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Sept06-FF.qxd 11/7/2006 2:04 PM Page FC1 PHYSICS IN CANADA LA PHYSIQUE AU CANADA Vol. 62 No. 5 September / October 2006 septembre / octobre 2006 Sept06-FF.qxd 11/7/2006 2:29 PM Page FC2 Sept06-FF.qxd 11/7/2006 2:04 PM Page 225 Vol. 62 No. 5 PHYSICS IN CANADA LA PHYSIQUE AU CANADA TABLE OF CONTENTS / TABLE September / October 2006 septembre / octobre 2006 DES MATIÈRES Editorial : Neutron and X-Ray Scattering at Major Facilities, by J. Katsaras, Guest Editor Éditorial : Diffusion des neutrons et des rayons X dans les grandes installations de recherche, par J. Katsaras, rédacteur honoraire 225 226 PHYSICS AND EDUCATION / LA PHYSIQUE ET L’ÉDUCATION Small-Angle Neutron Scattering and Biomolecules, by/par J. Katsaras et al. 233 Neutrons and Transition Metal Oxides: A Match Made in Heaven, by/par J.E. Greedan 241 Stop That Corrosion - If You Can, by/par Z. Tun et al. 249 FEATURE ARTICLES / ARTICLES DE FOND Quantum Magnetism and Superconductivity, by/par W.J.L. Buyers and Z. Yamani 257 Polarized Neutron Reflectometry as a Unique Tool in Magnetization Reversal Studies of Thin Films and Multilayers, by/par H. Fritzsche et al. 265 Diffraction Studies of Gas Hydrates with an Emphasis on CO2 Hydrate, by/par B.H. Torrie et al. 273 Phase Transitions in Organic-Inorganic Perovskites, by Ian Swainson 279 Revealing the Microstructure of Polymeric Materials using SANS, by B. Frisken 285 Use of Neutron Diffraction for Development of Metal Hydrides: Case of BCC Alloys, by J. Huot et al. 289 Neutrons and Muons as Complementary Probes of Exotic Magnetism and Superconductivity, by C. Wiebe 295 Status of the Canadian Macromolecular Crystallography Facility: Design and Commissioning of the 08ID-1 Beamline at the Canadian Light Source, by P. Grochulski et al. 301 Phonon Spectroscopy and X-Ray Scattering using Synchrotron Radiation, by J.S. Tse and D.D. Klug 305 Synchrotron Advances at the Frontiers of Food Physics: Studies of Edible Fats such as Chocolate Under Shear, by G. Mazzanti et al. 313 DEPARTMENTS / RUBRIQUES Erratum and Letter / Erratum et communication 229 FRONT COVER / COUVERTURE AVANT 2006 Congress / Congrès 2006 230 News (IUPAP Prize) / Informations (Priz de l’UIPPA) 232 From bottom left, clockwise, a selection of figures from the articles by Fritzsche et al. (fig. 6, pg. 268), Greedan (fig. 10, pg. 246), Swainson (fig. 3, pg. 280), Huot et al. (fig. 1, pg. 289), and Katsaras et al. (fig. 1, pg. 234). Cover design by Alastair McIvor, National Research Council, Chalk River. Call for Suggestions/Nominations (Council/CNILC) Appel de candidatures (Conseil/CNILC) 256/272 News (37th Olympiad) / Informations (37ième Olympiad) 278 Institutional, Corporate and Sustaining Members / Membres institutionnels, corporatifs, et de soutien 284 Books Received / Livres reçus Book Reviews / Critiques de livres 321 322 Employment Opportunities & Commercial Ads / Postes d’emplois et publicités commerciales 331 Art of Physics / Art de la physique IBC Advertising Rates and Specifications (effective January 2006) can be found on the PiC website (www.cap.ca - PiC online). / Les tarifs publicitaires et dimensions (en vigueur depuis janvier 2006) se trouvent sur le site internet de La Physique au Canada (www.cap.ca PiC Électronique). En partant du coin en bas à gauche, dans le sens des aiguilles d’une montre, une sélection de figures tirées des articles de Fritzsche et al., (fig. 6, p. 268), de Greedan (fig. 10, p. 246), de Swainson (fig. 3, p. 280), de Huot et al. (fig. 1, pg. 289) et de Katsaras et al. (fig. 1, p. 234). Montage par Alastair McIvor, Conseil national de recherches, Chalk River. Sept06-FF.qxd 11/7/2006 2:04 PM Page 226 EDITORIAL PHYSICS IN CANADA LA PHYSIQUE AU CANADA The Journal of the Canadian Association of Physicists La revue de l'Association canadienne des physiciens et physiciennes ISSN 0031-9147 EDITORIAL BOARD / COMITÉ DE RÉDACTION Editor / Rédacteur en chef -- E D I T O R I A L / ÉDITORIAL -- NEUTRON AND X-RAY SCATTERING AT MAJOR FACILITIES DIFFUSION DES NEUTRONS ET DES RAYONS X DANS LES GRANDES INSTALLATIONS DE RECHERCHE Béla Joós, P.Phys. Physics Department, University of Ottawa 150 Louis Pasteur Avenue Ottawa, Ontario K1N 6N5 (613) 562-5800x6755; Fax:(613) 562-5190 e-mail: [email protected] Associate Editor / Rédactrice associée Managing / Administration Francine M. Ford c/o CAP/ACP Book Review Editor / Rédacteur à la critique de livres Andrej Tenne-Sens c/o CAP / ACP Suite.Bur. 112, Imm. McDonald Bldg., Univ. of / d' Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 (613) 562-5614; Fax: (613) 562-5615 Email: [email protected] Advertising Manager / Directeur de la publicité Michael Steinitz, PPhys Department of Physics St. Francis Xavier University, P.O. Box 5000 Antigonish, Nova Scotia B2G 2W5 (902) 867-3909; Fax: (902) 867-2414 Email: [email protected] Board Members / Membres du comité : Rod H. Packwood (613) 225-6156 Email: [email protected] René Roy, phys In 1895 Wilhelm Conrad Röntgen, a professor of physics and the director of the Physical Institute of the University of Würzburg (Germany) discovered a new form of radiation, which he called X-rays. Years later, James Chadwick, a professor of physics at Cambridge University discovered the neutron, a neutral particle in the nucleus of an atom. For their discoveries, Röntgen and Chadwick were awarded, respectively, in 1901 and 1935, the Nobel prize in physics. The theoretical beginnings of synchrotron radiation go back to Thomson's discovery of the electron in 1897. Subsequently, Larmor derived an expression from classical electrodynamics describing the power radiated by an accelerated charged particle, which Liénard extended for a relativistic particle undergoing centripetal acceleration in a circular trajectory. The radiated power of a relativistic particle is proportional to (E/mc2)4/R2, where E is particle energy, m is the rest mass, and R is the radius of the trajectory. By 1945, Julian Schwinger – yes, Schwinger of relativistic quantum electrodynamics fame - worked out the classical theory of radiation from accelerated relativistic electrons. On 24 April 1947, Elder, Gurewitsch, Langmuir and Pollock observed the bluish-white light of synchrotron radiation using General Electric’s 70 MeV (mega electron volt) electron synchrotron at Schenectady, New York. David J. Lockwood, PPhys In 1942, Enrico Fermi supervised the design and assembly of an "atomic pile" graphite blocks, uranium, and cadmium control rods - in the squash courts beneath the University's football stadium. The world’s first controlled nuclear reaction took place on December 2, 1942. Interestingly, 18 months earlier in Canada, George Laurence, then on staff at the National Research Council (NRC), constructed his own atomic pile in the basement of the NRC’s laboratories at 100 Sussex Drive. But for a small amount of boron impurity in the graphite, Canada’s atomic pile might have been the first in the world to go critical. In June of 1944, the National Research Council established the “NRC Atomic Energy Project” at Chalk River. ANNUAL SUBSCRIPTION / ABONNEMENT ANNUEL: The first controlled nuclear reaction in Canada took place on September 5, 1945, when the Zero Energy Experimental Pile (ZEEP) reactor went into operation. The ZEEP reactor was designed to produce only a few watts of heat, and was used to provide data for the design of the 25 MW (mega watts) NRX (National Research eXperimental) reactor, for a time the most powerful reactor in the world. Ten years later, the completion of the National Research Universal (NRU) reactor in 1957 was a landmark achievement in Canadian science and technology. Operating at 120 MW of power it was the most powerful reactor of its time, and even today, produces some of the most intense thermal neutron beams from a core flux of 3x1018 neutrons/m2/s2. In 1994, Bertram N. Brockhouse was awarded the Nobel Prize in physics for his development of neutron spectroscopy and the triple-axis spectrometer while using the intense neutron beams provided by the NRX and NRU reactors. Département de physique, de génie physique et d’optique Université Laval Cité Universitaire, Québec G1K 7P4 (418) 656-2655; Fax: (418) 656-2040 Email: [email protected] Institute for Microstructural Sciences National Research Council (M-36) Montreal Rd., Ottawa, Ontario K1A 0R6 (613) 993-9614; Fax: (613) 993-6486 Email: [email protected] $40.00 Cdn + GST or HST (Cdn addresses), $40.00 US (US addresses) $45.00 US (other/foreign addresses) Advertising, Subscriptions, Change of Address/ Publicité, abonnement, changement d'adresse: Canadian Association of Physicists / Association canadienne des physiciens et physiciennes, Suite/Bureau 112, Imm. McDonald Bldg., Univ. of/d' Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 Phone/ Tél: (613) 562-5614; Fax/Téléc. : (613) 562-5615 e-mail/courriel : [email protected] Website/Internet : http://www.cap.ca Canadian Publication Product Sales Agreement No. 0484202/ Numéro de convention pour les envois de publications canadiennes : 0484202 © 2006 CAP/ACP All rights reserved / Tous droits de reproduction réservés WWW.CAP.CA (select PIC online / Option : PiC Électronique) 226 PHYSICS IN CANADA Neutron and X-ray scattering have become indispensable tools in a wide range of condensed-matter research fields (e.g. crystallography, structure of surfaces and interfaces, disordered systems, etc.). A highlight of note is the important role X-rays have played in macromolecular structure determination starting with the structure The contents of this journal, including the views expressed above, do not necessarily represent the views or policies of the Canadian Association of Physicists. Le contenu de cette revue, ainsi que les opinions exprimées ci-dessus, ne représentent pas nécessairement les opinions et les politiques de l'Association canadienne des physiciens et des physiciennes. September / October 2006 Sept06-to-trigraphic.qxd 11/8/2006 9:42 AM Page 227 PRÉFACE of DNA and continuing to the recent Nobel prize awarded to Roger Kornberg for his studies of the molecular basis of eukaryotic transcription using the Stanford Synchrotron Radiation Laboratory. The 13 articles in this issue cover a range of scientific topics. What they all have in common is neutron and X-ray scattering carried out at major facilities for condensed matter research. The Canadian facilities used were the Canadian Light Source (CLS), the Tri-University Meson Facility (TRIUMF) Centre for Molecular and Materials Science and the Canadian Neutron Beam Centre (CNBC). In Canada, the Canadian Light Source (CLS), located at the University of Saskatchewan, is a 2.9 GeV (giga electron volt) state-of-the-art, third generation synchrotron light source estimated to meet ~ 90% of the current and future demands of the Canadian research community. The CLS consists of a 250 MeV electron Linac, a booster to ramp the beam to 2.9 GeV, and the main ring, which is designed to operate at 2.9 GeV and currents up to 500 mA. Presently there are 7 beamlines being commissioned, with another 7 under construction. TRIUMF, located at the University of British Columbia, is one of the three subatomic research facilities in the world that specialize in producing intense beams of protons. The cyclotron, the biggest in the world, is capable of accelerating 20 000 billions particles/second (~ 300 Microamps). The proton beams produced by the cyclotron, strike different kinds of targets, producing neutron, pion, and muon beams, which can be used for different types of experiments. More recently, the ISAC (Isotope Separation and ACceleration) facility allows for the production of some of the most intense beams of exotic ions (isotopes) in the world, making TRIUMF an internationally-recognized centre for the study of nuclear astrophysics. NRC operates today’s CNBC at Chalk River. Presently, the facility is comprised of 5 thermal instruments, which are located at the NRU reactor. The University of Western Ontario recently led 12 other universities in procuring funds from the Canada Foundation for Innovation to add a new, world-class neutron reflectometer to the CNBC facility. The reflectometer is expected to begin operation in 2007, to support a wide range of nanotechnology applications never before possible in Canada. The CNBC primarily operates as an accessible international user facility, supported in part by a Natural Sciences and Engineering Research Council of Canada (NSERC) Major Resources Support (MRS) grant, which is presently administered through McGill University. Neutrons, which possess a magnetic moment (spin ½ particles), are ideally suited to the study of magnetic structures and magnetic fluctuations. The article by Fritzsche et al. describes how polarized neutrons are used to study magnetic thin films and multilayers, while Buyers and Yamani describe how neutrons have played a pivotal role in the discovery of new phases of matter in quantum gapped systems, a highly-correlated heavyfermion system, and superconductors. Adding to the neutron/magnetism flavour, is Wiebe’s article on neutrons and muons as complementary probes for exotic magnetism and superconductivity. Powder diffraction, because of its ease of use and quick turnover of samples, is one of the most widely used techniques to study structural properties of materials. Neutron powder diffractometers, although less commonly available than their x-ray counterparts, are “workhorse” instruments found in practically all major neutron laboratories. As a result, it is not surprising to see 4 articles in this issue based on neutron powder diffraction for their science (i.e., Greedan, Swainson, Torrie et al., and Huot et al.). Before small-angle neutron scattering (SANS), studies of polymer structure were, for the most part, limited to light and smallangle x-ray scattering techniques. The unique role of SANS in the case of hydrogenous materials lies in the difference in the coherent scattering length between hydrogen (bH = -0.37 × 10-12 cm) and deuterium (bD = 0.67 × 10-12 cm). This difference results in a marked difference in scattering power (contrast) between hydrogenous and deuterated monomer units. Canada has SANS expertise, even though we lack a proper SANS instrument. Here the articles by Katsaras et al. and Frisken demonstrate the versatility of SANS, and the power of contrast variation. Neutron reflectometry is a technique used to probe the structure of surfaces, thin-films and buried interfaces, as well as processes occurring at surfaces, e.g. corrosion. In their article, Tun et al. report on neutron reflectometry studies of passive oxide layers on titanium and zirconium, materials of interest to the nuclear industry. March 2006 saw an important milestone for the CLS, and the Canadian crystallography community, with the first results coming off the Canadian Macromolecular Crystallography Facility (CMCF) beamline. The images were of a protein crystal, PEP carboxykinase. In this issue, Grochulski, Blomqvist and Delbaere of the CMCF team describe, in detail, the 08ID-1 beamline which was used to collect the data. The report by Grochulski et al. is followed by the articles of Tse and Klug, and Mazzanti et al. describing diverse topics such as X-ray phonon spectroscopy and synchrotron X-ray studies of chocolate under shear. John Katsaras National Research Council, Chalk River Guest Editor, Physics in Canada DIFFUSION DES NEUTRONS ET DES RAYONS X DANS LES GRANDES INSTALLATIONS DE RECHERCHE En 1895, Wilhelm Conrad Röntgen, professeur de physique et directeur de l'Institut de physique de l'Université de Würzburg (Allemagne), découvre une nouvelle forme de radiation qu'il nomme rayons X. Plusieurs années plus tard, James Chadwick, professeur de physique à l'Université Cambridge fait la découverte du neutron, une particule électriquement neutre qui est un constituant du noyau de l'atome. Röntgen et Chadwick ont reçu le Prix Nobel de physique pour leurs découvertes, respectivement en 1901 et 1935. Les premières théories sur le rayonnement synchrotron remontent à la découverte de l'électron par Thomson en 1897. Par la suite, Larmor calcule une expression au moyen de l'électrodynamique classique décrivant le rayonnement produit par une particule chargée accélérée, que Liénard applique à une particule relativiste soumise à une accélération centripète dans une trajectoire circulaire. La puissance de rayonnement d'une particule relativiste est proportionnelle à (E/mc2)4/R2, où " E " représente LA PHYSIQUE AU CANADA septembre / octobre 2006 227 Sept06-to-trigraphic.qxd 11/8/2006 9:42 AM Page 228 FOREWORD l'énergie des particules, " m ", la masse au repos et " R ", le rayon de la trajectoire. Vers 1945, Julian Schwinger - oui, " LE Schwinger " qui a connu la gloire grâce à son travail sur l'électrodynamique quantique relativiste - met au point la théorie classique du rayonnement produit par des électrons relativistes accélérés. Le 24 avril 1947, Elder, Gurewitsch, Langmuir et Pollock observent une lumière blanche bleuâtre émise par le rayonnement synchrotronique en utilisant un synchrotron à électrons de 70 MeV (mégaélectrovolts) à Schenectady, New York. En 1942, Enrico Fermi dirige la conception et la construction d'une " pile atomique " - en superposant des briques de graphite, de l'uranium, et des barres de commande de cadmium - sur les courts de squash situés sous les gradins du stade de football de l'Université de Chicago. Le 2 décembre 1942, il réussit la première réaction nucléaire contrôlée. Fait intéressant, 18 mois plus tôt, le Canadien George Laurence, alors membre du personnel du Conseil national de recherches du Canada (CNRC), avait construit sa propre pile atomique dans le sous-sol des laboratoires du CNRC au 100, promenade Sussex. N'eut été d'une petite quantité d'impureté de bore, la pile atomique construite au Canada aurait été la première pile à fonctionner au monde. En juin 1944, le Conseil national de recherches mettait sur pied le " NRC Atomic Energy Project " (Projet de l'énergie atomique du CNRC) à Chalk River. Au Canada, la première réaction nucléaire en chaîne contrôlée a lieu le 5 septembre 1945, lorsque le réacteur de recherche ZEEP (pile expérimentale d'énergie zéro) est mis en service. Le ZEEP a été conçu pour produire uniquement quelques watts de chaleur et a été utilisé pour fournir des données pour la conception du réacteur NRX (réacteur national de recherche expérimental) de 25 MW (mégawatts), qui a été, pendant un certain temps, le réacteur le plus puissant au monde. Dix ans plus tard, la construction du réacteur national de recherche universel (NRU) fut une réalisation historique en 1957 dans le domaine des sciences et de la technologie au Canada. Ce réacteur qui fonctionne à des niveaux de puissance de 200 MW était le réacteur le plus puissant de l'époque, et même aujourd'hui il produit certains des faisceaux de neutrons thermiques les plus intenses dans un flux de 3x1018 de neutrons/m2. En 1994, Bertram N. Brockhouse remporte le Prix Nobel de physique pour le développement de la spectroscopie neutronique et l'invention du spectromètre neutronique à trois axes en utilisant les faisceaux de neutrons intenses produits par les réacteurs NRX et NRU. La diffusion des neutrons et des rayons X est devenue un outil essentiel à une vaste gamme de champs de recherche sur la matière condensée (p. ex., la cristallographie, la structure des surfaces et interfaces, les systèmes désordonnés, etc.). Un fait marquant digne d'être souligné est le rôle important qu'ont joué les rayons X dans la détermination de la structure macromoléculaire, en commençant par la structure de l'ADN, jusqu'aux études de Roger Kornberg sur le fondement moléculaire de la transcription eukaryote entreprises au Laboratoire de rayonnement synchrotron de Stanford (Stanford Synchrotron Radiation Laboratory) qui lui ont valu le Prix Nobel en 2006. Les 13 articles publiés dans ce numéro traitent de divers sujets scientifiques qui ont tous en commun la diffusion des neutrons et des rayons X, effectuée principalement dans des grandes installations de recherche dans le cadre de la recherche sur la matière condensée - notamment le Centre canadien de rayonnement synchrotron (CCRS), le Centre for Molecular and Materials Science de la Tri-University Meson Facility (TRIUMF) et le Centre canadien de faisceaux de neutron (CCFN). 228 PHYSICS IN CANADA Au Canada, le Centre canadien de rayonnement synchrotron (CCRS), situé à l'Université de la Saskatchewan, est une source de rayonnement synchrotron de troisième génération à 2,9 GeV (gigaélectrovolts) à la fine pointe de la technologie pouvant satisfaire selon les estimations près de 90 p. 100 des demandes actuelles et futures de la communauté des chercheurs canadiens. Le CCRS comprend un accélérateur linéaire d'électrons de 250 MeV, un injecteur permettant d'accélérer l'énergie du faisceau jusqu'à 2,9 GeV et l'anneau principal conçu pour fonctionner à 2,9 GeV, et alimenté par des courants pouvant atteindre 500 mA. Il y a actuellement 7 faisceaux dont la mise en service est en cours et 7 autres qui sont en construction. Le grand accélérateur TRIUMF, situé à l'Université de la Colombie-Britannique, est l'une des trois installations de recherche subatomique au monde qui se spécialisent dans la production de faisceaux intenses de protons. Le cyclotron - le plus gros au monde -peut accélérer 20 000 milliards de particules par seconde (~ 300 Microamps). Le faisceau de protons produit par le cyclotron heurte différents types de cibles produisant des faisceaux de neutrons, de pions et de muons, pouvant être utilisés pour effectuer différents types d'expériences. Plus récemment, ISAC (pour " Isotope Separation and ACceleration ", ou séparation et accélération d'isotopes) permet la production de faisceaux d'ions exotiques (isotopes) parmi les plus intenses au monde, faisant de TRIUMF un des centres de recherche mondiaux pour l'astrophysique nucléaire. Le Conseil national de recherches du Canada exploite le Centre canadien de faisceaux de neutrons (CCFN) à Chalk River. L'installation comprend 5 instruments thermiques, qui se trouvent dans le réacteur NRU. L'Université de Western Ontario à la tête d'une demande impliquant 12 autres universités a obtenu récemment des fonds de la Fondation canadienne pour l'innovation en vue d'installer au CCFN un nouveau réflectomètre à neutrons de calibre mondial. Le réflectomètre devrait entrer en service en 2007, afin de soutenir une vaste gamme d'applications des nanotechnologies qu'il était impossible de réaliser auparavant au Canada. Le CCFN est exploité principalement comme une installation accessible aux utilisateurs de divers pays et soutenue en partie par la subvention Accès aux grandes installations (AGI) octroyée par le Conseil de recherches en sciences naturelles et en génie (CRSNG), qui est administrée par l'intermédiaire de l'Université McGill. Les neutrons, qui ont un moment magnétique (particules à spin ½), sont idéaux pour étudier les structures et les fluctuations magnétiques. L'article de Fritzsche et coll. décrit de quelle manière les neutrons polarisés sont utilisés pour étudier les films minces magnétiques et les multicouches, alors que Buyers et Yamani expliquent le rôle crucial qu'ont joué les neutrons dans la découverte des nouvelles phases de la matière dans les systèmes à fossé quantique, un système de fermion lourd à forte corrélation et des supraconducteurs. L'article de Wiebe sur les neutrons et les muons comme étude supplémentaire sur le magnétisme exotique et la supraconductivité contribue à la connaissance des neutrons et du magnétisme. En raison de la facilité de son utilisation et du renouvellement rapide des échantillons, la diffusion des poudres est l'une des techniques les plus couramment utilisées pour étudier les propriétés structurales des matériaux. Les diffractomètres à neutrons, bien qu'ils soient moins accessibles que les diffractomètres à rayon X, sont des instruments d'une très grande utilité que l'on September / October 2006 Sept06-to-trigraphic.qxd 11/8/2006 9:42 AM Page 229 PRÉFACE trouve dans pratiquement tous les grands laboratoires de neutrons. Il n'est par conséquent pas étonnant de voir que 4 articles publiés dans ce numéro soient basés sur une telle diffusion de neutrons dans le cadre d'études scientifiques (Greedan, Swainson, Torrie et coll., et Huot et coll.). faces enfouies ainsi que les processus se produisant à la surface comme la corrosion. Dans leur article, Tun et coll. présentent leurs études de réflectométrie des neutrons des couches d'oxyde passive appliquées au titane et au zirconium, des matériaux intéressants pour l'industrie nucléaire. Avant que n'advienne la diffusion de neutrons à petit angle (DNPA), les études sur la structure des polymères étaient pour la plupart limitées aux techniques de diffusion de la lumière et de diffusion radiologique à petit angle. Le seul rôle de la DNPA en ce qui a trait aux matériaux hydrogéniques réside dans la différence entre la longueur de diffusion cohérente de l'hydrogène (bH = -0,37 × 10-12 cm) et du deutérium (bD = 0,67 × 10-12 cm). Cet écart entraîne une différence marquée dans la diffusion par la poudre (contraste) entre les unités d'hydrogène et les unités monomères deutérées. Le Canada bénéficie de l'expertise de la DNPA bien qu'il ne possède pas un instrument approprié pour la DNPA. Dans leurs articles, Katsaras et coll. et Frisken mettent en évidence la versatilité de la DNPA et la puissance de la variation des contrastes. En mars 2006, le CCRS et la communauté canadienne des cristallographes ont franchi une étape importante avec les premiers résultats obtenus par le faisceau lumineux du Canadian Macromolecular Crystallography Facility - CMCF (installation canadienne de cristallographie macromoléculaire). Les images étaient celles d'un cristal de protéine, la PEP carboxykinase. Dans ce numéro, Grochulski, Blomqvist et Delbaere de l'équipe du CMCF présentent en détail le faisceau lumineux 08ID-1 utilisé pour recueillir les données. Le rapport de Grochulski et coll. est suivi d'articles rédigés par Tse et Klug, et Mazzanti et coll. portant sur divers sujets, tels que la spectroscopie des phonons par rayon X et des études par rayons X du chocolat soumis à une pression de cisaillement émis par synchrotron. La réflectrométrie des neutrons est une technique utilisée pour étudier la structure des surfaces des films minces et des inter- John Katsaras Conseil national de recherches du Canada, Chalk River Rédacteur en chef invité ERRATUM IN MEMORIAM - PHILIP R. WALLACE P.R. Wallace on the band structure of graphite was published in 1949. The year should have read 1947. 2006 JULY/AUGUST PIC This obituary, which was printed in the 2006 July/August issue, contains a factual error. Using a quote from an article by MMR Williams published in Prog. Nucl. Energy in 2000, it was stated that the now classic paper by This Physical Review article is now gaining great prominence because of graphene, the name given to a single sheet of graphite. The material’s unique band structure and ease of fabrication are creating great enthusiasm for its potential in generating exciting new quantum physics and new electronic applications. LETTER / COMMUNICATION BOOK REVIEW - “AGAINST THE TIDE” 2006 JULY/AUGUST PIC In a recent volume of your Journal (Vol. 62, No. 4, 2006) there appeared what seemed at first to be a long-delayed review of my autobiography, Against the Tide (IOP Publishing, 2000), written by Professor T.W. Johnston, a plasma physicist, researching into controlled fusion in the Université du Québec. In his first paragraph his ‘verbatim’ quotation from the Publisher's review is rather spoilt by some undisclosed editing, for example by removing references to Rhodes and to the Chairman of Oxford University's Mathematical Institute. However by his third paragraph it is clear that the Professor is really engaged on another mission of much greater importance. Now I have admired and frequently referenced the comprehensive work The Particle Kinetics of Plasmas (1964), written by the Professor and two past colleagues, Drs. Shkarofshy and Bachynsky, although disappointed by some of the unphysical mathematical constructs in Chapters 9 and 10. These speculations help me to understand why, instead of genuinely reviewing my autobiography and giving the Reader even the briefest explanation of my tokamak theory, the Professor diverts attention to my incidental and entirely orthodox statements about plasma pressure. But after this detour he enthusiastically joins the Fusion Lobby with an ex cathedra declaration that my theory of transport is completely wrong. It seems that the wide range of observational support that he could have hardly avoided seeing, counts for nothing − not even a single mention in dispatches! So what is wrong with Chapter 10, entitled “Collisionless Plasmas in Strong Magnetic Fields"? By Newton's second law of motion, particles that do not collide conserve momentum and can not exert any sort of force. But scalar pressures parallel and perpendicular to the magnetic field are found in this “overreached" chapter, spoiling an otherwise scholarly text. There is no problem with magnetic pressure and even if the perpendicular pressure pz is somehow due to magnetic pressure in disguise, what about pk2? Particles moving parallel to the magnetic field hit nothing and are not affected by the magnetic field B, so where is the pressure force? Dr. Ware's biassed review of my Principles of Magnetoplasma Dynamics (OUP, 1987), to which Professor Johnston alludes with approval, was also preoccupied with denying Newton's second law (see Article 5 on my website). Incidentally there is a spectacular blunder in Chapter 9; the free space permeability μ0 and a magnetization current jm are not good bed-fellows; recall that jm = L H M where M / B(μ0-1 - μ-1). Professor Johnston confidently asserts “The equations used for basic tokamak theory (including neo-classical theory) are derived from fundamental kinetic equations by very careful approximation and there is no justification for inserting such ad hoc (more properly ad hominem) forces derived from one man's intuition". Logical positivism in attack mode! The positivist Pierre Duhem was probably too polite to use similar language about Maxwell's displacement current, imaginatively derived from elasticity theory, but Maxwell's great success with the speed of light must have annoyed him. See pp. 80-86 of The Aim and Structure of Physical Theory, Atheneum, New York, 1962. (cont’d on pg. 232) LA PHYSIQUE AU CANADA septembre / octobre 2006 229 Sept06-FF.qxd 11/7/2006 2:04 PM Page 230 2007 CONGRESS 2007 CAP CONGRESS Joint with CLS Users’ Advisory Group Meeting, 2007 June 15-17 June 17-20 University of Saskatchewan Saskatoon, Saskatechewan CALL FOR ABSTRACTS The 2007 congress of the Canadian Association of Physicists (CAP) will be held from June 1720, 2007 at the University of Saskatchewan in Saskatoon, Saskatchewan, in conjunction with the CLS Users’ Advisory Group meeting from June 15-17. The CAP Divisions are working hard to establish a very exciting program with talks and posters in the following topics of physics : Medical and Biological Physics Nuclear Physics Optics and Photonics Particle Physics Physics Education Plasma Physics Theoretical Physics Women in Physics Atmospheric and Space Physics Atomic and Molecular Physics and Photon Interactions Condensed Matter and Materials Physics History of Physics Industrial and Applied Physics Instrumentation and Measurement Physics Abstract submission forms can be found through the CAP's website at http://www.cap.ca Deadline: March 1, 2007 The HERZBERG MEMORIAL PUBLIC LECTURE, to be held on Sunday evening, June 17th, will be given by the 2001 Nobel Prize winner, Dr. Carl E. Wieman, of the University of Colorado (as of January 1, Dr. Wieman will be located at the University of British Columbia). Bookmark the CAP's congress site and keep visiting for details of the technical sessions, invited speakers, and other congress arrangements as they unfold. WE LOOK FORWARD TO SEEING YOU IN SASKATOON IN JUNE !! FUTURE CAP CONFERENCES 2008 Annual Congress June 8 - 11, 2008 (to be confirmed) Laval University, Québec, QC WWW.CAP.CA 230 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:04 PM Page 231 CONGRÈS 2007 CONGRÈS DE L’ACP 2007 17-20 juin Université de la Saskatchewan Saskatoon, Saskatechewan Conjointement avec la réunion du << CLS Users’ Advisory Group >>, 15-17 juin 2007 APPEL DE RÉSUMÉS Le congrès de 2007 de l’Association canadienne des physiciens et physiciennes (ACP) se tiendra du 17 au 20 juin 2007 à l’Université de la Saskatchewan, à Saskatoon, Saskatchewan. Ce congrès aura lieu conjointement avec la réunion du << CLS Users’ Advisory Group >> du 15 au 17 juin. Les divisions de l’ACP travaillent fort à établir un programme très excitant, comprenant des exposés et des affiches sur les sujets suivants en physique : Physique atmosphérique et de l’espace Physique atomique et moléculaire et interactions aves les photons Physique de la matière condensée et matériaux Histoire de la physique Physique industrielle et appliquée Physique des instruments et des mesures Physique médicale et biologique Physique nucléaire Optique et photonique Physique des particules Enseignement de la physique Physique des plasmas Physique théorique Les femmes en physique On peut trouver les formulaires de soumission de résumé sur le site de l’ACP à l’adresse http://www.cap.ca Date limite : 1er mars 2007 Le CONFÉRENCE PUBLIQUE COMMÉMORATIVE HERZBERG, qui aura lieu le dimanche soir, 17 juin, sera donnée par le récipiendaire du Prix Nobel en 2001, Dr. Carl E. Wieman, de l’Université du Colorado (dès le 1er janvier, il sera à l’Université de la Colombie-Britannique). Ajoutez le site du congrès de l'ACP à vos signets et venez y consulter les détails des sessions techniques, la liste des conférenciers invités et les renseignements pratiques à mesure qu'ils se complètent. AU PLAISIR DE VOUS ACCUEILLIR À SASKATOON EN JUIN!! PROCHAINS CONGRÈS DE L’ACP Congrès annuel 2008 8 - 11 juin 2008 (à confirmer) Université Laval, Québec, QC WWW.CAP.CA LA PHYSIQUE AU CANADA septembre / octobre 2006 231 Sept06-FF.qxd 11/7/2006 2:04 PM Page 232 NEWS NEWS / INFORMATIONS INTERNATIONAL UNION OF PURE AND APPLIED PHYSICS - YOUNG SCIENTIST PRIZE IN COMPUTATIONAL PHYSICS We would like to draw attention to the Young Scientist Prize in Computational Physics which has recently been established by the C20 Commission on Computational Physics of IUPAP. The award is aimed at recognising outstanding achievements of scientists at an early stage of their careers in the broad field of computational physics. Name of the Award: International Union of Pure and Applied Physics Young Scientist Prize in Computational Physics Frequency/Venue: C Triennially, up to three International Union of Pure and Applied Physics [IUPAP] Young Scientist Prizes in Computational Physics will be awarded. C They will be announced and presented at the annual Conference on Computational Physics (CCP). C It is intended that one award be made each year. However, in any given year, the selection committee may, at its discretion, may decide not to make an award. If so, multiple awards may be made in the following year. C [It is proposed that the first award be made at CCP2007 in September 2007, in Brussels] Criteria for selection: C The recipients of the awards in a given year should on January 1 of that year have a maximum of 8 years of research experience (excluding career interruptions) following their PhD. C The recipient should be the principal performer of original work of outstanding scientific quality in Computational Physics. C A previous recipient will not be eligible for another award. Nomination procedure: C The awards will be advertised electronically by the C20 Commission on its web page [see www.iupap.org] and elsewhere. C The deadline for nominations is 1st March. C Self-nominations will not be considered. C Nominations shall be made to the Chairman of the C20 Commission by electronic mail [[email protected]] and should include the following: B A letter of not more than 1,000 words evaluating the nominee's achievements and identifying the specific work to be recognised. B A Curriculum Vitae including all publications. B A brief biographical sketch. The selection committee: The selection committee consists of the Members and Associate Members of the C20 Commission The selection committee may consult with appropriate external assessors. Type of Awards: C The Awards will be US$1000 each, plus a medal and certificate to be provided by IUPAP. C The award money will normally be given as a contribution towards the expenses for attending the CCP. C The winner will be invited to present a paper at the CCP. LETTER / COMMUNICATION (CONT’D FROM PG. 229) These so-carefully derived equations yield energy losses ~ 10-4 times those observed − the so-called neo-classical ‘correction' reduces this factor to a mere 10-2 or so. But are the fundamental equations really to be trusted? Boltzmann's famous kinetic equation is both fundamental and wrong − at least for the purpose of finding energy losses from tokamaks. His collision integral is valid only to first order in the Knudsen number expansion; at higher orders the hypothesis of molecular chaos on which he based his theory fails. See Article 3 on my website. Turbulence is the scapegoat for fusion theorists' 40-year failure to discover why − so far as conserving mass and energy is concerned − tokamaks resemble canoes made from barbed wire. There are several varieties of turbulence and all need the help of ‘adjustable' constants; but what is wrong with the turbulence escape? Just the incidental fact that it is not supported by observations. Sufficient microturbulence to increase the thermal diffusivity in the electron gas by the required several orders of magnitude would, by Spitzer's extension of Lorentz's theory of conductivity, have a similar effect on electrical resistivity, yet observations of the voltage drop around a tokamak torus give values only a little larger than predicted by classical theory. A pity, for by choking the toroidal current to negligible values, a good dose of turbulence would have put paid at an early stage to tokamak research and saved the vast sums of public money being lavished on this 50 year-old international sport, speculated to deliver energy to the grid as soon as 2045. The only recognition of this simple fact about turbulence that I have found is in Kikuchi et al. (Nuclear Fusion, 30(2), 341, 1990); the authors come very close to heresy. Referring to observations in tokamak JT60 they remark: “However, it is surprising to observe such classical behaviour in the ‘diffusion-driven' current when other transport coefficients are anomalous." Your reviewer claims that my theory involves “major surgery of the fundamental equations." It certainly does not; all the basic MHD equa- 232 PHYSICS IN CANADA tions are unchanged. He failed to notice that I have merely extended the usual constitutive equation (Fourier's law) for the heat flux vector q − an approximation valid to first order in the Knudsen number Kn − to second-order in Kn to obtain for either of the ion or electron fluids, q = − κ∇T − o 5 kB p τ B × ∇ v i ∇T, 2 2Q B (1) where LE v is the deviator of the fluid velocity gradient, kB is Boltzmann's constant, p is the pressure, Q is the particle charge, B is the magnetic induction, T is the temperature and τ is related to the bounce time of the particles trapped in the tokamak field. In tokamak conditions the last term in (1) is dominant by orders of magnitude and allowed me to explain many apparently distinct tokamak observations: 6H thermal diffusivity, energy confinement time, L and H modes, the L6 transition, internal transport barriers, sawtooth oscillations, major disruptions, etc., with numerical values close to those observed without any empirical fiddling. No other theory manages to explain convincingly any of these phenomena. There is a corresponding successful theory for particle diffusion, based on second-order (in Kn) viscosity. See Theory of Tokamak Transport, Wiley-VCH, 2006, the Preface of which is on my website. For a brief account of the fusion saga including the physical principles involved in my theory, the Reader is referred to Article 1 on my website, which I wrote for the 2006 Balliol College Annual Record, the Editor of which insisted that it should be intelligible even to classicists and other arts graduates. To see how the lieutenants of Fusion Research protect their status and incomes, Article 9 is instructive. There is much more to say of course, but I shall close by thanking the Journal Editor for accepting this rebuttal and Professor Johnston for the glimpse of my obituary he allowed me in his final paragraph. L. C. Woods Emeritus Fellow of Balliol College, Oxford, UK September / October 2006 Sept06-FF.qxd 11/7/2006 2:04 PM Page 233 LA PHYSIQUE ET L’ÉDUCATION ( SMALL-ANGLE NEUTRON ... ) SMALL-ANGLE NEUTRON SCATTERING AND BIOMOLECULES by J. Katsaras, T.A. Harroun, J. Pencer, T. Abraham, N. Kučerka and M.-P. Nieh S oft materials, both polymeric and biologically relevant, are “heavy” atoms. In the case of polymeric materials, neurich in hydrogen. By coincidence, neutrons have the unique trons are used to precisely locate hydrogen atoms [9,10]. capability of scattering differently from hydrogen (coherent scattering length of hydrogen, bH = -0.37 × 10-12 cm) com(iii) 1H has a negative scattering length giving it “contrast” pared to its isotope deuterium (bD = 0.67 × 10-12 cm). As a when surrounded by other, positive scattering length result of this marked difference in scattering power (contrast) atoms. For biological samples intrinsically rich in hydrobetween native hydrogenated materigen, judicious substitution of 2H for 1H als and their counterparts synthesized a powerful method for selectAs a result of a marked dif- provides from deuterated monomer units, neuively tuning the contrast of a given tron scattering techniques have proven ference in scattering power macromolecule. By doing so, one can to be powerful tools for the study of accentuate, or nullify, the scattering soft condensed matter systems. Here, (contrast) between native from particular parts of a macromolecuwe will discuss the small-angle neu- hydrogenated materials and lar complex. This powerful technique is tron scattering (SANS) technique, commonly referred-to as “contrast variwhich is presently playing a pivotal their counterparts synthe- ation” [11-13]. role in extracting unique structural sized from deuterated information from intrinsically disor(iv) Neutron energies are similar to the monomer units, neutron dered systems. energies of atomic and electronic processes, i.e. meV to eV range. scattering techniques have This allows for the study of the NEUTRONS proven to be powerful tools various dynamic properties (i.e., Neutrons are electrically neutral, subtranslations, rotations, vibrations atomic, elementary particles, found in for the study of soft conand lattice modes) exhibited by all atomic nuclei, except hydrogen densed matter systems. molecules and eV transitions with(1H). They are approximately 1,840 in the electronic structure of matetimes more massive than an electron rials [14-16]. and have a nuclear spin of 1/2. Neutrons are only stable when bound by an atomic nucleus, while unstable free neu(v) Because they possess a magnetic moment (spin 1/2 partrons have a mean lifetime of approximately 900 s, decaying ticles), neutrons are ideally suited to the study of magnetinto a proton, an electron, and an antineutrino [1,2]. ic structures (short- and long-range) and short wavelength magnetic fluctuations. It is important to note that Because neutrons interact with atomic nuclei the scattering the cross-sections for magnetic scattering are of the same “power” (cross-section) of an atom is not strongly related to magnitude to those for nuclear scattering [17-18]. its atomic number. Neighbouring elements in the periodic table can therefore, have substantially different scattering SMALL ANGLE NEUTRON SCATTERING (SANS) cross sections [3]. More importantly, the interaction of a neutron with the nucleus of an atom allows neutrons to interact Small angle neutron scattering (SANS) probes structure differentially with an element’s isotopes. The classic example in materials of length scales ranging from tens of angstroms is the isotopic substitution of 1H for deuterium (2H) in poly(10-9 m) to hundreds of nanometers (10-7 m) [19]. The length [4,5] meric materials . As a result of their intrinsic properties, scale, d, is determined by the neutron wavelength, λ, and the neutrons are used as follows: scattering angle, θ, through the relationship (i) Since they interact weakly with atomic nuclei, neutrons are highly penetrating. This feature allows neutrons to probe samples in complex sample environments, without the need to engineer neutron “windows” or ports into the sample enclosure. This enables the measurement of bulk processes under realistic conditions [6-8]. (ii) Because the scattering ability of an atom is not strongly related to its atomic number, neutrons are used extensively to locate “light”, low atomic number atoms among λ = 2d sin θ/2, John Katsaras <[email protected]>a,b,c, Thad A. Harrounc, Jeremy Pencera, Thomas Abrahama, Norbert Kučerkaa, and Mu-Ping Nieha; aCanadian Neutron Beam Centre, National Research Council Canada, Chalk River Laboratories, Chalk River, ON, K0J 1J0; bBiophysics Interdepartmental Group, Guelph-Waterloo Institute for Physics, Guelph, ON, N1G 2W1; cDepartment of Physics, Brock University, St. Catharines, ON, L2S 3A1 LA PHYSIQUE AU CANADA septembre / octobre 2006 233 Sept06-FF.qxd 11/7/2006 2:04 PM Page 234 PHYSICS AND EDUCATION ( SMALL-ANGLE NEUTRON ... ) commonly referred-to as Bragg’s Law. Through the use of cold (i.e. long wavelength) neutrons and the appropriate beam collimation, length scales approaching tens of micrometers are possible [20,21]. In general, SANS can provide information regarding a particle’s size and shape, distribution of scattering inhomogeneities, conformational changes and molecular associations in solution. More importantly, because of the properties of neutrons individual components within a macromolecule can be systematically manipulated either through isotopic labelling or the judicious use of solvents. Below we will discuss SANS instrumentation and provide a few examples of SANS data obtained from lipid/water and surfactant/water systems. SANS INSTRUMENTATION Figure 1 shows a schematic of a typical SANS instrument located at a neutron source capable of producing long wavelength (λ ~ 5 – 20 Å) or commonly referred-to, “cold neutrons” [22]. Velocities (i.e., wavelengths) of the incoming neu- trons are chosen by a mechanical velocity selector, basically, a high-speed rotor. The helically twisted rotor blades are coated with 10B, a neutron absorbing material, and reasonably monochromatized neutrons (bandpass, Δλ/λ of ~ 10%) are obtained by varying the rotor speed (revolutions/minute, rpm). Those neutrons whose velocities are not synchronized to the rotor speed are absorbed by the 10B coated blades. Monochromatic neutrons are then transported over meters and are collimated through a series of nickel-coated guides, which take advantage of the wave-like properties of neutrons. The propagation characteristics of neutrons involves the refractive index (n) of the medium. Since the critical angle (θc) depends on the refractive indices of the media that the neutrons traverse, when nmedium < nair neutrons are transported along the length of the guide by a mechanism known as total external reflection (θincident < θc). For neutrons n = 1 – (λ2p/2π) and the scattering length density, ρ is equal to Σbi/V, where bi is the coherent scattering length and V is the sample volume. Neutron guides are made of optically flat glass whose interior is generally coated with nickel or its isotope 58Ni (larger θc and increased Δλ/λ). Since, for neutrons, the index of refraction of 58Ni is slightly less than one, then all neutrons with an angle < θc (i.e., < 0.5° for λ = 5 Å neutrons) are transported. Recently developed supermirrors made up, for example, of Ni/Ti multilayers can increase the effective θc by up to a factor of 3, compared to pure Ni [23]. They do so not only by utilizing the total external reflection component, but also the superimposed constructive interference (Bragg reflection) from the successive layers of Ni, effectively extending the plateau of total external reflection. The desired energy neutrons impinge on the sample, which when scattered, are usually detected by a 3He-filled two-dimensional (2D) detector. SANS INFORMATION AT A GLANCE: FRACTAL DIMENSIONALITY Fig. 1 234 Schematic of a typical SANS instrument utilizing long wavelength or commonly referred-to cold neutrons. Velocities (i.e., wavelengths) of incoming neutrons are chosen by a mechanical velocity selector (a). For a given cylinder length, L, and a spiral pitch, p, if the cylinder spins on its axis at an angular velocity ω ω/2π π) are transmitonly neutrons of velocity, V (= pω ted. Reasonably monoenergetic cold neutrons are transported over meters and collimated through a series of nickel-coated or supermirror (e.g., Ni/Ti multilayers) guides (b). The evacuated guides, which transport cold neutrons via total external reflection, are made of optically flat glass and their interiors are coated with either nickel, or its isotope 58Ni (larger λ), or multilayers of critical angle, θc, increased Δλ/λ Ni/Ti, which offer an even greater θc. Neutrons then interact with the sample (c), which scatters neutrons usually detected by a 3He-filled 2D detector (neutron + 3He 6 3H + 1H + 0.76 MeV) (d). The flight path in which the 2D detector is housed is evacuated, resulting in a reduced background. PHYSICS IN CANADA For objects with a radius of gyration, RG , and Q << 1/RG where Q = 4π/λ sin θ/2, plotting ln[I(Q)] vs Q2 results in a straight line of slope –RG2/3, commonly referred to as a Guinier plot. However, when Q >> 1/RG I(Q) decays as Q-α, where α is the fractal dimension of the scattering object. In this case, fractal refers to a complex structure made up of geometrical objects (self-similarity). The magnitude of α permits for the geometry (i.e. morphology) of the scattering object to be determined. In the case where the Q-range of the scattering data is sufficiently large (over one decade in Q) [24], one can estimate α by simply determining the slope of the line from a log-log plot of I(Q) vs Q. Table I shows the fractal dimensions corresponding to various morphologies adopted by biomolecules and polymeric systems. SANS can also be used to characterize the stability of biological membranes interacting with additive molecules. Of special interest are pharmacologically important molecules that, in appropriate concentrations help to either stabilize the lipid bilayer or cause it to undergo structural change (e.g., lamellar to hexagonal transition). For example, non-ionic surfactant molecules such as, N-dodecyl-N,N-dimethylamine (DDAO) September / October 2006 Sept06-FF.qxd 11/7/2006 2:04 PM Page 235 LA PHYSIQUE ET L’ÉDUCATION ( SMALL-ANGLE NEUTRON ... ) destabilize dioleoyl phosphatidylcholine (DOPC) bilayers forming mixed micelles whose shape changes, as a function of increasing DDAO concentration, result in rod-like particles (e.g., tubular or cylindrical micelles) and hard sphere objects (e.g., globular micelles) [25]. TABLE 1 lipid, such as dihexanoyl phosphatidylcholine FRACTAL EXPONENTS FOR VARIOUS (DHPC) [44,45]. In this sysMORPHOLOGIES tem, a typical saturated acyl chain lipid, such as dimyristoyl phosphatidylcholine (DMPC, di-14:0 hydrocarbon chains), MORPHOLOGIES OF “BICELLE” MIXforms a disk-shaped bilayTURE LIPIDS DETERMINED BY SANS er whose edges are stabiAmphipathic phospholipids are one of the main lized by a curved monolaycomponents of biological membranes. They are er of detergent [46]. Since composed of hydrophobic fatty acid chains and their discovery, bilayered hydrophilic headgroups (Fig. 2), and along with micelles have been used in cholesterol are the primary constituents of cell a number of studies membranes. In purified forms, lipid/water sysattempting to elucidate the tems form a variety of interesting structures structure of proteins under (e.g., lamellar, cubic and hexagonal phases, physiologically relevant micelles, etc.) (Fig. 3) which for a number of reac o n d i t i o n s [39,45,47,48]. sons have been the focus of both experimenHowever, as we will show, the bilayered micelle morpholotal [26-32] and theoretical interest [33-38]. Many of these strucgy is just one of many structures that these lipid mixtures are tures exhibit features on length scales ranging from nanomecapable of adopting. ters to microns. In the recent past there has been a great deal of scientific activity in a system forming bilayered micelles, or commonly referred-to ‘‘bicelles’’ [39-40]. As we shall show below, neutron scattering has proven extremely useful in characterizing these systems. Although bicelles were commonly formed in aqueous solutions of ionic surfactants and alcohols [41-43], for biologists a more pertinent system is where the detergent molecules have been substituted by a short chain phospho- Fig. 2 Chemical composition and space-filling model of 1-stearoyl-2-oleoyl-sn-glycero-3phosphocholine (18:0-18:1 PC). This lipid is composed of a hydrophilic phosphorylcholine headgroup, a glycerol backbone, and two hydrophobic hydrocarbon chains. Fig. 3 COMPLETE UNBINDING OF LAMELLAE: FORMATION OF UNILAMELLAR VESICLES Figure 4 shows SANS profiles of varying wt% DMPC/DHPC lipid mixtures doped with the negatively charged lipid, dimyristoyl phosphatidylglycerol (DMPG) [49]. A 25 wt% sample was diluted in single steps, at 45oC, to final wt% concentrations of 18.0, 12.5, 9.0, 5.0, 2.5, 1.25, 0.5, and 0.1. The profiles for lipid concentrations, clp $ 2.5 wt% exhibit quasiBragg maxima, characteristic of equidistant lamellae (i.e., multibilayers). As a function of increasing amounts of water, the lamellar repeat spacing (d-spacing) varied linearly with changes in clp-1, from 104 to 1348 Å with the lamellar reflec- Example morphologies adopted by lipids: (a) Prolate micelle; (b) Inverse prolate micelle; (c) Hexagonal; (d) Inverted hexagonal (e) Micelle; (f) Inverted micelle; (g) Unilamellar vesicle; (h) Bilayered micelle; (e) Bilayer; (j) Cubic. LA PHYSIQUE AU CANADA septembre / octobre 2006 235 Sept06-FF.qxd 11/7/2006 2:04 PM Page 236 PHYSICS AND EDUCATION ( SMALL-ANGLE NEUTRON ... ) range, representative of isolated bilayers. The data were fit using a model of noninteracting polydisperse ULV. Fig. 4 SANS profiles of (DMPC/DHPC/DMPG) samples prepared and diluted at 45 °C. For all samples, the molar ratios of ([DMPC]+ [DMPG])/[DHPC] and [DMPG]/[DMPC] were fixed at 3.2 and 0.01, respectively. Bragg maxima are evident for 2.5 wt % # clp # 25 wt % samples, the result of multibilayers with a precise lamellar periodicity, d-spacing. For samples < 2.5 wt %, the multilamellar stacks unbind forming variable size ULV. Note that the SANS profiles decay monotonically and lack the oscillations which are characteristic of monodisperse ULV. So what happens if we take some of these morphologies, cool them down to 10oC and reheat back to 45oC? Figure 5 includes SANS data of 1.25 and 2.5 wt% samples. At 10oC the data do not show any sharp peaks and are well described by the bicelle morphology. The data can be best fit to a bilayered disk morphology using a combination of the core-shell-discoidal (CSD) model and the Hayter-Penfold structure factor, SHP(Q), resulting in a disk core radius, R, of 590 and 220 Å for the 1.25 and 2.5 wt% samples, respectively. Not surprisingly, both samples have the same bilayer thickness (42 Å). On reheating to 45oC, the lamellar morphology is recovered in the case of the 2.5 wt% sample. However, of greater interest is that on reheating the 1.25 wt% sample to 45oC, the scattering pattern shows an oscillatory behavior as a function of Q, the fingerprint of monodisperse ULV, instead of the monotonic decay seen initially at 45oC. The data were fit to a ULV model with a SHP(Q) structure factor and a Schulz size distributionyielding an average core radius<Ri>of ~300 Å, a bilayer thickness of 33 Å, and a polydispersity of 0.14. Whereas the ULV were initially large and highly polydisperse (Fig. 5), after temperature cycling they became smaller and more monodisperse. The formation of polydisperse ULV from lamellae is not surprising, since the unbinding of the bilayers does not select any particular length scale. However, the situation is very different when ULV are formed from bicelles, whereby the bilayered micelle morphology dictates the size of ULV formed. Figure 6 pictorially summarizes the various morphologies observed by Nieh et al. [49]. SANS AND CONTRAST VARIATION Fig. 5 SANS profiles of 2.5 and 1.25 wt% samples prepared at 45°C (top curve) on cooling to 10°C (middle), and on reheating to 45°C (bottom). The arrow represents the sequence of temperatures. The lamellar phase is recovered in the 2.5 wt % sample, whereas for the 1.25 wt % sample, initially polydisperse ULV become monodisperse on reheating (profile exhibits an oscillatory behaviour as a function of Q). The solid lines are fits to the data. tions moving systematically to lower values of Q. However, at clp # 1.25 wt% the lamellar reflections disappear, the result of a complete unbinding transition whereby, the extended lamellar stacks have disintegrated forming variable radii unilamellar vesicles (ULV). The scattered intensity for clp # 1.25 wt% follows a Q-2 dependence over an extended Q 236 PHYSICS IN CANADA For polymeric materials rich in hydrogen, the use of contrast variation and SANS makes for a powerful combination. By judiciously exchanging the molecule’s hydrogen atoms for deuteriums, or by changing the solvent’s scattering length density (ρ), one can enhance the “visibility” of a molecule’s moieties. For example, the optimum contrast conditions for studying the overall bilayer structure are a fully hydrogenated lipid in 100% D2O solvent. On the other hand a solvent composed of 50:50 D2O:H2O provides the best contrast for lipids with perdeuterated chains while the same lipid in a pure D2O provides information mainly about the lipid’s headgroup. The data obtained from these experiments can then be analyzed using either model dependent or model independent methods. A model independent method based on the Guinier approximation (i.e., low Q region) provides a reasonably straightforward procedure for extracting the bilayer’s structural parameters [13]. By analyzing the SANS data obtained at several different contrast conditions, the average bilayer scattering September / October 2006 Sept06-FF.qxd 11/7/2006 2:04 PM Page 237 LA PHYSIQUE ET L’ÉDUCATION ( SMALL-ANGLE NEUTRON ... ) Fig. 6 Schematic summary of the morphological transformations observed by Nieh et al. [49]. On diluting below a critical lipid concentration clpu at T > TM (chain melting transition of DMPC), extended bilayer sheets unbind into a polydisperse ULV dispersion. On cooling below TM and clpu $ clp $ 1.25 wt %, polydisperse ULV transform into an isotropic bicellar solution, which on reheating to T > TM, gives rise to monodisperse ULV. For clp # 0.5 wt % polydisperse ULV are trapped and cannot, at low T, transform into bicelles. Monodisperse ULV can also be obtained by diluting the bicellar phase below clpu at T < TM, followed by heating above TM. In the case of very dilute mixtures, i.e., clp # 0.1 wt % and T < TM, bilayered micelles do not reform. Instead, oblate ellipsoids are created. The dashed lines indicate plausible transformations not probed by the experiments carried out by Nieh et al. [49]. length density is evaluated from the quadratic dependence of the intensity at the origin versus the solvent scattering length density. The radius of gyration (RG) is evaluated from the slope of the KratkyPorod plot and then plotted against the inverse of the difference between the solvent and bilayer average scattering length densities. In such a graph, one can obtain RG at infinitely large contrast corresponding to a point at the graph’s origin. Compared to a single SANS measurement, this value - obtained from multiple contrast variation experiments is a more precise measure of the bilayer’s apparent thickness and can be used to study the relative changes in a bilayer using a modelfree approach. Contrast variation experiments analyzed using a model-based approach enables one to increase the number of independent model parameters leading to more realistic models with better resolved structural features. Scattering curves obtained at different contrast conditions (Fig. 7) are used to capture the different features of the bilayer. A single molecular model of the bilayer is then used to simultaneously fit the different contrast scattering curves. This model is made up of the probability distributions corresponding to the different functional groups (e.g., choline headgroup, hydrocarbon chains, etc.) of a bilayer (inset to Fig. 7). MORPHOLOGY OF GEMINI SURFACTANT AGGREGATES Fig. 7 SANS curves obtained at different contrast variation conditions. ULV composed of fully hydrogenated DPPC and DPPC with perdeuterated hydrocarbon chains (d62-DPPC) were prepared in three different D2O:H2O (100%, 70% and 50%) mixtures. A molecular model of the bilayer is shown in the inset to the figure. The bilayer profile is represented by probability distribution functions corresponding to solvent molecules, the PC headgroup, and the CH2 and CH3 making up the lipid’s hydrocarbon chains. The aggregation behaviour of Gemini surfactants is another problem that has been examined with SANS. Gemini surfactants are composed of two or more pairs of hydrophilic and hydrophobic groups connected to each other with a spacer (Fig. 8). In order to modify the surface tension of a solution, only small amounts of Gemini surfactants are required as their critical micellar concentration (cmc) in aqueous solutions is much lower than the cmc of conventional surfactants having the same hydrophilic and hydrophobic LA PHYSIQUE AU CANADA septembre / octobre 2006 237 Sept06-FF.qxd 11/7/2006 2:05 PM Page 238 PHYSICS AND EDUCATION ( SMALL-ANGLE NEUTRON ... ) Fig. 8 α’The molecular structure of α,α [2,4,7,9-tetramethyl-5-decyne-4,7-diyl] ω-hydroxyl-polyoxyethylene]. bis-[ω groups. One example of what SANS can achieve in studying the structure of such surfactant systems is the molecule α,α’-[2,4,7,9tetramethyl-5-decyne-4,7-diyl]-bis-[ω-hydroxyl-polyoxyethylene] (Fig. 8), which contains 10 ethylene oxide (EO) segments. Conclusions from previous studies were that the system underwent two possible transitions namely a monomer 6 micelle I and a micelle I 6 micelle II at 0.9 and 2 wt%, respectively [50-53]. However, recent SANS data, outlined below, Fig. 9 have contradicted these findings [54]. SANS scattering curves of Gemini surfactants at concentrations varying from 0.5 to 5 wt%. Figure 9 shows SANS patterns for various surfactant concentrations [54]. At low concentration (0.5 wt%) and a Q-regime of < 0.02 Å–1, I(Q) decays as Q-4 decay indicating the presence of large particles (> 50 nm) in solution - denoted later on as “clusters”. Between 0.03 and 0.1 Å-1 I(Q) plateaus and decays as Q-2 for Q > 0.1 Å-1, characteristic of particles with a much smaller length scale, possibly monomer surfactant molecules. As the surfactant concentration increases to 1 wt%, the slope of the scattered intensity decreases at small Q values, indicative of scattering contributions from larger sized “clusters”. Moreover, the intensity plateau starts to decay earlier than that seen in the 0.5 wt% sample, implying that the smaller aggregates are getting larger at higher concentrations, presumably due to micellation. The SANS data of the 1 wt% sample also shows a slight upturning at very low Q (< 0.005 Å–1), implying either the coexistence of micelles with small amounts of clusters, or that the size of the clusters, at this concentration, are so large that they are beyond the SANS detecting limit. Above 2 wt% this low Q behaviour disappears completely, indicating that either the clusters have become too large to detect or that they no longer exist. Analysis of the SANS data can reveal the size and aggregation number of the surfactant. For Q· RG # 1 (corresponding to a Q range of 0.01 < Q < 0.04 Å-1) I(Q) can be related to the radius of gyration, RG , aggregation number, ns and the second virial coefficient, A2 (an index for interparticle interaction), as follows 238 PHYSICS IN CANADA Fig. 10 Zimm plot constructed for SANS data of surfactants with concentrations between 1.1 to 5 wt%. The Q values range from 0.008 to 0.1 Å-1. September / October 2006 Sept06-FF.qxd 11/7/2006 2:05 PM Page 239 LA PHYSIQUE ET L’ÉDUCATION ( SMALL-ANGLE NEUTRON ... ) ⎛ 1 + 2A 2 φ + ) ⎜⎝ vsn s φ 1 = I( Q) Δρ 2 ( 1 − Q 2 R 2G / 3 + ∼ ( 1 + Q 2 R G2 / 3 + Δρ )⎛ 1 + 2A 2 φ + ⎜ ⎝ vs n s 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 6. 7. 8. where νs is the volume of one aggregate and Δρ is the difference in scattering length density between the solvent (i.e., D2O) and the surfactant. This equation is the basis of the Zimm plot. By plotting the extrapolated φ=0 (justifies neglecting intermolecular interferences i.e., structure factor) values from φ/I(Q) versus Q2 plots, a straight line is obtained 9. R G3 . On the other hand, by plotting 3 ⋅ v s n s Δρ 2 10. the extrapolated Q=0 (justifies the treatment of intramolecular interference i.e. form factor) values, a line is obtained with 11. slope 12. with slope 2A 2 . Δρ 2 A Zimm plot (Fig. 10) can therefore be (cφ+Q2), constructed with φ/I versus where c is an arbitrary constant allowing for the various φ lines to be separated. The obtained RG , ns and A2 values for micelles are (14.7 ± 3.5) Å, (17.2 ± 0.2), and (-2 ± 6) x 10-5 mol/cm3, respectively. From the analysis of the SANS data the two morphological transitions identified were clusters/monomers 6 clusters/micelles and clusters/micelles 6 micelles. CONCLUDING REMARKS With regards to polymeric materials, SANS is arguably the single most important neutron scattering technique. 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Greedan T ransition metal oxides (TMO) have been perhaps the most ments of similar Z due to the somewhat random variation of intensively studied class of inorganic solids for the past two b with Z. Several useful situations exist, for example the trio decades. It is common to attribute this sustained interest in of elements important in organic and bio materials part to the high Tc cuprate phenomenon which emerged in C (b = 6.65 fm), N (b = 9.36 fm) and O (b = 5.80 fm) and the the late 1980’s and the colossal magneto resistance manthird row p-block elements Al (b = 3.45 fm), Si (b = 4.15 fm), ganates of the 1990’s. In fact new oxide P (b = 5.13 fm), S (b = 2.85 fm) and materials seem to emerge at regular (b = 9.58 fm). For the 3d transition metal oxides Cl intervals, for example the recent dis- Transition elements a particularly useful pattern covery of superconductivity in (TMO) have been perhaps exists as seen in Fig. 1, where the b’s for NaxCoO2 • yH2O [1]. In addition adjacent elements vary widely, permitTMO’s such as LiCoO2 are the basis of the most intensively stud- ting facile discrimination which would the science and technology of lithium ied class of inorganic solids be very difficult with x-rays. Also, note batteries as cathode or positive electhat, unlike for x-rays, neutrons can trode materials, another very active for the past two decades. have negative scattering amplitudes. research area, currently. Neutron scat- The pairing of transition The physical interpretation of this is tering has been an essential tool for that the neutron wave changes phase by probing the complex physics underly- metal oxides and neutron π upon scattering. While neutron scating the behaviour of the materials diffraction extends back to tering lengths can not be calculated which exhibit these phenomena but in from first principles, all of the relevant fact the pairing of transition metal the beginnings of neutron values have been measured and tabuoxides and neutron diffraction extends lated [4]. Examination of such tables beam science in the early shows back to the beginnings of neutron another useful property of neubeam science in the early 1950’s. 1950’s. trons in that different isotopes of the Significantly, the first experiments to same element can scatter neutrons very confirm Néel’s prediction of antiferrodifferently. The most famous example magnetism were performed by Shull, Strauser and Wollan is provided by the stable isotopes of hydrogen, 1H and 2H, for using neutron powder diffraction on MnO, FeO, CoO and which the scattering amplitudes are – 3.74 fm and 6.67 fm, NiO in 1951[2,3] respectively. Why are neutrons so indispensable in the study of transition metal oxides? The basic reasons stem from the composition of the neutron and the nature of the interaction between neutrons and matter. The neutron is comprised of two down quarks and one up quark, so, it is electrically neutral and has a spin of one-half. Thus, neutrons are not scattered by electron density fields, as are x-rays, but are scattered only by other nucleons, i.e. the nuclei of atoms and, as will be discussed shortly, by magnetic fields. Neutrons are, thus, highly penetrating and the scattering amplitude of the neutron nucleus interaction is to a first approximation independent of atomic number but strongly dependent on the composition of the nucleus of a given element. These amplitudes are called “scattering lengths”, b. An important implication is that “light” or low Z elements scatter neutrons as efficiently as “heavy” or high Z elements. For example the elementally averaged scattering lengths for O (b = 5.80 fm) and Ba (b = 5.06 fm) or W (b = 4.77 fm) are comparable. [Note: 1 fm = 10-15m]. This is far from the case with x-ray scattering where the amplitude depends directly on Z. Even 7Li (b = – 2.22 fm), which is nearly invisible to x-rays, especially in a powder experiment, can be seen easily with neutrons. As well, it is often possible to discriminate between ele- Fig. 1 Variation of the neutron scattering length versus atomic number (Z) for the 3d transition elements. Due to the above reasons neutron diffraction is an important tool in the determination and refinement of crystal structures, especially those containing both light elements (such as lithium, boron, oxygen, etc.) and heavy elements and, J.E. Greedan <[email protected]>, Brockhouse Institute for Materials Research & McMaster University, Dept of Chemistry, London, ON L8S 4M1 LA PHYSIQUE AU CANADA septembre / octobre 2006 241 Sept06-FF.qxd 11/7/2006 2:05 PM Page 242 PHYSICS AND EDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) where appropriate, elements with similar Z. For diffraction studies the key quantity is the structure factor defined below for both x-rays and neutrons: F(hkl) = Σ fi exp 2πi(hxi + kyi + lzi) [ x-rays] F(hkl) = Σ bi exp 2πi(hxi + kyi + lzi) [neutrons] where h, k and l are the Miller indices of a given reflection, fi is the x-ray scattering amplitude, xi , yi and zi are the fractional coordinates of atoms within the unit cell and the summation, Σ, includes all atoms within the cell. At this stage it should be noted that fi is strongly attenuated as the scattering angle increases but that bi does not change with angle due to the fact that the nucleus is a point scatterer. In general the neutron diffraction pattern of a transition metal oxide will contain more information than an x-ray diffraction pattern covering the same range of momentum transfer with comparable resolution and overall counting statistics. But, the singular reason that neutrons and transition metal oxides constitute such a perfect pairing is that neutrons are sensitive to the magnetic fields which result from the presence of unpaired electrons at the transition metal site. The variety of magnetic phenomena which follow from the presence of these “local” magnetic moments and their interactions can be probed with unique precision and accuracy using neutron scattering. The key quantity is the so-called magnetic scattering length, p, defined as: p = e 2γ/2mc2 where e and m are the electronic charge and mass, c is the speed of light and γ is the nuclear magneton. In appropriate units p = 2.696 fm, i.e., the same order of magnitude as the nuclear scattering lengths of most elements and is interpreted as the scattering amplitude associated with a magnetic moment of one Bohr Magneton at zero scattering angle. One Bohr Magneton is the magnetic moment of one unpaired electron spin. Thus, the total magnetic scattering amplitude is obtained by multiplying by the magnetic moment for the transition metal ion in question which for the spin only case (usually a good approximation for 3d electrons) is pgSf and where orbital magnetism cannot be ignored (usually the case for 4f electrons), pgJJf. In these expressions g = 2.00, S is the total spin quantum number, gJ is the Lande factor for f electron configurations and J is the total angular momentum quantum number. The common factor, f, is called a “form factor” and arises due to the fact that the magnetic fields are electronic in origin and thus, there is a strong attenuation with increasing scattering angle. This is similar to the situation for the atomic scattering factor in x-ray diffraction but in most cases the attenuation is even more severe. Thus, given that the amplitudes for the magnetic and nuclear scattering are on the same scale for neutrons, the magnetic component is easily detected. This is unlike the case for x-ray magnetic scattering where the magnetic component is only of order 10-4 or less of the electron density scattering. scattering angle and contributes to the background at low scattering angles due to the strong influence of the form factor. When the local magnetic moments are ordered to form an infinite magnetic lattice, i.e., long range magnetic order, the magnetic scattering concentrates in Bragg peaks which reflect the dimensions and symmetry of the “magnetic” unit cell. One can define a magnetic structure factor as below: F(hkl) = Σ pigSifi exp 2πi(hxi + kyi + lzi) [magnetic neutron diffraction] where the sum is now over all of the magnetic atoms in the magnetic unit cell. The total neutron diffraction pattern (assuming an unpolarized neutron beam) for a magnetically ordered material such as a transition metal oxide is thus a superposition of the chemical and magnetic contributions. This is expressed in the equation below: F2(hkl)Total = F2(hkl)Chem + q2F2(hkl)Magn where the factor q2 = sin2 α and α is the angle between the scattering vector (normal to the (hkl) plane) and the magnetic moment vector. This factor arises because what is actually measured in a magnetic neutron diffraction experiment is the component of S or J normal to the scattering vector. Often the magnetic cell has either larger dimensions or different symmetry than the “chemical” cell, so the magnetic Bragg peaks are easily detected. In principle both the chemical and the magnetic structure, i.e. the magnitude and spatial distribution of the magnetic moments, can be determined simultaneously from a neutron diffraction pattern. EXAMPLES FROM EXPERIMENTS AT THE CANADIAN NEUTRON BEAM CENTRE AND/OR BY CANADIAN SCIENTISTS The following examples involve studies using the powder neutron diffraction technique either carried out at the [b] [a] Fig. 2 The details of the magnetic contribution depend on whether the local magnetic moments are random or ordered in the solid. The former case is called paramagnetism and the resulting magnetic scattering is incoherent with respect to 242 PHYSICS IN CANADA September / October 2006 (a) The ideal cubic perovskite unit cell showing the A-site ions at the corners (spheres) and the octahedral coordination of the B-site ions (polyhedra). The oxygen atoms are small spheres at the corners of the octahedra; (b) The unit cell of La1/3NbO3 showing the ordering of La3+ vacancies and the doubling of the ideal perovskite cell in one direction. Sept06-FF.qxd 11/7/2006 2:05 PM Page 243 LA PHYSIQUE ET L’ÉDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) Canadian Neutron Beam Centre or by Canadian scientists at international sites concentrating mainly, but not exclusively, on transition metal oxides. No attempt is made to provide a comprehensive survey. The structure of defect perovskites of the type Ln1/3MO3. Perovskites represent a vast family of oxide materials of general composition ABO3. The ideal, cubic structure is shown in Fig. 2a wherein the small cation B is octahedrally coordinated by O2-. These octahedra share corners to form a three dimensional network and the large cations, A, reside in the large interstices in this network. It has been known for some time that some perovskites can tolerate an unusually large concentration of vacancies on the A-site, for example materials of the type Ln1/3MO3, where Ln is a trivalent lanthanide ion and M is a pentavalent transition metal ion such as Nb5+ or Ta5+ [5]. The earliest studies, using x-ray diffraction, indicated that the Ln3+ ions were not distributed randomly over the A-sites in the pseudo-cubic cell but ordered to produce a super cell requiring the doubling of one pseudo cubic axis as shown in Fig. 2b. Fig. 3a shows an x-ray powder diffraction pattern from a fairly recent study of La1/3TaO3 which is consistent with the structure shown in Fig. 2b [6]. In this case the TaO3 octahedra are well-aligned with no evidence of tilting away from the crystallographic axes, i.e., the Ta – O – Ta angles are all exactly 90o or 180o. Of course the x-ray data are sensitive to the very heavy elements, La and Ta and there is relatively little information about the oxygen atoms. A very different picture arises when neutron diffraction data are considered as done by Dr. C.A. Bridges and the author at McMaster University [7]. In Figs. 3b and 3c are displayed the neutron powder diffraction data obtained for the very similar perovskite, Ce1/3NbO3, at a so-called “spallation source”, the Intense Pulsed Neutron Source at the Argonne National Laboratory. Fig. 3b shows the result of a refinement of the neutron data using the model found from an analysis of the x-ray powder data. Note the presence of several strong reflections which are not accounted for by the model. Upon further analysis, it was discovered that these new reflections result from subtle tiltings of the NbO3 octahedra which leave the Fig. 3 Nb5+ and Ce3+ positions essentially unchanged but which result in significant shifts in the O2- positions relative to those in Fig. 2b. Fig. 3c shows a refinement of the neutron powder data taking these octahedral tiltings into account and the fit is seen to be much improved. In Fig. 4, the structures derived from the x-ray data (4a) and the neutron data (4b) are compared which illustrate the subtle shifts in the oxygen positions which are easily detected by neutrons but are essentially invisible to xrays. Cation Order/Disorder in the Battery Cathode Material Li(Ni1/3Co1/3Mn1/3)O2 As already mentioned, transition metal oxides are the cathode materials of choice in modern lithium battery technology. The first lithium battery to be a commercial success, marketed by SONY, uses LiCoO2 as the cathode or positive electrode. Lithium battery cathodes must be capable of storing and releasing Li+ ions reversibly at room temperature as illustrated by the electrochemical half reaction below: LiCoO2 ] Li+ + “CoO2” + eIn practice not all of the Li+ can be extracted from LiCoO2 due to the inherent instability of Co4+ under ambient oxygen partial pressure. The reversibility of this reaction is due to the crystal structure which is of the layered NaCl type, Fig. 5a, in which it is seen that the Li+ and Co3+ ions do not randomly occupy the Na+ sites in the NaCl structure but instead order in separate layers which are normal to the body diagonal of the NaCl cell. Li+ is removed reversibly from the Li layers and re-inserted during charging and discharging of the bat- (a) Rietveld fit of x-ray powder diffraction pattern for La1/3NbO3 to the model shown in Fig. 2b. The fit is clearly excellent [Ref 6, reproduced with permission of Elsevier]; (b) Fit to the neutron powder data for Ce1/3NbO3 using the model derived from x-ray powder diffraction, illustrated in Fig. 2b. The crosses are the data, the solid line is the fitted model, the vertical tic marks locate Bragg reflections and the bottom curve is the difference between the data and the model. The inset shows major peaks not accounted for in the model and the fit is seen to be poor [Ref. 7, reproduced with permission of the International Union of Crystallography]; (c) Fit to a model derived from an analysis of the neutron diffraction data in which the NbO3 octahedra tilt along the unit cell axes and the light atoms (oxygen) move from the ideal positions. The fit is seen to be much improved [Ref 7, reproduced with permission of the International Union of Crystallography]. LA PHYSIQUE AU CANADA septembre / octobre 2006 243 Sept06-FF.qxd 11/7/2006 2:05 PM Page 244 PHYSICS AND EDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) Fig. 4 (a) Projection of the crystal structure of Ce0.33NbO3 from x-ray powder diffraction data compared with the result from neutron power diffraction. The Ce3+ and O2- ions are shown as spheres while the NbO3 corner sharing octahedra are shown in polyhedra representation. Note the subtle tilting of the octahedra which shift the oxygen atoms from their idealized positions (Fig. 2b). These small shifts are easily detected in the neutron experiment but missed in the x-ray data due to the low scattering power of oxygen. Fig. 5 tery. There are nonetheless many problems with LiCoO2, due mainly to the toxicity and cost of Co but also to the instability of Co4+ as mentioned earlier, so there is considerable impetus to replace this material. One promising candidate is Li(Co1/3Mn1/3Ni1/3)O2. The structural questions concerning this oxide revolve around issues such as whether the three elements are randomly distributed within the transition metal layer or ordered, whether the Li+ ions can mix with the transition metal ions as is the case in LiNiO2 and whether changes in structure occur when large amounts of Li are removed. In fact two possible cation ordering schemes had been proposed [8], which are illustrated in Fig. 5. This is of course an ideal problem for neutron diffraction, given the ease of discrimination among the three transition elements (Fig. 1) and the Li+ positions can be determined with great accuracy as well. These questions were recently addressed by two Canadian groups, at NRC (P.S. Whitfield and I.J. Davidson) and the University of Waterloo (L.F. Nazar) [9,10] using both synchrotron x-ray diffraction and neutron diffraction methods. By comparing calculated neutron diffraction patterns for the two cation ordering schemes and a random model with the observed data, the NRC group were able to show, Fig. 6, that neither cation ordering scheme could be detected in the neutron data, indicating that long range order does not exist. A more detailed analysis of the results showed a very minor, 2%, mixing between Li+ and Ni2+. Fig. 6 The Waterloo group studied the effect on structure upon electrochemical removal 244 PHYSICS IN CANADA The ordered NaCl structure of LiCoO2 is shown in (a). The large open spheres are oxide ion, the smaller black and hatched spheres are Co2+ and Li+. Two possible cation ordering schemes are proposed for Li(Ni1/3Co1/3Mn1/3)O2. In (a) ordered occurs within the transition metal ion layers and in (b) the transition metal ions order into separate layers [8] [Ref. 9, reproduced with permission of Elsevier]. of Li, i.e. the structures of Lix(Ni1/3Co1/3Mn1/3)O2. An important result from their research that a structure change occurs for very low Li contents (x = 0.04) as well as a significant contraction of the c-axis in strongly Li depleted phases. Both observations explain the problems of reversibility and electrochemical cycling in this composition range. Nonlinear Optical (NLO) Materials – Heavy Metal Borates This is an example from the laboratory of Professor J. Barbier of McMaster University. In this group the crystal and structural chemistry of metal borates is investigated as part of a search for new NLO compounds. For such materials a noncentrosymmetric structure is necessary and this often can be achieved by incorporation of so-called “lone pair” cations (a) Calculated neutron powder patterns for the cation ordered models for Li(Ni1/3Co1/3Mn1/3)O2 and a random model compared with (b) the actual data for λ = 2.37 Å neutrons. Clearly, there is no evidence for long range cation ordering [Ref. 9, reproduced with permission of Elsevier]. September / October 2006 Sept06-FF.qxd 11/7/2006 2:05 PM Page 245 LA PHYSIQUE ET L’ÉDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) such as Pb2+ or Bi3+. A recent case concerns BaBiBO4 for which only powder samples were available [11]. The accurate location of the B atoms or even O in the presence of very high Z elements such as Ba and Bi presents a significant challenge. The heavy atoms could be located from analysis of x-ray powder data and approximate positions for B and O were also suggested. However, a detailed structure refinement could only be carried out using neutron data. (11B enriched starting materials are generally available to avoid the strong neutron absorber, 10B). The detailed analysis was necessary to determine if the structure was indeed non-centrosymmetric. Fig. 7 shows a socalled Rietveld refinement of the high angle neutron data for BaBiBO4 and the resulting crystal structure. Fig. 8 Refinement in a non-centrosymmetric model was shown to be slightly but significantly superior to that in a centric model. This was confirmed by measuring the optical properties in which a high second harmonic generation efficiency was observed. Two possible models for the structure of ammonium cyanate, NH4CNO, involving (a) N – H – O hydrogen bonds and (b) N – H – N hydrogen bonds. The carbon atoms are not shown [Ref. 14, reproduced with permission of the American Chemical Society]. Hydrogen Bonding in Ammonium Cyanate, NH4CNO While clearly not a transition metal oxide, this example is nonetheless compelling in its illustration of the singular power of neutrons to detect light atoms (H or D) and to distinguish between atoms of similar Z (N and O). This work is a collaboration among several laboratories including that of Prof. R.R. Tykwinski of the University of Alberta and J.D. Dunitz of the ETH in Zürich [12]. The solid state transformation of ammonium cyanate to urea, H2N – C O – NH2, observed by Wöhler, a pioneer of organic chemistry, was first studied more than 170 years ago [13]. The mechanism is still Fig. 9 Fig. 7 Rietveld refinement of the neutron powder diffraction pattern of BaBiBO4 on a non- centrosymmetric model consistent with NLO properties and a model of the refined structure. The Ba2+ and O2- ions are shown as large and small spheres, the BO3 groups as planar triangles and the unusual distorted five-fold pyramidal site for Bi3+ is apparent [Ref. 11, reproduced with permission of Elsevier]. Rietveld refinement of neutron powder data for ND4NCO. The refined structure is consistent with the model in Fig. 8b, i.e., with N – H – N hydrogen bonding [Ref. 14, reproduced with permission of the American Chemical Society]. under investigation. It is of course important to understand the structure of ammonium cyanate, the starting compound. Two possible models for this structure, focussing on the environment about the NH4+ (ammonium) ion, are shown in Fig. 8. There is a clear choice between (a) N – H – O and (b) N – H – N hydrogen bonding linkages. Earlier studies of this problem using laboratory x-ray powder data, supported by calculations, had supported formulation (a) [14]. However, subsequent analysis of high quality synchrotron x-ray data showed that there was in fact no significant difference between the two models and that x-ray data, even of the highest quality, could not solve this problem. To quote the authors “Chastened by our experiences with the use of x-ray powder diffraction to tackle this problem, we turned to neutron powder diffraction of a deuterated sample ND4NCO.” Fig. 9 shows the Rietveld refinement of the data on model (b). Attempts to refine on model (a) were significantly inferior. Thus, the solid state structure of ammonium cyanate has been established, unequivocally, by neutron diffraction. LA PHYSIQUE AU CANADA septembre / octobre 2006 245 Sept06-FF.qxd 11/7/2006 2:05 PM Page 246 PHYSICS AND EDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) MAGNETIC NEUTRON DIFFRACTION unit cell must be twice the value of the chemical or nuclear unit cell along the c-axis direction. We conclude this survey of The temperature dependence for activity in Canadian neuthe strongest magnetic Bragg tron powder diffraction peak is shown in Fig. 12 to be with some examples in consistent with a Tc = 155K, just which magnetic scattering is at the peak in the χT vs T plot. A highlighted. Most of these Rietveld refinement of the full involve projects from the data set using models for both author’s laboratory somethe crystal and magnetic structimes in collaboration with tures yields the result shown in others. the inset in which it is seen that within the layers the Fe and Re Magnetic Structure of the spins are coupled ferrimagnetiQuasi-Two Dimensional cally while overall the layers are Ferri-magnets, the Pillared coupled antiferromagnetically. Perovskites La5Re3MO16, Magnetic moments in the M = Mn, Fe, Co,Ni ordered state can be refined for each atom and are 1.53(13) μB for Oxides of this unusual comRe5+ and 3.10(15) μB for Fe2+. position were discovered Note that the spins for both ions about 10 years ago, indepoint directly along the c-axis pendently, by two Fig. 10 The crystal structure of La5Re3MO16. Note the corner direction. This is determined by sharing octahedral layers (light grey and dark grey) groups [15,16]. While the the absence of reflections of the of composition Re5+M2+O77- which are pillared by chemical formula appears type (0 0 ½) which indicates that edge-sharing dimeric Re2O99- units(black). The La3+ complex, the crystal strucions are shown as white spheres. the moment direction must be ture is easy to understand, along c. Now, the bulk properties Fig. 10. It consists of infinite can be understood. Upon coolsheets of corner sharing octahedra, as found in the perovskite ing ferrimagnetic correlations develop within the layers as structure of composition Re5+M2+O77-, which are “pillared” manifested in the sharp increase in χ just above 155K, below by edge-sharing octahedral dimeric units, Re2O98-. The which the layers begin to couple antiferromagnetically which dimeric pillaring units are diamagnetic so the magnetic ions gives rise to the sharp drop with decreasing temperature. are in the perovskite-like layers which are > 10.3 Å apart. A typical example is La5Re3FeO16. The bulk magnetic properThe work described above is exemplary of that which has ties are very unusual, showing a sharp in the susceptibility been carried out over a period of several years in the author’s near 155K followed by a sharp decrease. To understand the microscopic magnetic structure, neutrons are needed. Fig. 11 shows the low angle part of the diffraction pattern for two temperatures, 160K, 13K and the difference plot for 13K – 160K. Difference plots are very useful devices for locating magnetic reflections which are present only below the “critical” or ordering temperature, Tc. In the inset to Fig. 11, four such magnetic reflections are indexed. That these peaks are seen only at low scattering angles is a reflection of the form factor, f, discussed previously. Note that the l Fig. 11 index is half integral, indicating that the magnetic 246 PHYSICS IN CANADA Low angle part of the neutron powder diffraction pattern for La5Re3FeO16 at 160K, 13K and the difference, 13K – 160K, showing the magnetic contribution and indexation of the magnetic peaks. Note that the c-axis for the magnetic cell is doubled relative to the chemical cell. September / October 2006 Sept06-FF.qxd 11/7/2006 2:05 PM Page 247 LA PHYSIQUE ET L’ÉDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) Fig. 13 (a) The “pyrochlore” lattice consisting of a three dimensional array of corner-sharing tetrahedra; (b) Geometric frustration of three spins on a triangle and four spins on a tetrahedron. Li+ into the cubic spinel LiMn2O4 as below: Fig. 12 Temperature dependence of the strongest magnetic reflection ( -1 +/-1 ½) showing Tc = 155K and the refined magnetic structure of La5Re3FeO16 which consists of ferrimagnetic Fe 8 Re 9 layers coupled antiferromagnetically. laboratory by undergraduates, exchange students, graduate students and postdoctoral fellows including Thomas Langet, Aurilien Gourrier, Andrew Green, Chris Wiebe, Heather Cuthbert and Lisheng Chi. Unexpected Two Dimensional Spin Correlations in the Three Dimensional Frustrated Spinel Oxide, Li2Mn2O4 This study was done in collaboration with Dr. A.S. Wills of University College London. Spinel oxides have attracted much attention lately in the context of the study of geometrically frustrated magnetic materials. The formula of a spinel oxide is AB2O4 where A ions occupy tetrahedral sites and B ions octahedral sites in a cubic close packed array of O2- ions. The B sites form what is called a “pyrochlore” lattice consisting of a three dimensional array of corner sharing tetrahedra as shown in Fig. 13. If the Fig. 14 nearest neighbour spin coupling constraint is for anti parallel spins, this lattice is “frustrated” in that only 2 of the 4 spin pairings can be satisfied simultaneously. As part of a long established and ongoing study of frustrated systems, the spinel Li2Mn2O4 was prepared by room temperature introduction of Li – n butyl (hexane) + LiMn2O4(s) 6 Li2Mn2O4(s) + n- octane(hexane) Thus, a metastable form of “LiMnO2” can be prepared with Mn3+ ions on a slightly distorted (Mn3+, 3d4, is a so-called Jahn-Teller ion and the structure is distorted from cubic to tetragonal) pyrochlore lattice. The stable form of LiMnO2 has a different structure. Again the bulk susceptibility of this material is unusual,with a broad maximum near 200 K and a sharp increase below ~ 50K with no discernable paramagnetic regime [17]. Again, neutron diffraction is needed to probe the magnetic correlations and the results appear in Fig. 14. Remarkably, the magnetic reflections have the asymmetric shape, called the Warren line shape, associated with correlations in two dimensions, yet the Mn3+ sublattice is three dimensional! The two observed peaks can be indexed as (20) and (13) on a particular type of two dimensional magnetic structure called the /3 x /3 Kagomé structure. (The Kagomé lattice consists of a planar array of corner sharing triangles and the pyrochlore lattice is built up of alternating Kagomé and triangular planar lattices.) See the original paper for more details [17]. Low angle part of the neutron diffraction pattern of Li2Mn2O4 showing the development of the asymmetric “Warren” peaks with decreasing temperature. The two peaks can be indexed as (20) and (13) suggesting short range order on the Kagomé planes in the pyrochlore structure [Ref. 17, reproduced with permission of the American Chemical Society]. LA PHYSIQUE AU CANADA A correlation length for the short range two dimensional ordering can be derived from a detailed fitting of the Warren peak shape and the temperature dependence is shown in Fig. 15. Note the sharp, first order like increase below 45 K and that the length scale remains finite at ~ 90 Å. There is still no detailed model to explain this remarkable result. septembre / octobre 2006 247 Sept06-FF.qxd 11/7/2006 2:05 PM Page 248 PHYSICS AND EDUCATION ( NEUTRONS AND TRANSITION METAL OXIDES ... ) blet (100)/(001) arises from an induced moment on the Nd3+ sites and the higher one (110)/(011) is due to the Ti3+ spins. This enhanced resolution makes possible for the first time the unambiguous determination of the magnetic structure of NdTiO3, shown on the right hand side of the figure. CONCLUSION An attempt has been made to show the scope of problems which can be addressed using neutron diffraction, mainly the powder method, in the study of transition metal oxide materials using examples carried out by Canadian scientists at the CNBC or elsewhere. Neutron diffraction is not merely complementary to x-ray diffraction but is an essential tool in the study of these systems. Perhaps B.N. Brockhouse said it best, “If neutrons did not exist they would need to be invented.” Fig. 16 The two strongest magnetic reflections for NdTiO3 showing clear Fig. 15 The temperature developresolution into doublets. This perment of the two dimensional mits the unambiguous determinaspin-spin correlation length tion of the magnetic structure in Li2Mn2O4. Note the first shown at the right. order like increase near 45K [Ref. 17, reproduced with REFERENCES permission of the American Chemical Society]. 1. K. Takada, H. Sakurai, E. Takayama-Muomachi, The Magnetic Structure of the Perovskite NdTiO3 using High Resolution Neutron Powder Diffraction 2. 3. The rare earth titanium perovskites, LnTiO3, where Ln3+ is a lanthanide, have been studied for more than 25 years due to a remarkable set of electronic properties. The parent compounds are Mott-Hubbard insulators, rather than metals, as expected from band theory due to a strong electron-electron correlation energy. Unique among rare earth transition metal perovskites, the sign of the spin-spin correlations between the transition metal ions changes from antiferromagnetic to ferromagnetic as the size of the rare earth ion decreases across the lanthanide series. The materials for Ln = La – Sm are antferromagnetic while those for Ln = Gd to Lu are ferromagnets. Considering the antiferromagnetic series, there are two important issues – one is the anomalously low ordered moment at the Ti3+ site of ~ 0.5 μB where ~ 1 μB is expected for a S = ½ ion and the second is the exact magnetic structure in the antiferromagnetic state. Surprsingly, the detailed magnetic structure is not known with certainty for the LnTiO3 antiferromagnets due to two factors – lack of true single crystals due to micro-twinning and the general use of low resolution data in older studies in which key magnetic reflections are not measured separately. To remedy this situation neutron diffraction data were obtained on nearly stoichiometric NdTiO3 using high resolution conditions (ë = 2.37 Å) at the CNBC [18]. 4. Data were obtained at 3.8K (Tc = 88K for the sample studied). The magnetic reflections are very weak relative to the structure reflections ( 1% < of the most intense structure peak) due of course to the very small magnetic moments involved. In Fig. 16 the magnetic reflections are isolated and the resolution into two sets of doublets is clear. The lower angle dou- 248 PHYSICS IN CANADA 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. September / October 2006 F. Izumi, R. Dalanian and T. Sasaki, Nature 422, 53 (2003). L. Néel, Ann. Phys. 17, 64 (1932). C.G. Shull, W.A. Strauser and E.O. Wollan, Phys. Rev. 83, 333 (1951). International Tables for Crystallography, Volume C., A.J.C. Wilson, ed. Kluwer Academic Publishers, Dordrecht, the Netherlands, 1992, pp. 384-391. P.N. Iyer and A.J. Smith, Acta. Cryst. 23, 740 (1967). A.M. Abakumov, R.V. Shpanchenko and E.V. Antipov, Mat. Res. Bull. 30, 97 (1995). C. Bridges, J.E. Greedan, J. Barbier, Acta. Cryst. B56, 183 (2000). Y. Koyama, I. Tanaka, H. Adachi, Y. Makamura and T. Ohyuku, J. Power Sources 119-121, 649 (2003). P.S. Whitfield, I.J. Davisdon, L.M.D. Cranswick, I.P. Swainson and P.W. Stephens, Solid State Ionics 176, 463 (2005). S.-C. Yin, Y.-H. Rho, I.P. Swainson and L.F. Nazar, Chem. Mater. 18, 1901 (2006). J. Barbier, N. Penin, A. Denoyer and L.M.D. Cranswick, Solid State Sci. 7, 1055 (2005). E.J. MacLean, K.D.M. Harris, B.M. Kariuki, S.J. Kitchin, R.R. Tykwinski, I.P. Swainson and J.D. Dunitz, J. Am. Chem. Soc. 125, 14449 (2003). F. Wöhler, Pogg. Ann. 12, 253 (1828). J.D. Dunitz, K.D.M. Harris, R.L. Johnston, B.M. Kariuki, E.J. MacLean, K. Psallidas, W.B. Schweizer and R.R. Tykwinski, J. Am Chem. Soc. 120, 13274 (1998). M. Ledesert, PH. Labbe, W.H. McCarroll, H. Leligny and B. Raveau, J. Solid State Chem. 105, 143 (1993). C.R. Wiebe, A. Gourrier, T. Langet, J.F. Britten and J.E. Greedan, J. Solid State Chem. 151, 31 (2000). A. S. Wills, N.P. Raju, C. Morin and J.E. Greedan, Chem. Mater. 11, 1936-1941 (1999). A.S. Sefat, J.E. Greedan and L.M.D. Cranswick, Phys. Rev. B74, 104418 (2006). Sept06-FF.qxd 11/7/2006 2:05 PM Page 249 LA PHYSIQUE ET L’ÉDUCATION ( STOP THAT CORROSION ... ) STOP THAT CORROSION - IF YOU CAN by Zin Tun, Jamie Noël and Dave Shoesmith I technique offers some unique capabilities. This brings us to n Spring 1836, Michael Faraday received a letter from the topic of this article. At Chalk River we have an ongoing Prof. Schoenbein, Professor of Chemistry at the University of research program to study passive oxide layers with neutron Bâle [1]. Schoenbein lamented how slow German periodicals reflectometry (NR). Instead of iron, our experiments have were in getting scientific papers published, and apologized been on titanium (Ti) and zirconium (Zr), two metals that are for taking the liberty of writing directly to Faraday. of interest to the nuclear industry. Schoenbein further presented observations he had made recently by dipping iron wires into a NEUTRON REFLECTOMETRY strong nitric acid where, under certain conditions, iron seemed to be fully The scientific study of pasprotected from the acid. Faraday sive oxide on metals started NR is a relatively new neutron scattering technique that allows determination repeated Schoenbein’s experiments for of near-surface layer structure of a flat in 1836 continues to this verification, carried out investigations of his own, and proposed tentatively day. It is fair to question if sample to a resolution of 1 or 2 nanometers in the direction normal to the samthat the passivation of iron was caused by the growth of a thin oxide layer on there is anything more to ple. As the measurements are limited to the wire. This body of work was pub- discover in such an old area small scattering angles, individual atoms are not observed by NR. Instead, lished in the Philosophical data analysis yields a function known [2] of research. After all, we Magazine later in the year. as the scattering-length density (SLD). The scientific study of passive oxide on now know Faraday’s pro- The SLD is the product of coherent neumetals thus started continues to this posal is basically correct [3]. tron scattering-length (usually denoted by b) and number density of constituent day. It is fair to question if there is isotopes of a particular layer. If a layer anything more to discover in such an contains more than one isotope, the old area of research. After all, we now layer SLD is the all-inclusive sum performed over all isotopes know Faraday’s proposal is basically correct [3]. The continpresent. We herein report specular reflectivity measurements ued interest in the phenomenon is due to several factors, each where the scattering vector q is kept perpendicular to the surproviding a compelling reason. First, the problem is interestface of the sample, taken to be the z-direction. Consequently, ing in its own right, involving the not well-understood solidspecular reflectivity provides no in-plane sensitivity. The state ion transport. Also there remains some fundamental SLD profiles we report are functions of z only, and they are issues not fully resolved. For instance, even the composition the xy-sum of SLD contributed by all isotopes that lie at the and structure of the oxide are still matters of controversy [3]. particular depth z. Second, we all realize that metal passivity, if it were fully understood and controlled, would have major impact, not Neutron scattering cross-sections are small compared to those only for industry but for the whole society. This promise drives researchers to continue looking for a unifying model or that give rise to X-ray or electron diffraction. Consequently, explanation, such as a recipe for growing an passive oxide diffraction signals from a nanometer scale layer would be too that would effectively stop corrosion of any metal under any weak to measure with neutrons. NR overcomes this difficulenvironmental condition. We are fully aware that a general ty by making use of total external reflection of neutrons when recipe may not exist given that intrinsic properties of metals they strike the sample surface at a small enough grazing (alloys included) and their oxides vary enormously. angle. Just as for visible light, below the critical angle, θc, the Nevertheless, even if we do not achieve such a lofty goal, the reflectivity of the interface is unity, i.e. the entire incident research will still be worthwhile since we will no doubt come beam is reflected. Once the grazing angle exceeds θc, the across some interesting phenomena as we work in this rich reflectivity drops quickly but this drop can be measured with field of research. Finally, the very fact that a thin layer of great precision for at least 5 or 6 orders of magnitude. The atoms, often not more than 10 crystallographic unit cells if it details of this drop are what conveys the information about were an ordered structure, is capable of stopping this the layer structure. For instance, for a sharp interface omnipresent agent of destruction - corrosion - is intriguing. It between two different media, the drop follows the well has captured many researchers’ interest in the past and is likely to do so in the foreseeable future. CHANCE FAVOURS THE PREPARED MIND, BUT … The chance of observing an interesting phenomenon increases if one uses a new experimental technique, especially if the Z. Tun <[email protected]>, National Research Council, Chalk River, ON K0J 1J0; J. Noël and D. Shoesmith, Dept.. of Chemistry, Western Ontario, London, ON N6A 5B7 LA PHYSIQUE AU CANADA septembre / octobre 2006 249 Sept06-FF.qxd 11/7/2006 2:05 PM Page 250 PHYSICS AND EDUCATION ( STOP THAT CORROSION ... ) Fig. 2 Fig. 1 Fresnel equation (dashed curve) plotted as a function of the scattering vector q. This is the expected variation of reflectivity if the interface causing the reflection is a sharp boundary between two media. For this plot we assume the media to be air and Si. In the case where there is a thin layer of a third material on the surface (assumed to be Au for this example) an interference pattern will be observed (solid curve). known Fresnel equation. In the case of a more complicated example, if the sample consists of several layers, each with a well defined thickness and SLD, an interference pattern appears superimposed on the Fresnel Law (Figure 1). Broad interfaces, in general, can be thought of as a series of “microlayers” whose SLD follows a profile defined by a sigmoidal function of a finite width. For data analysis, one proposes a layer profile model whose calculated reflectivity is at least approximately similar to the observed reflectivity. Much in the same way as for crystallographic structure refinement, the residual discrepancies between Robs and Rcal are then minimized by least-squares refinement of the model parameters, i.e. the thickness, SLD, and interface width of the layers are refined. One advantage of NR that is very much relevant to our research is its ability to detect the presence of hydrogen or Hcontaining species. 1H (or natural H which is 99.99% 1H) is one of the few isotopes whose neutron scattering length, b, is negative, meaning the Fermi pseudo potential between a proton and a neutron is attractive instead of repulsive. Therefore, during an experiment where an in-situ chemical reaction is in progress, a decrease in the SLD of a layer, for example, may signal H ingress into a layer. One can verify this tentative result by repeating the experiment in a deuterated environment, for 2H (or D), unlike H, has a very large positive b. If the hypothesis about the H-ingress is correct, the SLD of the layer should increase in the deuterated experiment. 250 PHYSICS IN CANADA Two possible geometries of performing neutron reflectometry on a thin metal film (e.g. Ti film of several tens of nanometers) deposited on a Si substrate. The circular substrate of 100 mm diameter and 6 mm thickness is shown edge-on, and the arrows represent incoming and reflected neutron beams. Another advantage of NR is that the scattering geometry makes it particularly easy to combine NR with many other experimental techniques. The θ/2θ scan performed for NR is almost a straight-through geometry (often 2θ < 10o), providing un-obscured frontal view of the sample surface and direct access for other probes for simultaneous investigation. The geometry is depicted in Figure 2a. On the other hand, if the sample needs to be enclosed in a special environment (controlled humidity, high vacuum, etc.) one can easily design an enclosure with two small windows. Yet another possibility is to use a substrate that is highly transparent to neutrons to support the thin film sample. Most popular substrates are Si or sapphire. In that case, the beam can be arranged to strike the thin-film sample from the substrate side as shown in Figure 2b. Note that the space away from the neutron beams is then entirely clear and open for whatever experiments one wishes to perform simultaneously. Figure 3 is an example of such an experiment where a specially designed cell allows simultaneous performance of NR and electrochemistry on a working electrode. These possibilities make NR very versatile and have produced many ingenious experiments worldwide. PASSIVE OXIDE ON Ti Using a cell based on the same design as the one depicted in Figure 3, Wiesler & Majkrzak [4,5] carried out NR on a Ti thin film in contact with (0.1 mole/dm3) H2SO4 solution. In this pioneering work, the authors grew anodic oxide on the already existing passive oxide in two ways – either by applying anodic potential abruptly or by slowly ramping (1 mV/s) the potential to its final value. They found that slightly denser packing results if the potential is slowly ramped, and the denser oxide thus formed dissolves slower in the acid. They also made observations on the loading of H into the oxide and the underlying metal by reversing the bias to cathodic polarity. September / October 2006 Sept06-FF.qxd 11/7/2006 2:05 PM Page 251 LA PHYSIQUE ET L’ÉDUCATION ( STOP THAT CORROSION ... ) anodization, and used up some 38 D of the underlying metal in the process. These changes correspond to anodization ratio α = (tE – tOC)/(E – EOC) = 25.4 D/V and the Pilling Bedworth ratio (volume of oxide produced per volume of metal consumed) RPB = 1.72 ± 0.04. These values compare well with literature values: the most commonly accepted value for α for Ti is 25 ± 5 D/V [9], while RPB, depending on the crystallographic structure of the oxide, is expected to be 1.77, 1.82, and 1.96, respectively, for rutile, brookite and anatase structures. We note that the observed RPB was very low, barely acceptable compared to the formation of rutile, the highest density form of TiO2. This suggests the resultant oxide was free of major voids and cavities. Fig. 3 Schematic of a cell to perform neutron reflectometry and electrochemical reactions simultaneously. The working electrode (WE) is a metal thin film deposited on low-resistance Si, while a Pt foil serves as the counter electrode (CE). A saturated calomel electrode (SCE), connected to the main body of electrolyte via a capillary and a porous ceramic junction acts as the reference electrode (RE) of the cell. In the 1990s, research groups at AECL’s Whiteshell Laboratories had a strong interest in the corrosion properties of Ti because the metal was being considered as a container material for underground spent nuclear fuel disposal (Canadian Nuclear Fuel Waste Management Program). Wiesler & Majkrzak’s work inspired us and we set out to do similar NR experiments combined with insitu electrochemistry. However, there is one major difference: instead of H2SO4 we chose to work with aqueous NaCl solution (0.27 mole/dm3) as the containers would come into contact with near-neutral pH, saline underground water. In addition to a better understanding of the corrosion mechanism, we needed a good estimate of the threshold polarization that would initiate H adsorption into Ti. Our results have been reported in several papers [6-8]. One of the highlights of the work is being able to shed light on the mechanism of ion transport across an existing oxide layer during anodization. Figure 4 shows the SLD curves of the Ti film exposed to the electrolyte solution both before (i.e. at the open circuit potential, EOC) and after being anodized to E = 2 V. Ti is another one of the few isotopes with negative scattering length, and hence the SLD of the metal layer is below zero. The scan at 2 V was performed several hours after setting the Fig. 4 potential to ensure we measured the long time equilibrium behaviour of the oxide layer. As expected, the oxide layer, originally at tOC = 47 D, thickened to tE = 112 D by Another important result depicted by Figure 4, as deduced from least-squares refinement with various models, is that the outer layer of the anodized oxide (i.e. the part that was in contact with the electrolyte) has a lower SLD than the original oxide. Three possibilities present themselves to explain the low SLD region: a) this region of oxide is porous, b) it is oxygen deficient, i.e. TiOx with x < 2, or c) it contains some form of hydrogen. Possibility a) can be ruled out on the basis that the observed RPB is very low, indicating the resultant oxide is highly compact. Since the Ti oxides are insoluble in water, an argument such as “RPB is actually high but it appears low as part of the oxide had dissolved away before NR was started” is not credible. Possibility b) can be rejected on the grounds that oxygen deficiency, if any, should occur deep within the oxide layer, not on the surface. This leaves possibility c) which is most likely since incorporation of H (as OH species) during anodization is indeed a known phenomenon (e.g. the observation of absorbed OH by angle resolved XPS as reported by Tun et al. [8]). Scattering-length density (SLD) profile of a Ti thin-film deposited on a Si substrate. The SLD of the metal layer is negative since the scattering length of Ti is negative. The oxide layer, 47 Å prior to anodization (open-circuit EOC = – 0 56 V ), thickened to 112 Å after acquiring equilibrium at 2 V applied potential. LA PHYSIQUE AU CANADA septembre / octobre 2006 251 Sept06-FF.qxd 11/7/2006 2:05 PM Page 252 PHYSICS AND EDUCATION ( STOP THAT CORROSION ... ) mobility), and react with Ti. Meanwhile, Ti migrates out (with 35% mobility) and reacts with O (as OH or water) at the oxide/electrolyte interface. Thus we end up with an inner layer of H-free oxide and an outer layer of H-containing oxide. If we accept this picture of oxide growth, the fact that the H-containing region ends just at the right depth so that the H-free region happens to have the same thickness as the original air-grown oxide is an accident. While there is nothing preventing such a fortuitous outcome, we thought it was desirable to look for alternative models of solid-state oxide growth where the amount of H-free oxide is necessarily conserved. The alternative model we favour is the point-defect model (PDM) [11]. The basic idea is depicted in Figure 6. According to this model, field-driven migration of one of the species, say O, is initiated when an O atom near Fig. 5 Visualization of field-assisted ion transport across an existthe metal/oxide layer hops into a defect site in the ing oxide layer. Most of potential drop between the metal of metal. This creates a vacancy in the oxide, which is anode and cathode takes place within the oxide which is an filled by an O atom at a shallower depth of the oxide, insulator or a large-gap semiconductor. The resulting elecleaving its original site vacant. This sequence of vacantric field within the oxide layer drives cations and anions in cy creation and subsequent filling by a nearby ion propopposite directions. agates outward through the existing oxide until, finally, the vacancy created at the oxide/liquid interface is filled Having thus explained the low SLD region, we are confrontby an O atom (or an OH ion) derived from the solution. The ed with yet another question: Is the high SLD region the origmetal ions can also migrate through the existing oxide by a inal oxide? From the peak value of SLD and the thickness, similar vacancy transfer process running in the opposite the high SLD region seems to be very similar to the original direction. oxide; it is tempting to think that they are one and the same. One could argue that the high SLD region is the original The O in the original air-grown oxide is H-free and, since this oxide that has “sunk” closer to the Si/Ti interface because number of O atoms is conserved according to PDM, the thicksome amount of metal has been removed and transported ness of H-free oxide would be conserved. The newly incorpoacross the original oxide to form new oxide (the low SLD rated O by anodization is contaminated to some extent with region) at the oxide/electrolyte interface. Note also that this H, causing the extra thickness of the oxide produced by consideration is valid regardless of which of the three possianodization to have a lower SLD. The fact that we do not bilities as explained above is responsible for the low SLD need to invoke a fortuitous outcome makes the PDM more region. However, such an interpretation is not consistent attractive. However, we recognize that a more direct experiwith known transport numbers for anodization of Ti. mental evidence is needed to decidedly settle this issue. Exclusive outward growth of the oxide would require very high Ti mobility. Using α-particle emitters implanted prior to anodization, Khalil and Leach [10] determined from the energy-loss spectrum that the emitter layer was buried within the thickened anodized oxide, at a depth of 35% of the increase in the oxide layer thickness. This corresponds to 35% metal and 65% oxygen mobility. Clearly, an alternative explanation is needed. It is important to first recognize that our desire to talk about the original oxide comes from the field-assisted ion transport (FAIT) model. The basic concept of this mechanism is depicted in Figure 5. Differently charged ions migrate through an existing oxide and react with respective counter ions at the metal/oxide or oxide/liquid interface. According to this simple-minded picture of FAIT, the original air grown oxide is merely a passive screen. Within the FAIT, we are then led to the following picture at the molecular level: What is attracted towards the anode is OH. Presumably H is stripped by the very large potential gradient within the existing oxide, H remains within the shallower depths while O continues to pass through (with 65% 252 PHYSICS IN CANADA Fig. 6 September / October 2006 Visualization of point-defect model of ion transport. When an ion within the existing oxide hops to a neighbouring lattice vacancy (defect), it creates a vacancy at its original site. Sept06-FF.qxd 11/7/2006 2:05 PM Page 253 LA PHYSIQUE ET L’ÉDUCATION ( STOP THAT CORROSION ... ) recorded over a frequency range spanning from a few mHz to ~100 kHz. Currents as low as a few nano-amperes are recorded. The data are then analyzed in terms of an equivalent circuit where a capacitor, for example, would represent the charge storage capacity of the double-layer on the electrode surface and a resistor parallel to it would represent charge leakage whose origin could be an electrochemical reaction or an electronic or ionic current. Only a preview of our NR and EIS results is provided here as we intend to publish a full account of these experiments elsewhere. Fig. 7 Scattering-length density (SLD) profile of a Zr thinfilm deposited on a Si substrate before anodization (labeled EOC), after attaining equilibrium at 1 V (E = +1V) and subsequently at 3 V (E = +3V). The SLD curves of our Zr thin film sample obtained at open circuit (EOC = –0.17 V) and two anodizing potentials are shown in Figure 7. Actually, NR (and EIS) data were collected at anodic potentials starting from 0 to 3 V in steps of 0.5 V. To ensure long time equilibrium behaviour was recorded, the NR scans, each typically taking 6 h, were repeated until no further change was discernable in the measured reflectivity. Depending on whether the NR scan was initiated immediately after the potential was applied or delayed by several hours, it took two or three repeats to achieve stability. EIS scans were always started immediately after setting the Repeating NR with a solution made of D2O instead of H2O may provide further evidence, but a fresh look with an entirely different technique may provide a more convincing outcome. PASSIVE OXIDE ON Zr Another metal that is of interest to the nuclear industry is Zr. Our studies of Zr are more extensive than those on Ti since we managed to carry out electrochemical impedance spectroscopy (EIS) concurrently with NR. Combining NR and EIS, though simple in theory, is very challenging because of electrical interference. Following the timehonoured approach of trial and error, we learned not only that the cell must be electrically isolated from the common ground of the neutron instrumentation, but also that no metal part of the cell must come close (within about 2 inches) to any grounded object (e.g. the top metal plate of the θ rotary drive) even when these parts themselves are electrically isolated from the EIS circuit. EIS is a familiar technique for electrochemists. By superimposing a small AC ripple of variable frequency on the DC bias applied for anodic or cathodic polarization of the working electrode, the AC response Fig. 8 of the electrode (i.e. current) is Impedance of the thin-film Zr electrode before it was anodized (labeled EOC), and after being anodized to a potential of 1 V (1V) and 3 V (3V). LA PHYSIQUE AU CANADA septembre / octobre 2006 253 Sept06-FF.qxd 11/7/2006 2:05 PM Page 254 PHYSICS AND EDUCATION ( STOP THAT CORROSION ... ) Fig. 9 Equivalent circuit proposed for the analysis of observed frequency dependence of Zr electrode impedance. potential. Each typically taking ~ 2 h to complete, we collected 12 to 18 completed EIS scans at each potential. Just as Figure 4 does for Ti, Figure 7 shows thickening of oxide at the expense of the Zr metal. The numerical values of α and RPB, 34 D/V and 1.57 respectively, are in good agreement with the literature values [12,13]. However, a two-oxide model such as that used for the anodized Ti oxide does not give a stable or significantly improved least-squares refinement at any of the potentials where we have made measurements. We concluded that there is no basis for invoking two types of oxide, and adopted a single oxide layer throughout for reporting the NR results. The impedance of the cell as measured by EIS at the same three potentials is shown in Figure 8. While many equivalent circuits with different levels of sophistication could be proposed, the circuit shown in Figure 9 is one of the simplest for an electrochemical cell. It consists of a capacitor, Cox, to represent charge storage capacity across the oxide layer and a parallel resistor, Rox, included to model possible charge leakage. The series resistor Rs represents the solution (electrolyte) resistance. For a good insulating oxide layer and an ionic solution such as the one we used Rox >> Rs. At the lowest frequency (almost DC), Cox is not conducting since its magnitude of impedance 1/ωC64, and we essentially have the two resistors Rox and Rs in series. We identify |Z| . Rox, and expect the phase, Θ, to be zero. As the frequency increases, Cox begins to conduct making the |Z| fall and Θ 6 –90°. Once Cox is fully conducting (frequency ~ 0.1 Hz) the circuit is essentially Rs and Cox in series, whose real part is Rs and the imaginary part (–ι/ωCox). As the frequency increases further, the real part remains constant but the imaginary part decreases. Eventually, as the imaginary part becomes comparable to, and then smaller than Rs in magnitude, Θ rotates back from –90° to zero and |Z| . Rs. Figure 10 shows the impedance Z of the equivalent circuit whose components Rs, Rox and Cox have been adjusted to obtain the best fit to the EOC data. The calculated Z shows all the expected trends discussed above. The calculated Z vs. frequency is in good agreement with the EOC curve of Figure 8 for all frequencies below ~ 5 kHz. At higher frequencies, however, the observed Z deviates from the model both in magnitude and in phase. This feature is likely to be an artefact, as it is not reproduced by EIS (ex-situ) measurements with simplified cell geometry. For instance, using a cell where the distance between the Zr working electrode and the counter electrode is reduced (~1 cm), and no capillary for the reference electrode in place, Z is observed to behave exactly as depicted in Figure 10 up to 1 MHz in frequency. Fig. 10 The impedance of the proposed equivalent circuit whose parameters have been least-squares fitted to the EOC result depicted in Figure 8. 254 PHYSICS IN CANADA September / October 2006 We are now ready to examine how NR and EIS could complement each other and lead to results that could not be obtained by using either of them alone. To this end, we need to first find correlations between the changes recorded by NR and EIS at various stages of the experiment. The EOC curve of Figure 8 shows that, prior to anodization, the low-frequency |Z| was very high, indicating the original passive oxide layer was continuous and provided good protection against corrosion. The high |Z| persisted as we increased polarization to anodic potentials of 0 V, 0.5 V and 1 V (only 1 V curve is shown in Figure 8 for clarity). At the next higher potential, 1.5 V, the low-frequency |Z| suddenly dropped and never recovered. As the 1.5 V curve is similar to the 3 V curve, only the latter is shown in Figure 8. The oxide layer thickness determined by NR, on the other hand, increased monotonically with the potential as shown in Figure 11. Note that there is no discernable discontinuity or anomaly of the oxide thickness at or around 1.5 V. It turned out that the expected discontinuity occurred for the SLD of the oxide layer. While the oxide SLD decreased with every potential increase (as seen in figure 7), the Sept06-FF.qxd 11/7/2006 2:05 PM Page 255 LA PHYSIQUE ET L’ÉDUCATION ( STOP THAT CORROSION ... ) Unexpectedly, the above monotonic trend revealed an underlying difference between the behaviour probed by NR and EIS. The solid-state ion transport across existing oxide no doubt continues many hours after the anodization potential was set. The behaviour of the cell current monitored by EIS, on the other hand, is distinctly different: it shoots up at the moment of the application of the potential, but decays to a small value within minutes. Over longer periods stretching beyond the first hour, the current is either very stable or drifts slightly. The drifts, typically very slow (over tens of minutes), may be in either the positive or the negative direction. This behaviour of the cell current, thus, stands in stark contrast with the unidirectional thickening of the oxide layer. Fig. 11 Chronological variation of oxide layer thickness observed by neutron reflectometry at EOC (–0.17 V), and at set anodic potential increased in steps from 0 to 3 V at intervals of 0.5 V. Time sequence of repeated scans at a given potential is denoted by Δ), squares (~), and circles (o). triangles (Δ largest drop occurred for the potential increase from 1 to 1.5 V. Moreover, the second largest drop of oxide SLD occurred for the next potential increase, from 1.5 to 2 V. Higher subsequent potentials brought about further decreases of the oxide SLD but they were all very small. The explanation that is consistent with both the EIS and NR observations is that a significant number of cracks developed within the oxide layer at 1.5 V, and they were immediately filled with H2O. This inrush of water led to a step in the oxide SLD, as well as a large drop in Rox as even a few saline water pathways can effectively short-circuit the oxide capacitor. A more detailed inspection of Figure 11 reveals a trend that very convincingly demonstrates the reliability of the NR data. The figure shows the results obtained by repeated NR scans using different symbols; triangles (Δ) are yielded by the scans carried out immediately after potential increase, squares (~) by the subsequent scan, and circles (o) by yet another scan if carried out. Lapse time between these scans is typically 6 h. Circles are the best estimate we have for the equilibrium oxide layer thickness, i.e. the thickness we would get at infinitely long time. A circle represents the very first point of the plot at EOC since the oxide layer does not thicken by just filling the cell. Thus chronologically encoded, the plot shows a remarkable trend – the change is monotonic with the symbols appearing always in the order Δ, ~, o. This shows that the variation of dox detected by NR are real, even when the thickening is only a matter of a few Angstroms (between ~ and o). In retrospect, the fact that NR and ESI expose different processes is not surprising. Anodization involves mass and/or charge transport between layers of the working electrode, arising from motion of neutral atoms, electrons or ions. Movement of neutral atoms is detected only by NR, electrons only by EIS, and ions by both. This is perhaps the most compelling reason for performing NR and EIS concurrently in the study of passive oxide layers. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. M. Faraday, Experimental Researches in Electricity, Vol. 2, pp. 234–239, Dover Publications, Inc., New York, (1965); republication of the original publication by Richard & John Edward Taylor in 1844. M. Faraday, Lond. and Edinb. Phil. Mag. 4, 53 (1836). H.H. Uhlig, “Passivity of Metals”, in Proceedings of the 4th International Symposium on Passivity, pp. 24–25, R.P. Frankenthal and J. Kruger editors, Electrochem. Soc. Inc., Princeton, New Jersey (1978). D.G. Wiesler and C.F. Majkrzak, Physica B198, 181–186 (1994). D.G. Wiesler and C.F. Majkrzak, Mat. Res. Soc. Symp. Proc. 376, 247–257 (1995). J.J. Noël, B.M. Ikeda, N.H. Miller, S.R. Ryan, D.W. Shoesmith, S. Sunder and Z. Tun in Surface Oxide Films, Proceedings Vol. 96-18, pp. 246–257, J.A. Bardwell editor, Electrochem. Soc. Inc., Pennington, New Jersey (1996). Z. Tun, J.J. Noël and D.W. Shoesmith, Physica B Condensed Matter 241-243, 1107–1109 (1998). Z. Tun, J.J. Noël and D.W. Shoesmith, J. Electrochem. Soc. 146, 988–994 (1999). See Tun et al. (1999) [Ref. 8] and references therein. N. Khalil and J.S.L. Leach, Electrochim. Acta 31, 1279–1285 (1986). D.D. Macdonald, J. Electrochem. Soc., 139, 3434–3449 (1992). P. Meisterhahn, H.W. Hoppe and J.W. Schultze, J lectroanal. Chem. 217, 159–185 (1987). Values of specific gravity for Zr, ZrO2 (zirconia), and ZrO2 (baddeleyite) are 6.49, 5.6, and 5.8 respectively, giving RPB = 1.56 for zirconia and 1.50 for baddeleyite. LA PHYSIQUE AU CANADA septembre / octobre 2006 255 Sept06-FF.qxd 11/7/2006 2:05 PM Page 256 CALL FOR NOMINATIONS-SUGGESTIONS CALL FOR NOMINATIONS-SUGGESTIONS / APPEL DE CANDIDATURES CANADIAN NATIONAL IUPAP LIAISON COMMITTEE Nominations are invited to fill one position (term ending Dec. 31, 2006) on the Canadian National IUPAP Liaison Committee (CNILC) for a term of three years commencing January 1, 2007 (ends Dec.31/09). Although there are no restrictions on who is nominated, efforts will be made to ensure that there is a broad representation on the Committee covering the areas of geographic location, physics sub-discipline, and language requirements. The final decision remains with the CNILC Secretariat. The current members of the Committee are: G.W.F. Drake (Chair) L. Marleau (term ends Dec.31/06) E. Hessels (term ends Dec.31/08) P. Hawrylak (Secretary) J.W. McDonald (term ends Dec.31/07) C. 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L’échéance pour la présentation des candidatures a été fixée au 9 décembre 2006. * Position sur le Comité exécutif 256 PHYSICS IN CANADA September / October 2006 Sept06-to-trigraphic.qxd 11/8/2006 3:04 PM Page 257 ARTICLE DE FOND ( QUANTUM MAGNETISM ... ) QUANTUM MAGNETISM AND SUPERCONDUCTIVITY by William J.L. Buyers and Zahra Yamani T magnetic moment that precesses around the sum of the static he spin of the neutron allows neutron scattering to reveal and dynamically varying field of its neighbours. This is the the magnetic structure and dynamics of materials over site-based picture of localized spins. nanometre length scales and picosecond timescales. Neutron scattering is particularly in demand in order to understand In metals the situation is entirely different. The conduction high-temperature superconductors, which lie close to magarises from band-based electrons in which it is the electron netically ordered phases, and highly correlated metals with momentum that is well defined at the giant effective fermion masses, which Fermi surface rather than the electron lie close to magnetic order or pass through a mysterious phase of hidden In this article, examples are position. Although embedded in a liqorder before becoming superconduct- given of quantum phenome- uid of high-velocity conduction electrons, local spins may still behave indeing. Neutron scattering also is the probe of choice for revealing new na where neutron scattering pendently provided their energy scale, phases of matter and new particles, as has played a defining role given by the exchange coupling, J, is much less than the eV bandwidth of the seen in the surprising behaviour of challenges current fast conduction electrons. The conducquantum spin chains and ladders that electron spin responds adiabaticalwhere mass gaps and excited triplons understanding of con- tion ly to the motion of the slow local spins. replace conventional spin waves. This is the picture for the rare earth Examples are given of quantum phe- densed matter. metals, except for a few mixed-valent nomena where neutron scattering has examples. The decoupling works played a defining role that challenges because the small-radius 4f magnetic shell lies inside the 5s current understanding of condensed matter. shell and so is shielded from the destructive influence of its neighbours. Even in this weakly coupled system the spin INTRODUCTION excitations of the f electrons are not eigenstates - the indirect Magnetism is at the heart of fundamental processes. The way coupling through the conduction electron sea shortens their in which black holes suck in matter from neighbouring stars lifetime. They acquire a relaxation rate, seen as a spectral line is a fundamentally magnetic process and not just caused by width, proportional to the imaginary part of the conduction gravity[1]. The magnetic moment of the neutron allows scienelectron (Lindhard) spin susceptibility χ”(q,ω) because coutists to study magnetism in materials at the nanoscale and pling, I, of the local f-spin to the conduction electron spin below. The pattern of neutron scattering and its velocity discauses an indirect (RKKY) exchange between f-moments of tribution reveals the structure and dynamics of the atomic the form J(q,ω)=I2χ(q,ω). The same indirect coupling, now magnetic moments or spins. Spins in condensed matter through the charge susceptibility, gives phonons in metals a belong to the overall electron system and arise from unpaired spectral broadening, and this is only removed for energies electrons in one of the outer orbital shells of the atom. The below the pairing gap in its conduction electron charge ground state of the spin depends on whether it is surrounded response when the metal becomes superconducting below by and exchange coupled to other well-defined spins as in Tc [2]. insulators, or whether the spins are embedded in a liquid of conduction electrons that may screen their moment and Nonetheless, when the coupling to conduction electrons is damp out their excitations. strong by exchange or by hybridization, the spins behave as if they are free at high temperature but are progressively In insulators an integral charge state is determined by chemiscreened on cooling by coherent reorganization of the concal valency and the environment allows the several unpaired duction electrons. The effect is described as Kondo screening electrons to form localized states of definite orbital and spin when the spin of the atomic core and of the conduction elecangular momentum linked by spin-orbit coupling. Hund’s tron can reorganize without substantial change of charge state rule is king. At each site we have an independent atom the and is described as mixed valency when hybridization symmetry of whose orbit is lowered by the electrostatic field changes the occupancy and effective charge. of its neighbours. The Pauli exclusion principle leads to an effective coupling, J, between neighbouring spins that may be ferromagnetic (parallel) or antiferromagnetic (antiparallel). The latter is more prevalent in nature because the magnetic William J.L. Buyers <[email protected]> and atoms in insulators establish superexchange bonds through Zahra Yamani, Canadian Neutron Beam Centre, National Research Council, Chalk River, Ontario, Canada K0J 1J0 shared non-magnetic neighbours such as O2- in MnO or F- as in KMnF3. The atom behaves magnetically as if it has a fixed LA PHYSIQUE AU CANADA septembre / octobre 2006 257 Sept06-FF.qxd 11/7/2006 2:05 PM Page 258 FEATURE ARTICLE ( QUANTUM MAGNETISM ... ) Examples of exotic or unconventional phenomena discovered with neutron scattering include magnetic solitons [4,5], and the quantum gap (Haldane gap) between the ground state and a triplet of massive spin particles that appears for integer but not half-integer spin chains. One-dimensional chains of spins are created by chemically separating chains of magnetic ions by ligands of non-magnetic ions. Clever solid-state chemists are responsible for creating the wide variety of 1D, 2D and 3D magnetic systems where singlet ground state, spin liquid and quantum phenomena may be investigated. Solitons in an Ising-like antiferromagnetic chain, where the spins point up or down, must be excited in pairs by the neutron flipping a spin (Sz → -Sz), thereby creating two domain walls or solitons costing energy 2J because there are two wrong bonds with ferro- instead of antiferro-orientation. This is because neutron scattering only connects states linked by the spin operator – it is a spin-one probe. The Ising spin exchange JSzi Szi+1 in the presence of weak transverse coupling allows each soliton to hop two sites at a time away from the initially localized soliton pair (Fig. 2). These solitons can be visualized as a place where we have Fig. 1 Energy levels of Co++ in the antiferromagnet KCoF3. The spin waves twisted the rest of the chain through 180º to are transitions from the ground to all excited states and form a lowest make a π soliton. Because the initial excitation band up to the illustrated single-ion spin-flip frequency of 7 THz and carried spin one, we find that each soliton is a down to a gap frequency set by the exchange mixing of higher spinspin one-half particle. A single soliton may be orbit states [3]. thermally excited with an activation energy J, half the spin wave energy. This simple examIn pure metallic systems spins normally condense into a state ple from the Ising chain has given rise to the concept of spinons, the basic particle in the S=½ isotropic (or Heisenberg) whose symmetry is lowered as a result of formation of magchain, later used for high-temperature superconductivity. netic order, a spin-density wave, a charge density wave, or a Because they are created in pairs, conservation of momentum superconducting paired state, while some systems remain ensures that there is a continuum of spinon excitations paramagnetic to the lowest temperatures. instead of sharp spin waves, a continuum that extends down to a lower limit set by the Bethe ansatz. A spin or orbital excitation appears as a collective excitation of the ordered state whose energy-momentum dispersion relation is a direct measure of the magnetic forces between any two atoms. Their energies give information on the local crystal field, the spin-orbit coupling and the interatomic exchange as shown in Fig. 1 for the insulator KCoF3. Although it has become customary in orbitally ordered materials such as manganites to treat the orbitons separately from the spin waves, spin wave and orbital states are not distinct as they are coupled by spin-orbit interaction. They together form the collective magnetic dipole excitations of the electronic system and should be included in an extension of the standard model [3]. EXOTIC PARTICLES More than just measuring the strength of interactions, as may be done in well-understood systems where the magnetism appears in the form of well-defined spin waves, the neutron is uniquely suited to discovering new phenomena that are not contained within accepted textbook lore. 258 PHYSICS IN CANADA Fig. 2 September / October 2006 Solitons hopping along a chain of S=½ spins [5]. Because the excitation is topological (half the spin chain is turned over at each thickly marked wall) as opposed to the sinusoidal spin-wave pattern, the soliton response looked at with a Fourier probe such as neutron scattering appears as a continuum. Sept06-FF.qxd 11/7/2006 2:05 PM Page 259 ARTICLE DE FOND ( QUANTUM MAGNETISM ... ) When the spins interact with isotropic rather than the above Ising exchange, classical thinkers, and most scientists, expected that the spin spectrum would be gapless. Instead Haldane conjectured [6] that the chains of integral-spins would exhibit a mass gap but those of half-integral spins would not. The Haldane gap was not expected, at least not by those that wave their fingers to illustrate rotational invariance and at the same time consider a long wavelength spin wave to be a precession of a classical spin! Before Haldane, Kadanoff’s postulate of Universality had wide acceptance because both experimental results on different materials and theoretical calculations with S=½ and S= 4 (i.e., classical result) gave phase transitions with the same properties. Renormalization group theory offered a mechanism for universal properties to arise since under repeated renormalization transformations some parameters are attenuated and become irrelevant while others remain relevant. Haldane’s conjecture was controversial mainly because it contradicted Universality. While it is sometimes valid to take a site-based view where the spin precesses in the field of its neighbours, this largely works only when there is a static field (a magnet with long-range order), in high dimensions, and in lattices without frustration (competing exchange fields). In one dimension there can be no long-range order and the spins can attempt to form bond order where pairs of spins form a singlet ground state. These singlet pairs may then interact and it is not obvious a priori whether this will give a lower overall ground state than the site-based approach. Anderson showed that the 2D triangular lattice preferred a ground state of resonating valence bonds over the Néel state, but the situation for one dimension (1D) was unknown until the work of Haldane [6]. The Haldane conjecture remained controversial, as well as being counter-intuitive, until the spin gap was discovered directly in neutron scattering experiments at Chalk River involving a University of Toronto student [7]. The isotropically coupled S=1 Ni2+ chains in CsNiCl3 were the test bed. The conventional (linear spin wave theory) view was that the lowest spin excitations were gapless Goldstone bosons but as shown in Fig. 3 the integral Ni2+ spins exhibit a large gap, about 40% of J. This result was soon confirmed in Europe on an organic material [8] and in CsNiCl3 polarized neutron scattering showed that the gap states were triplets [9]. In recent years the unusual temperature dependence of the gapped triplet states, which has given rise to the new name for a particle, the triplon, have been fully explored by Kenzelmann et al. [10]. The spin triplons increase their energy on heating, whereas spin-wave energies decline in ordered systems (Fig. 4). Within the non-linear sigma model, this is because, to conserve the total moment, the triplon energies must rise to counteract their increase in population through thermal excitation. A useful picture for a singlet with a gap to excited states is the valence bond solid described in the review by Affleck [11], in which each of the two electrons of an S=1 atom form a singlet pair with one electron of a neighbouring atom, one to the left and one to the right. This global singlet state is the exact solution of a closely related Hamiltonian. For S=½ the sole electron can form only one singlet bond, all to the left or all to the right, but then there are two degenerate states, no singlet and no gap. The discoveries of the quantum gap presaged the large current body of research on singlet-to-triplet excitations or Fig. 3 The Haldane spin gap discovered in the integer-spin chain system CsNiCl3 in its 1D phase [7]. The Ni2+ (S=1) chains lie along the hexagonal z direction [0 0 1]. If the excitations were conventional spin waves all freη,η η, 1) quencies along the 1D zone centre Q =(η would lie at zero, since there is no longrange order, but the quantum disordered ground state leads to a mass gap of 0.32 THz to a triplet of spin excitations with only short-range spin correlations. The weak coupling perpendicular to the chains along η,η η, 0) leaves a residual in-plane dispersion. (η Fig. 4 Haldane gap triplet energies rise with temperature in accordance with the self-consistent non-linear sigma model [10]. LA PHYSIQUE AU CANADA septembre / octobre 2006 259 Sept06-FF.qxd 11/7/2006 2:05 PM Page 260 FEATURE ARTICLE ( QUANTUM MAGNETISM ... ) triplons, as found in even-leg spin ladders and in systems formed from integer-spin triangle motifs. The solitons in magnetic chains led to the now pervasive modern concept of spinons. HIDDEN ORDER An enigmatic problem in the field of strongly correlated heavy fermion systems is the nature of the hidden order that sets in below the large specific heat jump at T0 = 17 K in URu2Si2. In addition, a superconducting phase occurs in URu2Si2 below 1.2 K. The heavy-fermion epithet stems from the fact that the Sommerfeld specific heat coefficient, γ=C/T, usually taken as a measure of the electronic density of states at the Fermi surface, is large above T0, 160 mJ/mol-K2. This is a hundred times larger than that of a simple metal like copper and suggests that the effective electron band mass is a hundred times the free electron mass. Clearly the proximity to a magnetic or exotic transition is causing the large mass, through spin or hybridization effects. Since evidence of heavy charge masses has been seen in de Haas-van-Alphen experiments, the strong spin response must be producing a slowing of the electron velocities, although the spins can themselves contribute to the giant specific heat. The charge and spin spectra must be renormalized downward to a few meV in energy to add to specific heat. Although a second order transition occurs at 17 K with substantial associated entropy, the nature of the order has remained a mystery for over 20 years [12,13]. Landau theory tells us that the small antiferromagnetic moment of 0.03 μB that develops below 17 K cannot possibly explain the large specific heat jump (entropy) associated with a second order local spin transition. It would require ordering of a moment Fig. 5 260 ~100 times larger! Antiferromagnetism therefore cannot be the hidden order parameter. The system seems rather to have condensed into a new phase of matter for which the order parameter and associated symmetries differ from conventional expectations. The properties are typical of ordering due to broken symmetry but, since its origin has not yielded to practically every known experimental technique, we refer to it as ‘hidden’ order. Strong hybridization is expected between the conduction and the 5f electrons and prevents application of either a purely localized or itinerant electron model. Local probes and pressure experiments suggest that the weak moment may be a parasitical phenomenon that forms in a very small volume fraction. The small moment may be simply a quixotic distraction from the real bulk order parameter that causes the large loss of electronic density. What is clearly a bulk property of the hidden order phase is the unusual spectrum of magnetic excitations (Fig. 5). Neutron scattering has shown [13] that they form well-defined propagating collective modes over most but not all of the Brillouin zone. Moreover they carry a large spin matrix element of 1.2 μB and are thus a property of the bulk or dominant phase. What is unusual is that the spin motion is entirely longitudinal along the tetragonal c direction. Contrast this with a spin wave of a magnetically ordered system where the motion is transverse to the moment. Also unusual is that while the well-defined excitations suggest a localization of the 5f moment, along the tetragonal [0 0 1] direction the lifetime shortens and damps out the response and so suggests decay into an itinerant-electron continuum. Itinerant spins are also suggested by long-range (RKKY) exchange that produces the several extrema in the dispersion relation. Over the last two decades many searches have been carried out for the hidden order and the evidence is either absent or contrary to models involving charge-density wave formation, quadrupolar ordering, multispin correlators [14], crystal fields [15], or orbital currents [16]. The frequency of gapped spin excitations versus wave vector in URu2Si2 at 4 K well within the hidden order phase [13]. Long-range exchange through the electron liquid causes several minima with the minimum gap at Q = (1, 0, 0). For directions within the tetragonal basal plane the excitations are long-lived, but those propagating in the c direction along (1, 0, ζ) are damped out at large wave vector. PHYSICS IN CANADA September / October 2006 Fig. 6 The temperature dependence of the incommensurate fluctuations at (1.4, 0, 0) and E=0.25 THz (~1 meV) energy transfer [17]. The fit gives an activation temperature of 110±10 K, the coherence temperature for the charge transport not the spin excitation energy. Sept06-to-trigraphic.qxd 11/8/2006 3:04 PM Page 261 ARTICLE DE FOND ( QUANTUM MAGNETISM ... ) A significant new result came from a search for an exotic form of magnetism predicted to arise below T0 from orbital currents where the weak moment would result from electron currents flowing around the atoms in a unit cell [16]. The orbital moment theoretically predicted was not observed. Wiebe et al [17] made a more important observation, however. Above the 17 K transition the spectral weight moves to the incommensurate wave vector (1.4, 0, 0) of the second minimum (Fig. 5) and the spectrum becomes gapless. The onset of the collapse of the gap was measured by probing the fluctuations at 0.25 THz, well below the gap frequency of 1.2 THz. The important result is that the incommensurate scattering is activated with a temperature T* = 110 K, the coherence temperature (see Fig. 6). Thus in the precursor phase to hidden order there are gapless incommensurate spin fluctuations over a finite region of the Brillouin zone. These can give rise to a term in the specific heat linear in T that can be misconstrued as electronic specific heat. The specific heat will jump at T0 and decrease below as the spin gap is formed. The large linear-in-T specific heat then may be thought of as coming from the spin fluctuations rather than from a Aheavy-electron@ charge band. Theorists often like to work with the Aone band does all@ approach with a Hubbard model that tries to reproduce both the charge and the spin response. Whereas most focus on the fermions determining the charge transport properties, the new results require more attention to the bosons of the spin response. The hidden order phase is robust and persists to a field of 35 T [18]. These exotic results have led to exotic theories, most recently to the suggestion that a Pomeranchuk instability of the electron liquid has grossly changed the Fermi surface [19]. SUPERCONDUCTORS Neutron scattering is particularly well suited to explore the intimate relation between magnetism and high-temperature superconductivity. The superconductors consist of squarelattice CuO2 planes of S=½ copper spins, into which holes have been created in the plane by the chemical removal of electrons from oxygen ligands, a process known as doping. Neutron scattering can show how the spin spectrum evolves as the superconducting transition temperature increases and then decreases as the electronic doping is increased beyond a critical value, pc~5%, into the phase known as the superconducting dome. The S=½ holes sit equally on the four oxygen neighbours and, from a distance, screen the copper moment to form a spin singlet. The resonating valence bond (RVB) ground state has been adduced to account for the precursor state that connects a Mott insulator (LaCuO4 or YBa2Cu3O6) to the hole-doped state where high-temperature superconductivity takes place [20]. The RVB state consists of sets of singlet pairs between copper spins at all distances with a symmetry similar to that of a superconducting pair. In conventional (phonon or S-wave) superconductors the pairing gap occurs for all directions of Fermi momentum, kF. In contrast the spins of the RVB pair lie on different atoms and the gap has d-wave symmetry with nodes along the directions kx = ±ky. Although there is a large amount of neutron beam research on La2xSrxCuO4 and YBa2Cu3O6+x, most is for relatively highly doped materials. In recent years attention has shifted in three continents to underdoped materials where superconductivity is weaker but magnetic fluctuations are stronger [21,22,23]. With the advent of high quality crystals from University of British Columbia it has been possible to study highly-ordered ortho-II crystals that display greater electronic order and thus a larger Tc for the same oxygen doping. With these crystals the hour-glass spectrum of incommensurate spin modulations at low energy, a resonance localized in Q and in ω, and a cone of damped highenergy spin waves has been well-established in recent work at Chalk River and at ISIS in the UK [24,25]. Here we focus on systems that lie much closer to the critical onset of superconductivity where the destruction of spin order and spin wave propagation seems the most crucial requirement for the onset of this anisotropic superconducting charge pairing. A recent study [26] has shown that high-temperature superconductors close to the edge of the superconducting dome behave quite differently from both their more highly doped counterparts and from their antiferromagnetic parent compounds. Although no Bragg peak, and so no long range order, is observed for lightly doped superconductors, subcritical 3D antiferromagnetic correlations are formed. This is evident from fact that the spin scattering is centred at integer values of L for zones (½,½,L) (Fig. 7 ). Thus the doped holes prevent the formation of the long range ordering but there is a memory of the phase that would be formed by further reduction of the hole content. Compared to the higher doped materials with a high-energy resonance (33 meV for YBCO6.5) at a commensurate position and no elastic central mode [25], the energy spectrum of lightly doped superconductors consists (Fig. 8) of a central mode coupled to a broad inelastic peak with a relaxation of Fig. 7 In YBCO6.35 with Tc=18 K, the antiferromagnetic correlations coupling the planes extend over only 15 Å along the c-axis [27]. LA PHYSIQUE AU CANADA septembre / octobre 2006 261 Sept06-to-trigraphic.qxd 11/8/2006 3:04 PM Page 262 FEATURE ARTICLE ( QUANTUM MAGNETISM ... ) insulator. It suggests a frozen glass state that inhibits the transition to magnetic longrange order and provides the random spin environment that allows superconductivity. Fig. 8 Two magnetic energy scales near the onset of superconductivity in YBa2Cu3O6.35, a narrow central mode with FWHH<0.08 meV, and faster relaxational excitations peaked at ~2 meV. The line is from a model where the soft relaxational magnetic mode of the superconducting phase is coupled to an elastic (central) mode and drives up its intensity to divergence as a quantum phase transition to the ordered magnetic phase is approached [26]. The nearly-elastic mode arises from the slow tumbling of about a hundred copper spins that are nearly ordered. One of the most remarkable features of the cuprate superconductors is the characteristic spin excitation energy known as the Aresonance@. It tracks Tc as the doping is varied (Fig. 11). The spin spectrum exhibits a peak whose enerFig. 9 The central peak grows on cooling gy scales as Eres~ with no change at Tc = 18 K as if the 6kBTc. Inclusion of spins ignore superconducting transithe results [26] for tion. p=0.06 (YBa2Cu3 O6.35) shows that the inelastic spin energy, albeit reduced by an order of magnitude in energy from that of optimally doped YBCO and heavily damped (Fig. 8), is a critical spectral feature of superconductivity. Fig. 11 shows it is the soft mode of the superconducting dome. 2.5 meV. Both are centred on the commensurate antiferromagnetic position but are broad in momentum. Correlation lengths associated with both modes are short ranged (longer in the basal plane than along the c-axis). The intensity of the central mode increases on cooling from 80 K and saturates at a low temperature of order of 10 K with no suppression at Tc (Fig. 9). The general behaviour as holes are added is that the strong antiferromagnetism of the parent insulators is rapidly broken up, carriers form to conduct electricity and heat, and the spin excitations evolve into strongly damped paramagnons [25]. Long-range antiferromagnetism has been destroyed and a superconducting phase is entered with only ~5% of hole doping. This is much less than the percolation limit of ~50% localized vacancies for a dilute 2D lattice, and clearly shows that holes produce a large spatial extent of weakened AF coupling. Possibly local ferromagnetic correlations ensue (Fig. 10). Perhaps the most surprising property, observed with polarized neutron scattering [26], is that the spin orientation is isotropic, unlike the XY order of the insulator. We can infer that the superconductor is in a spin ‘hedgehog’ phase. Such preservation of spin rotational invariance is a very different topology than the collinear spins of the antiferromagnetic 262 PHYSICS IN CANADA Fig. 10 A doped hole on the oxygen neighbours puts the CuO4 into a singlet state and may cause ferromagnetic bonding. Even a low doping of ~5% destroys the antiferromagnetic order because every hole affects many sites. September / October 2006 Sept06-FF.qxd 11/7/2006 2:05 PM Page 263 ARTICLE DE FOND ( QUANTUM MAGNETISM ... ) Fig. 11 The characteristic energy of the inelastic spin response tracks the superconducting transition temperature Tc(p) as the doping p in the CuO2 planes is increased. In cuprate superconductors the reason for the remarkable tracking of the superconducting transition temperature with the resonance energy (Fig. 11) has not been explained satisfactorily. While a number of theories based on a Fermi liquid coupled to a spin susceptibility have attempted to explain individual experiments at large, near-optimum doping where the electrons form a Fermi liquid, these theories are unlikely to work in the region near the lower edge of the superconducting dome that we have studied. There the electronic hole density is small, there is considerable doubt as to whether a sharp Fermi surface exists, and the resistivity is insulator-like, falling with increasing temperature, thus mirroring the decrease in χ”(q,ω) with frequency. Moreover the spin fluctuations are so strong (recall from Fig. 9 they ignore Tc) that a description based more on states, RVB or otherwise, that pre-exist at a less-than-critical doping would seem a better starting point. In this regard we suggested that the resonance can be regarded [24] as an image of the two-particle pairing states, states that are allowed in the particle-hole spectrum detected by neutrons only by dint of the superconducting order. Because the pairing gap is d-wave of the form cos(kx)-cos(ky), the spectrum of spin states coupled incoherently to all electron momenta should exhibit an anisotropic rise to a peak at the maximum d-wave gap followed by a sudden fall. This asymmetric resonance spectrum is very close to what was observed in an oxygen-ordered crystal of YBCO6.5 (Fig. 12 based on [24]) and may be a fingerprint of superconducting pairing. Moreover, in the normal phase almost half the resonance weight has already formed on cooling to just above the superconducting transition temperature. We believe that this fingerprint shows that incoherent superconducting pairs are present in the normal phase. By contrast conventional phonon-mediated superconductors show an extremely nar- Fig. 12 The spin resonance peaked at 33 meV in YBCO6.5 in its superconducting phase (8 K) and in its normal phase (85 K) above its superconducting transition temperature of 59 K. The π,π π) selects spin two-dimensional wave vector (π fluctuations that have opposite sign (are of antiferromagnetic symmetry) between neighbouring Cu atoms in the square lattice. For this AF phasing there is no gap in an ordered antiferromagnet. In the superconductor with its d-wave gap for pairing charge carriers, the spin response is shifted upward. The presence of a similar but weakened spectrum above Tc. indicates that local incoherent pairs have already formed in the normal phase [24] within vortexantivortex fluctuations. row temperature range for critical fluctuations. When we reduce the doping to the edge of the superconducting phase we have seen that the spin fluctuations are strong and in this interpretation are dominated by incoherent pairs, so much so that they show little change in their growth rate on cooling through Tc. Needless to say this concept is highly controversial, for it would suggest that the lightly-doped but nonsuperconducting antiferromagnet would carry some of the same local pairing symmetry as the superconductor. CONCLUDING REMARKS The power of neutron scattering is that it provides direct access to the energy, momentum and spin of the fundamental particles in condensed matter systems. Other spectroscopic LA PHYSIQUE AU CANADA septembre / octobre 2006 263 Sept06-FF.qxd 11/7/2006 2:05 PM Page 264 FEATURE ARTICLE ( QUANTUM MAGNETISM ... ) techniques are generally less direct, such as the local probes of muon spin resonance and NMR. The positive muon traps and interacts strongly on the large eV scale with its immediate electronic environment drawing a screening electron around it; the field it measures may in some systems be different on the meV scale of spin fluctuations than the unperturbed field of the system. Other probes give an average of the charge but not spin spectra, or are averages over many particles such as thermal and electrical conductivity and specific heat. Neutron scattering has allowed new phases of matter to be discovered as we have seen for quantum gapped systems, for a highly-correlated heavy-fermion system, and for the quantum antiferromagnet doped to form a superconductor. 12. 13. 14. 15. 16. 17. ACKNOWLEDGEMENTS WJLB benefited as a member of the Canadian Institute for Advanced Research and both authors recognize technical and scientific support from CNBC, Chalk River, and NIST, Gaithersberg, MD. We are grateful to C. Stock, and to many colleagues, for their insight and help over several years. 18. REFERENCES 19. 1. 20. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 264 J.M. Miller et al., “The magnetic nature of disk accretion onto black holes”, Nature 441, 953 (2006). J.D. Axe and G. Shirane, “Influence of the Superconducting Energy Gap on Phonon Linewidths in Nb3Sn”, Phys. Rev. Lett. 30, 214 (1973). W.J.L. Buyers, T.M. Holden, E.C. Svensson, R.A. Cowley and M.T. Hutchings, “Excitations in KCoF3. II. Theoretical”, J. Phys. C4, 2139 (1971). S.E. Nagler, W.J.L. Buyers, R.L. Armstrong and B. Briat, “Propagating Domain Walls in CsCoBr3”, Phys. Rev. Lett. 49, 590 (1982). S.E. Nagler, W.J.L. Buyers, R.L. Armstrong and B. Briat “Solitons in the one-dimensional antiferromagnet CsCoBr3”, Phys. Rev. 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Birgeneau, “Central mode and spin confinement near the boundary of the superconducting phase in YBa2Cu3O6.353 (Tc=18 K)”, Phys. Rev. B73, 100504(R) (2006). C. Stock et al., private communication. Sept06-FF.qxd 11/7/2006 2:05 PM Page 265 ARTICLE DE FOND ( POLARIZED NEUTRON REFLECTOMETRY ... ) POLARIZED NEUTRON REFLECTOMETRY AS A UNIQUE TOOL IN MAGNETIZATION REVERSAL STUDIES OF THIN FILMS AND MULTILAYERS by H. Fritzsche, Z. Yamani, R. Cowley and R.C.C. Ward T understand the magnetization reversal process and to distinypically, the magnetization reversal behavior of thin magguish between a domain wall movement and a rotation netic films and multilayers is studied with magnetometers process because generally magnetic domains give rise to elec(e.g. a vibrating sample magnetometer or a superconducting trical noise and reduce the performance of a sensor [13]. quantum interference device) or with the magneto-optical Exchange-bias systems consisting of a ferromagnet in direct Kerr effect. In this article we show how Polarized Neutron contact with an antiferromagnet repreReflectometry (PNR) can be used as a sent an essential component of thin-film tool to measure hysteresis loops and to study the magnetization reversal In this article we show how systems used as sensors. PNR shed behavior of magnetic multilayers in Polarized Neutron Reflecto- light on the asymmetric magnetization reversal of these exchange-biased more detail. We will discuss the For the instrumental setup needed to perform metry (PNR) can be used as multilayers [11,14,15,16,17]. PNR experiments along with the theo- a tool to measure hystere- Co/CoO system PNR experiments revealed a rotation process of small retical background of this technique. In contrast to conventional magne- sis loops and to study the domains for increasing fields and a motion for decreasing tometers capable of measuring only magnetization reversal domain-wall fields during the first cycle of a hysterethe average magnetization of a multilayer, PNR is able to determine the behavior of magnetic multi- sis loop. magnetization profile and can distinIn this article we provide an introducguish between the magnetizations of layers in more detail. tion to the theoretical description of different magnetic layers in a multilayPNR along with some model simulaer. This feature of PNR being elementtions of reflectivity curves followed by a description of the specific, will be demonstrated with the magnetization reveressential components needed to set up a polarized neutron sal study of a (6 nm ErFe2 / 6 nm DyFe2) multilayer, where reflectometry experiment. How PNR can yield layer-sensiwe were able to follow the magnetization reversal of the ErFe2 tive information for a magnetization reversal of a multilayer and DyFe2 magnetizations independently. consisting of two different ferromagnetic layers is shown for INTRODUCTION the case of a (6 nm ErFe2 / 6 nm DyFe2) multilayer. These types of multilayers are of technological interest because they During the last two decades Polarized Neutron Reflectometry have potential applications for sensors and magnetic read (PNR) has become a very powerful and popular technique in heads. the study of magnetic properties of thin films and multilayers. PNR has drawn a lot of attention of the scientific commuTHEORETICAL DESCRIPTION OF PNR AND nity due to the study of the oscillatory exchange coupling in MODEL SIMULATIONS Fe/Cr [1,2], Co/Cu [3] or Fe/Nb [4,5] multilayers. PNR is the method of choice to prove the antiferromagnetic coupling of The scattering geometry of a typical reflectometry experiment the magnetizations of ferromagnetic layers (e.g. Fe) separated is shown in Fig. 1. The neutron beam hits the surface at an by non-ferromagnetic layers (e.g. Cr) because the antiparallel angle θ and the reflected intensity is simply measured as a alignment of the magnetic layers gives rise to an additional function of θ, which is typically in the range between 0 and 2°. peak in the reflectivity curve. Even more complicated strucThe interfaces of the samples are arranged perpendicular to tures such as a non-collinear 50° coupling [6] or a helical magthe scattering vector netic structure [7] can be determined by PNR. Another area 4π where PNR has been applied very successfully is the determi(1) q = kf − ki = sin(θ) nation of the absolute magnetic moment of ultrathin Fe and λ Co films [8,9,10] to study surface and size effects. Here, the big with k i and k f being the incoming and outgoing neutron wave advantage of PNR is that the substrate does not contribute to vector and λ the neutron wavelength. The neutron spins are the magnetic signal unlike in conventional magnetometry measurements where the diamagnetic signal of the substrate dominates over the tiny magnetic signal originating from the H. Fritzschea <[email protected]>, sample. a b b a Only recently PNR was used to study the magnetization reversal of thin films [11,12]. Thin magnetic films are used as magnetic field sensors and therefore it is very important to Z. Yamani , R. Cowley , R.C.C. Ward ; National Research Council Canada, CNBC, Chalk River Labs, Chalk River, ON, K0J 1J0, Canada; bOxford Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK LA PHYSIQUE AU CANADA septembre / octobre 2006 265 Sept06-FF.qxd 11/7/2006 2:05 PM Page 266 FEATURE ARTICLE ( POLARIZED NEUTRON REFLECTOMETRY ... ) Fig.2 The scattering length density (SLD) for spin-down neutrons (left) and spin-up neutrons (right) for the case of bulk Fe. The SLD is composed of a nuclear and a magnetic part. Vj± = Fig. 1 Scattering geometry for a neutron reflectometry experiment with the scattering angle θ, scattering vector q, P the external magnetic P field H ext, and the magnetic moment of the spin-up neutrons ( μP+) and spin-down neutrons ( μP-). The spin-flip (SF) axis as well as the non-spin flip (NSF) axis is indicated along with the crystallographic orientation used for the experiments on the (ErFe2 / DyFe2) multilayer. oriented either parallel to the external field (spin-up neutrons) or antiparallel (spin-down neutrons) to the external field which is in the film plane (see Fig. 1). The interaction with the film is reduced to a one-dimensional problem, which can be described for grazing incidences with an effective potential that is a sum of a nuclear and a magnetic component (the Zeeman interaction). For the case that the sample’s magnetization is parallel to the external field this potential Vj in layer j is given by: Vj = 2π 2 N j b nuc − μ ⋅ Bj j m PHYSICS IN CANADA ( ) (3). PNR is very sensitive to magnetic structures because the nuclear and magnetic SLDs are of the same order of magnitude. The nuclear SLD depends on the elements and their isotopes in the sample [18,19]. A diagram of the SLD and the simulated reflectivity curves for the case of bulk Fe saturated along the external field (Nbnuc = 801.9 μm-2 and Nbmag = 498.5 μm-2) is shown in Fig. 2 and Fig. 3, respectively. The solid line in Fig. 3 denotes R+, the reflectivity of spinup neutrons, the dashed line is R-, the reflectivity of down neutrons. The reflectivity of the sample can be calculated by solving the Schrödinger equation using the above mentioned potential. The simulations presented here were calculated with software based on the Parratt formalism [20]. The critical edge qc up to which total reflectivity (R=1) is observed is different for spin-up and spin-down neutrons and depends on the SLD in the following way: (2) where m and μ6 denote the neutron mass and magnetic 6 moment and Nj , bjnuc, and B j denote the atomic density, coherent nuclear scattering length, and magnetic induction in layer j. The first term in Eq. (2) results from the interaction of the neutron with the nucleus, while the second term results from the interaction of the neutron with the magnetization of the sample. The product Njbjnuc is known as the nuclear scattering length density (SLD). The magnetic part of the potential depends on the orientation of the magnetic induction with respect to the magnetic moment of the neutrons. It is important to note that we are not sensitive to a perpendicular magnetization component in the PNR setup sketched in Fig. 1. The magnetic contribution to the potential can also be expressed in terms of a magnetic SLD Njbjmag, which makes it convenient to discuss the sample’s properties in terms of SLDs. According to Eq. 2 the potential V+ for spin up and Vfor spin down neutrons is different and they can be expressed in terms of a magnetic SLD as follows: 266 2π 2 N j b nuc ± N j b mag j j m September / October 2006 Fig. 3 Simulated reflectivity curves of a bulk Fe sample for spin-up neutrons (R+, solid line) and spin-down neutrons (R-, dashed line). Sept06-FF.qxd 11/7/2006 2:05 PM Page 267 ARTICLE DE FOND ( POLARIZED NEUTRON REFLECTOMETRY ... ) to an additional peak at q = 2π/dAF. The existence of this additional peak shows immediately that the ferromagnetic layers are oriented antiparallel with respect to each other. As the total magnetization of the multilayer is zero, the critical scattering vector for spin-up and spin-down neutrons are identical. So far we only discussed cases where the magnetization is collinear with the external field. The big advantage of PNR is that it is also sensitive to in-plane magnetization components perpendicular to an external field. These perpendicular components (parallel to the [001] direction in Fig. 1) give rise to a so-called spin-flip process, i.e. an incoming spin-down neutron will be reflected as a spin-up neutron Fig. 4 Simulated reflectivity curves and magnetic structure of a ferromagnetically and vice-versa. The spin-flip scattering is proportional to |μ6xB6| and is maximum aligned (4 nm Fe / 1 nm Cr)20 multilayer in an external magnetic field Hext. -1 Clearly observable is the chemical peak at q = 0.127 Å due to the chemical if the whole magnetization is perpendicumodulation of the multilayer. lar to the external field or the neutron spin, respectively. As shown in Fig. 6, the antiferromagnetic structure of a Fe/Cr multilayer can be observed as a peak in the spin-flip reflectivities R-+ and R+- if q c± = 16 π N( b nuc ± b mag ) (4). the magnetization of the Fe layers is perpendicular to the external field. At the same time no antiferromagnetic peak The simulated reflectivity curves of a ferromagnetically can be observed in the non-spin flip reflectivities R++ and R--. aligned (4 nm Fe / 1 nm Cr)20 multilayer along with the magThe two superscripts of the reflectivities denote the spin state netic structure of the multilayer is depicted in Fig. 4. In this of the neutrons before and after reflection from the sample. case, the chemical period dchem is identical to the magnetic This sensitivity of PNR to magnetization components parallel period and leads to a Bragg peak at q = 2π/dchem. Analogous and perpendicular to the external field has been exploited, e.g. + to the case of bulk Fe, the critical scattering vector qc for to study the spin-flop transition in an antiferromagnetically spin-up neutrons is larger than the critical scattering vector coupled Fe/Cr multilayer [21]. At low fields the magnetizaqc- for spin-down neutrons. For the case of an antiferromagtion is collinear with the external field. When increasing the netic alignment of the Fe layers, as shown in Fig. 5, the magexternal field the whole magnetic structure rotates at a certain netic period dAF is now twice the chemical period and leads field value from a collinear alignment like in Fig. 5 to a perpendicular arrangement as shown in Fig. 6. So, where conventional magnetometers would simply measure an averaged zero magnetization, PNR can determine the magnetic structure of the magnetic multilayer in more detail and even distinguish between the two types of antiferromagnetic alignment shown in Figs. 5 and 6. More detailed information on the theoretical description of PNR and fitting algorithms can be found elsewhere [22,23,24]. INSTRUMENTAL SETUP Fig. 5 Simulated reflectivity curves and magnetic structure of an antiferromagnetically aligned (4 nm Fe / 1 nm Cr)20 multilayer with its magnetizations collinear with the external field. Clearly observable is the chemical peak at q = 0.127 Å-1 due to the chemical modulation of the multilayer and the AF peak at q = 0.065 Å-1 due to the magnetic modulation of the multilayer. LA PHYSIQUE AU CANADA The C5 triple axis spectrometer at the neutron reactor NRU in Chalk River was used to perform the neutron reflectometry experiments described in the next section. The (111) reflection of a Cu2MnAl septembre / octobre 2006 267 Sept06-FF.qxd 11/7/2006 2:06 PM Page 268 FEATURE ARTICLE ( POLARIZED NEUTRON REFLECTOMETRY ... ) As the polarizer delivers only spin-down neutrons, we need a device called “spin flipper” (SF1) located after the polarizer to convert spin-down neutrons into spin-up neutrons in order to be able to measure the reflectivity curve of spin-up neutrons as well. Another spin flipper is needed in front of the analyzer (SF2) to determine the spin state of the reflected neutrons. At reactor sources Mezei-type spin flippers [26] are commonly used. They consist of two solenoids with rectangular cross section. One solenoid flips the neutron’s spin and the other one compensates the stray fields. The field produced by the compensation Fig. 6 Simulated reflectivity curves and magnetic structure of an antiferromagnetically coil is collinear with the guide aligned (4 nm Fe / 1 nm Cr)20 multilayer with its magnetizations perpendicular to the field, whereas the flip field is -1 external field. Clearly observable is the chemical peak at q = 0.127 Å in the nonperpendicular to the guide field. spinflip reflectivities R- - and R++ due to the chemical modulation of the multilayer Therefore, the neutron’s spin -1 -+ +and the AF peak at q = 0.065 Å in the spin-flip reflectivities R and R due to the precesses in the flip field and magnetic modulation of the multilayer. one has to adjust the magnetic field produced by this solenoid Heusler crystal is used to polarize and analyze the neutrons’ by tuning the current through the flipper coil in order to spin state at a wavelength of λ=0.237 nm in combination with achieve exactly a π rotation when the neutrons pass through a pyrolitic graphite (PG) filter which reduces the higher order the magnetic field region. A magnetic guide field of at least contributions of a monochromator (λ/2, λ/3, etc.) [25] by a a few Gauss is always needed along the neutron path in order factor of about 1000. The distances from the monochromator to preserve the spin polarization. to the first slit, first slit to second slit, and second slit to samThe polarization of the beam can be determined by measurple were 0.16 m, 1.44 m, and 0.18 m, respectively. A sketch of ing the flipping ratio F, i.e. F- = I --/I -+ for spin-down neuthe setup is displayed in Fig. 7. The components needed are trons or F+ = I++/I+- for spin-up neutrons, respectively. The a monochromator (M) and analyzer crystal (A), slit systems polarization of the neutron beam can be deduced via: (S1, S2, S3, and S4), spin flippers (SF1 and SF2), a PG filter (F), a sample, and a detector (D). The slits S1 and S2 define the I −− ( 1 − 1 / F ) I −− − I − + F−1 (8). collimation of the beam, whereas the slits 3 and 4 reduce the P = = = −+ −− −− background. The detector is a 5 bar 3He gas detector. I +I I ( 1 + 1 /F ) F+1 The maximum achievable polarization by using the (111) Bragg reflection of a Cu2MnAl Heusler crystal can be easily calculated from the different structure factor for up neutrons and down neutrons. The intensity I+ and I- for up and down neutrons, respectively, is simply, ignoring element-specific Debeye-Waller factors: I+ ~ I0 × (bnuc, Mn – bnuc, Al + bmag, Mn)2 ~ I0 × 2.09 (5) I- (6) ~ I0 × (bnuc, Mn – bnuc, Al - bmag, Mn)2 ~ I0 × 249.7 where bnuc, Mn = -3.73 fm denotes the nuclear scattering length of Mn, bnuc, Al = 3.449 fm denotes the nuclear scattering length of Al, and bmag, Mn = 3.2H2.695 fm denotes the magnetic scattering length of Mn with 3.2 μB per Mn atom at room temperature. The neutron beam polarization P is defined as: P= I− − I+ I− + I+ (7) Fig.7 and in the case of a perfect Heusler crystal the maximum achievable polarization is 98.3%. 268 PHYSICS IN CANADA September / October 2006 Neutron reflectometry set-up using a polarizing monochromator (M) and analyzer crystal (A), slit systems (S1, S2, S3, and S4), spin flippers (SF1 and SF2), a PG filter (F), and a detector (D). Sept06-FF.qxd 11/7/2006 2:06 PM Page 269 ARTICLE DE FOND ( POLARIZED NEUTRON REFLECTOMETRY ... ) The square root is used here because the neutrons are reflected twice, from the monochromator and the analyzer, using for both the same type of crystal, in our case a Heusler crystal. In our setup we typically achieve flipping ratios higher than 25 corresponding to a polarization of about 96%. The experiments on the (6 nm ErFe2 / 6 nm DyFe2)40 multilayers were carried out in a magnetic field of up to 6 T using a cryomagnet because the rare earth / iron alloys are wellknown for their huge magnetic anisotropies and therefore, a large external magnetic field is needed to saturate the sample’s magnetization along certain crystallographic directions. The additional measures needed to maintain the neutrons’ polarization in the presence of huge magnetic stray fields of a cryomagnet is described elsewhere [27]. MAGNETIZATION REVERSAL OF A (6 nm ErFe2 / 6 nm DyFe2)40 MULTILAYER During the last decade there has been an increasing interest in thin films and multilayers composed of rare earth materials because they have many potential technical applications as sensors and magnetic read heads. In the (ErFe2 / DyFe2) multilayer system both the DyFe2 and the ErFe2 layers are hard magnets but with different easy axes in the bulk samples. The term “easy axis” describes the direction in which the magnetization prefers to lie without an external field. Bulk DyFe2 has the crystallographic <100> directions as easy axes, whereas bulk ErFe2 has its easy axes along the <111> directions. This can lead to very complex magnetic structures when considering that additional anisotropies such as interface, shape, and strain anisotropy, are present in these thin magnetic films [28,29,30]. On top of that there exists an exchange interaction between the Fe atoms of adjacent layers that strongly favors a parallel alignment of the magnetizations. tion. The sample’s orientation with respect to the magnetic field and the neutron spins is depicted in Fig. 1. After having reached the negative saturation the magnetic field was ramped down to zero and reversed to positive values. The shown reflectivity curves were recorded at a field of 0.4 T (top panel), 1 T (middle), and 6 T (bottom). Only the non-spin flip reflectivities for down neutrons (R--, open circles) and upneutrons (R++, closed circles) are shown, the measured spinflip reflectivities R-+ and R+- were zero within errors. In the top panel of Fig. 8 it can be clearly seen that the critical scattering vector up to which total reflectivity occurs, is larger for R-- than for R++. That proves that the magnetization in a positive field of 0.4 T is still reversed, i.e. antiparallel to the applied field. In positive saturation, as shown in the bottom panel, the critical scattering vector for R-- is much smaller than that for R++. The coercive field is about 1 T as can be seen in the middle panel because the reflectivity curves for spin-up and spin-down neutrons are very similar, especially the critical scattering vectors for both cases are very close to The magnetic structure of both the ErFe2 and DyFe2 is called ferrimagnetic because the magnetic moment of the Fe atoms is antiparallel and unequal to the magnetic moment produced by the rare earth atoms Dy and Er. Below room temperature the magnetic moment produced by the rare earths is larger, and therefore the net magnetization of the layers points always along the direction of the rare earth magnetization. The sample was grown using the molecular beam epitaxy facility in the Clarendon Laboratory, Oxford. Sapphire substrates with a (11⎯20) orientation were cleaned and 100 nm niobium was deposited as a chemical buffer layer, followed by a 2 nm iron seed to improve the crystal growth [31]. The multilayer was then grown by co-deposition of the elementary fluxes with a layer thickness of 6 nm for both layers, repeating the (ErFe2 / DyFe2) sequence 40 times. Finally the multilayer was covered with a 10 nm thick yttrium layer as a protection against oxidation. Both layers, DyFe2 and ErFe2, had a (110) surface orientation. In Fig. 8 a series of reflectivity curves are shown during a magnetization reversal cycle at a temperature of T = 100 K. Prior to the measurements the sample has been saturated in a field of –6 T with the field along the in-plane [1⎯10] direc- Fig. 8 Measured neutron reflectivities R++ (solid circles) and R- - (open circles) of a (6 nm ErFe2 / 6 nm DyFe2)40 multilayer along with the fits (solid and dashed line, respectively) at a temperature T=100 K, in an external magnetic field of 0.4 T (top panel), 1 T (middle panel), and 6 T (bottom panel). Prior to the measurements, the magnetization of the sample was reversed in a field of –6 T, the field was always applied along the [1⎯⎯1 0] in-plane direction. LA PHYSIQUE AU CANADA septembre / octobre 2006 269 Sept06-FF.qxd 11/7/2006 2:06 PM Page 270 FEATURE ARTICLE ( POLARIZED NEUTRON REFLECTOMETRY ... ) Fig. 9 Magnetization component along the external field of the DyFe2 layers (solid circles), ErFe2 layers (open circles), and the average magnetization of the (6 nm ErFe2 / 6 nm DyFe2)40 multilayer (triangles) as a function of the external field at a temperature of 100 K. Prior to the measurements, the magnetization of the sample was reversed in a field of –6 T, the field was always applied along the [1⎯⎯1 0] in-plane direction. each other. For a completely demagnetized sample the spinup reflectivity would equal the spin-down reflectivity. An important observation was that no increased spin-flip signal was observed at 1 T. That means that there is no homogeneous in-plane rotation of the magnetization. The magnetization must be reversed either by domain wall movement or a magnetization rotation perpendicular to the sample’s surface because in PNR we are not sensitive to magnetization components perpendicular to the sample’s surface. The reflectivity curves shown in Fig. 8 were fitted using the Parratt formalism [20]. The solid line represents the fit to the spin-up reflectivity, whereas the dashed line represents the fit to the spin-down reflectivity. From the fit data we can infer the magnetization component of the DyFe2 and ErFe2 layer parallel to the external field independently. The values are shown in Fig. 9 with the closed circles representing the magnetization component of the DyFe2 layers and the open circles representing the magnetization component of the ErFe2 layers. The average value, as it would be measured by classical magnetometry is displayed as triangles. It can be clearly seen that the behavior of the two magnetizations is different. The magnetization curve of the DyFe2 represents an easy axis loop with a very fast switching from negative to positive saturation. In contrast, the ErFe2 magnetization curve represents a hard axis loop where the magnetization rotates continuously towards the direction of the magnetic field. This nicely shows the capability of PNR to be elementspecific. This property of PNR to be element-specific is underlined in Fig. 10 where simulated reflectivity curves are shown for three different cases of a magnetic structure giving a zero sig- 270 PHYSICS IN CANADA Fig. 10 Simulation of R++ and R- - for different magnetic structures in a (6 nm ErFe2 / 6 nm DyFe2)40 multilayer: in the top panel for the case where the magnetization of the DyFe2 layers is antiparallel to the external field, the magnetization of the ErFe2 layers parallel to the external field, the middle panel with swapped magnetization directions, i.e. the DyFe2 layers parallel, the ErFe2 layers antiparallel to the external field, and the bottom panel for the case of zero magnetization in both layers. nal in a classical magnetometer. In the top panel the magnetization of the DyFe2 (MDyFe2 = -0.13 T) is antiparallel to the external field, whereas the magnetization of the ErFe2 layer (MErFe2 = 0.13 T) is parallel to the external field. This corresponds to the magnetic structure at the coercive field as deduced from our PNR data at a magnetic field of 1 T (Fig. 8, middle panel). As can be seen in the middle panel of Fig. 10, where the directions of both magnetizations are swapped, the intensity ratio of R++ to R- - at the Bragg peak position is swapped as well. So, it is easy in a PNR experiment to distinguish between these two cases and it shows that the PNR data in Fig. 8 (middle panel) could not have been fitted with a magnetic structure where the directions of both layer magnetizations are reversed. For comparison, the case for zero magnetization, where R++ = R- -, is displayed in Fig. 10 (bottom panel). September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 271 ARTICLE DE FOND ( POLARIZED NEUTRON REFLECTOMETRY ... ) The reason for this element-specific magnetic information is the different nuclear SLD of DyFe2 (Nbnuc = 729 μm-2) and ErFe2 (Nbnuc = 554 μm-2). So, this type of element-specificity of PNR would not work for systems where the nuclear SLDs are identical or very close to each other. CONCLUSION The magnetization reversal experiments described here demonstrate the unique capabilities of Polarized Neutron Reflectometry for determining the magnetic structure of multilayers with different magnetic layers. PNR can determine complicated magnetic structures inaccessible to standard magnetometry techniques. PNR is capable of measuring element-specific hysteresis loops, i.e. PNR can distinguish the magnetization of different magnetic layers, where standard magnetometry techniques would only measure the average magnetization. 9. 10. 11. 12. 13. 14. 15. 16. ACKNOWLEDGMENT 17. We are indebted to Zin Tun, CNBC, for his continuous efforts during the past decade to install and improve the neutron reflectometry set-up on C5 and for his time to explain to us how to use his set-up properly. 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In particular, no bona fide scientist will be excluded from participation on the grounds of national origin, nationalitiy, or political considerations unrelated to science.” Application forms and additional information can be obtained from the IUPAP website: http://www.iupap.org or from the Secretary of the Canadian National IUPAP Liaison Committee : “To secure IUPAP sponsorship, the organizers have provided assurance that (Conference name) will be conducted in accordance with IUPAP principles as stated in the ICSU Document “Universality of Science” (sixth edition 1989) regarding the free circulation of scientists for international purposes. In particular, no bona fide scientist will be excluded from participation on the grounds of national origin, nationalitiy, or political considerations unrelated to science.” Pour obtenir des formules de demande et toute autre information, il suffit de visiter le site suivant : http://www.iupap.org ou de s’addresser au secrétaire du Comité national canadien de liaison avec l’UIPPA : P. Hawrylak Institut des sciences et des microstructures Conseil national de recherches Canada (M-50) Ottawa, Ontario K1A 0R6 P. Hawrylak Institute for Microstructural Sciences National Research Council of Canada (M-50) Ottawa, Ontario K1A 0R6 Télphone : (613) 993-9389 Télécopieur : (613) 990-0202 Courrier électronique : [email protected] Tel: (613) 993-9389 Fax: (613) 990-0202 E-mail: [email protected] PROFESSIONAL CERTIFICATION PROFESSIONNELLE Details regarding the certification process, as well as all forms required to apply for certification, can be found in the "Professional Certification" section of http://www.cap.ca. 272 PHYSICS IN CANADA L'information relative au processus de certification, ainsi que les formulaires requis, sont disponibles sous la rubrique "Certification professionnelle" du site Internet de l'ACP qui se lit ainsi : http://www.cap.ca. September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 273 ARTICLE DE FOND ( DIFFRACTION STUDIES OF GAS HYDRATES ... ) DIFFRACTION STUDIES OF GAS HYDRATES WITH AN EMPHASIS ON CO2 HYDRATE by B.H. Torrie, O.S. Binbrek, I.P. Swainson, K.A. Udachin, C.I. Ratcliffe and J.A. Ripmeester U nder the right conditions of high pressure and low temrounding water so knowledge of the density is critical for peratures, water will form cages around a variety of simple modeling this dispersal method. Gas hydrates are non-stomolecules. The cages are interconnected to form a crystal chiometric compounds since the cage occupancies vary structure and space filling requirements dictate that there be depending on how the hydrate is formed and therefore the more than one type of cage. Cage type is also determined by density also varies. The purpose of the research described in the size of the molecule that is enclosed. There are three comthe rest of this article is to develop a fuller understanding of mon structures labelled I, II and H how the CO2 molecules occupy the with the structure of H being detercages in the hydrate, and to determine mined by an NRC group using neu- Gas hydrates are a potential how practical it is to determine the dentron diffraction at Chalk River in the sity of the samples using single crystal source of huge quantities of and powder diffraction techniques. 1980’s [1]. natural gas and can also be Why are gas or clathrate hydrates of The structure of CO2 hydrate has been interest? The right conditions for the used to store natural gas investigated in the past by a Japanese [3] formation of the hydrates are found in and hydrogen and to group and a U.S. group working [4]at coastal waters and under permafrost. the Argonne National Laboratory , Natural gas hydrates have been found sequester carbon dioxide. both using powder neutron diffraction. off the west coast of Vancouver Island A much more detailed structure was and in the Mackenzie Delta and many determined using single crystal X-ray similar places around the world. The components of the natdiffraction at NRC [5]. ural gas come from two sources, the decay of organic matter formed in the oceans or discharged from the continents, BASIC DIFFRACTION THEORY known as biogenic gas, or from the thermal cracking of Since physics departments often neglect to teach basic crystalhydrocarbons that have migrated from deeper sources, lography, a mini-course is included here so that you can betknown as thermogenic gas. It has been estimated that the ter understand the rest of this paper. A comparison between total fuel in gas hydrate form exceeds that from coal, oil and diffraction from a grating and crystal diffraction should be other sources of natural gas combined. Unfortunately these helpful. If a plane wave is incident on a reflection grating, hydrates are widely dispersed in awkward locations so gas then diffraction from the grating lines produces cylindrical hydrates are tomorrow’s fuel, not today’s. Of more immediwaves that combine to give a diffraction pattern made up of ate interest is that synthetic gas hydrates can be formed from lines of various orders at the detector. The more grating lines natural gas. In the case of methane, the resulting crystals are that contribute to the pattern, the sharper the diffraction lines metastable for several days at ambient pressure just below [2] will be. Similarly, when a plane wave is incident on a crystal, 0C. Research in Norway indicates that natural gas the wavelets produced by the scattering centres combine to hydrates can be formed, sent to markets in ships and decomgive a diffracted plane wave. Conditions are such that a scatposed to release the gas at a cost which is comparable to the tering plane can be defined that acts like a mirror with the cost of shipping liquid natural gas which is the alternative in angle of incidence equal to the angle of reflection for the plane current use when pipelines are not practical. waves. The ‘mirror’ is called a Bragg plane. There are many parallel Bragg planes in a crystal and, if the condition for conIn a similar vein, gas hydrates can be used to store hydrogen. structive interference is satisfied, the plane reflected waves There has been much hype about the hydrogen economy of the future but, until a safe and economical method of storing hydrogen has been developed, a hydrogen based economy is Bruce Torrie <[email protected]>a, Omar Binbrekb, not practical. Experimental and theoretical work at NRC has Ian Swainsonc, Konstantin Udachind, Christopher advanced the knowledge of storing clusters of hydrogen in d and John Ripmeesterd; a Department of Ratcliffe hydrate cavities. Another gas hydrate of interest is formed from water and CO2. It has been proposed that this greenhouse gas, produced by the burning of fossil fuels, could be pumped into the oceans at an appropriate depth where it would form a hydrate that would sink to the ocean floor. Obviously this will only happen if the CO2 hydrate is denser than the sur- Physics, University of Waterloo, Waterloo, Ontario, N2L 3G1; b Department of Physics, University of Petroleum and Minerals, Dhahran, Saudi Arabia; c National Research Council of Canada, Steacie Institute for Molecular Sciences, Chalk River Laboratories, Chalk River, ON, K0J 1J0; d Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, ON, K1A 0R6 LA PHYSIQUE AU CANADA septembre / octobre 2006 273 Sept06-FF.qxd 11/7/2006 2:06 PM Page 274 FEATURE ARTICLE ( DIFFRACTION STUDIES OF GAS HYDRATES ... ) will combine to give a Bragg reflection. The more planes that contribute to the reflection, the sharper the reflection will be. Scattering centres and Bragg planes are somewhat artificial constructs but because a crystal is made up of three-dimensional repeating units, there are associated scattering centres made up of atoms or groups of atoms that repeat in space and through these centres it is possible to construct planes of various orientations that again repeat in space. Three other concepts need to be introduced to give a basic understanding of crystal diffraction. Bragg peaks will be broadened by a combination of two instrumental effects. If the incident wave is not plane, meaning that the incident beam diverges or converges, then the peaks will be broadened if the incident wave if not monochromatic. Most sources of neutrons, as found at Chalk River and other places, tend to be weak compared to modern laboratory Xray sources or synchrotron X-ray sources so a more relaxed geometry is used to increase the intensity but this also broadens the diffraction peaks. There are also sample dependent effects to consider. If the spacing between the Bragg planes varies because of strains in the crystal, then the peaks will again be broadened. Also, the atoms in the crystal are in constant thermal motion and this alters the interference condition as a function of time. Diffraction measurements give a time average of this motion which can be analyzed in terms of a thermal ellipsoid since the amplitude of the motion varies with direction depending on the nature of the interatomic bonding. Thermal motion reduces the intensity of Bragg peaks at high scattering angles. Bragg planes are labeled with three Miller indices, h k l, that give the orientation and spacing between the planes. For a cubic crystal, such as CO2 hydrate where the basic building block is a cube, the planes parallel to the cube faces are labeled (100), (010) and (001). More generally, the planes are labeled (hkl) where h, k and l are the reciprocals of the intersection points of the Bragg plane with the cell sides. For example, the plane parallel to the z-axis and intersecting the x and y-axes at the length of one cell side away from the ori- Fig. 1 274 Small (dodecahedral) Cage of Type I Gas Hydrate PHYSICS IN CANADA gin is labeled (110) and the separation between all such adjacent planes is l/sqrt(12 + 12 + 02) = 1/sqrt(2) as a fraction of a cubic cell side. For the plane (hkl) the separation is l/sqrt(h2 +k2 + l2). Two planes will have the same separation if (h2 +k2 + l2) is the same for both. An example of this is (334) and (035). In a single crystal diffraction pattern the diffraction spots for these reflections are well separated since the interplanar angle is 31.5o. What happens if a powdered sample is used instead of a single crystal? An ideal powder contains crystallites with all possible orientations so the diffraction spots are expanded into rings which overlap completely in our example. Since the rings have finite widths, for the reasons discussed above, there will also be partial overlap of rings when the sums of the squares of the Miller indices are only approximately equal. The density of rings increases with scattering angle so there is considerable overlap at high angles. Let us look a little more carefully at what happens when a single crystal sample is replaced with a powder sample. There will be a loss of information about interplanar angles since an array of diffraction spots, located by two angles, has been replaced by an array of diffraction rings, or more commonly with a slice through the rings since the detector only operates in a plane, that are located by one angle. For simpler unit cells there is enough information in the low angle non-overlapping powder peaks to determine the unit cell dimensions and angles so the geometrical loss is not important. Details of the structure, though, are contained in the peak intensities and some of this information is lost due to peak overlap when a powder is used rather than a single crystal. MODELS FOR CO2 HYDRATE CO2 hydrate forms a type I gas hydrate with a cubic structure and a unit cell (basic repeat unit) containing 46 water molecules in a framework of two dodecahedral and six tetrakaidecahedral cages as shown in Figures 1 and 2. Each cage can hold one CO2 but the larger cages tend to be fully occupied and smaller cages only partially occupied with the Fig. 2 September / October 2006 Large (tetrakaidecahedral) Cage of Type I Gas Hydrate Sept06-FF.qxd 11/7/2006 2:06 PM Page 275 ARTICLE DE FOND ( DIFFRACTION STUDIES OF GAS HYDRATES ... ) merge. This is particularly true of the carbon sites at the centre of the large cage. The result will be indistinguishable from what would be obtained with a single site occupied by an atom with large thermal motion. The smearing is obviously more of problem at high temperatures for both the carbon and oxygen atoms. INSTRUMENTATION The single crystal measurements were made on a Bruker Smart CCD X-ray Diffractometer as found at the Steacie Institute for Molecular Sciences, NRC, Fig. 3 Possible locations for the oxygen Ottawa. Similar instruments can Fig. 4 Possible Locations for the oxygen atoms of CO2 in the small cage. be found at a number of atoms of CO2 in the large cage. Black atoms are for the Argonne Canadian universities. With this Markings of atoms is the same as in model, others for the NRC model Figure 3. instrument a single crystal difexcept for the clear atom that fraction pattern was recorded at marks the centre. 173 oK and the structural (NRC) model was refined with the SHELXTL software package [6]. occupancy depending on preparation conditions. In the simpler (Argonne) model the carbon atoms sit in the centre of The second instrument that was used is the C2 powder neuboth cages and oxygens are disordered among a collection of tron diffractometer, also operated by the Steacie Institute, but equivalent positions located one C-O bond length away from located at Chalk River on the NRU nuclear reactor. Details of the centres. The possible positions of the oxygen atoms in this instrument can be found on the web, but the following space is illustrated by the dark spheres in figures 3 and 4. In differences from the first instrument are of note. X-rays are the small cage the oxygens lie on a spherical shell and in the scattered by electrons and scattering intensity increases in a large cage the oxygens lie in a donut shaped ring. For the regular fashion throughout the periodic table as the number more complex (NRC) model, the carbon atoms still are locatof electrons increases. There are exceptions, but that is the ed in the centres of the small cages but the oxygen atoms general trend. Neutrons are scattered by nuclei and the scatoccupy three sets of equivalent positions. In other words, tering intensity varies in an irregular fashion throughout the there are three times as many possible positions for the oxyperiodic table. Light atoms are much easier to locate with gens, 36 in total, as in the simpler model as shown by the neutrons than X-ray but the most important light atom, dark spheres in figure 3 but the occupancy of any one site has hydrogen, has a large incoherent scattering cross-section so it been reduced by a factor of three. For the large cages, the caris routine to use deuterated samples to remove most of the bon atoms reside in a cluster of 16 equivalent positions surincoherent background. Although not of interest for the rounding the centre and the oxygens reside in a broadened present study, neutrons have a spin which interacts with donut with 32 possible sites. The oxygen sites are shown by atomic spins so magnetic materials can be studied. An the spheres marked with quadrants in figure 4. In the advantage and a disadvantage of neutrons is that the interacArgonne model there are two occupancies, one for each cage tions with matter are weak. The advantage is that samples type. In the NRC model there are 3 occupancies for the small can be surrounded by cryostats and pressure chambers withcage and 2 occupancies for the large cage. out a large reduction in signal strength but the disadvantage is that scattering from the sample is weak although fairly uniformly distributed over the sample, i.e. there is little attenuaOBJECT OF RECENT NEUTRON EXPERIMENTS tion of the incident beam within the sample due to scattering Obviously the NRC X-ray experiment was very successful in or absorption which require corrections to be applied to Xleading to the development of a very sophisticated model for ray data. CO2 hydrate but there was a desire for a faster method of measuring occupancies. The growth of single crystal samThe C2 instrument was used to record a powder profile at the ples is time consuming which is an impediment to making same temperature of 173oK as was used for the single crystal measurements on a number of samples prepared under difmeasurements. The sample was prepared using well ferent conditions. Powder samples, on the other hand, can be crushed frozen deuterium oxide in a metal reaction vessel prepared much more readily but there is a loss of information placed in a bath at -15oC before slowly adding CO2 gas. in going from a single crystal diffraction pattern to a powder Reaction conditions were 40 bars of CO2 at a temperature of pattern as discussed above. With lower resolution the collec5oC for 24 hours to give a composition similar to that of the tions of atomic sites shown in figures 3 and 4 will tend to single crystal sample of reference 6. LA PHYSIQUE AU CANADA septembre / octobre 2006 275 Sept06-FF.qxd 11/7/2006 2:06 PM Page 276 FEATURE ARTICLE ( DIFFRACTION STUDIES OF GAS HYDRATES ... ) b a Fig. 5 a) X-ray powder profile (top) and neutron powder profile (bottom) in the range 1 to 2 Å; b) X-ray powder profile (top) and neutron powder profile (bottom) in the range 2 to 3 Å. ANALYSIS As a test of what is possible the single crystal X-ray results were transformed into an X-ray powder pattern using GSAS [7], i.e. the atomic positions, occupancies and temperature factors were used as inputs to generate an idealized powder pattern that is background and noise free. To do this conversion it is necessary to specify instrumental parameters for the X-ray powder diffractometer so these parameters were taken from the X-ray powder diffraction example in the GSAS manual. The assumed diffractometer is a conventional Bragg-Brentano type using CuKá radiation. Neutron and X-ray powder profiles are compared in figure 5. The single crystal diffraction results contain 478 unique peaks whereas the derived powder pattern contains only 140 unique peaks for a reduction of more than a factor of three. Similarly the neutron powder pattern contains only 178 unique peaks for a reduction of something less than a factor of three. These reductions reflect the overlap mentioned above but the exact numbers depend on the fact that the wavelengths and scattering angle ranges of the three instruments were somewhat different. Certain aspects of the structure are well known and will not change significantly from one crystal to the next. For example, the CO2 molecules interact only weakly with the cages that they occupy so the molecule should retain an O-C-O angle of 180o and a typical C-O bond length of 1.16 Å. The geometry of the cages is also well known and can be transferred from one diffraction study to the next with only minor adjustments. Temperature factors should be similar since the temperature was the same in all cases. . The first question to address is whether the sophisticated model used with the single crystal data can be applied to powder data. To answer this question it is useful to use the idealized X-ray powder profile. If the model fails with this manufactured profile then it is unlikely to work with any real X-ray or neutron powder profile. First of all the profile was 276 PHYSICS IN CANADA tested against the fixed atom model that was used to generate it. You might think that the fit would be perfect but there is quantization noise that depends on scaling. The larger the scale factor, the smaller the quantization noise. With a scale factor that gives approximately the same number of counts per peak as in the single crystal work, the fitting process gives a κ2 = 0.1760E-1. Next step is to reduce the number of variables since the number of unique peaks is reduced as pointed out above. This was done by fixing the cage structure and using a rigid body representation of the CO2 molecule. Occupancies and temperature factors tend to be highly correlated so temperature factors were included to test for correlation effects. Similar atoms should have similar thermal motions so it was assumed that the framework oxygens, hydrogens, carbons and oxygens in CO2 for each of the two cage types had common temperature factors. Isotropic thermal motion was assumed to give a further reduction in the number of variables. The total number of variables is now 24 compared to 108 in the single crystal study. Note that the 108 includes instrumental parameters that are not varied in the analysis of the idealized powder pattern. The resulting fit could be regarded as unsatisfactory or satisfactory depending on your goal. The exactitude of the single crystal results has been lost. The centres of the molecules in the large cage moved within the carbon blob in the centre of the cage as is expected and the orientations of the molecules in both cages changed significantly but still basically define a spherical shell or donut as in figures 3 and 4. In spite of these differences, the occupancies are in good agreement with the single crystal values. The occupancies are 41%, 59% summing to 100% (large cage) and 38%, 19% and 14% summing to 71% (small cage) for both. For completeness, the simpler Argonne model was also used to fit the manufactured X-ray powder data. In this case the carbon atom in the large cage is fixed in the centre so the carbon blob only manifests itself as a large temperature factor. Again the orientations of the molecules change significantly September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 277 ARTICLE DE FOND ( DIFFRACTION STUDIES OF GAS HYDRATES ... ) but the occupancies are only slightly changed at 101% and 71%. The above results gave us confidence that a powder pattern can be used to determine occupancies but not the details of arrangement of the CO2 molecules in the cages. Therefore the analyses were repeated using the two models with a real neutron powder pattern. From figure 5 it can be seen that the real pattern differs from the idealized X-ray pattern in having a background, Poisson noise and decreased resolution associated with increased peak widths. With the sophisticated model, positional and orientational parameters again tend to wander away from the single crystal values but the occupancies are only slightly different. For the large cage the occupancies are 42% and 60% summing to 102% and for the small cage the occupancies are 38%, 17% and 17% summing to 72%. With the simpler model the occupancies are 102% and 77%. An anomalous feature of this set of results is that the isotropic temperature factors for the oxygen atoms in the small cages is very high. It can also be seen from the correlation table in GSAS that the occupancies and temperature factors are highly correlated. If the temperature factors of the oxygens in the two types of cages are arbitrarily constrained to have the same value then the occupancies become 101% and 73%. A less arbitrary approach would be to make the measurements at a lower temperature so that thermal motion is less pronounced and there would be less interaction between occupancies and temperature factors. We have done this with the sample used here and other samples with the expected decrease in the occupation factors for the small cages. SUMMARY Gas hydrates are of interest because they are a future source of large quantities of natural gas. They also offer a possible means of storing natural gas for shipment and hydrogen to fuel the hydrogen economy. This article concentrated on one aspect of using hydrates, which is for sequestering CO2 at the bottom of the oceans. The molecules occupy cages in the hydrate structure and occupancies depend on preparation conditions. Cage occupancies were determined in diffraction experiments and from this information the densities of CO2 hydrates can be calculated. REFERENCES 1. 2. 3. 4. 5. 6. 7. J.A. Ripmeester, J.S. Tse, C.I. Ratcliffe, and B.M. Powell, Nature 325, 135 (1987). J.S. Gudmundsson, M. Mork, and O.F. Graff, 4th International Conference on Gas Hydrates, page 997, Tokyo, May 19-32 (2002). T. Ikeda, O. Yamamuro, T. Matsuo, K. Mori, S. Torii, T. Kamiyama, F. Izumi, S. Ikeda, and S. Mae, J. Phys. Chem. Solids 60, 1527 (1999). R.W. Henning, A.J. Schultz, V. Thieu, and Y.J. Halpern, J. Phys. Chem. A 104, 5066 (2000). K.A. Udachin, C.I. Ratcliffe, and J.A. Ripmeester, J. Phys. Chem. B 105, 4200 (2001). G.M. Sheldrick, Acta Crystallogr. A46, 467 (1990). A.C. Larson and R.B. Von Dreele, General Structure Analysis System, LAUR 86-. 748, The Regents of the University of California. LA PHYSIQUE AU CANADA septembre / octobre 2006 277 Sept06-FF.qxd 11/7/2006 2:06 PM Page 278 INTERNATIONAL PHYSICS OLYMPIAD 37TH INTERNATIONAL PHYSICS OLYMPIAD, SINGAPORE 2006 BY ANDRZEJ KOTLICKI AND GUILLAUME CHABOT-COUTURE The 37th International Physics Olympiad (IPhO) was held in Singapore from 7th to 17th of July, 2006. A total of 93 countries participated in the competition making it the largest Olympiad in our history. The number of participating countries increases almost every year with very rapidly increasing participation from Asia but only 2 countries from Africa. Similarly to the competitions held in Korea and Indonesia, the Olympiad was quite clearly an event of primary importance to the Singaporean government and its educational authorities. The president of Singapore himself was scheduled to speak at the opening ceremony but, he was force to cancel at the last minute due to sickness (reported in the press). In his place several top government officials participated in the opening ceremony and stressed in their opening addresses the paramount importance of science, technology and education for the Singapore’s development. Four Nobel Price Laureates and a Templeton Prize Laureate gave lectures to the participants and socialized with them. The social program was very entertaining and interesting with visits to research centers, historical sites, a night safari and a continuous “flow” of excellent Singaporean food. The students were delighted by this exotic experience, most of them on their first ever international trip. The academic part of the competition was organized by faculty members from the two major Singaporean Universities: the National University of Singapore (theoretical problems) and the Nanyang Technological University (experimental problem). The problems were quite interesting and well prepared. They did not concentrate on extensive math but required creative thinking and the ability to describe physical reality using appropriate formulas and approximations. Marking by the academic committee was very thorough and fair, and in most cases, agreed closely with the marking of the leaders. The marking moderations (the process of establishing the final mark acceptable by both leaders and the local marking team) were performed in a good collegial atmosphere with very few real controversies. Canada was represented by the following students: Mr. Boris Braverman, from Sir Winston Churchill High School, Calgary, Alberta Mr. Lin Fei from Don Mills Collegiate Institute, Toronto, Ontario Mr. Patrick Kaifosh from University of Toronto Schools, Toronto , Ontario Ms Lu Liu from Waterloo Collegiate Institute, Waterloo, Ontario Mr Devin Trudeau from Dover Bay Secondary School, Nanaimo , B.C. The team leaders were: Dr Andrzej Kotlicki from the Department of Physics and Astronomy of the University of British Columbia and Guillaume Chabot-Couture, a former member of the Canadian team at the IPhO in 2000, and at present, a PhD student at Stanford University. 278 PHYSICS IN CANADA The Canadian team had their best performance ever, winning two gold medals (Boris and Lin), the forth and fifth gold medals in the history of Canadian participation at the IPhO, one bronze medal (Patrick) and a honorary mention (Devin). Boris was 10th overall among over 400 participants. A total of 37 gold medals, 48 silver medals, 83 bronze medals and 81 honorary mentions were awarded. The following 85 countries participated in the 37th International Olympiad: Albania, Argentina, Armenia, Australia, Austria, Azerbaijan, Belarus, Belgium, Bolivia, Bosnia & Herzegovina, Brazil, Brunei Darussalam, Bulgaria, Cambodia, Canada, China, Chinese Taipei, Colombia, Croatia, Cuba, Cyprus, Czech Republic, Denmark, Ecuador, Estonia, Finland, France, Georgia, Germany, Ghana, Great Britain, Greece, Hong Kong , Hungary, Iceland, India, Indonesia, Iran, Ireland, Israel, Italy, Japan, Jordan, Kazakhstan, Korea South, Kuwait, Kyrgyzstan, Laos, Latvia, Liechtenstein, Lithuania, Macau, Macedonia, Malaysia, Mexico, Moldova, Mongolia, The Netherlands, Nigeria, Norway, Pakistan, Peru, Philippines, Poland, Portugal, Romania, Russia, Saudi Arabia, Serbia, Singapore, Slovakia, Slovenia, Spain, Sri Lanka, Suriname, Sweden, Switzerland, Tajikistan, Thailand, Turkey, Turkmenistan, Ukraine, USA, Uzbekistan and Vietnam The following 8 countries send observers to the 37th International Olympiad and plan to participate in the future: Bangladesh, Cameroon, Montenegro, Myanmar, Nepal, New Zealand, Puerto Rico, Zimbabwe. The best score (47.2 points) was achieved by Mailoa Jonathan Pradana from Indonesia, the absolute winner of the 37th IPhO. The following limits (out of 50) for awarding medals and honourable mentions were established according to the Statutes: Gold Medal 37 points, Silver Medal 29 points, Bronze Medal 21 points, Honourable Mention 14 points. Acting on behalf of the organizers of the next International Physics Olympiad, Prof. Sepehry Rad announced that the 38th International Physics Olympiad will be organized in Isfahan, Iran on July 13th – 21st , 2007. He showed a movie about the preparation and site of the coming Olympiad and cordially invited all the participating countries to attend the competition. After the final national selection held at the end of May and hosted by the University of Toronto had chosen the current five best young Canadian physicists, they were invited to an intensive training on the Canadian west coast at Department of Physics and Astronomy of the University of British Columbia before leaving for Singapore. This two day intensive training aimed at better preparing them for the international competition consisted of lectures and exams. The former also included problem solving sessions on advanced topics in physics while the latter were tailored to be 5 hours long to match the duration of the exams at the IPhO and to make sure that the students could adequately manage their time throughout the competition. After all the tricks and Olympiad wisdom had been passed on, the team was off to their tropical destination on the other side of the world. September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 279 ARTICLE DE FOND ( PHASE TRANSITIONS ... ) PHASE TRANSITIONS IN ORGANIC-INORGANIC PEROVSKITES by Ian Swainson T he name perovskite refers to a mineral found over a large Amines can be created with arbitrarily long carbon chains region of (P-T) in the earth’s mantle, with predominant comand bulkier groups such as phenyl rings. Amines larger than position MgSiO3. More generally, perovskite refers to the MA, FA and TMA do not fit in the interstices of the ABX3 structure type consisting of octahedra that are fully cornerframework. They tend to crystallize as layer perovskites, typbonded and form a 3d-framework [1]. The general formula ically in the A2BX4 stacking type (Fig. 1). Here, the interlayer for this structure type is ABX3, in which the BX6 octahedra are spacing is free to expand according to the cation size. usually anionic so that counterions, A, are found in the interPerovskites with organic cations and an inorganic layer or stices between the octahedra, which framework have recently become form variable geometry cages (Fig. 1). The name perovskite refers known as organic-inorganic perovskites The term perovskite is often expanded (OIPs), or hybrid perovskites [2]. Sn2+ further to include structures more cor- to a mineral found over halides have taken a special interest rectly termed layered perovskite-relatof changes in the conductivity a large region of (P-T) in because ed structures, formed by concatenation of the inorganic component at structurof corner-bonded octahedra in a single the earth’s mantle, with al transitions; semiconductor–metal plane, leaving two unbonded, apical X and semiconductor-insulator transiatoms protruding above and below the predominant composition tions are common, and some Sn2+-comlayers (Fig. 1). These structures will be MgSiO . pounds can have a large electrical 3 loosely termed layer perovskites here. mobility [2,3,4]. There are a large variety of additional structural forms that are related in various ways to the fundaOne group of very famous transitions in perovskites is the set mental perovskite structure [2], but we will not discuss them of tilt transitions, which can be viewed as changes in the confurther here. formation of the framework, driven by rotations of octahedra. The highest symmetry form has space group Pm3m where The most familiar perovskites have simple A cations, but it is the macroscopic symmetry demands undistorted, untilted possible to substitute organic molecular cations, most comoctahedra. In the case of the OIPs the amines have to be orimonly amines. Short chained protonated amines such as entationally disordered in this symmetry as they sit on point methylammonium (MA) of formula CH3NH3+, tetramethysymmetries that are higher than their molecular symmetry. lammonium (TMA) of formula (CH3)4N+ and the planar forTilting of the octahedra about one of the pseudo-cubic axes mamidinium ion (FA) of formula NH2-CH=NH2+ can be causes antiferro- tilting in neighbouring octahedra connected placed into the ABX3 structure. Neutron and synchrotron in the plane normal to that axis (Fig. 2). In the next plane radiation have proved to be essential to study the phase below, to which the octahedra are corner-connected, combehaviour in these compounds. mensurate tilting patterns may be in-phase or out-of-phase. Fig 1 Untilted perovskites and layered perovskite-related structure types. Left: isolated layers of corner-linked octahedra stacked in a primitive tetragonal lattice, typical of ABX4 structures, Middle: isolated layers stacked in a body-centered tetragonal lattice characteristic of A2BX4. Right: octahedral frameworks in a primitive cubic lattice, characteristic of ABX3 true perovskite structures. In the classic direct-space studies of tilt transitions of Glazer [5,6] these tilt patterns were denoted with symbols such as a0b+c -, where a superscripted + refers to in-phase rotations, a superscripted - to out-of-phase rotations, and a 0 refers to no rotation. a, b and c refer to differing magnitudes of rotation about the three pseudo-cubic axes. More recently a group theoretical study has shown that only two irreducible representations, labelled M3+ and R4+, are responsible for these two commensurate styles of tilting, and both are associated with the zone boundary of the Brillouin Zone (BZ) (Fig 2) of the parent Pm3m structure [7,8]. This work demonstrated that only 15 pure tilt structures exist, which had previously been a matter of some debate. A third approach, using an idealized form of lattice dynamics, called the Rigid Unit Mode (RUM) Ian Swainson <[email protected]>, National Research Council of Canada, Steacie Institute for Molecular Sciences, Chalk River Laboratories, Chalk River, ON, K0J 1J0 LA PHYSIQUE AU CANADA septembre / octobre 2006 279 Sept06-FF.qxd 11/7/2006 2:06 PM Page 280 FEATURE ARTICLE ( PHASE TRANSITIONS ... ) initio code FOX [11] has proved very useful in solving the structures. Use of the group analysis codes Isotropy [12] and Isodisplace [13] greatly simplifies the relationship between these OIP superstructures and the underlying tilt structures. Fig 2 Top Left: One layer in a perovskite ABX3 framework. Top Right: The act of rotating one octahedron clockwise about an axis perpendicular to the page is to impose antiferro rotations about all neighbouring octahedra in the plane. For the neighbouring layers, connected above and below the page, the commensurate tilt patterns are limited to being exactly in-phase, or out-of-phase. Below: The Brillouin Zone of the untilted cubic parent structure. The M and R points are shown, with which the M3+ and R4+ irreducible representations governing in- and out-of-phase tilting are associated. The lines, T, joining these points represent the freedom of phasing of the tilts between the two commensurate choices. Rx, Ry and Rz represent tilts about the x, y and z-axes associated with certain wavevectors. In a free refinement of the geometry of the MA cation in the ordered phase of MAPbBr3 from neutron data (Fig. 3) it was found that the MA cation is in almost ideal trans configuration, while the PbBr6/2 octahedra are fairly distorted [14]. This observation agrees with Raman data [15,16,17] which shows that the lowest frequency internal mode of MA is higher in frequency than the highest frequency mode associated with the octahedral network, implying the cations are far stiffer than the octahedra. A simplistic view of bond-strength-bond length rules would imply that if the B-X bond length is shortened the octahedra might be expected to be more rigid, and one might expect less distorted octahedra. Yet the change from MAPbBr3 to MAPbCl3 (Fig. 4) shows a strong increase in distortion of the octahedra. A simple picture was offered of the relative rigidities of the two ions and the result of placing the same rigid cation inside a smaller cage as an explanation for the increased distortion in MAPbCl3 [18]. Another effect on changing from Br to Cl, is that there is also an increasingly strong hydrogen bonding interaction between the halide and MA. LONE PAIR DISTORTIONS IN OIPS In MAPbCl3, not only do the X-B-X angles and B-X bond lengths distort further, but the octahedra also become noncentrosymmetric with Pb moving off the centroid [18]. This is due to the creation of a stereoactive lone pair on the Pb2+ ion. Going down the periodic table, Group 14 elements have an approach (e.g., [9]), is capable of examining non-high-symmetry points of the BZ and shows that rotational freedom exists associated with the edges of the BZ, linking the M and R points [9]. This demonstrates that neighbouring planes of octahedra are not restricted to the two commensurate tilt patterns, but have continuous freedom in the phasing of the tilts. Knop et al. [10] studied the dynamics of the MA cation and performed calorimetric measurements of the transition in the methylammonium lead halides, but at this time the structures of many of the phases was unknown. We have examined the sequence of transitions in methylammonium salts MAPbBr3, MAPbCl3 and MASnBr3 using neutron and synchrotron powder diffraction. Synchrotron data has proved very useful in indexing unknown low-temperature phases, and greatly simplifies the solution of structures, by being strongly dominated by the metal-halide framework. Neutron data are essential for refining the geometry of the cations, and for testing the orientation of these ions in the cages. Since superlattices can be generated when the amines orientationally order in the tilt systems, the direct space ab 280 PHYSICS IN CANADA Fig 3 September / October 2006 View of the ordered structure of MAPbBr3 Sept06-FF.qxd 11/7/2006 2:06 PM Page 281 ARTICLE DE FOND ( PHASE TRANSITIONS ... ) rather than 6-coordinated. In the cubic phases of these compounds dynamical flipping of the 3+3 distortion is associated with high ionic conductivity [24]. In addition subtle effects such as the coexistence of two different crystallographic forms at the same temperature occur; the protonated form of MAGeCl3 transforms fully to the Pm3m symmetry on heating, whereas the only 7% of the deuterated form only transforms into the cubic phase prior to melting, the majority remaining in the untransformed rhombohedral phase [24]. TMAGeCl3 shows evidence of two phases coexisting over a large temperature interval on cooling: a monoclinic form, and an orthorhombic form [25,26]. It has been suggested that the softness of the material may allow untransformed domain walls of the orthorhombic phase to exist between monoclinic domains [24]. Phase coexistence over wide temperature intervals shows that there is very little energy difference certain states, and the strong isotope effect in MAGeCl3 suggests that subtle changes in the interaction between amine and GeCl6/2 are at the root. It remains to be seen to what extent similar disorder effects extend to Sn(II) salts. INCOMMENSURATE PHASES IN THE OIPS Fig 4 View of the ordered structure of MAPbCl3 increasing preference to keep their outer s2 electron pair as a lone pair than for it to participate in bonding, so that Pb is far more commonly found as a formal 2+ ion than a formal 4+ ion. These lone pairs can become non-spherical, and stereochemically active by hybridization with p-orbitals. The structural effect of this non s-wave lone pair is that the Group 14 element is driven off-centre resulting in alternating long and short bonds to each pair of halides in trans configuration across the octahedron. The spontaneous displacements of ions with d0 electronic configurations, such as Ti4+, are commonly referred to as a second-order Jahn-Teller effect; the stereoactivity of the lone pair of the Group 14 elements represents another class of this effect [19,20]. We have recently been studying the phases of MASnBr3 below room temperature. We find that the upper structural transition contains a tilt and a lone pair distortion. This transition is also a semiconductor to insulator transition [21], and at this point MASnBr3 changes colour from red to yellow [22]. If we extend our view for one moment to non-perovskite structures such as those containing Sb3+, an ion which has the same electronic configuration as Sn2+, there have been interesting observations of coupling between hydrogen bonding and the orientation of the lone-pair inside the octahedron [23]. The polarization of the electrons on the terminal Cl atom by the amine is coupled to polarization of electrons within the Sb-Cl bond; i.e. H-bonding interactions may be coupled to orientations of the stereoactive lone pair. This effect is worth examining further in the OIPs, since the orientation of the lone pairs is likely coupled to the ordering of the cations. The lone pair distortions are usually strong for Ge2+, and GeCl3-based OIPs are usually described as 3+3 coordinated (i.e. 3 short bonds opposite 3 long bonds in the octahedron) As the amines begin to orientationally order on cooling, it is not uncommon to observe that OIPs pass through incommensurate phases over some temperature interval. These have been observed in both ABX3 and A2BX4 OIPs. A simple phenomenological picture of phonon-induced incommensuration arises from the model of Heine and McConnell [27]. This is essentially a strong phonon anti-crossing interaction in which a strongly temperature-dependent optic or librational mode attempts to cross through a lower frequency mode, which in practice is usually a transverse acoustic phonon. Modes with the same symmetry are forbidden from crossing and repel. If these modes have a different symmetry at high-symmetry points at the centre and boundaries of BZs but the same in the interior then modes can soften at an incommensurate position. One of the most famous cases of incommensurates in insulators, and certainly amongst the OIPs, comes from the propylammonium tetrachlorometallates, where a variety of metals show similar effects. PA2MnCl4 shows a sequence of transitions α−β−γ−δ−ε−ζ, where α has the I4 / mmm symmetry of an untilted A2BX4 lattice, and β is a pure tilt phase of space group Cmca. Phase δ is also Cmca with the same basis (a reentrant of phase β). γ and ε are incommensurately modulated phases, and ζ a low temperature commensurately modulated phase [28,29,30]. The γ, ε and ζ modulated phases are all associated with instabilities at different points in the Brillouin Zone. γ−PA2MnCl4 is characterized by transverse modulations running along c with amplitudes parallel to the layer axis b of the Cmca lattice and the critical wavevector associated with this transition lies on the surface of the BZ along the H-line of buckling modes (Fig. 5). The amplitude of the incommensurate distortion decreases to zero at the γ-δ transition. Thus the Cmca β-phase “reappears” as the δ-phase. The second incommensurate phase, ε appears below this as a second order transition with a different wavevector, k = (1/3 + δ)a* [31], lying along the Σ−direction, and the lock-in to the commensurately modulated ζ−phase occurs along a third direction at k = (a* ± b*)/3 [28,29,30,31]. LA PHYSIQUE AU CANADA septembre / octobre 2006 281 Sept06-FF.qxd 11/7/2006 2:06 PM Page 282 FEATURE ARTICLE ( PHASE TRANSITIONS ... ) Using the Rigid Unit Mode (RUM) approach one can calculate the RUM spectrum of the tilted layers (Fig 5); i.e., all possible modes that do not distort the octahedra. The untilted α-phase has a potential RUM instability at all wavevectors and does not give much information as to the origin of the wavevectors associated with the observed incommensurate phases [33]. Pure tilts exist at |k|=a*/2, while in the interior of the BZ buckling modes occur where the octahedra are both tilted and displaced perpendicular to the layer. The buckling modes are “transverse” waves that buckle the plane of octahedra, rather like buckling a piece of paper. However, this plane is decorated with corner-bonded rigid octahedra, so a better analogy may be made to the flexing of chain mail. If we take the Cmca structure seen in the β and δ-phases as the parent of the modulated phases we find only two orthogonal planes of “buckling” modes and a single line of tilts at their intersection [33]. The wavevectors associated with the γ, ε and ζ phases all lie on these planes. The related salt PA2CdCl4 shows a commensurately tilted structure at base temperature in place of the modulat- Fig 5 ed ζ-phase of PA2MnCl4; the wavevector associated with this ordering lies at the Y-point, on the line of pure tilts (Fig. 5). it is a true ABX3 perovskite, the modulated structure has been described in terms of (fused) “layers” [26], and that the major distortion is a “shear wave”. These planar shear waves are “frozen” transverse acoustics. Hence, although they differ in their RU and non-RU character, the incommensurate distortions in A2BX4 and ABX3 have a similar origin in that they are caused by the onset of ordering of organic cations interacting with transverse acoustic modes. The reasons for the difference in the RU character lies are the higher flexibility of layers compared to frameworks, and the free adjustability of the interlayer distance in the former structure type. THE EFFECT OF PRESSURE ON OIPS Rigid Unit Mode distribution in the Brillouin Zone of the commensurately tilted Cmca-structure of PA2MCl4. Two planes of buckling modes intersect in a single line of pure tilts along Γ−Δ Δ−Y. γ, ε, and ζ represent the wavevectors associated with the modulated phases of PA2MnCl4, and PACC represents the wavevector associated with the final tilted form of PA2CdCl4. Historically there was much discussion of the interaction between the PA chains determining the modulations; the PA chains are fairly rigid and themselves show few degrees of internal freedom. But it is clear that the layers determine the low-energy choices available for modulation, since the observed wavevectors all lie in the planes of RU buckling modes. These RUMs are a special class of acoustic modes. This implies that the most constrained component (inorganic layers) governs the behaviour of the whole system. For the true ABX3 perovskites there are few RUMs, which exist as solely a line of tilts linking the M and R points along the edge of the BZ of the untilted phase (Fig. 2); in principle one could observe incommensurate pure tilt structures associated with this line, but that is not what is seen. Instead the k-vectors associated with the incommensurate distortion lie in the interior of the BZ. Acoustic modes are again involved and the motions can be viewed as buckled layers, but the octahedra are now forced to distort. Perhaps the best-studied example is δ-TMAGeCl3. Although 282 PHYSICS IN CANADA There have been only a limited number of investigations of the response of these compounds to applied pressure. Lee et al [34] examined the response of tin-based compounds. One interesting claim was that FASnI3 was the most compressible perovskite known with a bulk modulus of 8 GPa - about three times more compressible than NaCl. TMAGeCl3 has been reported as having a bulk modulus of 9 GPa [25]. This softness has been invoked as an explanation for the observation of two crystalline forms of TMAGeCl3 coexisting at low temperatures. Using a diamond anvil cell in conjunction with synchrotron powder diffraction Lee et al. (2003) showed transitions between the Pm3m initially to Im3 and finally ending in a reversible amorphization. Very similar behaviour was found for FASnI3, MASnI3 and (MA1/2FA1/2)SnI3. The space groups Im3 , I4/mmm, and Immm reported in the study of Lee et al. [34] correspond to the a+a+a+, a0b+b+ and a+b+c+ tilt systems with in-phase tilting, associated with differing order parameter directions of the M3+ irreducible representation [7]. Two interesting observations can be made from this study. First, that the initial phase entered in the SnI6/2 OIPs is Im3 , independent of the composition of the organic cation; and second that none of the reported phases is compatible with full orientational ordering of the organic cations. We have collected additional, unpublished, neutron data that suggest that the preference for Im3 may extend to being independent of the composition of the inorganic component as well. Thus, the initial response of OIPs to pressure appears almost monotonous compared to the variety of different ordered and incommensurate phases September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 283 ARTICLE DE FOND ( PHASE TRANSITIONS ... ) seen on cooling at ambient pressure. The early appearance of Im3 for all compositions strongly suggests that it is coupling to volume that favours its formation. The a+a+a+ tilt system, in which all three tilts are activated with the same magnitude, guarantees maximum volume reduction for minimum tilt angle, and keeps the organic cations on high point symmetries. Our neutron data show that this phase is stable over a wide temperature interval on cooling, suggesting that the overall tendency for cation ordering is strongly reduced under pressure. It is not clear at this time why in-phase tilting is preferred over out-of-phase tilting under pressure, to what extent this is true of OIPs in general, and whether, upon loss of crystallinity, the orientational disorder of the cations changes from dynamic to a glassy static disorder. CONCLUSIONS The organic-inorganic perovskites show a complex set of transitions, associated with tilt instabilities, ordering of orientationally disordered cations, stereoactive lone pair distortions, and incommensurate instabilities, which are due to interactions between acoustic modes and the cations. 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LA PHYSIQUE AU CANADA septembre / octobre 2006 283 Sept06-FF.qxd 11/7/2006 2:06 PM Page 284 DEPARTMENTAL, SUSTAINING, CORPORATE-INSTITUTIONAL MEMBERS DEPARTMENTAL MEMBERS / MEMBRES DÉPARTMENTAUX - Physics Departments / Départements de physique (as at 2006 November 1 / au 1er novembre 2006) Acadia University Bishop's University Brandon University Brock University Carleton University Collège François-Xavier-Garneau Collège Montmorency Concordia University Dalhousie University Lakehead University Laurentian University McGill University McMaster University Memorial Univ. of Newfoundland Mount Allison University Okanagan University College Queen's University Royal Military College of Canada Ryerson University Saint Mary’s University Simon Fraser University St. Francis Xavier University Trent University Université du Québec à Trois-Rivières Université de Moncton Université de Montréal Université de Sherbrooke Université Laval University of Alberta University of British Columbia University of Calgary University of Guelph University of Lethbridge University of Manitoba University of New Brunswick University of Northern British Columbia University of Ottawa University of Prince Edward Island University of Regina University of Saskatchewan (and Eng. 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McDonald Bldg., Univ. of/d’Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 Phone / Tél : (613) 562-5614; Fax / Téléc : (613) 562-5615 ; Email / courriel : [email protected] INTERNET - HTTP://WWW.CAP.CA 284 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 285 ARTICLE DE FOND ( REVEALING THE MICROSTRUCTURE ... ) REVEALING THE MICROSTRUCTURE OF POLYMERIC MATERIALS USING SANS by Barbara Frisken O ne class of soft materials where small angle neutron scatINTRODUCTION TO BLOCK COPOLYMERS tering is especially useful is polymeric materials built from Design of nano-structured polymeric materials can be conmulti-component polymers. These polymers phase separate trolled through the chemical structure of the polymer. on microscopic length scales to form well-defined microstrucPolymers are built up from individual tures. In the case of polymers consistunits, called monomers. If these ing of two blocks of different This article will review monomers are all the same, the polymer monomers, hexagonal cylinders, closepacked spheres, bi-continuous phases SANS techniques used to is known as a homopolymer. For example, homopolymers such as and other structures can be achieved reveal structure in block poly(styrene) or poly(methacrylate) are by changing the relative length or the degree of segregation of the blocks. copolymer materials with composed of multiple units of styrene and methacrylate, respectively. The tendency of these materials to selfassemble leads to a wide variety of particular examples from Copolymers consist of different important applications ranging from work done by Canadian monomers which can be organized randomly or in blocks, known as random high-impact plastics to foams. This or block copolymers, respectively. The article will review SANS techniques researchers. simplest type of block copolymer is the used to reveal structure in block diblock, which contains a block of type copolymer materials with particular examples from work “A” monomers and a block of type “B” monomers. Other done by Canadian researchers. examples include triblocks, which can either repeat a block (ABA triblocks) or contain three distinct blocks (ABC triblocks). Figures 1a and 1b show sketches of an AB diblock and a BAB triblock polymer, respectively. Block copolymers can also be assembled with branched architecture, such as star-branched block copolymers. Mixtures of different polymers tend to phase separate easily, as the energy of interaction increases with the number of monomers that make up the polymer. Polymers containing two or more blocks are only able to phase separate on microscopic length scales because the different blocks are physically joined. This leads to self-assembly into one of a variety of ordered structures as determined by the fractions of the molecule taken up by the different blocks and the interaction between the blocks. Fig. 1 Schematic diagrams of block copolymer architecture and assemblies. (a) A-B diblock, (b) B-A-B triblock, (c) disordered phase of diblock polymer and (d) ordered (lamellar) phase of diblock polymer (see Ref. 1). The structural organization of block copolymers in the melt, i.e. a bulk polymer sample with no solvent, is determined by the degree of polymerization N, the overall volume fraction occupied by each component, and the A-B segment-segment interaction parameter [1]. At high enough temperatures, entropy dominates and an isotropic or disordered phase with different blocks interpenetrating each other exists throughout the sample. As the temperature drops, the interaction parameter increases and fluctuations in the density from the mean density develop. Eventually the polymer microphase separates at the order-disorder transition. A disordered melt and an ordered (lamellar) phase are sketched in Figs. 1c and 1d, Barbara Frisken <[email protected]>, Dept of Physics, Simon Fraser University, Burnaby BC V5A 1S6. LA PHYSIQUE AU CANADA septembre / octobre 2006 285 Sept06-FF.qxd 11/7/2006 2:06 PM Page 286 FEATURE ARTICLE ( REVEALING THE MICROSTRUCTURE ... ) respectively. Different ordered structures can be achieved by controlling the chemical structure of the polymer. For example, if the volume fraction occupied by the A block of a diblock copolymer is small, the sample will separate into micelles, small generally spherical aggregates, of A blocks in a B matrix. At a slightly higher volume fraction of A, the sample will microphase separate into A cylinders in a B matrix. At equal volume fractions for the A and B blocks, the microstructure after separation will be lamellar, or layered. There are other phases including a bicontinuous phase known as the gyroid phase or “plumber’s nightmare” that occurs at volume fractions intermediate between the cylindrical phase and the lamellar phase. Sketches of these four phases are shown in Fig. 2. For volume fractions of B less that 0.5, the opposite structures occur. These structures persist as the melt is cooled into the solid phase. This capacity for structural organization on nanometer length scales leads to a wide range of applications [2]. By combining two or more types of monomers in a polymer, composite materials can be built which combine the properties of different monomers to create unique materials. For example, combining blocks of poly(butadiene), a rubbery polymer, and poly(styrene), a glassy polymer, results in a microphase separated structure of glassy domains in a rubbery matrix that is both rigid and tough, especially if the copolymer is a triblock with the rubbery block in the middle. Thermoplastic elasticity due to microphase separation has application in high-impact plastics and pressure-sensitive adhesives. Block copolymers are also used as compatibilizers to stabilize polymer blends. An A-B copolymer can stabilize a mixture of A and B polymers by segregating at and stabilizing the interface between the two phases, in the same way that a surfactant stabilizes a dispersion of oil droplets in an aqueous phase. Surfactant-like behaviour that occurs when block copolymers are blended with homopolymers has application in foams, oil additives, thickeners and dispersion dispersive agents. Research on fundamental aspects of these materials focuses on three main areas: the melt phase at high temperature where the polymer is fluid, the solid phase that exists below the glass transition of the polymer, and the behavior of block copolymer when dispersed in various solvents. The microphase separation and ordering, both equilibrium [1] and non-equilibrium [4], is the focus of many studies of both the melt and solid phase. When copolymer is added to a solvent at low concentration the molecules disperse completely. But at higher concentrations, entropy favours aggregation of the molecules into micelles. Work on copolymer solutions has focused on the size and structure of these micelles and is driven by goals of understanding what structures occur in copolymer samples cast from solution and by the use of copolymers as compatibilizers. BLOCK COPOLYMERS AND SANS Scattering experiments are useful tools for determining the microstructure and related behavior of these materials. The length of the structures (10-1000 Å) and the wavelengths of the radiation available for scattering means that small angle scattering of x-rays and neutrons is appropriate for the determination of ordering in both melt and dispersion. In both SAXS and SANS experiments, the intensity of radiation scattered I is measured as a function of scattering angle, which is related to the scattering wavevector q = 4π ⎛ θ ⎞ sin ⎜ ⎟ . Small λ ⎝2⎠ angle x-ray scattering (SAXS) and small angle neutron scattering (SANS) are complementary; SAXS provides superior resolution, while SANS allows use of contrast variation, achieved mainly by exchange of deuterium for hydrogen within the polymer, to reveal different parts of the microstructure. SANS is also useful for samples that are otherwise strongly scattering; the scattering cross section of samples for neutrons is generally very small. The variety of SANS experiments involving block copolymers is extensive [5-7]. Selective deuteration of some fraction of polymer molecules has been used to observe the conformation of the polymer chain in the melt. Selective deuteration of one block or even part of a block has been used to determine intramicellar structure and to enhance contrast between blocks in the melt. Variation of the deuterium content of the solvent has also been used to enhance some aspect of the structure. This can help determine which structural aspects are responsible for different features observed in the scattering data. Fig. 2 286 Schematic diagrams of ordered phases of block copolymer melts. Clockwise from top left (a) micellar, (b) cylindrical, (c) lamellar and (d) bi-continuous phases. (Adapted from Ref. 3 and used with permission.) PHYSICS IN CANADA The rest of this article will focus on the work of several Canadian groups, particularly investigations of micellar structure, novel nanostructures, and microscopic order in conducting polymers. COPOLYMERS IN SOLUTION The dilute regime of a polymer solution is defined as concentrations below which chains of adjacent polymers begin to September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 287 ARTICLE DE FOND ( REVEALING THE MICROSTRUCTURE ... ) overlap. Scattering studies below the overlap concentration yield information about the radius of gyration, the molecular weight and the packing of the chains. In copolymers, there is a second concentration that is important at low concentrations: the critical micelle concentration. While the polymer will always fully disperse at low enough concentration due to the entropy of mixing, the entropy of the system can be maximized by self-assembly of the polymer into small aggregates or micelles at concentrations above a critical concentration. Scattering studies can yield information about the shape and size of these micelles. An example of the latter type of experiment which makes interesting use of selective deuteration can be seen in an investigation of the coronal structure of star-like block polymer micelles [8]. Adi Eisenberg’s group at McGill is particularly interested in the formation of micelles of ionomers, lightly charged polymers. In this particular series of experiments, they used the block ionomer micelles as a model system to investigate the behavior of polymer-coated colloidal particles. The block copolymer consisted of poly(styrene) (PS) and poly(acrylic acid) (PAA) and the micelles were formed in tetrahydrofuran (THF), a good solvent for PS, with the PAA forming the core and the PS the corona. In order to study the structure of the corona, the PS block was partially deuterated. The scattering length densities of PS, PAA and THF are similar; that of poly(d-styrene) (dPPdS) signficiantly different. By placing the deuterated segment at different distances from the core, the researchers were able to study the structure of different parts of the corona. To distinguish between possible structures, the researchers examined the qdependence of the scattering. For a disordered system, scattering is large at small q or large length scales, where fluctuations of all sizes exist. The scattering decreases at larger q, typically as q-α, where different structures are characterized by different exponents α. They observed exponents of 5/3 for dPS units far from the core and 1 for dPS units closer to the core. From this they determined that the chain forms a flexible “blob” far from the core, but closer to the core the chain stiffness increases consistent with an increase in the polymer density and a breakdown of the blob model, as predicted by Gast et al. [9]. NOVEL NANOSTRUCTURES Amphiphilic copolymers, which have a hydrophobic block and a hydrophilic block, can be used as surfactants in the design of new materials. Recently, Guojun Liu and coworkers in the Chemistry Department at Queen’s University reported the use of poly(acrylic acid)-poly(styrene) (PAA-PS) diblocks in the synthesis of polymer-coated cobalt nanocrystals for magnetic storage applications [10]. The particles were made by solution phase reduction of cobalt in the presence of the PAA-PS diblock. Because of strong binding that occurs between PAA and Co, the polymer chains remain stuck to the particles forming a core-shell structure. The presence of the polymer not only controls particle formation but also enables film formation; the particles can be solvent-cast to yield bulk films with magnetic properties. SANS was used to confirm the core-shell structure of these particles. Because the particles are metallic, they absorb light making particle characterization by light scattering unfeasi- ble. The weak interaction of neutrons with matter makes neutron scattering an ideal choice for studying such optically dense materials. Liu et al. [10] measured the intensity of scattered neutrons to determine the differential scattering cross section dΣ where dΩ I (q) ∝ dΣ (q) = K P (q) S (q) . dΩ (1) The factor K depends on the contrast and other sample parameters, P (q) is the particle form factor describing the size and shape of individual particles and S(q) is the structure factor describing the correlation between the particles. For a dilute sample, S(q) = 1. Liu et al. analyzed their data using the Guinier model where at small qRG # 1 the form factor can be written ⎛ 1 ⎞ P ( q ) ∼ exp ⎜ − q 2 RG2 ⎟ ⎝ 3 ⎠ (2) where is the radius of gyration of the particles. Using SANS, they confirmed a 12 nm polymer shell coating 11 nm Co nanoparticles. PROTON-CONDUCTING POLYMER FILMS Recently, we made use of contrast variation techniques to explore the structure of proton-conducting films cast from solutions of diblocks consisting of a fluorous block and a sulfonated polystyrene (S-PS) block [11]. Proton-conducting polymer membranes form the heart of the proton exchange membrane fuel cell where they provide both a proton-conducting path and mechanical strength. Studies have indicated a relationship between the nanostructure of these materials and their proton conductivity [12]. Block copolymers materials, where a range of architectures is achievable, allow for systematic investigation of this relationship. Because these samples absorb water, contrast variation can be achieved by varying the D2O content in the hydrated membranes. For example, in Fig. 3 we can see the strong effect of varying the D2O content of the absorbed water on data taken for one of these samples. There are two main features in the scattered intensity for these materials; one peak at around 0.01 Å-1 and a second peak at around 0.1 Å-1. As the relative amounts of H2O and D2O are varied, the magnitudes of these peaks increase or decrease and a third peak appears around 0.02 – 0.03 Å-1. The fact that the shape of the spectra changes as the contrast is varied tells us that the system is not a simple two-component system, but instead consists of at least three components. Consider scattering from a binary system consisting of a sphere in a matrix; shown in Fig. 4a. If the contrast is varied, by increasing the scattering from the matrix for example, the system still scatters like a sphere in a matrix but with a change in the overall amplitude, reduced if the contrast is decreased and augmented if the contrast is increased. If the system is more complicated, for example it consists of three components, the angular dependence of the scattered intensity can change. Figure 4b shows a core-shell particle; if the scattering amplitude of the matrix is matched to that of the shell, the LA PHYSIQUE AU CANADA septembre / octobre 2006 287 Sept06-FF.qxd 11/7/2006 2:06 PM Page 288 FEATURE ARTICLE ( REVEALING THE MICROSTRUCTURE ... ) of partially sulfonated diblocks consisting of a lamellar structure with 3 levels of scattering length density associated with fluorinated domains, hydrated sulfonated polystyrene domains and an interface layer of non-sulfonated polystyrene. Contrast variation techniques played an important role in confirming that our model was consistent with the data: the structure factor information was removed by dividing three of the scattering spectra by the fourth leaving data that depended on form factor only. A model function for core-shell disks was then successfully fit to the data used during these experiments were crucial to our successful modeling of the structure of these films. SUMMARY Fig. 3 Fig. 4 Scattering spectra from a series of fluorous-sulfonated poly(styrene) diblock films for four different solvent contrasts: H2O (squares), 50-50 (H2O-D2O) (diamonds), 30-70 (H2O-D2O) (circles) and D2O (triangles). As the D2O content of the solvent is varied, the shape of the scattering curves changes. (Reproduced from Ref. 11 with permission.) (a) When the contrast is varied in a two-component system, only the amplitude of the scattering changes. (b) When the contrast is varied in a three-component system, the angular dependence of the scattering intensity also changes as it appears that scattering is from an object of different structure. particle scatters like a smaller sphere while if it is matched to the scattering amplitude of the core, the particle scatters like a spherical shell. As these particles have different form factors, the shape of the spectra will change as the contrast is varied. We were able to study two series of samples, one consisting of S-PS blocks of different length but full sulfonation, and the other consisting of a constant S-PS block length but with varying levels of sulfonation. By varying the contrast between polymer film and solvent, we were able to study differences in the structure of the two series. We have developed a model that is consistent with all data within the series 288 PHYSICS IN CANADA The ability to vary the contrast between solvent and polymer or between different parts of the polymer molecule by selective deuteration or use of D2O makes SANS a powerful tool to investigate nanoscale structure in novel materials based on block copolymers. REFERENCES 1. For example, please see F.S. Bates and G.H. Fredrickson, “Block Copolymer Thermodynamics: Theory and Experiment”, Annu. Rev. Phys. Chem. 41, 525-557 (1990) and references therein. 2. A.-V. Ruzette and L. Leibler, “Block Copolymers in Tomorrow’s Plastics”, Nature Materials 4, 19-31 (2005). 3. C. Burger, S. Zhou and B. Chu, “Nanostructures of Polyelectrolyte-Surfactant Complexes and Their Applications” in Handbook of Polyelectrolytes and Their Applications, ed. by S.K. Tripathy, J. Kumar and H.S. Nalwa (American Scientific Publishers, Stevenson Ranch, California, 2002), vol. 3, pp. 125-141. 4. For example, please see G.H. Fredrickson and F.S. Bates, “Dynamics of Block Copolymers: Theory and Experiment”, Annu. Rev. Mater. Sci. 26, 501-50 (1996) and references therein. 5. R.W. Richards, “Small Angle Neutron Scattering from Block Copolymers”, Adv. in Polym. Sci. 71, 1-39 (1985). 6. I.W. Hamley, The Physics of Block Copolymers, Oxford University Press, Oxford (1998). 7. K. Mortensen, “Block Copolymers Studied with Small Angle Neutron Scattering”, in Scattering in Polymeric and Colloidal Systems, ed. W. Brown and K. Mortensen (Gordon and Breach Science Publishers, 2000). 8. M. Moffitt, Y. Yu, D. Nguyen, V. Graziano, D.K. Schneider and A. Eisenberg, “Coronal Structure of Star-Like Block Ionomer Micelles: An investigation by Small-Angle Neutron Scattering”, Macromolecules 31, 2190-2197 (1998). 9. K.A. Cogan, A.P. Gast and M. Capel, “Stetching and Scaling in Polymeric Micelles”, Macromolecules 24, 65126520 (1991). 10. G. Liu, X. Yan, Z. Lu, S.A. Curda and J. Lal, “One-Pot Synthesis of Block Copolymer Coated Cobalt Nanocrystals”, Chem. Mater. 17, 4985-4991 (2005). 11. L. Rubatat, Z. Shi, O. Diat, S. Holdcroft and B.J. Frisken, “Structual Study of Proton-Conducting Fluorous Block Copolymer Membranes”, Macromolecules 39, 720-730 (2006). 12. Y. Yang and S. Holdcroft, “Synthetic Strategies for Controlling the Morphology of Proton Conducting Polymer Membranes”, Fuel Cells 5, 171-186 (2005). September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 289 ARTICLE DE FOND ( USE OF NEUTRON DIFFRACTION ... ) USE OF NEUTRON DIFFRACTION FOR DEVELOPMENT OF METAL HYDRIDES: CASE OF BCC ALLOYS by J. Huot, L. Cranswick, I. Swainson W ith the growing concern about global warming, a To reach commercialization, the material should be safe and replacement to fossil fuels has to be found. Despite many of low cost. Despite intensive research a metal hydride meettechnological and economical problems, hydrogen is seriousing all these characteristics are yet to be found. Nevertheless, ly considered as an energy vector, mainly because of its benmetal hydrides could offer a technological solution for onefits in terms of air pollution, energy security, and renewabilboard or stationary applications [6]. More research on the ity [1,2]. In the perspective of a hydrodevelopment of new metal hydrides gen economy, a safe, low-cost and high and the understanding of the fundacapacity hydrogen storage method After a brief introduction of mental aspects of metal-hydrogen systhat could operate at or near room temis still needed. In this task, neutron systems, tem perature will be needed. These fea- metal-hydrogen powder diffraction is an important tool tures are especially important in the we will review the basic in the development and understanding case of mobile systems such as the fuel of metal-hydrogen systems. In this cell or hydrogen internal combustion facts that make neutron dif- paper we will discuss neutron diffracengine cars. Hydrogen could be stored fraction a unique tool for tion as a tool for studying metal-hydroin pressure tanks or in a liquid form gen systems. The emphasis will be on but these two technologies suffer structural determination of crystal structure characterization with important drawbacks such as high metal hydrides. Two types the BCC system as an example. But pressure and low volumetric capacity first, some basic facts of metal hydrides in the case of pressure tanks, or cryo- of metal hydrides will be should be presented. genic temperatures (below 20 K) and discussed: magnesium and important liquefaction energy in the METAL HYDRIDES [3] case of liquid . The class of materials solid solution BodyA simplified view of metal-hydrogen known as metal hydride seems to be a interaction is shown in Figure 1. First, it better candidate for the storage tech- Centred Cubic (BCC). should be realized that it is the hydronology for mobile systems [4]. Metal gen atoms which will enter the metal hydrides (MH) are chemical comlattice and not the hydrogen molecule. Therefore, the hydropounds of one or many metals (M) with atomic hydrogen gen molecule should be dissociated at the metal surface, dis(H) [5]. The advantages of metal hydrides are that they have solve at interstitial sites of the host metal and form a solid high volumetric storage capacity (higher than liquid hydrosolution (α phase). When the local hydrogen exceeds a cergen) and they could provide extremely pure hydrogen, which tain limit (which depends on the metal host), a hydride phase is essential for fuel cells. For most practical applications the starts to precipitate (β phase). This is the metal hydride phase absorption where the metal and the hydrogen form a chemical bond. The and desorpheat of formation for elements and intermetallics considered tion of for practical applications varies from 28 to 75 kJmol-1. The hydrogen has interested reader could consult review articles on the thermoto be at, or dynamics of hydrogen with metal and intermetallic close to, alloys [7,8]. room temperature and THERMODYNAMICS at pressure of around one The thermodynamics of hydrogenation is easily described by bar. The pressure-composition isotherms (PCT curves) as shown in m e t a l Figure 2. The reaction of a metal with hydrogen can be repreh y d r i d e sented as should also have fast sorption J. Huot1 <[email protected]>, L. Cranswick2, kinetics and I. Swainson2; 1 Physics Department, Université du be resistant Québec à Trois-Rivières, Trois-Rivières, Québec, Canada Fig. 1 Schematic of hydrogen dissociation at to poisoning G9A 5H7; 2 National Research Council, Steacie Institute the interface and solution of atomic by trace for Molecular Sciences, Chalk River Laboratories, Chalk hydrogen in the bulk. (Adapted impurities. River, Ontario, Canada K0J 1J0 from [9]) LA PHYSIQUE AU CANADA septembre / octobre 2006 289 Sept06-FF.qxd 11/7/2006 2:06 PM Page 290 FEATURE ARTICLE ( USE OF NEUTRON DIFFRACTION ... ) between 2 and 3 Å3 per hydrogen atom [10]. This translates to an expansion that could reach 30 vol.% in some systems and is often anisotropic. A hydrogen sublattice is formed and the crystal structure may change, typically with a reduction of symmetry. Nevertheless, the metal atom substructure does not change appreciably. At low temperature, the hydrogen sublattice may become ordered. During hydrogenation, the α and β phases coexists but because these two phases have quite different lattice volumes, a large number of lattice defects will be created. In ductile metals the crystal will be deformed while brittle metals (or intermetallic compounds) will disintegrate into small grain size powder. Defects will also cause a broadening of X-ray and neutron diffraction patterns. Fig. 2. Schematic of a pressure-composition isotherm. α is the solid solution of hydrogen and β is the hydride phase. The right-hand side plot is a van’t Hoff plot giving the enthalpy of hydride formation ΔH. (Adapted from [7]) x M + H 2 ⇔ MH x 2 (1) Region I of Figure 2 is for low hydrogen concentration. At low concentration (x « 1) hydrogen dissolves in the metal lattice and forms a solid solution phase (α phase). The crystal structure of the α phase is the same as the metal. On hydrogenation, hydrogen atoms will occupy specific interstitial sites. The interstitial sites in three major crystal structures of hydrides are shown in Figure 3. Only octahedral (O) and tetrahedral (T) sites are shown because they are the only ones occupied by hydrogen atoms. Some distinction should be made on the different structures. In the FCC lattice, the T and O sites are respectively enclosed in regular tetrahedral and octahedral formed by metal atoms. At low or medium H concentration, the preferred interstitial sites are octahedral. In the HCP (Hexagonal Close Packed) lattice, the tetrahedral or octahedral sites become distorted as the ratio of lattice parameters c/a deviates from the ideal value of 1.633. Tetrahedral sites are favoured at low H concentration in HCP metals. In Hydrogen concentration increases with hydrogen pressure until the equilibrium pressure of the hydride phase (β) is reached. The system has now three phases (α, β and hydrogen gas) and two components (metal and hydrogen). The Gibbs phase rule gives the number of degrees of freedom (f) as: f=C-P+2 (2) where C is the number of components and P is the number of phases. Therefore, at a given temperature, the hydrogen pressure is constant in the two-phase region (region II of Figure 2). The equilibrium pressure Peq at the α6β phase transition is then given by the van’t Hoff law. 1nPeq = − ΔH ΔS + RT R (3) where ΔH and ΔS are respectively the enthalpy and entropy of the α6β transition. Experimentally, the transition enthalpy and entropy are obtained by the van’t Hoff plot of plateau pressure against reciprocal temperature (Figure 2, right hand side). Once pure β phase is reached, hydrogen enters in solid solution in the β phase and the hydrogen pressure again rises with concentration (region III of Figure 2). CRYSTAL STRUCTURE With the formation of the β phase, the lattice expands and for most binary metal compounds the volume expansion is 290 PHYSICS IN CANADA Fig. 3 September / October 2006 Interstitial sites of hydrogen occupation (octahedral and tetrahedral) in fcc, hcp and bcc lattices. Sept06-FF.qxd 11/7/2006 2:06 PM Page 291 ARTICLE DE FOND ( USE OF NEUTRON DIFFRACTION ... ) FCC and HCP lattice, for each metal atom, there is one octahedral site and two tetragonal sites available for hydrogen. In BCC lattice, the polyhedron is greatly distorted. For the O sites, two metal atoms are much closer to the interstitial site than the other four metal atoms. Therefore, the O sites are subdivided in Ox, Oy, Oz sites according to the direction of the four-fold symmetry axis. In the same way, the T sites of BCC lattice are divided according to their symmetry axis and are noted Tx, Ty, Tz. The hydrogen atom has three octahedral and six tetrahedral sites available per metal atom. Hydrogen will preferably occupy the tetrahedral sites in BCC metals. USE OF NEUTRONS Neutron scattering is a unique probe for the study of structure and dynamics of condensed matter. Thermal neutrons (neutrons in thermal equilibrium with a moderator material near room temperature) have a wavelength comparable in magnitude with the interatomic distance of matter. Thus, material structure could be studied by neutron scattering. For structure determination, one advantage of neutrons over X-ray scattering is that neutrons are uncharged and thus interact only weakly in solids. This means they have a better penetration than X-ray and the bulk of material could be probed instead of mainly surface properties in the case of X-ray. The neutron scattering length depends on the nature of the nucleus and thus varies greatly from one element to another, contrary to X-ray scattering which is proportional to the number of electrons. The relative neutron and X-ray scattering for a few elements is presented in Figure 4. It can be seen that hydrogen and deuterium have a very large neutron cross section compared to other elements but they are essentially undetectable by X-ray. For hydrogen storage materials this is a very important feature: hydrogen could be located by neutron powder diffraction but not by X-ray powder diffraction. The fact that the cross section depends on the nature of the nucleus means that the scattered wave will vary between different isotopes. The scattering also depends on the interaction between the two spin states of the neutron-nucleus sys- Fig. 4 Scattering of X-ray and neutrons for some atoms. For X-ray the radii of circles are proportional to the atomic number, for neutron the radii are proportional to the scattering length. Negatives neutron scattering length are indicated by dark circles. (Adapted from [11]) tem. Here, we should make the distinction between coherent and incoherent scattering. As explained in Squires [12], the coherent scattering depends on the correlation between the positions of the same nucleus at different times, and on the correlation between the positions of different nuclei at different times. It gives interference effects and causes Bragg peaks. In the case of incoherent scattering, it depends only on the correlations of the same nucleus at different times; it does not give interference effects. Bragg scattering is determined by the coherent cross section. Therefore, for structural studies (neutron diffraction) the coherent part of the cross section is the significant parameter. In the case of hydrogen, the incoherent cross section is very large (80 barn) compare to the coherent one (1.76 barn). Consequently, the neutron powder diffraction of compounds with high proportion of hydrogen will show an extremely high background with only small Bragg peaks thus making analysis virtually impossible. Fortunately, for deuterium the coherent cross section is bigger than the incoherent part (respectively 5.59 and 2.05 barn). Thus, for structural characterization by neutron powder diffraction it is common practice to use deuterium instead of hydrogen. In most cases, it is difficult to obtain a good quality single crystal of metal hydride, therefore most of the structural measurements are performed by neutron powder diffraction. Sample containers are usually made of quartz or vanadium (sometimes steel is also used) and the pressure and temperature of the container can be controlled for in-situ experiments. Almost 60 years ago the first neutron diffraction measurement of metal hydride was performed on sodium hydride by Shull et al [13]. It is interesting to note that the maximum intensity on their NaD patter was 25 counts/min! On modern neutron diffractometers the intensity is many orders on magnitude higher, making measurements much faster and accurate and allowing in-situ experiments during hydrogenation/dehydrogenation. MAGNESIUM HYDRIDE Because of their high hydrogen storage capacity magnesium and magnesium based alloys could be attractive for energy storage material. However, due to the hydride stability and slow sorption kinetics, the actual applications are limited. Important efforts are directed in improving the hydrogen sorption properties by addition of catalysts, synthesis of new alloys, new composites, and new ways of synthesis. A powerful way of improving the hydrogen sorption properties is by energetic ball milling of hydrides [14]. In ball milling elemental powder is mixed with hardened stainless steel balls and loaded in a crucible. Spinning or shaking the crucible generates ball-powder-ball and ball-powder-wall collisions. These repeated high-energy impacts induce fracturing and cold welding of particles and define the ultimate structure of the powder [15]. As an example we present here the case of magnesium. Pure magnesium hydride (MgH2) was ball milled for 20 hours in a Spex Shaker mill. In Figure 5, X-ray and neutron powder diffraction patterns of ball milled magnesium hydride are shown. Neutron diffraction pattern was taken on the high-resolution neutron powder diffractometer C2 DUALSPEC at Chalk River. The neutron wavelength was LA PHYSIQUE AU CANADA septembre / octobre 2006 291 Sept06-FF.qxd 11/7/2006 2:06 PM Page 292 FEATURE ARTICLE ( USE OF NEUTRON DIFFRACTION ... ) Such formation of a metastable phase synthesized at room temperature by ball milling has also been seen in many other systems [20]. Fig. 5 X-ray and neutron powder diffraction of MgH2 ball milled 20 hours. 1.3287 Å and the sample holder was a cylindrical can made of vanadium. For the reasons cited above, this pattern was taken on a deuterated sample (MgD2). The X-ray pattern was taken on a commercial diffractometer (Siemens D5000) with a Cu Kα radiation (wavelength Kα1 = 1.5418 Å). Crystallographic parameters such as phase abundance, lattice parameters, refinement of atomic positions and occupancies, crystallite size and strain could be determined by Rietveld refinement. In the Rietveld method the leastsquares refinement is carried out until the best fit is obtained between the whole observed diffraction pattern and the assumed crystal structure [21]. This is an extremely powerful technique and is now extensively used for analysis of X-ray and neutron powder diffraction patterns. For example, Rietveld refinement of the powder diffraction patterns showed in Figure 5 indicated that the crystallite size of β-MgH2 and γ-MgH2 phases are respectively 11.9±0.1 nm and 17.1±0.7 nm. From neutron pattern, comparison of the Mg-D bond lengths indicated that in the β phase, the bond lengths are symmetrically stretched and compressed while in the γ phase, only one bond is stretched. It was proposed that, upon ball milling the phase transformation from β to γ is most likely associated with a micro-stress relaxation process [22]. This type of study could only be conducted with neutron diffraction. The effect of nanocrystallinity on the kinetics of hydrogen sorption is shown in Figure 6. Both absorption and desorption are much faster in the case of ball milled (nanocrystalline) magnesium hydride than for the unmilled sample. In desorption, the unmilled sample has an incubation time of almost 800 seconds while for the nanocrystalline material the desorption starts immediately with a high rate. The enhancement of hydrogen storage properties with nanocrystallinity has been observed for a wide variety of elements and intermetallics as well as for nanocomposites [23]. The differences between the X-ray and neutron diffraction patterns are obvious: the Bragg reflections are shifted because of the different wavelength of the two radiations but also the relative intensities are altered because deuterium atoms scatter neutrons much more than X-rays. Another striking feature of these patterns is the broadness b of the peaks; this indicates a the nanocrystallinity of the material. From the peaks’ full width at half maximum the crystallite size and strain could be determined. Usually, magnesium hydride has the stoichiometric tetragonal β-MgH2 phase [16,17]. In the case of ball milled magnesium hydride, another phase of magnesium hydride is produced, the orthorhombic (γ-MgH2) phase [18], as can be seen on the diffraction patterns of Figure 5. This orthorhombic (γMgH2) phase was first synthesized under highpressure and high tem- Fig. 6 Hydrogen sorption curves of unmilled MgH2 (filled marks) and ball milled (hollow marks) MgH2. (a) absorption at 573K under 1.0 MPa of hydrogen pressure. (b) desorption perature treatments (2.5-8 [19] at 623 K under a hydrogen pressure of 0.015MPa. Gpa and 250-900°C) . 292 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 293 ARTICLE DE FOND ( USE OF NEUTRON DIFFRACTION ... ) further heat treatment was performed on the Solid solution BCC alloys (mainly Ti-V-Cr buttons. The size of the and Ti-V-Cr based) are promising hydrogen button was 15 g. storage materials because of their relatively Neutron diffraction of high storage capacity and their ability to the arc melted alloy was absorb and desorb hydrogen in ambient performed on the highconditions [24]. This type of hydride is also resolution neutron powconsidered by Toyota Motor Corporation in der diffractometer C2 hybrid high-pressure/metal hydride storDUALSPEC at Chalk age tanks for vehicular applications [25]. An River (wavelength important characteristic of this type of 1.3287 Å). The button alloys is that usually two different strucwas wrapped in a thin tures are formed during hydrogenation platinum foil which process. First, for most BCC solid solution acted as an internal referalloys when the ratio of hydrogen atoms ence for lattice parameover the number of metal atoms in the structers calculation. The ture (H/M) is around 1 the hydride strucRietveld analysis of the ture is formed by a BCC metal sublattice, pattern was carried out which is sometimes deformed. When the using the softwares [30] H/M ratio is around 2 the hydride has the Fig. 7. Neutron diffraction pattern and Rietveld and refinement of TiV0.9Mn1.1. The short vertical EXPGUI [31]. Refinement of CaF2 structure where metal atoms form an GSAS bars indicate the position of Bragg peaks: the FCC sublattice and the hydrogen atoms upper row is for titanium, second row is plat- the neutron pattern of an occupy tetrahedral (T) sites surrounded by inum, third row is C14 phase, and fourth row alloy with TiV0.9Mn1.1 four metal atoms. From X-ray and neutron composition is difficult is the BCC phase. The bottom curve is the diffraction Nakamura et al [26,27] found that difference between experimental and calcubecause, as shown in for Ti1.0V1.1Mn0.9 solid solution BCC alloy lated pattern. Figure 4, the scattering the mono-hydride Ti1.0V1.1Mn0.9D2.0 has a cross section of Ti and pseudo-cubic NaCl structure where the hydrogen atoms Mn are almost the same, making them hard to distinguish occupy octahedral (O) sites surrounded by six metal atoms. with neutron radiation. Moreover, vanadium is difficult to In an investigation of Ti1.0V1.1Mn0.9Hx and Ti1.0V1.1Mn0.9Dx, locate because of its small cross section. Despite these disadCho et al [28] found a large difference between the equilibrium vantages, a good quality neutron diffraction pattern could pressures of the hydride and deuteride PCT isotherms. give precise information about the crystal structure. In However, the crystal structures, lattice parameters, and Figure 7 we present the Rietveld analysis of the neutron difphase abundance of the isotope hydrides depends only on fraction pattern of arc melted TiV0.9Mn1.1. The residue curve the hydrogen content and not on the type of isotope. is small, indicating a good fit of the pattern. SOLID SOLUTION BCC In almost all cases, the highest hydrogen storage capacity is In Rietveld method various values are used to indicate the reached when the alloy is single phase BCC solid solution. goodness of the fit. One of the most meaningful is the ‘RHowever, in one of the first paper on this subject, Iba and weighted pattern’ Rwp which measures the weighted differAkiba [29] identified a lamellar structure of 10 nm scale conence between the calculated and measured intensities. In the sisting of two BCC phases with a composition TiMn0.9V1.1. present case Rwp=5.67%, confirming the quality of the fit. In They postulated that the high capacity is considered to be Table 1 the identified phases (beside platinum) are displayed caused by interactions of these nano-composite phases long with their respective phase abundance and lattice through a coherent interface. In metal hydride materials, parameters. A small amount of pure titanium was identified. studies of the effect of phase coherency in multiphase alloys The phase identified as C14 is a member of the so-called has been limited. Therefore, we decided to investigate the ‘Laves phases’ structures. effect of coherency in multiphase BCC solid solution. For this, we selected an alloy close to the stoichiometry found by Iba TABLE 1 and Akiba [29]. In their case they CRYSTAL STRUCTURES OF TIV0.9MN1.1 AS DETERMINED FROM RIETVELD REFINEMENT. found that the alloy TiMn0.9V1.1 T HE VALUES IN PARENTHESES ARE THREE STANDARD DEVIATIONS AND REFER TO THE LAST DIGIT has the best storage capacity. For this study we selected the multiphase alloy TiMn1.1V0.9. Buttons Phase Space Group Abundance Lattice parameters of TiMn1.1V0.9 alloys were pre(%) (D) pared by arc melting chunks of C14 P 6 /mmc 32 (4) a =4.906(3) 3 pure metals (Ti sponge, c = 8.011(9) Mn chunk, V chunks) in an BCC I m -3 m 65 (1) a =3.018(1) argon atmosphere. The buttons were turned over 4 times and remelted in order to achieve Titanium P 63/mmc 3 (1) a =2.971(5) homogeneity of the alloy. No c = 4.63(1) LA PHYSIQUE AU CANADA septembre / octobre 2006 293 Sept06-FF.qxd 11/7/2006 2:06 PM Page 294 FEATURE ARTICLE ( USE OF NEUTRON DIFFRACTION ... ) TABLE 2 5. H. Kohlmann, in Encyclopedia of Physical Science and Technology, CRYSTALLOGRAPHIC PARAMETERS OF THE C14 PHASE IN TIV0.9MN1.1 AS DETERMINED edited by Robert A. Meyers FROM RIETVELD REFINEMENT OF NEUTRON DIFFRACTION PATTERN (Academic Press, San Diego, 2002), Vol. 9, pp. 441. 6. D. Chandra, J.J. Reilly, and Site Refined Atoms Occupancy R. Chellappa, JOM 56, 26 (2006). (Wickoff symbol) Coordinates 7. L. Schlapbach, I. Anderson, and J.P. Burger, in Electronic and 2a -Mn 0.65 Magnetic Properties of Metals and V 0.35 Ceramics Part II, edited by 4f z = 0.065 Ti 1.0 K.H. Jürgen Buschow (VCH, Weinheim, 1994), Vol. 3B, pp. 271. 6h x = 0.82356 Mn 0.58 8. M. Yamaguchi and E. Akiba, in V 0.42 Electronic and Magnetic Properties of Metals and Ceramics Laves phases are intermetallic compounds of AB2 in which, Part II, edited by K.H. Jürgen Buschow (VCH, Weinheim, in the case of metal hydrides, a strong hydride former occu1994), Vol. 3B, pp. 333. pies the A site and a weaker hydride former is on the B site. 9. L. Schlapbach, in Hydrogen in Intermetallic Compounds I, edited by L. Schlapbach (Springer-Verlag, Berlin, 1988), pp.1. There are three types of laves phases crystal structures; (i) 10. D.G. Westlake, Journal of the Less-Common Metals 90, 251 hexagonal C14 (MgZn2 type)+, (ii) cubic C15 (MgCu2 type), (1983). and (iii) hexagonal C36 (MgNi2 type). The difference 11. D.A. Neumann, Materials Today 9, 34 (2006). between these structures is explained by different stacking of 12. G.L. Squires, Introduction to the theory of thermal neutron scathexagonal atomic layers [32]. The appearance of this C14 tering. (Dover, Mineola, New York, 1996). Laves phase is expected because, as pointed out by Akiba 13. C.G. Shull, E.O. Wollan, G.A. Morton et al., Physical Review 73, [24] and Iba , these new BCC alloys have a nominal AB2 com842 (1948). position and are closely related to Laves phases. 14. J. Huot, G. Liang, and R. Schulz, Applied Physics A72, 187 (2001). In our Rietveld analysis the atomic occupancy and position in 15. C.C. Koch, in Processing of Metals and Alloys, edited by the C14 phase were refined. Atomic positions are noted by R.W. Cahn (VCH, Weinheim, Germany, 1991), Vol. 15, using the Wyckoff notation. The Wyckoff symbol describe pp. 193. 16. A.S. Pedersen, in Hydrogen Metal Systems I, edited by the special positions of the space group, beginning with a for F.A. Lewis and A. Aladjem (Scitec Publications, Zurich, the highest symmetry. For the C14 structure, position 2a is 1996), pp. 35. (0,0,0), 4f is (1/3,2/3,z), and 6h is (x,2x,1/4). In Table 2 the 17. A.A. Nayeb-Hashemi and J.B. Clark, in Monographs Series on refined parameters for the C14 phase are shown. Alloy Phase Diagrams (ASM International, Metals Park, Ohio, 1988), pp. 370. Titanium atoms are localized exclusively on the 4f site while 18. J. Huot, G. Liang, S. Boily et al., Journal of Alloys and the manganese and vanadium atoms are distributed on the 2a Compounds 293-295, 495 (1999). and 6h sites but with a different abundance. These abun19. J.-P. Bastide, B. Bonnetot, J.-M. Letoffe et al., Materials Research dances give a stoichiometry of TiV0.8Mn1.2 for the C14 phase. Bulletin 15, 1215 (1980). This is an example of the use of neutron diffraction as a tech20. Y. Chen, J.S. Williams, and G.M. Wang, Journal of Applied nique for structure determination and characterization. A Physics 78, 3956 (1996). 21. R.A. Young, in IUCr Monographs on Crystallography-5, edited complete description of the hydrogen sorption properties by R.A. Young (Oxford University Press, Oxford, 1993), and the effect of ball milling on the BCC solid solution alloys pp. 298. will be given in a forthcoming paper. 22. J. Huot, I. Swainson, and R. Schulz, Ann. Chim. Sci. Mat. 31, 135 (2006). In conclusion, neutron diffraction is a unique and powerful 23. J. Huot, in Nanoclusters and Nanocrystals, edited by tool for the structure characterization and the localisation of H.S. Nalwa (American Scientific Publishers, Stevenson hydrogen (deuterium) atoms. In the past it played a crucial Ranch, California, 2003), pp. 53. role in the understanding of metal hydrides and will remain 24. E. Akiba and H. Iba, Intermetallics 6, 461 (1998). a privileged tool for the development of new metal hydrides 25. D. Mori, N. Haraikawa, N. Kobayashi et al., Mater. Res. Soc. for practical applications. Symp. Proc. 884E, GG6.4.1 (2005). 26. Y. Nakamura and E. Akiba, Journal of Alloys and Compounds ACKNOWLEDGEMENT 345, 175 (2002). 27. Y. Nakamura, K.-I. Oikawa, T. Mamiyama et al., Journal of The authors wish to thank Prof. Louis Marchildon for useful Alloys and Compounds 316, 284 (2001). comments and Mr. Sylvain Pednault for drawing figures. 28. S.-W. Cho, H. Enoki, T. Kabutomori et al., Journal of Alloys and Compounds 319, 196 (2001). REFERENCES 29. H. Iba and E. Akiba, Journal of Alloys and Compounds 253-254, 21 (1997). 1. G.D. Berry and S.M. Aceves, Journal of Energy Resources 30. B.H. Toby, Journal of Applied Crystallography 34, 210 (2001). Technology 127, 89 (2005). 31. A.C. Larson and R.B. Von Dreele, Report No. LAUR 86-748, 2. M.L. Wald, Scientific American 290, 66 (2004). 1994. 3. R. Harris, D. Book, P. Anderson et al., The Fuel Cell Review 1, 32. F. Stein, M. Palm, and G. Sauthoff, Intermetallics 12, 713 17 (2004). (2004). 4. S. Ashley, Scientific American 292, 62 (2005). 294 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 295 ARTICLE DE FOND ( NEUTRONS AND MUONS ... ) NEUTRONS AND MUONS AS COMPLEMENTARY PROBES OF EXOTIC MAGNETISM AND SUPERCONDUCTIVITY by C.R. Wiebe M their respective strengths and weaknesses, and close by givany of the “big questions” in science have needed “big ing examples of recent problems in the field that can be illutools” to answer, such as the Hubble Space Telescope and minated by using both kinds of probes [3,4]. particle accelerators such as CERN. In the field of condensed matter physics, some of the “big questions” of the field are NEUTRON SCATTERING now being addressed with the creation of scientific centers such as the National High Magnetic Field Laboratory in Neutron scattering is a technique whereby neutrons, created Florida, the Canadian Light Source, by a source such as a nuclear reactor or and neutron sources such as NIST in accelerator (such as a spallation source), Gaithersburg, Maryland. New neu- In this paper, I will outline are directed at a material of interest, tron sources at Oak Ridge (the and the scattered neutrons are analyzed how neutron scattering can Spallation Neutron Source), and the to learn about how the constituent proposed facility at Chalk River will be used with muon spin atoms are located in space (chemical open new vistas of research in the near structure), how they are moving with future. However, there are some prob- relaxation (mSR) to gain a respect to one another (dynamics), and lems that neutron science is not well more complete picture of how magnetic spins order and interact suited to answer, and other probes of with one another (magnetic neutron exotic magnetism and solids are needed. In this paper, I will scattering). The simplest example of a outline how neutron scattering can be superconductivity in solids. neutron scattering experiment is a difused with muon spin relaxation (μSR) fraction experiment, where neutrons of to gain a more complete picture of a particular energy are scattered from a exotic magnetism and superconductivity in solids. I will dissolid of interest, and the pattern of intensity as a function of cuss examples of problems in the field that have been scattering angle is used to learn about how the atoms are addressed using these two complementary techniques. arranged within the material. Bragg’s law, 2d sinθ = λ, determines where the intensity of the neutron signal will peak due INTRODUCTION to constructive interference of neutrons that reflect from regularly spaced atomic layers. This is called an elastic scattering The great neutron scientist Bertram Brockhouse (Nobel experiment since the incoming neutron and the outgoing neuLaureate, 1994) once remarked that if Chadwick hadn’t distron have the same energy, and thus no energy has been lost covered the neutron, then it would have to be invented [1]. in the solid. Neutron scattering is an incredibly powerful technique for investigating different states of matter, and since If a crystal known as an analyzer is used before the neutron Brockhouse’s invention of the triple axis spectrometer, the detector (but after the neutrons have been scattered from the field has experienced a considerable amount of growth. sample), the energy of the outgoing neutron beam can be Neutron scientists around the world are now using neutrons measured, and an inelastic experiment can be conducted. to investigate diverse problems from protein crystallography, Energy can be transferred to the solid in a variety of different to dynamics in membranes, to spin glass behavior, engineerways, but in solid state physics, inelastic neutron scattering is ing applications, and of course, a wide variety of correlated [2] usually used to measure lattice vibrations (phonons) or magelectron systems . netic excitations (such as spin waves). An excitation, be it a phonon or spin wave, can be created or destroyed by an However, even though there are many problems that neutron incoming neutron, giving rise to a shift in energy of the outscattering can address, there are some fundamental systems going neutron beam. The wavevector of the momentum that have been difficult to characterize with neutrons due to transfer to the solid, Q, can be measured in addition to the limitations of the technique. It is rare when a single type of energy, and information about dispersion relations of the experiment can answer complex problems such as the nature vibrations can be obtained. of high temperature superconductivity in a system of ~ 1023 electrons. An entire arsenal of techniques have, in fact, been Most physical scientists have been exposed to x-ray diffracused to investigate solids for several decades, and the growtion at some point in their training, and one may ask the quesing consensus is that only a combination of probes can be used to make progress. In this paper, I will discuss how neutron scattering can be used with muon spin relaxation (μ SR) C.R. Wiebe <[email protected]>, Florida State to get a better picture of electronic behavior within solids. University/NHMFL, Tallahassee, FL, USA 32310-4005 I will give a brief introduction to both techniques, discussing LA PHYSIQUE AU CANADA septembre / octobre 2006 295 Sept06-FF.qxd 11/7/2006 2:06 PM Page 296 FEATURE ARTICLE ( NEUTRONS AND MUONS ... ) tion - why use neutron scattering instead of x-ray scattering? Neutron sources are far more expensive than conventional table-top x-ray sources in general – why do we bother with this technique? There are a number of distinct advantages that neutron scattering has over x-rays: (1) Neutrons are charge neutral. The consequence of this is that neutrons do not interact strongly with the charged electrons within solids, and they can penetrate to great depths (on the order of centimeters). The average x-ray from a conventional source only penetrates on the order of microns due to the charged nature of electromagnetic radiation. (2) Neutrons interact primarily through the strong force that is with the nuclei, compared to x-rays, which interact via the electromagnetic force with charges. Neutrons can see deep within the constituent atoms, and they are not affected much by electronic clouds. (3) Neutrons from a reactor have an average energy which is on the order of milli electron volts (meV), as compared to x-rays which have energies on the order of kilo electron volts (1 keV = 106 meV). The meV range is where many phenomena occur in solids, such as lattice vibrations, as compared to keV, which is a much higher energy scale. This makes inelastic scattering more convenient for neutron scatterers compared to x-ray scientists. (4) Neutrons have magnetic moments – they have spin. Due to the fact that neutrons have a quark structure, even though they have neutral charge they have a spin s = ½. Each neutron in an experiment can interact with the spins of a solid, which are usually from the constituent unpaired electrons. Therefore, neutrons can also give information about the magnetic structure of a solid (such as a ferromagnet, which has a permanent magnetic moment below a temperature TC), or about the magnetic excitations (such as magnons or spin waves). MUON SPIN RELAXATION (μSR) Given the many applications of neutron scattering, one may ask what sort of complementary information can be gained from the muon spin relaxation technique. To answer this question, one needs an introduction to μSR [4]. μSR stands for muon spin relaxation, muon spin rotation, or muon spin research – the name was chosen to draw an analogy to nuclear magnetic resonance, or NMR. NMR is most often used to look at what are called hyperfine interactions between the nuclei and the electrons in condensed matter systems, and thereby gain information about electron-electron interactions within the solid. μSR is a similar technique – that is, a μSR spectroscopist investigates how muons interact with electrons in a solid. However, the muons have to be implanted within a material, whereas with NMR, the nuclei already exist to be probed (or a material can be doped with a certain nuclei of interest). By monitoring the polarization of the muon spin as a function to time, the local magnetic field at each muon site can be obtained, and from this we can gain complementary information to neutron scattering measurements. (with a half life of 26 ns) that decay into the longer lived muons (with a half life of 2.2 μs). The decay of these pions is governed by the weak interaction, which insures that the resulting muons are 100% spin polarized. Since muons are charged (either negative or positive), we can use electric and magnetic fields to create muon beams which are then directed at our material of interest (see figure 1). The high energy of the muons is such that these beams can penetrate deep within solids, and through cryostats, magnets, and pressure cells which enable measurements at low temperatures, in reasonably high magnetic fields (up to about 7 T) and under pressure. Once the muons have penetrated within a material of interest, they are rapidly thermalized and reside within an electrostatically favorable place within the crystalline lattice (at a negatively charged site, for example, for positively charged muons). The actual experimental process of μSR involves injecting muons, one at a time, into a solid of interest, and measuring the time it takes to decay (see figure 2). The muon will decay into two neutrinos and a positron with a half-life of about 2.2 μs. Since this is, again, governed by the weak interaction, the resulting positron is preferentially emitted in the same direction of the muon spin at the time of the decay. This enables one to determine the evolution of the muon spin as a function of time by surrounding the target with a series of positron detectors, and measuring a large number of muon decays. The asymmetry, which is a subtraction of either forward – backward, or right - left detector counts, gives a measure of the polarization of the muon spin. Since the initial polarization of the muon beam is known (the beam is 100% spin polarized), one can accurately determine the local magnetic field at each muon stopping site within a material. In a given material, the muon spin precession signal will change above and below a magnetic transition due to the development of an internal magnetic field. In the paramagnetic phase, where the spins are rapidly fluctuating, the muon essentially sees a net field of zero, since the magnetic Fig. 1 Muons are usually created through high energy collisions of protons upon a target, which produces short-lived pions 296 PHYSICS IN CANADA September / October 2006 A typical schematic of an accelerator-based muon spin relaxation experiment. Muons are typically produced in a cyclotron, where protons are accelerated to high speeds and undergo collisions with a target. The decay products at the target include pions, which rapidly decay to muons and neutrinos. A crossed electric and magnetic field separates out unwanted decay products, and after the muon beam is collimated it is ready for use. Sept06-FF.qxd 11/7/2006 2:06 PM Page 297 ARTICLE DE FOND ( NEUTRONS AND MUONS ... ) spins cancel each other out on the average. However, within the ordered state, the muon spin precesses. This is similar to Larmor precession in NMR – the muon, possessing a spin, will precess with a frequency proportional to the internal magnetic field generat- Fig. 2 A closer look at muon spin relaxation. ed from the The muons are implanted at the left with a spin polarization in the direco r d e r e d tion of the beam. After implantation, moments. A the muons will feel a local spin envimeasurement ronment and the orientation will of this frechange. After decay, the positrons are quency will preferentially emitted in the direction determine of the muon spin, and are measured in the size of a series of detectors, which mark an this field. event on the electronic clock. The The amplidirection of the magnetic field in the tude of the experiment is perpendicular to the muon spin, indicating a transverse signal confield configuration (picture courtesy tains inforof A. Savici). mation about what volume fraction is ordered. So, for example, if only 20% of the sample is ordered and the rest is a paramagnetic, or fluctuating phase, will we only see a signal which is 20% of the maximum signal (sometimes called the asymmetry). This provides complementary information with neutron diffraction, which tends to measure only the average ordered moment within a material. Muons, being a local probe, give a measurement of the moment size (through the frequency of the precession), and the volume fraction. of experiment that can be done – a longitudinal field (or “LF”) experiment (where the field is applied along the same axis as the initial muon polarization), or a transverse field experiment (where the field is applied perpendicular to the initial muon spin polarization direction). Longitudinal field measurements are used to probe spin dynamics, since one is providing a bias direction for the magnetic spins within a solid with an applied field. However, the fluctuation rates that can be probed with μSR are much different than neutron scattering – on the order of 104 to 1012 Hz. This is a time scale which bridges what NMR and neutron scattering can measure (slow dynamics and fast dynamics, respectively), and is useful as a consistency check for these experiments. μSR has also seen a great deal of success in elucidating the spin dynamics of spin glasses, which tend to have time scales slower than what neutron scattering can resolve. Transverse field μSR measures a Knight shift, which is akin to the magnetic susceptibility. TFμSR is also used to measure the penetration depth within superconductors, which is probably the most successful application of this technique in condensed matter physics. The classification of superconductors based upon various symmetries of the pairing of the electrons (into s-wave, or d-wave states, for example) has been done through careful μSR measurements in a series of landmark experiments [4]. COMPARISON OF THE TECHNIQUES What are the advantages of μSR over neutron scattering? The table below summarizes and compares these two techniques. (1) Reciprocal space vs. real space probes. Neutron scattering is a reciprocal space probe; that is, it measures not the real space distribution of spins and atoms, but the Fourier transform of this. Any neutron data, to be interpreted properly, needs to be Fourier transformed to real space from the abstract world of “reciprocal space” to gain information that we can readily use. Muons, on the other hand, are real space probes. The muon signal that is obtained is actually measuring the local magnetic field at each muon site. The disadvantage to this is that the muons have resting sites that have to be elucidated to make sense of the resulting signal in many cases. Although the muons land randomly within the bulk of There are three different kinds of μSR experiments, which are classified according to the magnitude and direction of the applied magnetic field. If there is no magnetic field, the experiment is aptly named “zero field μSR” (of ZF-μSR). These sorts of experiments are excellent for probing magnetic transitions, and weak magnetic ordering. The muon is an extremely sensitive probe – fields on the order of a fraction of a gauss can be measured! If one applies a magnetic field, there are basically two types LA PHYSIQUE AU CANADA septembre / octobre 2006 297 Sept06-FF.qxd 11/7/2006 2:06 PM Page 298 FEATURE ARTICLE ( NEUTRONS AND MUONS ... ) samples, the actual stopping site within each unit cell is determined through electrostatics and can be difficult to infer from the data. There are some cases, such as in the determination of penetration depths within superconductors, where this is not crucial. However, this is in stark contrast to neutron scattering, where the neutrons can measure the entire sample at once without the need to determine “stopping sites”. peak, which corresponds to an ordered moment of about 0.03 μB was discovered, but this moment was too small to account for a large heat capacity anomaly at 17.5 K [7,8]. μSR measurements were among the first to offer a crucial piece of information about the nature of this “hidden order” state. One of the questions which have plagued experimentalists in this field is the role of impurities. Neutron scattering can detect magnetic impurities through their magnetic transitions, and it was thought that the small Bragg peak seen was actually due to a large moment in a small part of the sample, as opposed to a small moment spread out homogeneously in a large part of the sample. μSR, on the other hand, can distinguish between the two situations. A large moment, from say the ordered electrons on a uranium site in an impurity, would give rise to a large internal field developing at the transition temperature. The size of the volume fraction will determine the amplitude of the signal. In the case of URu2Si2, muon precession was observed below 17.5 K, confirming the existence of magnetic order discovered through neutron scattering [9]. However, the size of the oscillating signal was small, suggesting that only about 10% of the sample was ordered (see figure 3). Moreover, the internal field was large, giving a large precession frequency that could not be accounted for with the small moment predicted from neutron scattering. It appears, then, that in the case of URu2Si2, the hidden order phase must be unrelated to (2) Elastic and inelastic information. With different kinds of neutron scattering experiments, the elastic and inelastic information can be separated, through for example the triple axis spectrometer invented by Brockhouse. The resolution can approach the micro electron volt (μeV) regime! μSR has a deficiency in this regard, since the inelastic and elastic data are often superimposed upon one another. A LF experiment can sometimes determine the strength of the interactions between spins, but in general neutron scattering is a far superior technique for the spatial and energetic resolution of magnetic correlations within materials. (3) Time scales. Neutron scattering typically measures very fast time scales (108 to 1013 Hz) – after all, the neutrons themselves do not spend much time within solids. Modern techniques have pushed this time window to smaller time scales, but this still does not cover the dynamic range offered by μSR – 104 – 1012 Hz (eight orders of magnitude!). When both techniques are used together, this results in over nine orders of magnitude of correlation times available to probe. RECENT EXAMPLES FROM MODERN CONDENSED MATTER PHYSICS What questions can the combination of these techniques answer? Here are some prominent examples from the field of condensed matter physics: (1) Heavy fermion materials: Heavy fermion metals belong to a class of highly correlated electron materials with extremely high effective carrier mass (as shown through specific heat measurements) [5]. Most of these systems are composed of f-electron actinides and transition metals. The physical interpretation of this “heavy mass” for the constituent electrons is that the carriers themselves are not moving independently of one another, but they are strongly interacting with other electrons within the lattice. The physics behind these systems involves a competition between magnetic ordering of the f-electrons, through what is called the RKKY interaction, and a tendency to remain disordered, which is caused by scattering of conduction electrons with the f-electrons through the Kondo effect. URu2Si2 belongs to this class of materials, with an effective electron mass which is about 25 times a free electron mass [6]. At 17.5 K in this material, there is a “hidden” order transition, and at about 1 K, there is a superconducting transition. Oddly enough, most of the attention in this material has been focused on the 17.5 K transition and not the superconducting one. This is because despite two decades of research, physicists still do not know what is ordering. A very tiny magnetic Bragg 298 PHYSICS IN CANADA Fig. 3 September / October 2006 Zero field muon spin relaxation spectra in URu2Si2 above and below the transition at 17.5 K [9]. Note the small precession signal at 2.5 K, which indicates a small volume fraction of ordered spins (scenario (a) compared to scenario (b)). Sept06-FF.qxd 11/7/2006 2:06 PM Page 299 ARTICLE DE FOND ( NEUTRONS AND MUONS ... ) this small moment, since the entropy loss from the transition would be small if it came from an impurity phase. NMR measurements, over a decade later, confirmed the μSR measurements of sample inhomogeneity [10]. The question of the hidden order phase still remains open. However, recent neutron scattering results are suggesting that the answer may lie in an analysis of the inelastic spectrum. (2) Geometrically frustrated materials: Geometrically frustrated oxides usually consist of transition metal or rare earth magnetic ions that exist in triangular sublattices. If antiferromagnetic interactions exists between these species, a conventional Néel ground state cannot arise in many of these systems, and thus the material is said to be “frustrated”. A wide variety of unusual ground states can instead be favored, such as spin glasses in the absence of chemical disorder, “spin ice” ordering, and possible “spin liquid” states, where the moments remain fluctuating down to zero Kelvin [11]. μSR has played an important role in the investigation of these fascinating materials. Neutron scattering is typically used first as a technique to probe for magnetic ordering. However, in many of these systems, the time scale for the fluctuating moments is smaller than the neutron time window, and thus the characteristic features of frustrated systems are seen as broad lumps of scattering in the elastic channel. If the moment is too small, the magnetic signal can be dominated by the background, and these features can be completely lost. This was the case in the S=1/2 FCC systems A2BReO6 (A = Sr, B = Ca, Mg) [12,13]. Both of these materials have networks of face-centered cubic (FCC) Re S=1/2 ions that have very strong antiferromagnetic interactions. The FCC lattice can be thought of as a series of edgeshared tetrahedra (complex networks of triangles), so these systems were prime candidates for geometric frustration. Specific heat and susceptibility measurements revealed transitions at ~ 14 K and 50 K respectively for the Ca and Mg systems, but no magnetic Bragg peaks were detected by neutron scattering. It was μSR that revealed the nature of the ground state through the appearance of a characteristic lineshape in the ZF-spectra below the transition temperatures that was typical of spin glasses – the spins were frozen out into random orientations. Instead of a precession signal, a loss in the polarization and a signature minimum in the spectrum is noted (see figure 4). Despite the successes of these techniques in elucidating the low temperature ground states of frustrated systems, there are still discrepancies in the literature about the correct interpretation of the results. For example, the pyrochlore material Tb2Sn2O7, where the Tb3+ spins lie on the corners of corner-shared tetrahedra, has been the subject of continued debate. Neutron scattering clearly notes magnetic Bragg peaks appearing below 1.2 K [14], but μSR experiments suggest that this state is not ordered, but dynamic (ie. there is no precession signal) [15]. Apparently, the spins appear static within the neutron time window, but dynamic within the μSR time Fig. 4 (a) Spins with strong antiferromagnetic interactions which reside in triangular sublattices give rise to the condition of frustration at low temperatures; (b) Zero field muon spin relaxation data on the geometrically frustrated material Sr2CaReO6 [12]. The characteristic drop in polarization below 14 K is typical of spin glasses (the fit is to a function used by Uemura et al. for canonical spin glasses). window! This situation can arise if there is a large internal field which dampens out the expected precession signal for ordering in a μSR experiment (as expected for large ordered Tb moments). It is also possible that there are regions of ordered spins coexisting with dynamic spins that dominate the signal. The low ordered moment seen from neutron scattering is consistent with this result. (3) Superconductivity: Last, but not least, is the field of superconductivity, where perhaps μSR has had the greatest degree of success in determining the symmetry of the superconducting state, the presence of magnetism coexisting with superconductivity, and the physics of vortex dynamics [16]. The literature is replete with examples of the strengths of this method [4]. However, there are some notable examples of problems within the field that have needed both neutron scattering and μSR to address. The existence of magnetism within vortex cores, for example, remains a controversial question. LA PHYSIQUE AU CANADA septembre / octobre 2006 299 Sept06-FF.qxd 11/7/2006 2:06 PM Page 300 FEATURE ARTICLE ( NEUTRONS AND MUONS ... ) Neutron scattering observes an increase in magnetic Bragg peak intensity as a function of applied field in La2xSrxCuO4 (x=0.163), eluding to the presence of enhanced antiferromagnetism within the vortex cores [17]. Some μSR experiments suggest similar behavior in Pr2-xCexCuO4 through an analysis of the muon lineshape (which is a measure of the local field distribution at the muon site) [18]. However, the subject is still controversial. What is more certain is the advantage that μSR has in determining the symmetry of the superconducting state through penetration depth experiments as a function of temperature. While neutron scattering can indirectly determine this through inelastic scattering spectra, μSR has been instrumental in characterizing many of the known superconductors, and perhaps even more helpful in drawing upon universal behavior throughout the high-TCs (through, for example, the Uemura plot [19]). For as long as the problem of hightemperature superconductivity exists, these techniques will likely be used together to further our understanding of this phenomena. CLOSING REMARKS A wide variety of problems can be addressed through μSR and neutron scattering experiments which provide very complementary data due to the range of the interactions and the respective timescales. It is likely that with the advent of more powerful spallation sources, μSR will continue to thrive alongside of neutron scattering, and it is no accident that sources such as ISIS in the UK have muons and neutrons available at the same location for experiments. There is no shortage of important condensed matter systems that are waiting to be investigated. 300 PHYSICS IN CANADA ACKNOWLEDGEMENTS The author would like to thank the continued support and interest in the field from many colleagues over the years, including B.D. Gaulin, W.J.L. Buyers, J.E. Greedan, J.S. Gardner, G.M. Luke, and Y.J. Uemura. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. September / October 2006 B.N. Brockhouse, Rev. of Mod. Phys. 67, 735 (1995). See, for example, http://www.neutron.anl.gov/ for a reference on neutron scattering. G.L. Squires, “Introduction to the Theory of Thermal Neutron Scattering,” Dover Publications, England (1997). For an introduction to ìSR and various recent experiments, see http://cmms.triumf.ca/intro/muSRBrochure.pdf For an introduction to heavy fermions, please see Z. Fisk et al., Proc. Natl. Acad. Sci. 92, 6663 (1995). De Visser et al, Phys. Rev. B34, 8168 (1986). C. Broholm et al., Phys. Rev. B43, 12809 (1991). For a review, see V. Tripathi et al., J. Phys. Cond. Matt. 17, 5285 (2005). G.M. Luke et al., Hyperfine Interactions 64, 517-522 (1990). K. Matsuda et al., Phys. Rev. Letters 87, 087203 (2001). For a review of frustration see J.E. Greedan, J. Mat. Chem. 10, 3058 (2001). C.R. Wiebe et al., Phys. Rev. B65, 155325 (2002). C.R. Wiebe et al., Phys. Rev. B68, 134410 (2003). I. Mirebeau et al., Phys. Rev. Letters 94, 246402 (2005). P. Dalmas de Réotier et al., Phys. Rev. Letters 96, 127202 (2006). For example, see J.E. Sonier et al., Rev. Modern Physics 72, 769 (2000). For example, see B. Lake et al., Science 291, 1759 (2001). J.E. Sonier et al., Phys. Rev. Letters 91, 147002 (2003). Y.J. Uemura et al., Phys. Rev. Letters 66, 2665 (1991). Sept06-FF.qxd 11/7/2006 2:06 PM Page 301 ARTICLE DE FOND ( STATUS OF THE CMCF ... ) STATUS OF THE CANADIAN MACROMOLECULAR CRYSTALLOGRAPHY FACILITY: DESIGN AND COMMISSIONING OF THE 08ID-1 BEAMLINE AT THE CANADIAN LIGHT SOURCE by Pawel Grochulski, Ingvar Blomqvist, and Louis Delbaere T he 08ID-1 beamline is the initial phase of the Canadian Macromolecular Crystallography Facility (CMCF) [1] located at the Canadian Light Source (CLS), a 2.9 GeV ring. CLS produced "first light" on December 2003, and the first data collected at CMCF 08ID-1 was in May 2006. Grenoble, France (6 GeV) and Spring-8 in Nishi Harima, Japan (8 GeV). Electrons and other charged particles do not radiate while undergoing linear, uniform motion. However, when accelerated, a rearrangement of their electric We have designed, constructed and fields occurs. This field perturbation are commissioning a beamline which The 08ID-1 beamline is the traveling away from the electrons at the is illuminated by a small-gap in-vacu- initial phase to the velocity of light is called electromagnetum hybrid undulator (SGU), located ic radiation. An example of such radiain the upstream half of the straight Canadian Macromolecular tion is a TV antenna where electrons are section, and chicaned inboard by Crystallography Facility driven up and down the antenna, in a 0.75 mrad. The downstream half of this [1] located at the periodic fashion, at a frequency specific section is reserved for the 08ID-2 (CMCF) to a particular TV station. In the case of beamline SGU. The beamline contains Canadian sources, electrons at Light Source synchrotron white beam slits (WBS), a double crysspeeds very close to the speed of light tal monochromator (DCM) equipped (CLS), a 2.9 GeV ring. CLS are stored in an evacuated circular path. with an indirectly cryo-cooled first observed synchrotron radiation is produced "first light" on The crystal and a sagittally-focusing seccaused by the transverse acceleration ond crystal followed by a vertically December 2003,and the first due to magnetic forces. These magnetic focussing mirror (VFM). The beamline forces are due to either bending magis terminated by an innovative and data collected at CMCF nets along the ring or by special inservery robust endstation, including a 08ID-1 was in May 2006. tion device magnets such as, undulators MarMosaic225 CCD X-ray detector. and wigglers located in the straight sections of the synchrotron ring. The synFor the most part, the beamline components were manufacchrotron radiation from a bending magnet source is linearly tured by ACCEL Instruments GmbH (Germany), while the polarized in the plane of acceleration. In an undulator source, beamline controls, similarly for the CLS facility, are being the electron beam is periodically deflected by weak magnetic developed based on an EPICS platform and complemented fields, generating a large number of electron beam oscillations with an innovative user interface. The primary scientific goal of small amplitude where the electron emits radiation at the of the 08ID-1 beamline is to interrogate small protein crystals wavelength of its periodic, sinusoidal motion. Strong interfer(~20 μ) with large unit cells (~1000 Å). The beamline is ence effects occur in an undulator and the radiation has a high equipped with a Röntek Spectrometer System (XFLASH intensity line spectrum over a very restricted frequency 101A) capable of simultaneously carrying out multiwaverange. The spectral resolution of the radiation is proportional length anomalous diffraction (MAD), X-ray absorption near to the number of undulator periods - the synchrotron radiaedge structure (XANES), and X-ray fluorescence (XRF) in the tion wavelength can be altered by varying the magnetic field. case of protein derivatives containing heavy metal atoms. For an electron, its wavelength is determined by the undulaThere are ongoing efforts to equip the beamline with a robottor magnetic period divided by γ (due to relativistic Lorentz ic cryogenic sample changer thus enabling remote access to contraction - at the CLS γ=5675.3). On the experimental floor the facility. of a synchrotron this wavelength appears to the observer to be further reduced by another factor γ due to the Doppler effect. For example, an undulator with a period of 0.02 m is CLS STORAGE RING The Canadian Light Source (CLS) is a 2.9 GeV "third generation" synchrotron facility in the same class of synchrotrons as the Swiss Light Source in Villingen, Switzerland and SPEAR3 in Stanford California, USA. The leading edge synchrotron technologies are the APS in Chicago, USA (7 GeV), ESRF in Pawel Grochulski <[email protected]> 1,2, Ingvar Blomqvist 1 and Louis Delbaere 2; 1 Canadian Light Source, 2 University of Saskatchewan, Saskatoon, Saskatchewan, Canada LA PHYSIQUE AU CANADA septembre / octobre 2006 301 Sept06-FF.qxd 11/7/2006 2:06 PM Page 302 FEATURE ARTICLE ( STATUS OF THE CMCF ... ) generating synchrotron radiation in the X-ray regime [~0.02 m/(2(5675.3)2)= 3x10-10 m]. When the magnetic field of an undulator is increased and the pure sinusoidal transverse motion of electrons becomes distorted, generating higher harmonics of the single wavelength undulator radiation, this device is called a wiggler. The spectrum of a wiggler is similar to the spectrum generated by a bending magnet, but the photon beam is much more intense and the "critical energy" (Ec) is shifted towards a higher energy with respect to the bending magnet radiation. The critical energy is the point in the spectrum which divides equally the total integrated spectral energy. The CLS critical energy is Ec=7.572 keV and, for example, the superconducting wiggler of the CLS XAFS beamline has Ec= 10.7 keV. Both bending magnets and wigglers have a continuous spectrum over a broad range of energies, typically extending from infrared to hard X-rays. Electrons circulating in the storage ring are compressed into bunches and, thus the generated radiation is emitted in pulses. However, since the time between bunches is 2 ns, the case of the CLS, the source can be considered continuous for all crystallographic applications except nanosecond timeresolved experiments. The CLS ring currently runs at 200 mA and the size of the electron beam at the location of the insertion device is 1.09 mm x 0.05 mm full width at half-maximum (FWHM), horizontal (H) x vertical (V)) and with divergence of 100 μrad x 21 μrad (FWHM, H x V). MACROMOLECULAR CRYSTALLOGRAPHY Macromolecular crystallography is a method for determining the structures of large biological molecules such as proteins and nucleic acids. Scientists study the structures of biological molecules in order to (a) increase their understanding of structural biology and biochemistry, (b) develop and improve the design of ligands that bind to macromolecules in order to use these ligands as pharmaceuticals, and (c) develop a basis for modifying the structures of macromolecules themselves in order to alter their functions, sometimes with industrial applications [2]. on an X-ray CCD detector is defined by three properties; the amplitude, which is measured from the intensity of the spot; the wavelength, which is defined by the monochromator; and the phase, which is lost in the X-ray experiment. In order to determine the atomic positions from a diffraction pattern we need to know all three properties for each diffracted beam and then calculate the Fourier transform. Determining phases is the most challenging task in crystallography and today it is done mostly by the multiwavelength anomalous diffraction method (MAD), realized by tuning the wavelength of the monochromator to the absorption edge of a "heavy atom" (e.g. selenium) in the protein. CANADIAN MACROMOLECULAR CRYSTALLOGRAPHY FACILITY The Canadian Macromolecular Crystallography Facility will have more than 60 protein crystallographers, located across Canada, and consist of three beamlines, two insertion devices beamlines and one bending magnet beamline. The first insertion device beamline (08ID-1) was intended to be highly efficient and flexible, capable of satisfying the requirements of the most challenging and diverse crystallographic experiments, i.e. physically small crystals with large unit cell dimensions (Figure 1). The recently funded bending magnet 08B1 beamline is designed for high-throughput data collection, capable of being accessed remotely. The third, an undulator based 08ID-2 beamline, is envisioned to have microfocussing capabilities, but with some restrictions in energy. Since the 08ID-1 beamline is already in a chicaned position, 0.75 mrad inboard (Figure 1), the SGU for the 08ID-2 will be chicaned 0.75 mrad outboard, so the total separation between photon beams will be 1.5 mrad. It will allow for the separation between beams to be 30 mm at a distance of 20 m from the source. BEAMLINE DESIGN Insertion device The CMCF 08ID-1 beamline is illuminated by a hybrid invacuum small-gap undulator (SGU) (80 periods with a period length of 20.0 mm) operating at a minimum gap of 5.5 mm (Beff=0.923 T). The mechanical supports and vacuum cham- The first prerequisite for solving the three-dimensional structure of a macromolecule by X-ray crystallography is a well-ordered crystal that will strongly diffract Xrays. Crystallography depends upon directing a synchrotron X-ray beam onto a regular array of identical molecules so that the X-rays are diffracted in a pattern from which the structures of an individual molecule can be retrieved. The electrons in the atoms making up the crystal scatter X-rays in all directions, and only those which constructively interfere with one another, according to Bragg's Law, give rise to diffracted beams that can be collected as distinct diffraction spots. Each diffraction spot is the result of constructive interference from X-rays with the same diffraction angle emerging from all atoms of the crystal. For example, diffraction from the 1500 atoms of a myoglobin protein crystal results in about 25,000 diffracted beams [3]. Each diffracted beam, which is recorded as a spot Fig. 1 Layout of the CMCF "sector" 302 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:06 PM Page 303 ARTICLE DE FOND ( STATUS OF THE CMCF ... ) ber for the SGU have been manufactured by R.M.P.s.r.l. (Italy), while the magnetic structure, shimming and controls have been produced at the CLS (Figure 2). The electron beam is stabilized by the electron beam position monitors (BPMs) in the storage ring, however, a four blade X-ray BPM installed at 8.7 m from the center of the SGU will be used in the feedback system to maintain the stability of the X-ray beam to better than 0.5 μrad. The brilliance tuning curves for the small-gap in-vacuum undulator and a flux spectrum are shown in Figure 3. The measured filled integrals, RMS phase angle error and photon energies as functions of undulator gap are shown in Table 1. It is critical that the RMS phase errors are less than 2o for the range of energy of 6.5 to 18 keV since harmonics from 3 to 9 have to be used for those energies. The 08ID-1 beamline illuminated by the SGU located in the upstream of the straight section and chicaned inboard by 0.75 mrad. The downstream half of this section is reserved for the future SGU associated with the 08ID-2 beamline. The effective size of the source produced by the undulator is practically identical to the size of the electron beam in the undulator whereas, the divergences are different depending on the wavelength. the size of the white beam. The central unit of the optical system is a double-crystal Si(111) monochromator manufactured by ACCEL Instruments GmbH (Germany). The double crystal monochromator is located at 43.5 m from the source. The first monochromator crystal is cryogenically cooled, while the second is a sagittally-focussing crystal. All essential components of the monochromator are indirectly water-cooled to minimize thermal fluctuations. A quadrant of PIN diodes positioned upstream of a 0.5 μm-thick chromium foil located between the monochromator and the mirror serve as online beam position and intensity monitors [4]. Vertical focussing of the beam is achieved by a 1.1 m long dynamically bendable ULE (ultra-low expansion titanium silicate) flat mirror manufactured by InSync, Inc. (Albuquerque, NM, USA). It has a TABLE 1 RMS PHASE ANGLE ERROR (O) AND PHOTON ENERGIES AS FUNCTIONS OF THE UNDULATOR GAP (o ) X-ray optics The narrow bandwidth produced by the SGU cannot be used directly for macromolecular crystallography. A monochromator is needed to reduce bandwidth and to reject all of the emission spectrum, except the band centered at the selected photon energy. Since monochromator crystals let through certain multiples of the selected fundamental photon energy, there is a need for a low-pass filter such as, a mirror. In detail (Figure 4), the optics are comprised of a CVD diamond-based water cooled X-ray beam position monitor (BPM) followed by white beam slits that are used to define Fig. 2 SGU in the storage ring Fig. 3 Tuning curves of the small-gap in-vacuum undultor (top) and flux spectrum for a 10 mm gap of the SGU LA PHYSIQUE AU CANADA septembre / octobre 2006 303 Sept06-FF.qxd 11/7/2006 2:07 PM Page 304 FEATURE ARTICLE ( STATUS OF THE CMCF ... ) TABLE 2 SPECIFICATIONS OF THE CMCF 08ID-1 BEAMLINE WITH 200 MA RING'S CURRENT Δ Fig. 4 Layout of the CMCF 081D-1 beamline measured surface roughness of 1.5 Å RMS and 0.58 μrad RMS surface figure error without a bender and about 100% larger with a SESO (France) bender at different bending radii. The mirror is downward reflecting and fully adjustable in terms of height, angle, and the radius of curvature can be changed from infinity to 1.39 km. The active surface of the mirror has three stripes parallel made of platinum, palladium and un-coated regions that can be translated into the beam, depending on the X-ray energy, to remove higher harmonics. At the normal 2.2 mrad glancing angle the uncoated track is used for photon energies below 13.5 keV and the Pd-coated track for 13.5-18 keV. A lateral movement of the mirror substrate inside the vacuum tank allows the appropriate stripe to be moved into the beam. With a demagnification ratio of 6.8 and 11.8 in the horizontal and vertical directions, respectively, a source size limited focal spot of 160 x 50 μm2 (H x V) (FWHM) at the sample can be achieved. The mirror tank is followed by a double safety photon shutter. Experimental station The experimental hutch is shown in Figure 5. The monochromatic beam is led through an evacuated filter box and then through an exposure box. It also contains vertical and horizontal slits, an X-ray beam position monitor and the fast shutter. The protein crystal is mounted on a single axis goniostat with a fully motorized x-y-z stage. The accumulated mechan- ical errors amount to less than 6 μm at the sample position. Diffraction data are recorded using a MarMosaic225 CCD detector mounted in ACCEL's detector holder that can be raised and tilted in order to enable ultra-high resolution data collection. The beamline is equipped with a Röntek Spectrometer System XFLASH 101A to perform the X-ray spectroscopy for multiwavelength anomalous diffraction (MAD) and X-ray absorption near edge structure (XANES) on the same crystals, and the X-ray fluorescence (XRF) for metal detection in protein derivative crystals. Specifications of the beamline are shown in Table 2. Control system The beamline's control system is based on the EPICS platform [7], however all commissioning tools have been prototyped using MATLAB (The MathWorks, Inc.). This includes all scan and sample visualization tools. After the commissioning is finished the user's software will be converted to a browser based graphical user interface allowing remote access to the facility. A number of Linux based PCs are available for data transfer, storage and processing. ACKNOWLEDGEMENTS We are indebted to the entire CLS staff for their excellent work during the design, construction and commissioning, in particular Michel Fodje, Alan Duffy, Russ Berg, Mike McKibben and Tasha Summers. REFERENCES Fig. 5 304 End-station of the CMCF 08ID-1 beamline PHYSICS IN CANADA 1. P. Grochulski, I. Blomqvist, B. Yates, E. Hallin, E. & L. Delbaere, "Design of the 08ID-1 protein crystallography beamline at the Canadian Light Source", Acta Physica Polonica A101(5), 589-594 (2002). 2. Third-Generation Hard X-ray Synchrotron radiation Sources, ed. Dennis M. Mils, John Wiley & Sons, Inc., New York (2002). 3. C. Branden and J. Tooze, Introduction to Protein Structure, Garland Publishing Inc., New York and London (1991). 4. R.W. Alkire, G. Rosenbaum and G. Evans, "Design of a vacuumcompatible high-precision monochromatic beam-position monitor for use with synchrotron radiation from 5 to 25 keV", J. Synchrotron Rad. 7, 61-68, (2000). 5. M. Sanchez del Rio, R.J. Dejus, X-ray Oriented Programs 2.0, http://www.esrf.fr/computing/scientific/xop/ 6. C. Welnak, G.J. Chen and F. Cerrina, “SHADOW: a synchrotron radiation X-ray optics simulation tool”, Nucl. Instr. And Meth. A347, 344-347 (1994); SHADOW VUI, v 1.0, http://www.esrf.fr/computing/ scientific/xop/shadowvui/ 7. EPICS: http://www.aps.anl.gov/epics/ September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 305 ARTICLE DE FOND ( PHONON SPECTROSCOPY ... ) PHONON SPECTROSCOPY AND X-RAY SCATTERING USING SYNCHROTRON RADIATION by John S. Tse and Dennis D. Klug O INTRODUCTION wing to advances in the production of high intensity, coherence and highly monochromatized synchrotron radiaScattering techniques are important tools for research in tion in recent decade, x-rays scattering has become a highly material science and condensed matter physics. Through the desirable technique for the investigation of the dynamical observation of the distributions and fluctuations in space and properties of condensed matter. Scattering using x-rays offers time, the scattering of neutrons and photons can provide several advantages over neutrons. In unique insight into the arrangement this report, the basic theoretical ideas the dynamics of atoms in the conand recent dramatic developments in Scattering using x-rays and densed (liquid and solid) state. synchrotron-based inelastic x-ray scatoffers several advantages tering are outlined. Potential applicaThe theoretical framework of using tions of these techniques are illustrated over neutrons. In this (neutron) scattering experiments to through the study of the dynamics of obtain dynamical information was preclathrate hydrates. The specific appli- report, the basic theoretical sented in the seminal theoretical work cation of inelastic x-ray scattering for ideas and recent dramatic of van Hove [1] using a space-time corthe characterization of the phonons relation function formalism. The full and the role of the guest-host interac- developments in synchro- potential of this technique was fully tions on the phonon band structure is tron-based inelastic x-ray exploited in the pioneering experiments described. In addition, the application of Brockhouse [2]. It was demonstrated of nuclear resonant inelastic x-ray scat- scattering are outlined. that the inelastic scattering of thermal tering is used to reveal the large anharneutrons permit the measurement of monic nature of the guest host interacsmall energy transfers associated with tions in the Kr clathrate. lattice vibrations. In the ensuing years, incoherent inelastic neutron scattering (IINS) has developed into an indispensable tool for the investigation of the dynamical properties of crystalline solids, glasses, polymers and liquids. In contrast, the development of x-ray scattering as a probe of atomic dynamics have been relatively dormant until the late 1980s. The energy width characteristic of x-rays generated from conventional cathode tubes have a temporal lifetime of ca. 0.1 fs which is very short as compare to atom motions in the order of ps. Moreover, the energy of x-rays is much larger than the vibration energies and very high energy resolution, ca. 10-6 is needed in order to measure vibrational structures. Therefore, x-rays are often used for the determination of static atomic positions although there were several attempts to extract dynamical information from the analysis of diffuse scattering [3]. In the last two decades, the availability of high intensity, spatially coherent and tunable x-rays from synchrotron radiation has revitalized the interest of using x-ray in scattering experiments. In particular, advances in monochromator design have now making routine measurement in a few meV resolution possible [4]. The use of x-ray methods in place of neutrons offers several practical advantages. Since intense x-rays can be focused into Fig. 1 ω-Q) region accessible with difEnergy-momentum (ω ferent probes of inelastic scattering (taken from ref. 7). John S. Tse <[email protected]>, Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E2; Dennis D. Klug, Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6 LA PHYSIQUE AU CANADA septembre / octobre 2006 305 Sept06-FF.qxd 11/7/2006 2:07 PM Page 306 FEATURE ARTICLE ( PHONON SPECTROSCOPY ... ) very small spot size (e.g. microns) only a small volume of sample is needed for the experiment. This is particularly critical for measurements under extreme pressure and temperature conditions. Excellent examples are recent measurement of phonon dispersion of single crystals under high pressure and the dynamical structure of levitated molten liquid droplets [5]. Another distinct advantage is that x-ray scattering can access a wide range in energy and momentum which is not accessible to neutrons with conventional triple axis spectrometers. Figure 1 compares the accessible energymomentum regimes for a number of scattering techniques. Optical methods, such as Brillouin and Raman scattering are restricted to small momentum (< 10-3 Å-1) and intermediate energy transfers (10-6 – 1 eV). Neutron scattering can be used for momentum transfer larger that 10-2 Å. X-ray scattering with synchrotron radiation largely overlap with neutrons but become more accessible at the lower and higher energy and momentum transfer regimes where neutron scattering is limited by kinematic restrictions. In this article, the application of x-ray scattering will be illustrated with specific examples. We will focus on the investigation of the lattice dynamics of clathrate hydrates. It will be demonstrated that valuable dynamical information on the low energy lattice vibrations and localized motions of the guests can be obtained from x-ray scattering experiments and a new site specific nuclear resonant inelastic x-ray scattering spectroscopy [6]. THEORETICAL AND EXPERIMENTAL BACKGROUND Non-resonant x-rays scattering [7] A schematic of the geometry for a scattering experiment is shown in Fig. 2. The incident beam has a well defined energy Ei, momentum qi and polarization ei. The scattered beam at an angle 2θ within an angle element dΩ is defined by the scattering wave vector qf, energy Ef and polarization ef . Application of the conservation rules for energy and momentum transfer gives E = ω = Ei − E f and Q = (qi − q f ) d2σ ⎛ dσ ⎞ =⎜ ⎟ S ( Q , ω) dΩdω f ⎝ dΩ ⎠0 [2] where (dσ/dΩ)0 is the intrinsic cross-section and in the spacetime correlation formalism 1 e iωt dt Ψ i ∫ 2π S ( Q , ω) = ∑e − iQ ⋅rj ( t ) iQ ⋅rj ' ( 0 ) e Ψi [3] j , j' The function 〈…〉 in eqn. (3) describes the fluctuation or correlation of the scattering phase of particles at t=0 and at a different time t at a given state Ψi. Within the one-phonon approximation, eqn (3) can be simplified to S(Q,ω) = G(Q,q,j)F(ω,T,q,j) [4] The dynamical structure factor = G(Q,q,j) is given by G ( Q , q, j ) = unitcell ∑ f d (Q )e −Wd [Q ⋅ ed (q, j )] M d−1eiQ⋅d 2 [5] d fd(Q) is the atomic form factor of atom d and ed(q,j) is the component of the normalized phonon eigenvector of mode j with phonon wavevector q for atom d. e-Wd is the Debye-Waller factor for atom d and Md is the mass. The response function F(ω,T,q,j) for an undamped phonon is given by F ( ω, T , q , j ) = n + 1 /2 ± 1 /2 δ ω ∓ ωq , j ωq , j ( ) [6] where the upper and lower signs are for x-ray energy loss and energy gain, respectively. The essence of a scattering experiment is the direct measurement of S(Q,ω) which can be accomplished with a spectrometer with the conventional triple-axis design. A schematic drawing of a typical beamline (ID 16 ESRF) is shown in Fig. 3. Typically, the phonon disper- [1] For x-rays, the energy of the incident photon is much larger than the energy transferred (i.e. Ei 〉〉 E), then Q = 2 qi sin θ The double differential cross section is related to the scattering function S(Q,ω) by Fig. 2 306 Geometry for neutron and x-ray scattering. PHYSICS IN CANADA Fig. 3 A schematic drawing of the conventional triple-axis spectrometer and the layout of a synchrotron x-ray inelastic scattering beamline. September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 307 ARTICLE DE FOND ( PHONON SPECTROSCOPY ... ) sion of an oriented single crystal can be obtained from constant energy scans. For polycrystalline samples where there is no distinct orientation of the sample with respect to the direction of the incident beam and, as a result of orientation averaging, only the absolute value of the momentum transfer is well-defined. However, in order to obtain a dispersion relation of a material, it is necessary to measure the frequency as a function of a distinct wave vector. In polycrystalline samples, only orientationally averaged longitudinal phonon modes can be measured in the first Brillouin zone. Transverse phonons may appear in the spectra of the extended zones [7]. Nuclear resonant x-ray inelastic scattering Nuclear resonant x-ray inelastic scattering (NRIXS) is a new technique for lattice dynamics measurements [6-8] method, applicable to specific nuclei with non-zero nuclear moment analogous to Mossbauer spectroscopy , can provide information on the vibrational density of states. The basic principle is to tune synchrotron x-ray to match the excitation energy of a nuclear transition. For a clamped non-vibrating nucleus, the emitted radiation is very close to recoil free and therefore has the same energy as the transition between the nuclear ground and excited state. The emitted photon may then interact with other nuclei in the crystalline solid and shift the “recoil” energy (vibration coupled). The measurement of the resulting time delayed de-excitations contains information on the vibrations of the nucleus embedded in an Einstein solid. The nuclear resonant interaction cross section σ(Q,ω) is related to the nuclear resonance cross section σ0 and scattering function S(Q,ω) defined above but in this case, can be considered as the probability density for phonon excitation [6] σ ( Q , ω) = σ 0 ΓS ( Q , ω) [7] In effect, apart from a sharp resonance, the NRIXS spectrum is a convolution with the vibration profile. Within the harmonic approximation, the vibrational density of states of the nucleus can be obtained [8]. A schematic diagram illustrating the principle of NRIXS for 83Kr (I=9/2) is shown in Fig. 4. Since the linewidth of the exited nuclear state is extremely narrow (3.1 ns for 83Kr), monochromator with very high energy resolution (ca. meV bandwidth) is required. These monochromators are often constructed for multiple reflections from high index planes of single crystals. Therefore, the availability of monochromatic coherence from an intense incident x-ray source is a prerequisite for the experiment. The experimental setup for the measurements of nuclear inelastic scattering is illustrated in Fig. 5. ILLUSTRATIVE EXAMPLES In recent years, inelastic scattering employing synchrotron xray has been used to study the phonon dispersion of single crystals, amorphous solids and liquids. An excellent review of the state-of-the-art can be found in [7]. We will focus on a specific topic in this article, namely, the characterization of the lattice vibrations and low energy guest motions in clathrate hydrates. Clathrate hydrates are non-stoichiometric crystalline inclusion compounds with water molecules forming a threedimensional network (host) where small molecules or rare gas atoms (guests) can be encaged in the empty voids [9]. Fig. 4 Schematic illustration of the principle for nuclear resonant inelastic scattering (adapted from ref. 6). (a) The energy level diagram ω) (resoand the absorption spectrum S(ω nance) for 83Kr nuclear excitation. (b) The convolution of the resonance absorption with vibrational levels. The dashed arrows indicate the creation and annihilation of phonons. The dotted arrows indicate multiple-phonon processes. Fig. 5 Schematic layout of a typical nuclear resonant inelastic scattering beamline. The detector measures the time-delayed fluorescence after nuclear excitation. The intensity of inelastic scattering can be converted into vibrational density of states. LA PHYSIQUE AU CANADA septembre / octobre 2006 307 Sept06-FF.qxd 11/7/2006 2:07 PM Page 308 FEATURE ARTICLE ( PHONON SPECTROSCOPY ... ) tron scattering. Theoretical lattice dynamics calculations on a structure I Xe hydrate have shown that these avoided or anti crossings occur at very low frequencies (ω) and at small momentum transfer (Q) (Fig. 6b). The use of neutrons to determine the collective excitations is virtually ruled out due to restrictions in Q-ω space at Q values within the first Brillouin zone, and due to the incoherent contribution of the hydrogen atoms to the spectrum. On the other hand, xrays can access the small Q values needed and provide the necessary energy resolution. Furthermore, since polycrystalline samples were to be used in the experiment, an unambiguous assignment of the observed modes is only possible in the first Brillouin zone: due to the selection rules in the one-phonon approximation only the longitudiFig. 6 The three most common structures (type I, cubic Pm3n, type 2, cubic, Fd3m and nal modes can be observed in the type H, hexagonal, P6/mmm) of clathrate hydrate stable under ambient pressure(a) first Brillouin zone. Momentum and (b) calculated phonon dispersion curve along the [111] direction for a Xe transfers beyond the first Brillouin hydrate. Note the anti-crossing of the “localized” guest motions with the acoustic zone will excite several longitudibranches predicted at Q=0.02 and 0.1. nal and transverse phonons at once, thus giving information on Three structures have been observed to be stable under ambithe density of states of these modes. For a cubic system, such ent pressure (see Fig. 6a). In general, for very small or large as the low-pressure phase of clathrates, the crystal acoustic guests, the type II Fd3m structure is adopted. Another very vibrations transform as T1u symmetry at the Brillouin zone common structure is the type I Pm3n cubic structure [9]. Even center. Factor group analysis [13] has shown that guest vibrathough gas hydrates have a well-defined crystalline structions also contain T1u symmetry modes at the zone center. As ture, the temperature dependence of the thermal conductivithese largely non-dispersive (localized) modes move away ty is quite complicated but resembles that of a glass [10,11]. from the zone center, avoided crossings with strongly disperFurthermore, the magnitude of the thermal conductivity of sive acoustic branches having similar symmetry are expected different hydrates is only weakly dependent on the nature of to occur within the Brillouin zone. the guests. Several models have been proposed to account for this novel property. There is a consensus regarding the X-rays scattering experiments were performed at the beam resonant scattering model [10,12] that attributes the scattering line ID28 at the European Synchrotron Radiation Facility in of the thermal phonons to the local excitation of the guests. Grenoble [14]. By using the silicon [11,11,11] reflection order Central to the resonant scattering model is the suggestion of for both the monochromator and the analyzer an overall enersymmetry avoided crossings between acoustic lattice gy resolution at full width at half maximum of 1.5 meV at phonons and “localized” guest branches [12]. The existence of 21.747 keV was achieved. Inelastic scans were then recorded low energy “localized” guest vibrations has been confirmed at 100 K in the energy region of 220–20 meV with momentum by several quasi-elastic incoherent inelastic neutron scattertransfers of 1.5 nm-1 〈 ⎢Q ⎢〈11.0 nm-1. These momentum transing (INS) experiments [13]. However, there was no direct evifers were chosen to cover and extend the measurements dence confirming the crossing of the phonon branches. The beyond the first Brillouin zone. The size of the first Brillouin understanding of the nature of the thermal conductivity zone, determined from the d spacing of the first allowed [110] where localized oscillators are present is important in a wide Bragg peak, is ⎢Qmin⎢=3.8 nm-1. A selection of inelastic x-ray range of materials. For example, efficient thermoelectric spectra (IXS) of methane hydrate at different momentum materials will require low thermal conductivities as one of transfers are shown in Fig. 7. their essential properties and this will often be determined by the ‘rattling’ components giving rise to localized vibrations of The spectra display a well defined dispersive mode. The the material. position of the dispersive mode is found to scale linearly with the momentum transfer in the ⎢Q ⎢range 〈6.0 nm-1 (Fig. 7). Since most simple clathrate hydrates, such as methane and This dispersive excitation can be identified with the longiturare-gas hydrates commonly only exist in polycrystalline dinal acoustic (LA) host-lattice phonon branch. From the form, it is difficult to grow a large enough single crystal for slope of the dispersion of the longitudinal acoustic mode, an the measurement of the phonon dispersion curve using neuorientationally averaged sound velocity of 3950±50 m/s can 308 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 309 ARTICLE DE FOND ( PHONON SPECTROSCOPY ... ) sion, ranging from 6.9±0.2 meV at ⎢Q ⎢=8.0 nm-1 to 9.5±0.3 meV at ⎢Q ⎢= 11.0 nm-1. The spectra in the momentum transfers beyond the first Brillouin zone, ( ⎢Q ⎢= 5 to 11 nm-1) reflect excitations of both transverse and longitudinal phonons and expected to reflect features of the density of states (DOS) of methane hydrate. This is illustrated in Fig. 8 by comparing the INS spectrum of methane hydrate in deuterated water with the IXS spectra obtained at high momentum transfers. Fig. 7 Comparison of experimental x-ray inelastic scattering spectra of methane hydrate with momentum transfers within (a) the first and (b) beyond the first Brillouin zone (b) with the theoretical spectra computed from lattice dynamics calculations (c). be deduced. At ⎢Q ⎢≈3 nm--1, a second non-dispersive peak at 5 meV becomes visible. Both the position and intensity of this peak do not show strong variation with increasing momentum transfer. A plot of the dispersion relation of the dispersive lattice mode and the nondispersive guest modes is shown in Fig 8. In comparison to previous INS spectra, this feature in the IXS is assigned to the guest vibrations inside the large cage. It is important to note that these vibrations appear in the IXS spectrum after the intersection with the LA lattice mode at ⎢Q ⎢≈2.5 nm-1, which is well within the first Brillouin zone. This behavior is pointing towards a coupling between the localized guest vibrations and the acoustic host lattice modes. Additional information can be obtained from spectra at higher momentum transfers (Fig. 7). Due to the better contrast, the LA mode moves out of the energy window, Fig. 8 additional broad features can be observed at around 7–10 meV. It is found that the energy position of this peak displays a slight disper- The assignment of the IXS is in complete agreement with the calculated orientationally average scattering function S(Q,ω) using eqns. 4-6 (Fig. 7). The dynamical structure factor G(Q,q,j) was calculated from the eigenvectors generated from a lattice dynamics simulation and averaged over 239 different directions within the ⎢Q ⎢ range of 0 – 10 nm-1.. The phonon wave vector q was chosen such that q=GQ, where G was an appropriate lattice vector for Q values beyond the first Brillouin zone. Thus, the intensities of both the longitudinal and the transverse modes are calculated. The calculated Q-averaged phonon-dispersion is also in substantial agreement with experiment (Fig. 8). Methane hydrate transforms to two high pressure phases MH-II and MH-III at moderate pressure of 1 and 2 GPa, respectively [15]. High-energy resolution inelastic x-ray scattering and diamond anvil cell (DAC) techniques can be used to determine the orientationally averaged compressional sound velocities. Combining A comparison of experimental (left side) and calculated (right side) averaged longitudinal acoustic phonon dispersion curves of methane hydrate. Note the observed and predicted anti-crossing at Q~2nm-1. The circles and triangles on the experimental curves are points on the acoustic branch and the localized guest vibrations, respectively. LA PHYSIQUE AU CANADA septembre / octobre 2006 309 Sept06-FF.qxd 11/7/2006 2:07 PM Page 310 FEATURE ARTICLE ( PHONON SPECTROSCOPY ... ) anvil cell. As the sample is composed of 35% MH-III and 65% ice VI, the peak at 8.9 meV is assigned to the LA phonon branches of MHIII and ice VI. At ⎢Q ⎢≥ 6.5 nm-1 an additional excitation can be observed at ca. 12 meV. In the observed ⎢Q ⎢ range this mode displays only a very weak dispersion and is assumed to have a constant energy 11.7±0.2 meV within the experimental error. At the highest displayed wave vector ⎢Q ⎢=8.9 nm-1 a shoulder at ≈18 meV can be observed. Taking the relatively high momentum transfer into account, it is reasonable to assume that both are related to transverse phonons in either ice VI or MH-III. With the successful separation of the methane hydrate from the ice contributions, the phonon dispersion curves for MH-II and ice VI at 17 and 21 kbar, and for MH-III at 21 kbar was obtained. The longiFig. 9 Experimental IXS spectra for high pressure phases of methane hydrate. (a) MH-II tudinal, or compressional, velociand (b) MH-III. The arrows indicate highly dispersive excitations from the diaties of sound can be derived by fitmond anvil cell. ting a sine function to the dispersion curves and determining the these findings with the results from diffraction experiments, slopes in the ⎢Q ⎢6 0 limit. An orientationally averaged the elastic properties of the high-pressure phases of methane compressional sound velocity of ice VI=4700±100 m/s was hydrate can be derived [16]. determined for ice VI at T=298 K and 17 kbar. For MH-II, an orientationally averaged compressional sound velocity of A selection of inelastic x-ray spectra of the MH-II and MH-III 4200±100 m/s was deduced from the phonon dispersion samples at different wave vector transfers, or ⎢Q ⎢, between curve. For the MH-III sample, the orientationally averaged -1 2.0 and 8.9 nm are shown in Figs. 9a and 9b, respectively. compressional sound velocities at 21 kbar and T=298 K for ice The IXS data represent the orientationally averaged longituVI are 4950±100 m/s and 4600±100 m/s for methane hydrate, dinal acoustic dispersion. In the case of the MH-II, the enerMH-III. For a randomly oriented, non-textured powder the gy positions of the inelastic excitations were determined to be compressional velocity of sound, which is the same as the ori-1 E=5.9 meV,15.8 meV, and 22.5 meV at ⎢Q ⎢=2.0 nm . The entationally averaged longitudinal sound velocity, is defined two high-intensity peaks at E=15.8 meV and E=22.5 meV disas ν p = C / ρ where C is a combination of the elastic conplay strong dispersions and cannot be observed at wave vecstants (effective elastic modulus) and ρ is the density -1 tor transfers ⎢Q ⎢〉5 nm . From the ⎢Q ⎢ dependence of the of the material. On the other hand, the compressional energy positions of these two excitations, sound velocities of and shear sound velocities can as well be expressed by ≈12 000 m/s and ≈17 000 m/s were determined. These peaks 4 are assigned to the transverse and longitudinal acoustic ν p = ( 1 /ρ ) ⎛⎜ B + G ⎞⎟ , and ν s = G / ρ where B is the 3 ⎠ ⎝ phonons of the diamond anvils. The third dispersive excitais the bulk modulus and G is the shear modulus. The pressure tion is assigned to the orientationally averaged LA phonon evolution of B and G were determined separately from x-ray branches of the sample. As the sample is composed of diffraction measurements [17]. The bulk modulus and density 61% MH-II and 39% (mole) ice VI, this dispersive excitation -1 are B(MH-II)=14.4 GPa, r(MH-II)=1.07 g cm-3 and B(MHat 5.9 meV, at ⎢Q ⎢=2.0 nm has contributions from the III)=23.6 GPa, ρ(MH-III)=1.16 g cm-3. Therefore, for MH-II, LA phonon branches of both ice VI and MH-II. For -1 C =18.9±0.8 GPa, G=3.4±0.6 GPa, and vs =1800±150 m/s and ⎢Q ⎢≥ 6.9 nm an additional non-dispersive excitation is for MH-III, C=24.5±1.0 GPa, G=0.8±0.7 GPa, and observed at 11.9±0.2 meV and is tentatively assigned to the vs =800±400 m/s. TA phonons of either ice VI or MH-II. In the case of the MH-III at ⎢Q ⎢=2.8 nm-1 three inelastic excitations at E = 8.9, 22.2 and 31.8 meV can be observed. As in the case of MH-II, the two intense excitations at higher energies are assigned to the acoustic phonons of the diamond 310 PHYSICS IN CANADA The IXS experiments successfully demonstrated the occurrence of symmetry avoided crossing between the acoustic phonon branches of the lattice vibrations and the “localized” motions of the guest. However, the effects of the resonant scattering cannot be characterized. To resolve this problem a September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 311 ARTICLE DE FOND ( PHONON SPECTROSCOPY ... ) Fig. 10 Experimental NRIX spectra (a) and the “harmonic phonon density of states” (b) derived from the corresponding experimental spectra for enclathrated 83Kr in the clathrate hydrate. site-specific method sensitive only to the guest motions is required in order to provide an unambiguous characterization of the consequence of the guest–host interactions. The NRIXS technique can be used to characterize the dynamics of the guest atoms if it has low-lying nuclear levels that can be excited by synchrotron radiation. This is the case for 83Kr, which has a nuclear level of 9.4 keV so that nuclear resonance can be excited using synchrotron radiation sources. Therefore, for the Kr clathrate hydrate, nuclear resonant inelastic scattering is sensitive only to the 83Kr guest atoms in the clathrate cages and the ice lattice forming the cages is effectively invisible. Because of this unique property, a clathrate hydrate of Kr is studied. It is possible to give a detailed characterization of the localized vibrations of Kr atoms The NRIXS measurements were performed at sector 3-ID at the Advanced Photon Source [18]. A four-silicon-crystal highresolution monochromator based on a weak-link structure with 1 meV energy bandwidth was used in the experiment. The high resolution and high throughput of this high-resolution monochromator make it possible to measure the lowenergy phonon modes of 83Kr in the clathrate at its natural abundance (11.5%) of Kr. The experimental NRIXS spectra S(ω) (eqn. 7) of the Kr clathrate hydrate at 25, 63 and 158 K are shown in Fig. 10. The positive energy is the energy gain (phonon creation) and the negative is the energy loss (phonon annihilation) spectra. To extract information concerning the Kr vibration density of states (VDOS), the observed spectra were subjected to analysis based on harmonic approximation. This procedure has been used successfully for the determination of the VDOS for a variety of materials under ambient and extreme conditions. For example the Kr VDOS of solid Kr under high pressure obtained from NRIXS experiments are in excellent agreement with theoretical calculations. In the present case, following the same procedure, the extracted Kr VDOS yields an unphysical negative density of states (Fig. 10b) at 6–8 meV at the two lowest temperatures of 25 and 63 K. The failure of the harmonic model indicates a complete breakdown of the harmonic approximation. Therefore, the vibrations of Kr are clearly intrinsically anharmonic. The observable in a NRIXS experiment is related to the Fourier transform of the self-intermediate scattering function, L(k0 ,t), where k0 is the incident radiation wave vector and t is time. For systems with large anharmonicity, the harmonic assumption is no longer valid and the calculation of L(k0 ,t) from molecular-dynamics simulations is necessary for a direct comparison with experiment [6,18] L(k 0 , t ) = 1 N ∑e ik ⋅( ri ( t )− ri ( 0 )) = e ik0 ⋅ri ( t ) e − ik0 ⋅ri ( 0 ) [8] i The sum is taken over the N particles in the simulation box and ri(t) is the position of the ith atom at time t and is obtained from the trajectory of a molecular-dynamics simulation. The calculated S(ω) are convolved with the experimental resolution and compared with the background subtracted NRIXS spectra in Fig. 11a and b. The low-energy feature (~1–1.5 meV) in the calculated S(ω) is associated with the vibrations of Kr in the large cages. Owing to limited instrumental resolution, this peak is overwhelmed by the very strong elastic (zero-energy) peak and cannot be accurately extracted from the experimental data. Apart from this shortcoming, the higher-energy peak predicted at ~4.2 meV is clearly observed in the experiment. This peak is mainly attributed to the localized vibrations of Kr in the small cages. Molecular-dynamics calculations also reveal several weak features at ~2 meV and at ~2.8 meV. These features are also discernible from the NRIXS spectra. LA PHYSIQUE AU CANADA septembre / octobre 2006 311 Sept06-FF.qxd 11/7/2006 2:07 PM Page 312 FEATURE ARTICLE ( PHONON SPECTROSCOPY ... ) ω) for a Kr clathrate. Note the Fig. 11 A comparison of experimental (a) and theoretical (b) functions S(ω apparent absence of the predicted peak at ~0.8 meV in the experimental spectra is due to errors in the background removal of the large central elastic peak. SUMMARY In this short article, some applications of inelastic x-ray techniques using synchrotron radiation are illustrated through a specific example on the characterization of guest-host interaction in clathrate hydrates. It is shown that IXS experiments provide complementary information to neutron scattering on the phonon spectra and help to establishes that the avoidedcrossing of the “localized’ guest vibrations with the acoustic phonon branches of the host lattice with the same symmetry is responsible for the guest–host interactions. In combination with site specific NRIXS measurements and theoretical calculations, the unexpected anharmonic nature of the guest vibrations is clearly demonstrated. This large anharmonicity is the cause of the very low thermal conductivity of the clathrate hydrates and is a direct consequence of the coupling between the host and the guest vibration. 3. 4. 5. 6. 312 L. van Hove, Phys. Rev. 95, 249 (1954). B.N. 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Katoh, K. Aoki, K. Nagashima, Y. Yamamoto, and T. Yagi, J. Chem. Phys. 115, 7066 (2001). J.S. Tse, D.D. Klug J.Y. Zhao, W. Sturhahn, E.E. Alp, J. Baumert, C. Gutt, M.R. Johnson and W. Press, Nature Materials 4, 917 (2005). Sept06-FF.qxd 11/7/2006 2:07 PM Page 313 ARTICLE DE FOND ( SYNCHROTRON ADVANCES ... ) SYNCHROTRON ADVANCES AT THE FRONTIERS OF FOOD PHYSICS: STUDIES OF EDIBLE FATS SUCH AS CHOCOLATE UNDER SHEAR by G. Mazzanti, S.E. Guthrie, A.G. Marangoni and S.H.J. Idziak C hocolate and other lipid food materials can form different ural fats. This peculiar behaviour is very important for the crystalline structures (polymorphs) depending on the temchocolate industry, yet, despite great advances done by modperature and shear profiles used during their manufacturing. ern science, many of the reasons for its behaviour are unclear. These structures determine the quality of the products. Until Of particular interest is the number of distinct structural recently, only very empirical knowledge existed on the effects phases that it forms and the effect that shear flow has on the of shear. The use of synchrotron x-ray diffraction has allowed rate and paths of transformation between these different crysfor pioneering advances in our undertalline phases. This is only one example standing of the mechanisms of struc- The use of synchrotron x- of structure in foodstuffs, a field that ture formation during the crystallizing offers very exciting and complex chalof edible multicomponent lipid sys- ray diffraction has allowed lenges in soft condensed matter tems under shear. as has been recently highlightfor pioneering advances in physics, ed in very prestigious publications [1,2]. INTRODUCTION our understanding of the The food structures result from the combination of many different compoWhen the western botanists discov- mechanisms of structure nents in a variety of phases related ered the cacao trees in the new world, through several time and length scales. formation during the crysthey named them “Theobroma”, the Common food items such as butter, food of the gods, after the name given tallizing of edible multicommargarines, lard, shortenings, chocolate by the Mayas. The mystery that still and spreads rely on microstructured fat surrounds that ancient civilization ponent lipid systems under networks to provide excellent mouthsomehow remains also in the very shear. feel, sensorial properties and physical peculiar crystalline structure and attributes [3-6]. The levels of these strucphase behaviour that cacao butter, the tures are illustrated in Figure 1. main structural component of chocolate, displays among natThough it may not be obvious to many people who consume these foods, natural fats form real crystals. These crystals form clusters, which grow into larger aggregates called flocs, which eventually produce the fractal solid network that we can see, spread and chew. The characteristics of the microstructures depend largely on the type of crystal formed by the molecular composition of the fat (i.e. lipids) [7] as well as their crystalline size and spatial distribution [8]. Fig. 1 Schematic representation of different levels of structure in a bulk fat. The crystallite may have one or more domains of a thickness ξ, composed in turn of several lamellae of thickness d. Each lamella is formed by individual fat molecules called triacylglycerides (TAGs) organized with a characteristic longitudinal stacking and lateral packing. The type of crystals formed depends on the chemical composition of the material. The principal lipid components of most edible fats are triacylglycerols (TAG), resulting from the esterification of the long hydrocarbon chain fatty acids upon a glycerol backbone. Natural fats contain a broad variety of fatty acids, depending on the kind of fat, its geographic origin and the techniques used to extract and purify the fat. Thus, they are multicomponent systems, often with several thousand types of molecules. In addition, minor components, mostly polar lipids, act as impurities that alter the phase behaviour of the fats [9]. Some of these minor components, commonly referred to as surfactants and emulsifiers, are often employed as natural additives to improve the characteristics of the materials. G. Mazzanti[1], S.E. Guthrie[2], A.G. Marangoni[3], S.F.J. Idziak[2], ([email protected]), [1] Dalhousie University, Halifax N.S., [2] University of Waterloo, Waterloo, ON, [3] University of Guelph, Guelph, ON. LA PHYSIQUE AU CANADA septembre / octobre 2006 313 Sept06-FF.qxd 11/7/2006 2:07 PM Page 314 FEATURE ARTICLE ( SYNCHROTRON ADVANCES ... ) Fig. 2 Cartoon of two main types of longitudinal stacking of TAGs molecules, corresponding to (a) two (2L) or (b) three (3L) fatty acid lengths for tripalmitin. The dark atoms represent carbon, the light ones oxygen. The resulting lamellae have very different d-spacings. The complexity is increased by the fact that the same fat can crystallize in different classes of crystals. This peculiarity of some materials (that they can be crystallized with different spatial arrangements of the molecules in the crystals) has been called polymorphism, while the types of crystals are referred to as polymorphs, or polymorphic forms. The natural fat systems display a rich and complex crystalline polymorphism, strongly dependent on heat, mass and momentum transfer conditions during crystallization. TAG molecules in a fat crystal. These structures, and their crystallization behaviour, bear strong resemblance to those of alkanes [10-12], since the long hydrocarbon chains are the dominant portion of the molecules. The metastable α form, analogous to the rotator phase in alkanes [10], is associated with a hexagonal unit cell as shown in Figure 3a, where a segment of the hydrocarbon chain is shown represented by two consecutive carbon atoms (black dots) and their corresponding hydrogen atoms (white dots). The β’ polymorphic arrangement is consistent with an orthorhombic unit cell [13,14] as described schematically in Figure 3b, while the β polymorph has a triclinic unit cell [13], as illustrated in Figure 3c. Thus knowledge of the lateral packing (e.g. α, β’, β) and the longitudinal stacking (e.g. 2L) is required to fully describe the crystalline structure. Margarines and shortenings contain usually a mixture of β’ and β crystals. The crystal size and type is crucial for the structure of margarines, because an excess of β crystals results in a sandy texture and poor spread and melting characteristics. The polymorphic forms for cocoa butter are more complicated, and they have been traditionally numbered I to VI in roman numerals. The ideal crystal type for chocolate is in a type of β form known as form V (or βV) [15,16]. This polymorph is quite stable during storage, and melts in the mouth but not too fast at the touch of the hand. For all fats in general, the less stable polymorphs have a lower free energy barrier of formation, thus can be formed more readily than the more stable polymorphs [7], if the cooling rate is fast enough. Thus, very often to obtain a given polymorph one has to crystallize first one of the more unstable (and often undesirable) ones, which then has to be eliminated. This means that the state diagrams of these materials are time dependent [17], and give rise to processes such as chocolate tempering. This peculiar characteristic makes the phase landscape of natural multicomponent lipids extremely rich and complex, and makes the determination of an equilibrium phase diagram extremely difficult, if not impossible. Instead, state diagrams are used in lieu of phase diagrams and do not give the equilibrium behaviour, but rather give To better understand how this polymorphism happens, we need to look at the way the molecules are arranged in the crystals. The TAG molecules form lamellar structures by stacking pairs of molecules in the longitudinal direction, usually of two (2L) or three (3L) fatty acid lengths as shown in Figure 2. This produces crystals that form disclike structures with molecules arranged perpendicular to the flat surface. The more common polymorphic forms of natural fats, analogous to those formed by pure TAGs, are usually termed α, β’ and β in order of their increasing melting point, packing density and thermodynamic stability. This polymorphism is a conse- Fig. 3 Top view of the lateral packing of the fatty acid chains, showing the three characterisquence of the variety of tic sub-cells: (a) the hexagonal phase α, (b) the orthorhombic phase β’ and (c) and the arrangements of lateral packtriclinic phase β. ing of the CH2 groups of the 314 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 315 ARTICLE DE FOND ( SYNCHROTRON ADVANCES ... ) smaller repeating spacings of the lateral packing (Figure 3) produce wide angle x-ray reflections, while the longitudinal long spacings (Figure 2) produce x-ray reflections in the small angle region. These small angle reflections provide information on the longitudinal packing of the TAG molecules in the crystals, i.e. whether they are in the 2L or 3L arrangement. Very few exact structures have been completely elucidated to date, but the characteristic signatures of the different polymorphs have been widely documented [19,21]. As rich as the state diagram in Figure 4 may appear, it was developed under static conditions (no shear applied) and at a fast cooling rate. However, both cooling rates and flow conditions greatly affect the phase behaviour of natural fats, by drastically modifying the initial steps of the crystallization process. These steps depend on the dynamics of structure formation under different temperature and shear treatments [22,23]. Therefore, to truly understand how these structures are formed, it is necessary to study their development in time with enough detail. Fig 4 Time-Temperature state diagram of cocoa butter cooled very rapidly (Reprinted with permission from [8], © 2003 American Chemical Society). phase behaviour along a given timeframe, as illustrated in Figure 4 for cocoa butter [8,18]. In this paper we will continue to refer to the individual structures as phases, or forms, as is conventional in this area of study. The reader can perform a simple experiment to examine this phase behaviour by melting some chocolate and pouring three large drops onto a plate. Upon hardening, the drops will have a waxy, unpleasant mouth feel and will tend to melt quite profusely in the hand as well as the mouth (phase α). If the other drops are left on the plate at room temperature for several days, they will develop into the glossy phase β(V) which tends to melt less in your hands. After several months of poor storage on the plate, with temperature fluctuations, the third drop of chocolate will start to bloom, or form a white powdery texture on the surface. The represents the undesirable transition into phase β(VI). Melting point determinations are often used to classify these polymorphic forms, since the less stable a polymorph is, the lower its melting point. However, these Fig. 5 structures can only be identified, characterized and differentiated in an unambiguous manner by their distinctive xray diffraction patterns. The Synchrotron x-ray diffraction (XRD) allows probing the crystalline structures directly, in-situ and in real time, thus providing irreplaceable information necessary to understand the genesis and dynamics of structures that depend on the polymorphic state of the material [23]. To study the formation of these structures we need to capture x-ray diffraction patterns during the crystallization process, and this is only possible with the intensity provided by a synchrotron source. The experiments start from the liquid at high temperature and progress as the material is observed during the cooldown and, over time, at the final crystallization temperature. The use of synchrotron radiation has permitted the development of time resolved studies in the crystallization of fats, (a) The Couette cell consists of two concentric cylinders made of 0.5mm thick Lexan walls. The internal cylinder is stationary and has water flowing inside for temperature control. The outer cylinder rotates. (b) The synchrotron x-rays traverse the sample in a tangential manner before striking a two dimensional CCD x-ray detector. (c) The shear profile developed by the velocity gradient between the moving and stationary cylinders is given by γA = u / δ. (Adapted with permission from [22], © 2003 American Chemical Society). LA PHYSIQUE AU CANADA septembre / octobre 2006 315 Sept06-FF.qxd 11/7/2006 2:07 PM Page 316 FEATURE ARTICLE ( SYNCHROTRON ADVANCES ... ) which has opened a new era in the understanding of these processes. The pioneering static experiments [24] have evolved to include combined techniques such as DSC [25] and more recently the application of shear [22,26]. In our research team this has been accomplished using a Couette shear cell. Although the challenges due to the geometry of the cell and the variable conditions of the experiments are difficult, the results have been extremely rewarding so far, placing our Canadian group at the world forefront of this line of research. In this paper, we review our recent work studying the effects of shear on the crystallization dynamics of fat. Careful analysis of the x-ray diffraction patterns has led us to the discovery of new phases and transition mechanisms in cocoa butter [27], and to the mathematical modeling, for the first time, of the combined phase transition in palm oil and milk fat [9,28] as well as a description of orientation in fats. X-RAY SHEAR CELLS A custom fabricated x-ray compatible Couette shear cell was used to perform shear measurements in order to develop relatively high shear rates. This cell consists of two concentric Lexan cylinders, the outer of which rotates at a controlled rate while the inner remains stationary as shown in Figure 5a. A specially designed temperature controlled water system was developed to provide very good temperature control as well as the carefully controlled temperature ramps necessary while cooling the fat. The walls of the Lexan cylinders are sufficiently thin (and relatively high energy 1.1 Å wavelength x-ray were used) to allow x-ray to pass through and scatter from the sample as shown in Figure 5b. Shear rates (u/δ in Figure 5c) up to 2880s-1 were attainable with this system [22]. All measurements reviewed here were conducted at the ExxonMobil beamline X10A at the National Synchrotron Light Source in Brookhaven National Laboratory, Upton, NY, USA. A Bruker 1500 two-dimensional (2D) CCD detector was used to capture diffraction patterns. One important advantage of using a 2D detector is the possibility of studying orientation effects which can be seen by the anisotropic Fig. 6 316 Two-dimensional diffraction patterns of cocoa butter’s phase II (a) crystallized at 17.5 °C. (a) Static crystallization (b) Under a shear rate of 1440s-1. The diffraction ring occurs at a scattering angle θ = 1.27 deg, or q = 0.127 Å-1, which corresponds to a 2θ d-spacing of 49.47 Å indicating that the molecules are arranged in a 2L conformation in the layers. PHYSICS IN CANADA scattering illustrated in igure 6b, indicating orientation, as opposed to the uniform scattering seen in Figure 6a, indicative of scattering by an unoriented, powder-like material. Two dimensional x-ray images are useful for quickly evaluating the qualitative behavior of the fat. For more detailed quantitative analysis, the x-ray diffraction intensity from each 2D diffraction image was radially averaged and plotted as a function of the reciprocal lattice spacing q, where, 2 π 4π q= = sin θ , d is the interplanar spacing, and 2θ is the d λ Bragg scattering angle as seen in Figure 5b. This radial averaging is accomplished by circular integration of the x-ray intensity at each value of the radius. Also, azimuthal (or mosaic) plots were derived from the 2D diffraction patterns, by plotting the intensity measured along the circumference (χ angle) of the diffraction rings at a fixed radius. This allowed for the study of the crystalline orientation in hardening fats [22]. Time dependent crystallization studies can yield tens of thousands of two dimensional diffraction patterns, making data analysis a complex task. We designed a custom plug-in program for the ImageJ software, typically used by the optical microscopy community, which was used to perform radial averaging as well as the other data transformations done on the 2D images [22]. CRYSTALLINE ORIENTATION Figure 6a shows a typical small angle diffraction pattern of cocoa butter’s phase II (or α) crystallized statically, while Figure 6b shows the same phase crystallized under a shear rate of 1440s-1. The anisotropy of the scattering intensity around the ring clearly indicates crystallite orientation in the sheared sample, whereas the sample crystallized statically presents uniform intensity around the diffraction ring. The orientation of the particles is also evident from the x-ray scattering at small angles seen near the beamstop. Azimuthal Fig. 7 September / October 2006 Azimuthal intensity profiles from phase a of palm oil and cocoa butter, crystallized under a shear rate of 1440s-1, as a function of the azimuthal angle around the diffraction ring indicating the increased orientational ordering seen in cocoa butter. Sept06-FF.qxd 11/7/2006 2:07 PM Page 317 ARTICLE DE FOND ( SYNCHROTRON ADVANCES ... ) formation. The initial nucleation is characterized by the appearance of nuclei far apart from each other. These platelet-like nuclei [29] do not interact with each other. As they start to grow, the system becomes a disperse suspension of rapidly growing crystals. Eventually the crystals start forming clusters as they impinge upon each other. This produces aggregates crystallized under static conditions at a fast cooling rate, which are not spherulites, but rather clusters of randomly oriented crystallites as seen in Figure 1. Fig. 8 Two-dimensional diffraction patterns of cocoa butter’s phase V (a β polymorph) crystallized at 17.5 °C under a shear rate of 360s-1. (a) Pure cocoa butter. (b) Commercially available dark chocolate. (Adapted with permission from [22], © 2003 American Chemical Society). plots derived from the 2D images are shown in Figure 7 for palm oil and cocoa butter under a shear rate of 1440s-1. As can be seen, the degree of orientation, as determined from the width of the peak seen in the azimuthal scan (narrower is better oriented), is dependent on each particular material. All four fat systems studied displayed orientational ordering under shear, strongly suggesting that the shear-induced orientation effect is universal to all fats. In most cases, this orientation effects were evident from the onset of crystallization but did depend on shear rate [22]. This orientation was also observed in real chocolate, and not only in pure cocoa butter. Figure 8a shows a typical diffraction pattern for cocoa butter crystallized under shear after the phase transition to phase β(V). A commercially available dark chocolate cooled under a shear rate of 360 s-1 produced the diffraction pattern shown in Figure 8b demonstrating that the orientation effect remains after the transition to phase β(V). Recall that phase β(V) gives chocolate its ideal sensory attributes. Current studies indicate that this preferred orientation remains for long periods of time. Also seen in Figure 8b is the greatly enhanced smallangle scattering at the center of the chocolate scattering pattern which is due to the large amount of fine particulate matter present in real chocolate, such as cocoa powder and sugar. To understand how the orientation of fat crystallites happens, the different stages of the crystallization Fig. 9 process of these multicomponent lipid materials can be described. During its crystallization from the liquid state, the fat material goes through different steps, beginning with nucleation, and followed by unhindered growth and structure The presence of a moderate shear field hinders the formation of these clusters, but the exact response depends on the composition of the system and processing conditions, as illustrated by the different response of palm oil and cocoa butter in Figure 7. The orientation of suspended particles in a flowing system depends on the interaction of shear, inter-particle, and Brownian forces [30]. In low volume fraction particle suspensions, like the ones present at nucleation and the early stages of crystallization, inter-particle forces are negligible. Therefore, the distribution of particle orientations results from the interplay between ordering induced by shear forces and disordering induced by Brownian forces. If shear forces are prevalent, a particle rotates slowly when nearly parallel to the direction of flow, and much faster when perpendicular to it, resulting in a time-averaged distribution preferentially parallel to the direction of flow. Triacylglycerol systems tend to crystallize initially forming small disc-like platelets [29], so it is reasonable to assume that the nuclei are platelet-like shaped. The time dependent x-ray diffraction pattern analysis is therefore consistent with the formation of small asymmetric crystals, which in the presence of a shear field adopt a non-random distribution around an average preferred orientation (Figure 9a). Weak or no orientation was observed at low shear rates either due to a random distribution of anisotropic crystals (Figure 9b) or the formation of spherical particles upon platelet aggregation (Figure 9c). This process can be Idealized schematic of the behaviour of platelet crystallites. a) Under high shear rates, the crystallites adopt a preferred orientation parallel to the walls of the cell, as long as the shear forces prevail over the segregation and adhesion forces. b) At very low shear the crystallites may just tumble in the flow, since the segregation forces prevail over shear and adhesion forces. c) If the adhesion forces between crystallites prevail over the shear and Brownian forces, the crystallites will form spherical clusters. (Adapted with permission from [22], © 2003 American Chemical Society). LA PHYSIQUE AU CANADA septembre / octobre 2006 317 Sept06-FF.qxd 11/7/2006 2:07 PM Page 318 FEATURE ARTICLE ( SYNCHROTRON ADVANCES ... ) formally described using the concept of the Peclet number [22]. PHASE TRANSITION ACCELERATION A very important effect of shear forces is the acceleration of the transformation of crystalline fats to more stable polymorphs [22,26,31-33]. For example, the times required for the a to b’ transition in milk fat, milk fat TAGs and palm oil were reduced by up to an order of magnitude in sheared samples relative to statically crystallized samples (Figure 10 a,b,c). Other interesting findings include the comparison between milk fat TAGs and native milk fat, that suggests that polar lipids present in the native milk fat hinder crystallization events, stabilize the α phase, and delay the formation of the more stable β’ phase. Cocoa butter displays a very rich and complex set of polymorphic transformations. As illustrated in Figure 10d, under static conditions, phase α (II) persists for approximately 75 minutes while phase β’(IV) starts to emerge after 50 minutes. The desirable β (V) form of cocoa butter, present in high quality chocolate, requires at least an additional 15 hours to form through the tempering process [18,34]. However, when cocoa butter was crystallized under a shear rate of 1440s-1, the formation of the β’(IV) phase was not observed at lower temperatures, whereas the β(V) phase formed in less than 20 minutes [16,22,26,27]. The persistence time and the relative amount of phase α (II) remaining after the beginning of the phase transition was reduced as shear was increased, and at 1440 s-1 no evidence of the presence of phase α (II) was observed after the phase transition. This is especially important for the confectionery industry where a reduction in the time required to induce the formation of desirable crystalline structures is extremely valuable. At higher temperatures, the relative concentration of phases depends on the combination of shear rate, cooling rate, final crystallization temperature and time [27]. MATHEMATICAL MODELING OF THE PHASE TRANSITIONS Integrated peak intensities derived from the 2D x-ray diffraction patterns can be used to describe quantitatively the phase transition between α and β’ in palm oil, milk fat and similar systems (margarines and shortenings, for example) using a model based on the competition of three events [28]. The first event is the crystallization of phase α from a fraction of the liquid, that will be denoted A. This assumes that only a certain fraction of the original material can crystallize in phase α, mostly composed of the molecules with the highest melting temperature. The second event, after the onset of phase β’, is the crystallization of phase β’ from the liquid fraction. Phase β’ can be formed from the molecular composition found in the liquid fraction “A” as well as from an additional liquid fraction B. The third event is the direct transformation of existing phase α into phase β’. The concept of the solid fat content (SFC), which defines the relative fraction of solid material in the fat is useful to describe the amount of crystallized material, as a significant fraction of a “solid” fat such as butter is actually in the liquid state. The SFC was approximatFig. 10 Relative crystalline content represented by X-ray integrated intensity of the diffrac- ed to be proportional to the total tion peaks as a function of time. Phase α (circles) and phase β’ (squares) are for (a) integrated intensity under the xmilk fat, (b) milk fat triacylglycerols, and (c) palm oil. (d) Phase α (II) (circles), ray diffraction peak, even under phase β’(IV) (squares), and phase β (V) (triangles) are for cocoa butter. The results conditions of weak orientation. from static experiments are represented by open symbols, whereas the results from The driving force is the supersatthe experiments under shear are represented by solid symbols. It can be clearly uration σ defined as the ratio appreciated that the transition between phases happens much earlier and faster between the mass of the untrans-1 when the materials are crystallized under a shear rate of 1440 s . (Adapted with formed material (liquid or cryspermission from [22], © 2003 American Chemical Society). 318 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 319 ARTICLE DE FOND ( SYNCHROTRON ADVANCES ... ) The initial conditions are A t=0 = A*, B t=0 = B* and αSFC t=0 = 0. The system of differential equations was integrated numerically in MATLAB® and fit to the high resolution x-ray diffraction data. The fits were remarkably good for the experiments at different temperatures and shear rates, as seen in Figure 11 where the solid line represents the fit. The effort represents the first time that the multiple phase transitions in a real fat system have been successfully modeled. talline α) and the total mass of the material potentially crystallizable. The equilibrium value that the SFC tends to is called SFC*. The supersaturation is defined by Eq. ( 1). σ≈ SFC * −SFC SFC = 1− SFC * SFC * ( 1) The supersaturation σ is considered to follow the differential form of the Avrami equation [35] (also known as the Johnson-Mehl-AvramiErofeev-Kolmogorov (JMAEK) model [36]) given by: ni − 1 ∂σi = −ni ⋅ ki ⋅ σi ⋅ ⎡⎣ − ln ( σi ) ⎤⎦ ni ∂t (2) Where k is a time scaling constant and n is a Fig. 11 Solid fat content (SFC,%) of-1palm oil crystallized at 22°C and 90 s as a growth mode exponent for the ith phase that is function of time, estimated from the CONCLUSION AND FURcrystallizing (e.g. α, β’). The phase behavior of integrated intensities. The open THER DIRECTIONS the crystallizing fats was postulated to proceed squares represent phase α and the as follows: Phase α nucleates from the melt and The discovery of new areas in open triangles phase β’. The solid grows from a fraction of the liquid called A*. At line is the model estimate SFC for the fascinating world of the some later time, which depends on the shear phase α and for phase β’. soft condensed matter physics rate, the α crystals act as nucleation sites for the of edible materials has been formation of β’ crystals. The β’ crystals can made possible by the use of grow from the liquid fraction A*, from another liquid fraction synchrotron x-ray diffraction. In the field of multicomponent B* (of an average lower melting point), and at the expense of bulk lipid systems the finding of orientation under shear and α crystallites. The two liquid fractions, A* and A*+B*, repreits correlation to the reduction of the phase transition characsent the maximum crystallizable liquid that can go, at a given teristic times are particularly important. The possibility of temperature, into each one of the phases α and β’. quantitatively modelling these processes also offers the possibility to improve the design of industrial equipment and proThus the process can be modeled with three differential cedures. The relevance of these findings is therefore of interequations and one balance equation [28] as shown below. est both for the scientist and the engineer. ∂A ⎡ ⎛ A ⎞⎤ = −na ⋅ ka ⋅ A ⋅ ⎢ − ln ⎜ ⎟ ∂t ⎝ A * ⎠ ⎥⎦ ⎣ na − 1 na − nb − 1 ⎧ ⎫ + A B A ⎪ ⎡ ⎤ ⎪ ⎞ nb ⎛ ⎨nb ⋅ kb ⋅ ( A + B) ⋅ ⎢ − ln ⎜ ⎬ ⎟⎥ A + B⎪ ⎝ A * +B * ⎠⎦ ⎣ ⎪⎩ ⎭t > t o β ' Many aspects still await explanation, and it is the task of soft condensed matter physicists to seek them. The development of correlations between shear, temperature, rheology, thermology, structural characteristics and mechanical properties is now under way in our group thanks to the development of new tools such as the split Couette cell [37] and a micromechanical analyzer. REFERENCES ∂α SFC ⎡ ⎛ A ⎞⎤ = na ⋅ ka ⋅ A ⋅ ⎢ − ln ⎜ ⎟ ∂t ⎝ A * ⎠ ⎥⎦ ⎣ na − 1 na 1. 2. − 3. nc − 1 ⎧ ⎫ ⎡ ⎪ ⎛ α SFC ⎞ ⎤ nc ⎪ ⋅ ⋅ ⋅ − ln α n k ⎨ c c SFC ⎢ ⎬ ⎟ ⎜ ⎝ A * ⎠ ⎥⎦ ⎣ ⎪⎩ ⎪⎭ t >t oβ' 4. 5. 6. nb − 1 ⎧ ⎫ ∂B B ⎪ ⎡ ⎪ ⎛ A + B ⎞ ⎤ nb = − ⎨nb ⋅ kb ⋅ ( A + B) ⋅ ⎢ − ln ⎜ ⎬ ⎟ ∂t A + B⎪ ⎝ A * + B * ⎠ ⎥⎦ ⎣ ⎪⎩ ⎭t > t o β ' β 'SFC = ( A * + B*) − ( A + B) − α SFC 7. 8. 9. 10. 11. 12. A. Donald, Nature Materials 3, 579 (2004). R. Mezzenga, P. Schurtenberger, A. Burbidge, and M. Michel, Nature Materials 4, 729 (2005). S.S. Narine and A.G. Marangoni, Phys. Rev. E60, 6991 (1999). S.S. Narine and A.G. Marangoni, Food Res. Intl. 32, 227 (1999). A.G. Marangoni, Phys. Rev. B62, 13951 (2000). A.G. 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Fryer and K. Pinschower, MRS Bulletin 25, 25 (2000). S.T. Beckett, The Science of Chocolate (Royal Society of Chemistry, Cambridge, UK, 2000). J.H. Los, W.J.P. van Enckevort, E. Vlieg, and E. Floter, Journal of Physical Chemistry B106, 7321 (2002). K.F. van Malssen, R. van Langevelde, R. Peschar, and H. Schenk, J. Am. Oil Chem. Soc. 76, 669 (1999). R.L. Wille and E.S. Lutton, J. Am. Oil Chem. Soc. 43, 491 (1966). J. Schlichter-Aronhime, S. Sarig, and N. Garti, J. Am. Oil Chem. Soc. 65, 1140 (1988). K. Sato, Fett-Lipid 101, 467 (1999). G. Mazzanti, S.E. Guthrie, E.B. Sirota, A.G. Marangoni, and S.H.J. Idziak, Crystal Growth & Design 3, 721 (2003). G. Mazzanti, S.E. Guthrie, E.B. Sirota, A.G. Marangoni, and S.H.J. Idziak, in Soft Materials - Structure and Dynamics, edited by J.R. Dutcher and A.G. Marangoni (Marcel Dekker, Inc., N.Y., 2004). M. Kellens, W. Meeussen, R. Gehrke, and H. Reynaers, Chemistry and Physics of Lipids 58, 131 (1991). G. Keller, F. Lavigne, C. Loisel, M. 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Avrami, Journal of Chemical Physics 8, 212 (1940). W.A. Johnson and R.F. Mehl, Transactions of the American Institute of Mining and Metallurgical Engineers 135, 416 (1939). S.E. Guthrie and S.H.J. Idziak, Review of Scientific Instruments 76, 026110 (2005). Sept06-FF.qxd 11/7/2006 2:07 PM Page 321 LIVRES REÇUS BOOK REVIEW POLICY Books may be requested from the Book Review Editor, Andrej Tenne-Sens, by using the online book request form at http://www.cap.ca. CAP members are given the first opportunity to request books. Requests from non-members will only be considered one month after the distribution date of the issue of Physics in Canada in which the book was published as being available (e.g. a book listed in the January/February issue of Physics in Canada will be made available to non-members at the end of March). The Book Review Editor reserves the right to limit the number of books provided to reviewers each year. 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Le Directeur de la critique de livres se réserve le droit de limiter le nombre de livres confiés chaque année aux examinateurs. Il se réserve, en outre, le droit de modifier toute critique présentée afin d'en améliorer le style et la clarité. S'il lui faut reformuler une critique, il s'efforcera de conserver le sens voulu par l'auteur de la critique et, à cette fin, il pourra juger nécessaire de le consulter. BOOKS RECEIVED / LIVRES REÇUS The following books have been received for review. Readers are invited to write reviews, in English or French, of books of interest to them. Books may be requested from the book review editor, Andrej TenneSens by using the online request form at http://www.cap.ca. A list of ALL books available for review, books out for review, and copies of book reviews published since 2000 are available on-line -see the PiC Online section of the CAP's website : http://www.cap.ca. Les livres suivants nous sont disponible pour une évaluation critique. Celle-ci peut être faite en anglais ou en français. Si vous êtes intéressé(e)s à nous communiquer une revue critique sur un ouvrage en particulier, veuillez vous mettre en rapport avec le responsable de la critique des livres, Andrej Tenne-Sens par internet à http://www.cap.ca. Il est possible de trouver électroniquement une liste de livres disponibles pour la revue critique, une liste de livres en voie de révision, ainsi que des exemplaires de critiques de livres publiés depuis l'an 2000, en consultant la rubrique "PiC Électronique" de la page Web de l'ACP : www.cap.ca. GRADUATE TEXTS AND PROCEEDINGS GENERAL INTEREST DARWINISM AND ITS DISCONTENTS, MICHAEL RUSE, Cambridge University Press, 2006, pp8: 316; ISBN: 0-521-82947-X (hc); Price: $30.00. THE TROUBLE WITH PHYSICS: THE RISE OF STRING THEORY, THE FALL OF A SCIENCE AND WHAT COMES NEXT, Lee Smolin, Thomas Allen Publishers, 2006, pp: 343; ISBN: 978-0-618-55105-7; Price: . UNDERGRADUATE TEXTS A SHORT INTRODUCTION TO QUANTUM INFORMATION AND QUANTUM COMPUTATION, Michel Le Bellac, Cambridge University Press, 2006, pp: 167; ISBN: 0-521-86056-3 (hc); Price: $60.00. AN INTRODUCTION TO GENERAL RELATIVITY AND COSMOLOGY, Jerzy Plebanski and Andrzej Krasinski, Cambridge University Press, 2006, pp: 534; ISBN: 0-521-85623-X (hc); Price: $80.00. CLASSICAL MECHANICS, R. Douglas Gregory, Cambridge University Press, 2006, pp: 596; ISBN: 0-521-82678-0 (hc); 0-521-53409-7 (pbk); Price: $120/60.00. SPACE-TIME, RELATIVITY AND COSMOLOGY, Jose Wudka, Cambridge University Press, 2006, pp: 320; ISBN: 0-521-82280-7; Price: $55.00 -hc. THE IDEAS OF PARTICLE PHYSICS: AN INTRODUCTION FOR SCIENTISTS, G.D. Coughlan, J.E. Dodd, B.M. Gripalos, Cambridge University Press, 2006, pp: 254; ISBN: 0-521-67775-0 (pbk); 0-521-84728-1 (hc); Price: $50/100.00. AN INTRODUCTION TO UNCERTAINTY IN MEASUREMENT, L. Kirkup, R.B. Frenkel, Cambridge University Press, 2006, pp: 233; ISBN: 0-52184428-2 (hc); 0-521-60579-2 (pbk); Price: $80/$34.49. CHAOS AND COMPLEXITY IN ASTROPHYSICS, Oded Regev, Cambridge University Press, 2006, pp: 455; ISBN: 0-521-85534-9 (hc); Price: $80.00. CONDENSED MATTER FIELD THEORY, A. Altland, B. Simons, Cambridge University Press, 2006, pp: 624; ISBN: 0-521-84508-4 (hc); Price: $85.00. DISCRETE INVERSE AND STATE ESTIMATION PROBLEMS WITH GEOPHYSICAL FLUID APPLICATIONS, Carl Wunsch, Cambridge University Press, 2006, pp: 371; ISBN: 0-521-85424-5 (hc); Price: $125.00. FINITE-TEMPERATURE FIELD THEORY PRINCIPLES AND APPLICATIONS, Joseph I. Kapusta and Charles Gale, Cambridge University Press, 2006, pp: 428; ISBN: 0-521-82082-0 (hc); Price: $140.00. LIQUID CRYSTALLINE POLYMERS - SECOND EDITION, A. Donald, A. Windle, S. Hanna, Cambridge University Press, 2006, pp: 589; ISBN: 0521-58001-3 (hc); Price: $90.00. PATH INTEGRALS AND ANOMALIES IN CURVED SPACE, Florenzo Bastianelli and Peter van Nieuwenhuizen, Cambridge University Press, 2006, pp: 379; ISBN: 0-521-84761-3 (hc); Price: $120.00. STEPS TOWARDS AN EVOLUTIONARY PHYSICS, Enzo Tiezzi, WIT Press, 2006, pp: 157; ISBN: 1-84564-035-7 (hc); Price: $95.00. WEAK SCALE SUPERSYMMETRY FROM SUPERFIELDS TO SCATTERING EVENTS, H. Baer and X. Tata, Cambridge University Press, 2006, pp: 537; ISBN: 0-521-85786-4 (hc); Price: $80.00. LA PHYSIQUE AU CANADA septembre / octobre 2006 321 Sept06-FF.qxd 11/7/2006 2:07 PM Page 322 BOOK REVIEWS BOOK REVIEWS / CRITIQUES DE LIVRES A GUIDED TOUR OF MATHEMATICAL METHODS FOR THE PHYSICAL SCIENCES, SECOND EDITION, Roel Snieder, Cambridge University Press, 2004, pp: 507, ISBN 0521834929 (hc); Price: US$60 Reviewing this text was an enjoyable experience. As the name suggests, it gives the reader a tour of the mathematical methods used in physical sciences. But this tour is a very practical one, as it engages the reader in an active manner by describing the methods and then posing challenging problems. Most of the mathematical methods needed to solve problems in physical sciences are introduced here. All the methods are given due attention according to their complexity and usefulness. The advanced concepts, such as Cartesian tensors, perturbation theory, asymptotic evaluation of integrals, and variational calculus, are discussed in a very easy-to-understand manner. The author relates the mathematical methods to appropriate physical problems, which makes the text highly engaging. With plenty of problems and to-the-point approach, this book is an absolute essential for students of physics, chemistry, and other physical sciences as well as professionals working in related areas. Syed Naeem Ahmed Sudbury Neutrino Observatory/Queen’s University Ontario, Canada Book Review Editor’s Note: For a more detailed review of the first (2001) edition of this book, see the Book Reviews section of the March/April 2002 issue of Physics in Canada. The review is available on the Web at: http://www.cap.ca/BRMS/Reviews/Math-Sneider-Buckmaster.html ALL YOU WANTED TO KNOW ABOUT MATHEMATICS BUT WERE AFRAID TO ASK: MATHEMATICS FOR SCIENCE STUDENTS, VOLUME 2, L. Lyons, Cambridge University Press, 1998, pp: 382, ISBN 052143601X (pbk); Price: US$28 All You Wanted to Know About Mathematics but Were Afraid to Ask: Mathematics For Science Students, Volume 2 est un livre qui s’adresse aux étudiants effectuant un baccalauréat en physique ou en génie. On y retrouve plusieurs concepts mathématiques qui seront utiles aux futurs bacheliers. Il s’agit d’un petit livre contrastant avec les grands livres habituels de mathématiques de l’ingénieur. De plus, ces notions mathématiques sont toujours abordées avec des exemples physiques concrets. Cette méthode est efficace pour conserver l’intérêt et l’attention d’un lecteur qui pourrait rechercher l’utilité de ce qu’il apprend. On développe également de cette manière la capacité d’analyse de systèmes physiques avec des outils mathématiques. L’auteur fait preuve d’une certaine originalité pour nous captiver. Par exemple, au chapitre 15, on verra qu’il y a un lien entre la multiplication de matrices et le lavage et le séchage de nos mains! Par ailleurs, plusieurs schémas illustrent les différentes notions expliquées facilitant ainsi la lecture. De plus, le livre n’est pas une suite d’équations difficile à suivre. Il y a en fait beaucoup de texte pour expliquer les équations écrites. En somme, il s’agit d’un bon livre d’ordre général, pédagogique et permettant de comprendre les bases de la mathématique et non d’un livre spécialisé permettant d’approfondir certaines notions déjà acquises. 322 PHYSICS IN CANADA Ce deuxième volume contient les chapitres 9 à 16 et l’annexe C de la série. Il n’est pas nécessaire d’avoir lu le premier volume pour l’entamer en supposant que l’on dispose déjà de bonnes connaissances. Les notions abordées dans le premier livre étaient les équations simultanées, la géométrie tridimensionnelle, les vecteurs, les nombres complexes, les équations différentielles ordinaires, les dérivées partielles, les séries de Taylor et les multiplicateurs de Lagrange. Quelques problèmes à la fin de chaque chapitre permettent de s’assurer de la compréhension de la matière. Selon l’auteur, il est nécessaire que l’étudiant essaie chacun de ces problèmes puisqu’ils sont peu nombreux. Les réponses à ces problèmes ne sont cependant pas données. De plus, il n’y a malheureusement aucune référence vers d’autres livres ou articles concernant les sujets traités. Le chapitre 9 débute avec le calcul des intégrales de ligne. On introduit ensuite les intégrales multiples en divisant la carte de l’Angleterre en rectangles pour calculer la population totale, connaissant la densité de population de chacun des rectangles. On y voit un exemple original d’aborder un concept mathématique. La généralisation pour des intégrales à n dimensions est ensuite effectuée avant de s’attarder aux limites d’intégration et aux changements de variables. Au chapitre 10, les opérateurs gradient, divergence et rotationnel sont expliqués en détail. On exprime aussi ces opérateurs en coordonnées cylindriques et sphériques. Ensuite, le théorème de la divergence, le théorème de Stokes et le théorème de Green sont tour à tour décrits. Quelques exemples mathématiques et physiques terminent le chapitre. Les équations différentielles partielles font l’objet du chapitre 11. Il est intéressant que l’équation de conduction de chaleur serve de point de départ à l’explication. Graduellement, on introduit les notions de conditions frontières, la séparation des variables pour la résolution de problèmes ou encore la méthode d’Alembert. Les exemples importants de l’équation d’onde, des équations de Poisson et de Laplace ainsi que de l’équation de Schrödinger sont entre autres mentionnés. Les transformées de Fourier constituent un outil bien important dans plusieurs domaines de la physique et le chapitre 12 leur est consacré. De façon bien structurée, l’auteur donne les étapes que l’on doit prendre pour déterminer les coefficients de Fourier d’une fonction donnée et pour vérifier que la réponse calculée est plausible. Cette approche est particulièrement intéressante. Ensuite les applications physiques données, par exemple les circuits électriques, permettent de comprendre l’importance de bien étudier ces séries. Les deux chapitres suivants se consacrent à des notions de physique. Le chapitre 13 porte sur les modes normaux. Les deux pendules couplés identiques et différents sont le point d’ancrage du chapitre. Pour être général, l’auteur aborde également les modes non-normaux. À la fin du chapitre, l’auteur a eu le souci de faire un résumé des étapes à suivre pour résoudre ce genre de problèmes. Il y a également un résumé de la notation utilisée pour que tout soit le plus clair possible. Pour sa part, le chapitre 14 traite des ondes. L’équation d’onde, la vitesse de groupe et la vitesse de phase, l’énergie des ondes, la réflexion, la polarisation, les ondes longitudinales et l’interférence sont autant de notions qui seront développées. September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 323 CRITIQUES DE LIVRES Les matrices et les opérations possibles avec ces matrices sont expliquées en détail au chapitre 15. La partie sur les propriétés des matrices est particulièrement intéressante comme aidemémoire. Finalement, le chapitre 16 montre comment obtenir les vecteurs et valeurs propres d’une matrice et leur utilité. Un retour sur les modes normaux est aussi effectué. L’annexe C ne fait que la liste des principales équations de chaque chapitre, mais peut constituer un bon aide-mémoire qui évite de relire tout le livre inutilement. Bref, ce deuxième volume présente de façon originale et stimulante plusieurs notions des mathématiques utiles en faisant constamment des liens avec des problèmes physiques concrets. Il s’agit donc d’un bon outil pour tout étudiant entreprenant des études de baccalauréat en physique ou en génie. Quelques problèmes à la fin des chapitres permettent aussi de s’assurer de sa compréhension. Peu volumineux, il est probablement idéal pour une personne ne disposant que de peu de temps pour comprendre certains des sujets présentés. Évidemment, cette concision n’en fait pas un livre spécialisé, mais bien un livre général. Léo Barriault Université Laval Québec, QC, Canada BAYESIAN LOGICAL DATA ANALYSIS FOR THE PHYSICAL SCIENCES: A COMPARATIVE APPROACH WITH MATHEMATICA SUPPORT, Phil Gregory, Cambridge University Press, 2005, pp: 460, ISBN: 052184150X; Price: US$70 I became intrigued by Bayesian statistics several years ago when I saw some applications of the methods to problems in physics and the success that they had. A graduate student worked with me to apply the methods in some new areas. In order to get up to speed on the subject matter I audited a graduate course in Statistics that focused on Bayesian statistics. This led to an awareness of the works of the physicist E.T. Jaynes who, in addition to publishing some applications, commenced to write a book on the subject. The chapters were available on the web, and so I downloaded everything and became excited about the potential of this field. Dr. Jaynes died before finishing the book, but with the help of Larry Bretthorst and others, the book, Probability Theory: The Logic of Science, was published in 2003 (also by Cambridge). Hence, it was very interesting to read the preface to this work by Phil Gregory, indicating how he also was stimulated by the work of Jaynes. Much of the work in this text is based on material from Jaynes, Bretthorst and others, who were pioneers in many of the applications of Bayes statistics to the sciences. The book contains 14 chapters and 5 appendices. The author begins with an introduction to the concept of scientific inference, its relation to probability theory, and the role of Bayes’ theorem. The concept of marginalization and the advantages of this approach over the standard statistical methods are introduced in the early chapters. Some of the basics of logic are introduced next, with truth tables and Boolean algebra. This leads into the operations required for plausible inference and some of the rules associated with this. The author then gets into the meat of the matter by discussing parameter estimation, selection of priors, assigning probabilities and building likelihood functions. Along the way he employs examples from physics and astronomy to show the relevance of the developments and their applications. In order to help readers appreciate the role of Bayesian statistics, three chapters of the book are devoted to reviewing the standard frequentist approach. Sampling theory, probability distributions and related topics such as pseudorandom numbers are presented. Calculating statistics, chi-squared values and confidence intervals are presented in Chapter 6. Hypothesis testing forms the basis of the following chapter. The central topics of the book include the maximum entropy principle and its role in generating probability distributions. Its application to image reconstruction is one example that is included. Computing means and standard deviations using Bayes’ theorem are also covered: How do different samples compare? Parameter estimation is another primary application. This is applied to both linear and nonlinear models. The Markov-chain Monte Carlo method has a chapter to itself. This is also a valuable technique for parameter estimation. An example included in the text is the analysis of astronomical data that was used to discover an extra-solar planet in 2003. Another very well-known application is in spectral analysis. Here the work of Jaynes and Bretthorst and others was revolutionary in the ability to obtain spectral information from noisy data. The appendices provide the required mathematical material for singular-value decomposition, the discrete Fourier transform, as well as elaborating on some of the math in earlier chapters. The author includes Mathematica support in some sections by including the required commands in the text. In addition, he has made available a tutorial, to support the book, on a website. Each chapter also has problems to test the reader’s understanding. There is also a very comprehensive list of reference material at the end of the book. Overall, this is an excellent text to introduce readers to the many applications of Bayesian logic. Richard Hodgson University of Ottawa Ottawa, Ontario, Canada BIOHAZARD, Ken Alibek with Stephen Handelman, Random House, 1999, pp: 319, ISBN 0375502319 (hc); Price US$25 Biohazard is a real-life account of Ken Alibek’s experience in the Soviet Union’s biological weapons program from 1975 until the collapse of the Soviet Union. His story is more ominous in today’s climate of international suspicion than it was in 1999. The authors’ clinical descriptions of Frankensteinian science are worded with such serious clarity that what could normally be disregarded as fiction feels authentic and real. I opened the front cover skeptical of the insert’s claims and closed the back cover accepting every word. It is the lack of emotion in the authors’ writing which convinced me this is not a heroic drama but a factual insider’s account of a well-established program. Alibek describes the mass manufacture and weaponization of lethal viruses, bacteria and toxins created for the sole purpose of immobilizing and killing entire populations. From the exotic (Marburg and Ebola) to the traditional (smallpox and plague), Alibek discloses the former Soviet Union’s collection of killer bugs. There is even mention of a Chimera virus, a hybrid designed to trigger multiple diseases in concert. LA PHYSIQUE AU CANADA septembre / octobre 2006 323 Sept06-FF.qxd 11/7/2006 2:07 PM Page 324 BOOK REVIEWS The majority of this book focuses on the politics and agencies involved in the mass manufacture of biological weapons. It outlines how the Soviet Union maintained a trail of deception for two decades. Millions of dollars were funneled into a secret program to design viruses and bacteria meant to kill millions of people. A central theme emerges from the pages – secret government policies, left unchecked, can avoid social responsibility and steal potentially life-saving research away from its citizens. Absent from this book is an open discussion about the personal goals, values and principles of the scientists involved in this program. Personal beliefs remain justifiably silent in Alibek’s Soviet-era world. There is, however, a description of the psychological toll the secrets and lies have on the lives of those involved. At first, the authors’ lack of emotion and observational style portrays scientists detached from their work, detached from the moral consequences. Reading further, glimpses of frustration, guilt and denial unfold into disillusionment and horror. A memorable moment is when Alibek introduces the reader to a man involved in the accidental release of anthrax into the city of Sverdlovsk: “His face was riveted on an invisible spot in front of him, and his hands began to shake so violently that he had to put his teacup down. He looked as if he was about to burst into tears”. The authors’ words are just as relevant now as they were in 1999. The book actually made accurate predictions about our world that explain why the Russians will continue to invent biological weapons: “…the weakened Russian military machine confronts a greater variety of challenges…These include armed separatist movements in the Caucasus, civil wars in central Asia, the spread of Muslim fundamentalism from Iran and Afghanistan…Biological weapons can play an important part in such conflicts, often compensating for the weakness or ineffectiveness of conventional forces”. Today, we live in a world where terrorists in Afghanistan are reportedly pursuing biological weapons, Chechen rebels have terrorized Russian citizens, and in 2002 Russian security forces used a secret narcotic gas to save hostages in a Moscow theatre. The realization of some of Alibek’s general predictions place more weight upon his dire warnings. This story is the only one of its kind, as the principal author is the only man in the world who has written about the secret life of a biological warfare scientist. If Ken Alibek ever reads this, I ask him, please pick up a pen and write another book. Graeme Drysdale University of Regina Regina, Saskatchewan, Canada BOSONIZATION AND STRONGLY CORRELATED SYSTEMS, A.O. Gogolin, A.A. Nersesyan and A.M. Tsvelik, Cambridge University Press, 1999, pp: xxii+423, ISBN 0521590310 (hc); Price: US$100 Bosonization and Strongly Correlated Systems by Gogolin, Nersesyan and Tsvelik provides an extensive overview of important non-perturbative techniques for the study of manybody systems. The book surveys the many technical details of bosonization and provides important references for further details. The book itself would serve as a good reference to such topics; however, in its attempts to cover such a huge wealth of methods and results, many details are skipped and many steps are left unjustified. Thankfully, the authors present references 324 PHYSICS IN CANADA to more elaborate treatments in their discussions. For use as a reference, their terse style would suffice to remind the reader of a particular method or result if the material didn’t necessarily rely so heavily upon previously presented work. In the first part of their book, they present the many technical details associated with bosonization and the results of noninteracting fermions and bosons, including topics such as onedimensional fermions, the Gaussian model (of bosons), the structure of Hilbert space in conformal theories, Bose-Einstein condensation in two dimensions, non-Abelian bosonization, and various spin-chain models. In the second part, the authors apply the techniques developed in the first part to a variety of many-body systems, including interacting fermions with spin, a Tomonaga-Luttinger liquid, a variety of spin models, superconductivity in a doped spin liquid, and edge states in the quantum Hall effect. In the third part, the effects of impurities are examined. Topics include potential scattering, the x-ray edge problem, impurities in a Tomonaga-Luttinger liquid, and the multichannel Kondo problem. The book has a wealth of information and is a convenient reference to someone already working in the field. For newcomers, the authors direct the reader to good sources of further details, while trying to present the essential ideas and results for a coherent, if brief, presentation. Lara Thompson University of British Columbia Vancouver, BC, Canada DATA AND ERROR ANALYSIS, SECOND EDITION, William Lichten, Prentice Hall, 1999, pp: 188, ISBN 0133685802 (pbk, CDROM included); Price: US$27 The ability to accurately interpret data and error is a fundamental skill for scientists and engineers. This relatively short text (188 pp.) and accompanying CD-ROM (Windows and Macintosh compatible) provides an introduction to data and error analysis with “simple, handy rules for estimating errors, both by graphical and analytic methods”. It has a learn-by-doing approach as opposed to a rigorous theoretical one. The author addresses this in his introduction by noting that it helps “science students process their data without lengthy and boring computations” that entail long discussions and involved derivations. There are five chapters: “Measurement and Errors”, “Error Analysis for One Variable”, “Error Analysis for More than One Variable”,” Finding Relations Between Variables” (according to the Table of Contents, but entitled “Linear Regression: Fitting a Straight Line to a Set of Points” within the text), and “Using Trigonometric and Exponential Functions in the Laboratory”. Each chapter contains practice problems (with answers), examples, and figures which demonstrate methods. Chapter 1 covers introductory measurement topics and definitions such as the distinction between exact and approximate statements, possible sources of error, significant digits, relative error, and percentage error. Chapter 2 introduces statistical terms, common frequency distributions, grouping, and properties that can be analyzed for a given data set. Chapter 3 extends on previous concepts by considering more than one variable. September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 325 CRITIQUES DE LIVRES Topics include error propagation, correlation, independence, and methods for error analysis. In Chapter 4, step-by-step instructions and examples are provided for linearly fitting data, manually with graph paper and computationally with the method of least squares. Chapter 5 explores trigonometric, exponential and power-law functions because they are commonly used to describe relationships between variables. A mathematical review, data-analysis methods, plotting (semilog and log-log graphs), and example calculations are presented. Power-series approximations for small angles are listed for trigonometric functions as an alternative method of calculation, although the derivation is not included. Demonstrations of how linear regression can determine coefficients for linear, log, exponential, exponential with counts, and power-law fits are particularly useful. Detailed calculations are provided for applications such as measuring the time constant of an RC circuit and measuring radioactive-isotope lifetimes. There is a strong focus on the included programs and guides for calculators and computers. The lengthy “Appendix B” (85 pp.) gives procedures for specific calculators. Unfortunately, I could not test these procedures since my scientific calculator is not on the list. The CD-ROM contains Excel programs to practice calculations and create plots, a cT program for error analysis, and BASIC and Pascal programs. Excel is a good choice of platform since it is highly familiar and widely available. The included files are user-friendly and provide a valuable medium for learning, but the size of the data sets is limited to less than 40 data points. Thus, these files are best suited for students who simply want to understand concepts, since they can input small data sets and not have to program in all the calculation details. As I was unfamiliar with cT, an Internet search informed me that the cT programming language was developed at Carnegie Mellon University. Its main niche is “the creation of programs for education, and many prize-winning educational programs were written in cT, especially in the areas of physics”.l Although the language is no longer supported, these files do not require the user to know how to program in cT – it is a graphical user interface for learning text material interactively. These files are not meant for practical research purposes, for which there are many programming languages and software applications capable of computing and displaying large data sets more efficiently and adaptively. I would have liked to see additional references to Matlab or other software applications. A strength of this text is its multidimensional learning environment. There is a good emphasis on using computers to make the computational part of the methods easier and faster, even though it does not give the user the knowledge to program their own applications and, in my opinion, does not make sufficient use of the vast array of software and programming languages available. It is suited toward undergraduate scientists and engineers who are not yet comfortable with programming and/or mathematical derivations, but who need to perform data and error analysis for their coursework. Students with strong math and computer science skills may require a text with more theory and programming material. Due to its limited scope, I would treat this text only as an introduction. Other resources should be consulted for mathematical derivations, more complex functions, and a com- prehensive source of statistical methods, distributions and formulas. Reyna Jenkyns University of Victoria Victoria, British Columbia, Canada 1. See: http://vpython.org/cTtsource/cToverview.html INTRODUCTION TO CHAOS: PHYSICS AND MATHEMATICS OF CHAOTIC PHENOMENA, H. Nagashima and Y. Baba, Institute of Physics Publishing, 1999, pp: 166, ISBN 0750305088 (pbk); Price: US$27 This book attempts to introduce some of the ideas of nonlinear dynamics, largely through the mathematics of one-dimensional iterated maps. Although the authors do take the time to explain how 1D maps come about from specific physical phenomena, it is my opinion that this approach is not the best way to come to appreciate the physical meaning of chaos. But, as far as expositions on chaos that employ this approach, I would highly recommend the book. Despite the title of the book under review, it is unfortunately quite slim on physics. Keeping in mind this is a review in a journal for physicists, I think it is necessary to comment on whether this book would be a good book for physicists, or even more generally, who this book would be good for. I think it is useful for self-study if you want to do numerical experiments with 1D maps and want to get a deeper understanding of that topic. It would also be useful as a course text for a short undergraduate applied math course in discrete dynamical systems. However, for physicists who would like to learn about chaos, I think there are much better starting points. I would rather recommend reading something like the collection of articles in the book Exploring Chaos, edited by Nina Hall. For formal undergraduate courses, I would highly recommend Baker and Gollub’s excellent junior undergrad text Chaotic Dynamics, or Francis Moon’s Chaotic and Fractal Dynamics for a senior undergrad physics course. An initial qualm I had with the book was that it did not cover in detail a significant range of topics that I think are essential in any “non-popular” introduction to the subject. In other words, I thought the book was ‘too thin’. But, as I read on it became clear that what the authors did cover, they did with clarity and precision. It is an elegant book. It is well thought out, contains many helpful figures, and the writing is excellent. So, it is perhaps more fair to judge the book on what is actually there instead of on what is not. The book consists of four chapters, a long (indispensable) set of appendices, a reference list, and a set of solutions to problems given in the chapters. Chapter 1 gives an introductory discussion. Chapter 2 covers the Li-Yorke theorem, Sharkovski’s theorem, the topological entropy, and the Lyapunov number. This chapter is (necessarily) quite rigorous and technical. The derivations are clean, and there are sufficient examples and problems, but this material is pretty hard going and not easy to get through without some mathematical experience. Beware that there is not a shred of physics to be found in this chapter! Chapter 3 covers various routes to chaos, windows, and intermittency using the standard (and no doubt fine) examples of the tent and logistic maps. The analysis is all laid out and it is well written, and again there are many elegant figures. Of course, anyone who has already studied these topics in some depth can proba- LA PHYSIQUE AU CANADA septembre / octobre 2006 325 Sept06-FF.qxd 11/7/2006 2:07 PM Page 326 BOOK REVIEWS bly appreciate many of the fine tricks the authors perform, but someone who has not studied the subject before, after going through this chapter, might wonder if they are “getting it”? They might ask: “so, what is chaos anyway?” It is not that there are any secrets here; for example, the authors do explain (albeit tersely) where the chaos resides in the window of the logistic map, but there is a lot of mathematical subtlety here. The impression one might get from this type of presentation is that chaos means “complex structure”, which is of course really misleading. In Section 3.2, the authors pursue the problem of trying to find a condition that a 1D map must satisfy in order that an infinite sequence of pitchfork bifurcations exists. No doubt this is an interesting mathematical problem, but I wonder if knowing the answer is that the Schwarz derivative of the map is negative (a fabulous mathematical result) helps the physicist to better understand what chaos is. Perhaps this is a heretical remark. As for genuine physics, all the physics you get in this chapter is two sentences about a laser experiment in connection with the period-doubling route to chaos. Undoubtedly, for anyone new to chaos, it would take quite some effort to get through Chapters 2 and 3. The payoff for the physicist seems negligible. This is where I would again question the 1D iterated maps approach (see first paragraph). Chapter 4 is entitled “Chaos in realistic systems”. However, the first section of this chapter is the only place where the reader will see any physics really discussed in detail. Here, conservative versus dissipative chaos is distinguished using the examples of the simple harmonic and damped oscillators, respectively. (Of course, there is no chaos to speak of for the simple harmonic oscillator.) The rest of the chapter contains material on limit cycles, strange attractors, Poincaré sections and maps, Lyapunov numbers, fractal dimensions, and scaling indices. In particular, I liked the nice simple discussion of the Hausdorf dimension and how it leads naturally to the capacity dimension. On the whole, the chapter is well written, but it is just not educational. Let me be more specific. The material on the Rossler and Lorenz attractors is very sketchy. The Henon map is just barely mentioned but nevertheless one finds a figure of the Henon attractor. There is also a figure that shows a strange attractor obtained from “magnon chaos”, but the authors never explain what this is. “Magnon chaos” also creeps into the section discussing the correlation dimension and in the section on scaling indices. The latter section is another case in point. The last section in Chapter 4 is about scaling indices and their spectra. There is standard material here such as the relation between the generalized boxcounting dimension, the q-parameter, the index, and the spectrum (although this result is admittedly derived in an unconventional way), and there are the standard examples like the “weighted Cantor set”. As before, the derivations are very clean, but the discussion is simply too terse. The authors cover this topic without explaining what is really being done and why. The notion of a multifractal is entirely absent. A more pedagogical and more meaningful discussion (for example, like that in Hilborn’s text Chaos and Nonlinear Dynamics) is necessary in order to make what is there at all intelligible. The authors do try and bring in some physics. In addition to the “magnon chaos” experiments mentioned before, the authors very briefly discuss data from a Benard convection experiment reported in a beautiful Letter, but the reader cannot really get too much out of it since it is all wrapped up in two or three sentences. Undoubtedly, the reader would have to look up the original article to understand what is going on. I think the figure from the original paper is insufficient; perhaps it would have been better to just mention the paper and only give the reference. 326 PHYSICS IN CANADA The appendices elaborate on some of the finer points and get into some of the technicalities. One finds a lot of pure classical analysis in the appendices to Chapter 2 such as countable and uncountable sets, Lebesgue measure, and so on. I think this material is definitely helpful and the authors cover this material in a way that would be appealing to non-purist mathematicians. Personally, I found the appendix on “normal numbers” and periodic orbits with finite-fraction initial conditions very interesting. The appendices to Chapter 3 are mostly supplementary to Chapter 3, and it would have made more sense to include them in Chapter 3 itself. Appendix 3D, for instance, gives examples of invariant measure and it would have been helpful to include that stuff in the main text. Generally speaking, the appendices are quite beneficial. I did, however, have some specific qualms with the last three appendices. One of these is about chaos in a double pendulum. Here would have been a nice opportunity to discuss chaos in a conservative system. The contents of this section are disappointing. All the authors do is obtain the equations of motion using the Lagrangian formalism (through the Euler-Lagrange equations). So, they write these down, give a Mathematica program which “solves these equations”, and then finally display a single Poincaré section. It is simply not enough. I think it would have been illuminating to give a full discussion of this example, something more along the lines of what is done in Chapter 11 of Hand and Finch’s Analytical Mechanics. The last two appendices are about the “singular points” of the van der Pol equation and the Roessler model. In these two sections, the authors embark upon a quickand-dirty analysis of the linearized dynamics in the vicinity of the equilibrium points of these two systems (although they don’t say it, this is what they are really doing). Honestly, I am impressed at how much ground they cover in a few pages. But, I would seriously question the benefit of embarking upon this material in the final pages of the text. This stuff constitutes a subject in its own right and any meaningful exposition demands a systematic study. For example, the same material spans more than three full chapters in the classic Strogatz text Nonlinear Dynamics and Chaos. The book ends with a page of references and solutions to problems. There are very few references given (most of these are original papers). This is not really a shortcoming, but rather reflects the limited scope of the text. There are about 45 problems in the book and full solutions are given at the end of the book. The solutions are nicely laid out and detailed. In conclusion, this book offers some nice systematic discussions on certain properties of one-dimensional iterated maps and very sketchy discussions of many other topics and ideas encountered in the subject of nonlinear dynamics. I would recommend this book as a starting point for understanding many of the mathematical features of 1D maps, but for physicists who would like to learn about chaos, there are many better alternatives. Jamal Sakhr Harvard University Cambridge, Massachusetts, USA QUANTUM FINANCE: PATH INTEGRALS AND HAMILTONIANS FOR OPTIONS AND INTEREST RATES, Belal E. Baaquie, Cambridge University Press, 2004, pp: 314, ISBN 0521840457 (hc); Price: US$70 In this book, the author shows how to approach problems related to financial markets with mathematical techniques that are September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 327 CRITIQUES DE LIVRES traditionally used in quantum field theory. This approach is in contrast to the usual stochastic methods that are generally applied to handle such problems. In particular, the author shows that path-integral formalism can be applied to understand the dynamics of options and interest rates. The author devotes the first chapter to introduce the reader to the terminologies and basic mathematics of financial markets. This useful chapter makes the book appealing to readers who are not very familiar with the financial sector. It gives a very good, brief, and to-the-point introduction of the subject. The author then moves on to introducing and applying quantummechanical and field-theoretical methods to stock options and interest rates. With plenty of appendices at the end of each chapter, the author has done a fairly good job in defining complex concepts and mathematical methods. The author touches on all the relevant segments of options and interest rates, such as stochastic volatility, moments, forward rates, and hedging. For non-specialists, that is, readers who are not already familiar with quantum field theoretical methods, this book may be fairly challenging. However, to physicists and mathematicians, it provides an excellent introduction to this novel approach. Since most quantitative analysts in the financial sector have backgrounds in physics or mathematics, this book would be highly beneficial for them in analyzing the markets in a non-traditional way. The author has done a marvelous job in showing that the quantum field theoretical methods can be usefully applied to financial market analysis. It is not intended to be a practical guide to the subject and therefore lacks examples of actual data analysis. As the author notes, the book is a research tool that can be used by physicists and mathematicians interested in the financial sector. I recommend it highly for such a readership. Syed Naeem Ahmed Sudbury Neutrino Observatory/Queen’s University Ontario, Canada SOLAR SYSTEM DYNAMICS, C.D. Murray and S.F. Dermott, Cambridge University Press, 2000, pp: 575, ISBN 0521575974 (pbk) / 0521572959 (hc); Price: US$40/$90 This textbook comprehensively outlines the main techniques, both old and new, and mathematical tools of planetary and solar system dynamics, demonstrating how these apply to a wide array of interesting, modern problems. This widely acclaimed, authoritative book succeeds in bridging the gap between the classical and modern methods of celestial mechanics. The work is distinguished by the great care taken to convey understanding and by the emphasis placed on the phenomena of resonance. By laying out the basics of the two- and three-body problems and some perturbation theory, it goes on to explain the dynamical origin, evolution, and stability of the bodies in the solar system. Programs written in the computer algebra system Mathematica (available as a free download on the author’s website) were used to help produce many plots of data and graphics in the text; several of these (and more) are available online and greatly enhance the educational value of the book. Notable topics omitted are mentioned in the preface: lunar theory, geophysics, and Cassini states. Altogether, this is a great textbook from which to learn and it is very suitable for a graduate-level course on celestial mechanics and for self-study by either the professional or the technically-inclined amateur astronomer. My personal interests in astronomy typically fall within the confines of “practical” astronomy and related ephemerides. Several excellent books have been published on these subjects, notably Montenbruck and Pfleger’s Astronomy on the Personal Computer and the venerable standard reference Explanatory Supplement to the Astronomical Almanac. There are many other, however, less “practical” subjects that are not covered therein despite their intrinsic appeal. For instance, it is known that the phenomenon of resonance underlies much of the dynamical structure in the solar system (e.g., planetary ring structure) and that most dynamical systems are not deterministic (i.e., chaos rules). Murray and Dermott’s text covers both the theory of deterministic and nondeterministic motion. For example, Chapter 8 on “Resonant Perturbation” develops a theory-based (Hamiltonian approach) investigation of orbit-orbit resonance and Chapter 9 covers “Chaos and Long-Term Evolution” of orbits. As such, it provides comprehensive coverage. The problem sets are well-crafted in their own right and some successfully integrate interesting elements from some recent high-profile astronomical media events. Problems which pique the interest of the reader can serve as the basis for further investigation and this is facilitated by the inclusion of a fairly extensive list of (mostly modern) references. The list of references could be further aided by the addition of an author index. There are no colour plates or colour figures (although this not meant to be a “coffee-table book”). The figures consist mainly of diagrams, graphs, and only a few photos. Solar System Dynamics is thoughtfully laid out, is a joy to read, and is a thought-provoking, enthralling journey. The authors have accomplished their goal with great skill and sensitivity. Grant I. Nixon MDS Nordion Ottawa, Ontario, Canada SYMMETRIES IN PHYSICS: PHILOSOPHICAL REFLECTIONS, Edited by K. Brading and E. Castellani, Cambridge University Press, 2003, pp: 445, ISBN 0521821371 (hc); Price: US$100 This book is a collection of papers written by physicists, mathematicians, and philosophers on the subject of symmetries in physics. The contributions span a wide range of topics related to symmetries and symmetry breaking. It seems that the editors have spent considerable time and energy in selecting the articles as each one of them gives the reader a new flavour of the subject. Some of the articles have been written by prominent philosophers, physicists, and mathematicians, such as Hermann Weyl, Leibniz, Kant, Black, Curie, and Wigner. They introduce the reader to the initial thought processes that eventually led to the current philosophical foundations of the symmetries in physics. These classic articles are followed by new articles and commentaries on the same subject, keeping the reader engaged in the learning process. The editors have ensured that all of the fundamental symmetries in physics receive due exposure in the book. The introduction of complex ideas, such as gauge theories and spontaneous symmetry breaking, takes the reader to a higher level of understanding LA PHYSIQUE AU CANADA septembre / octobre 2006 327 Sept06-FF.qxd 11/7/2006 2:07 PM Page 328 BOOK REVIEWS in a philosophical sense. Most of the articles in the book deal with the philosophy of symmetries without going into complex mathematics. This makes the book appealing to non-specialists with little background in physics and mathematics. For philosophy students, this book provides an excellent introduction to the subject. Throughout the rest of the book, new pieces of code and relevant algorithms are presented which add more functionality to the basic program discussed in the previous chapters. Chapter 3 presents methods of calculating interatomic forces, two algorithms for integrating equations of motion, and code for setting up the initial state of the simulation. Highly recommended for students and researchers working in the fields of physics and philosophy of science. Measuring equilibrium properties of simple fluids is the topic of the next chapter. It is mostly concerned with structural properties of the system. Therefore, methods for calculating radial distribution functions as well as for studying packing arrangements through the Voronoi algorithm are discussed. Cluster analysis is also described. Syed Naeem Ahmed Sudbury Neutrino Observatory/Queen’s University Ontario, Canada THE ART OF MOLECULAR DYNAMICS SIMULATION, SECOND EDITION, Dennis C. Rapaport, Cambridge University Press, 2004, The next three chapters discuss how to calculate dynamical properties of a fluid, its transport coefficients, and how to perform a correlation analysis. Most physics students know that molecular dynamics (MD) simulation consists of numerically solving equations of motion for a system of interacting particles. In other words, their positions and velocities are calculated at a series of time steps. Some of those students would probably be able to write code simulating elastic collisions of billiard balls. If that is where your programming knowledge ends, and you always wondered about the details of MD code or your career choice calls for writing one, then this book is for you. Up to this point, all example simulations are performed in constant-energy and volume ensemble (NVE or microcanonical ensemble). Extending the functionality of the code so that it covers constant-temperature (NVT or canonical) and constant-pressure (NPT or isothermal-isobaric) ensembles is covered next, followed by studies of nonequilibrium dynamics, rigid and flexible molecules, as well as molecules with internal degrees of freedom and geometric constraints. As case studies, water, surfactants, and alkane chains are chosen, respectively. Chapter 12 is entirely devoted to the subject of three-body and many-body interactions and Chapter 13 discusses long-range interactions where the Ewald sums and multiple-moments expansion methods are described and implemented. Chapters 14 through 16 cover step potentials, time-dependent phenomena, and granular dynamics. pp: 549, ISBN 0521825687 (hc); Price: US$60 Dennis C. Rapaport is a professor at the Department of Physics of Bar-Ilan University in Israel. His research interests include not only performing MD simulations to study properties of a variety of physical systems but also designing simulation algorithms for parallel computers. He is also interested in interactive simulations. I think that The Art of Molecular Dynamics Simulation, Second Edition can be considered a classic in the field, and as part of a canon of books about application of computer simulations in physical sciences that includes Understanding Molecular Simulation by D. Frenkel and B. Smit, and Computer Simulation of Liquids by M.P. Allen and D. J. Tildesley. The Art of Molecular Dynamics Simulation is claimed by the author to be a practical guide to writing MD simulation code and I fully agree. In fact, an entire MD code is in the book. In that sense, it is unique because I do not think that there is any other book on that topic which includes working molecular dynamics source code. Due to its availability and popularity among potential readers, the author decided to use C as the programming language. Although an entire source code can be downloaded from the Internet, typing it in as you read could serve as a valuable programming exercise, especially for an inexperienced programmer. Personally, I found the author’s programming style a little difficult to follow, but this should not be a problem for a more experienced programmer. On the other hand, a complete lack of comments in the code is, in my opinion, a more serious drawback. The book covers a lot of material and it is difficult to list all the topics without actually rewriting its table of contents here. It starts with some introductory remarks in Chapter 1, where the author describes the very basics of MD code for studying monatomic systems interacting through Lenard-Johns potential. The main emphasis of this section is on the general methodology of MD simulation and the programming style used throughout the book. However, after working through those first 43 pages, the reader will be able to perform his or her first, very simple simulations of a soft-disk fluid. 328 PHYSICS IN CANADA Considering the rapid development of computer technology, and the increasing availability of multiprocessor computers at many universities, it was certainly a good choice on the author’s part to include a chapter about making your code run in parallel. Implementation of message passing, threads, and vector processing approaches are discussed in Chapter 17. Small tidbits of information regarding general functionality of the code are described in the next chapter. Those include generation of random numbers, sorting, some utility functions such as solving a system of linear equations, memory allocation, and sorting. The author’s choice of a standard structure for each chapter helps the reader to fully benefit from the material covered. He always starts with a presentation of necessary formulae and theoretical concepts. Detailed implementation remarks with the listing of actual code follows. A measurement section, which tells the reader how to set up a simulation run and presents some results which are useful for comparison purposes, concludes most of the chapters. It is also worth mentioning that each chapter ends with a selection of exercises for the reader. Their purpose is twofold. Some of them will ask him or her to perform simulation runs with different initial conditions than those described in the text. Those very often include references to original papers on a given topic which again allow for easy checking of validity of the results. Others are coding exercises which result in improving and extending the functionality of the code. In my opinion, a serious reader will have to work through those exercises. I have never used or written simulation code of any kind, neither have I a need to do so right now; however, I always wanted to know how such calculations are performed. The Art of Molecular Dynamics Simulation contains all information needed to satisfy September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 329 CRITIQUES DE LIVRES my curiosity and a lot more. I regard it as a very good book for anybody who wants or needs to write molecular dynamics simulation code. Source availability, choice of case studies, and a cookbook approach are its three major assets. A large number of relevant references to original journal articles as well as books on the topics of molecular dynamics simulation, properties of liquids, and statistical mechanics are included at the end of the book. Using them will certainly enhance and solidify the reader’s knowledge of the subject. been devoted to wind-wave investigation and this monograph by Peter Janssen is an important contribution. However, there is no such thing as a perfect book and The Art of Molecular Dynamics Simulation is certainly no exception (although in my opinion the author did a good job writing it). I have to admit that I found parts of the book difficult to follow — at least during the first read. This is probably a result of my lack of a thorough background in theoretical physics of fluids in particular and in computational physics in general. However, returning to a given section after browsing through some of the references allowed me to grasp a few more details rather quickly. Obviously, the level of difficulty Rapaport’s book will present to a reader will vary from person to person and will depend on a level of familiarity with classical and statistical mechanics, computer programming, and numerical methods. However, I do feel that a few concepts resurfacing throughout the book could be explained a little more thoroughly. For example, the concept of linked list and cluster analysis algorithm were new to me and I had to resort to browsing through some of the references given to understand them a little better. In my opinion, their importance in computer simulations warrants a more thorough discussion; perhaps a few simple diagrams would be very helpful. “Peter Janssen pays attention to the problem of interaction of atmospheric boundary layer and sea waves. Winds generate ocean waves but, at the same time, airflow is modified due to loss of energy and momentum to the waves; thus, momentum from the atmosphere to the ocean depends on the state of the waves. Wind-wave numerical simulation is made on the basis of the wave action balance equation.” One more negative aspect caught my attention, namely, a noticeable number of graphs, with multiple curves differing in a value of some parameter, which are presented without a suitable description. Although it is sometimes possible to find relevant information from the subsequent discussion in the text, it would improve the book if the author included appropriate legends. On the other hand, a serious reader will try to reproduce all those graphs from his own simulation runs, therefore he or she will be able to sort out that issue rather quickly. Perhaps that was the author’s intention. In summary, I can testify that Dennis C. Rapaport’s The Art of Molecular Dynamics Simulation, Second Edition will provide a source of countless hours of enjoyment for interested readers, studying a plethora of properties of liquids by means of molecular dynamics simulation. It will certainly improve the reader’s understanding of computer simulation methodology and classical and statistical mechanics. Through an excellent selection of exercises and references it will also serve as a starting point for studies at a much more advanced level than that covered by the book. Marek Bromberek Memorial University of Newfoundland St. John’s, NL, Canada THE INTERACTION OF OCEAN WAVES AND WIND, Peter Janssen, Cambridge University Press, 2004, pp: 292, ISBN 0521465400 (hc); Price: US$120 Je débuterai cette revue de littérature par l’introduction tiré du World Meteorological Organisation Bulletin, July 2005: “Surface gravity waves are well known, complicated phenomena, which have always been the subject of great interest. They are easily observed but difficult to describe mathematically. Many works have “About 20 years ago, the author was a member of the International Wave Modelling Group (WAMDI). At present, the resulting WAM model is being improved, tested and widely used both at the global scale and in local water areas. The operational WAM model variant assimilates satellite information for updating the wave forecast. Nowadays, it is one of the most popular wind-wave models used in many countries. Cette introduction de I.G. Lavrenov présente bien ce que constitue le chapitre 1, l’introduction, de l’ouvrage de P. Janssen. Le chapitre 2 sur le bilan d’énergie des vagues océaniques en eau profonde, présente la dérivation et la formulation des ondes linéaires, des ondes groupées et le bilan d’énergie. Le bilan d’énergie fait intervenir des termes sources comme le forçage du vent, l’interaction non-linéaire vagues-vagues et la dissipation par le déferlement. Ici on introduit succinctement ces termes sources; ils seront approfondis dans les chapitres suivants. Le chapitre 3 sur la génération des vagues par le vent, décrit principalement l’effet de la turbulence sur la génération, et l’effet à double sens du vent sur les vagues, et la cambrure des vagues sur l’écoulement du vent. Ici, il aurait été intéressant de présenter graphiquement cet effet à double sens à l’aide des profils du vent et la fréquence des vagues au fur et à mesure que s’installe cette interaction. Au chapitre 4, l’auteur présente plus spécifiquement les termes sources d’interaction non-linéaire vagues-vagues et de dissipation de ceux-ci. L’interaction vagues-vagues est un processus qui fait intervenir une représentation mathématique sophistiquée et encore une fois j’aurais aimé que l’on présente de façon conceptuelle la physique se rattachant à ce phénomène de façon moins abstraite. La dissipation des vagues fait intervenir l’équation de V. Zakharov. Enfin le chapitre 5 présente l’aspect de la prévision des vagues à l’aide du modèle numérique du European Centre for MediumRange Weather Forecasts (ECMWF) et l’analyse résultant des observations conventionnelles des bouées en mer (plus spécifiquement distribuées sur la côte est de l’Amérique du Nord) et les observations de hauteur de vague provenant de l’altimètre à bord du satellite ERS-2. C’est un chapitre très intéressant, mais il ne constitue pas le pôle principal de l’ouvrage. Ce chapitre mentionne aussi les recherches en cours qui pourront devenir dans un futur rapproché les points majeurs d’avancées dans le domaine, comme par exemple le rôle des vagues dans la circulation océanique et les courants. Personnellement, j’ai lu cet ouvrage avec beaucoup d’intérêt et il pourrait être utile aux étudiants, ingénieurs et scientifiques qui sont intéressés par la génération des vagues et les problèmes reliés à leurs prévisions et leurs formations. André April Institut des sciences de la mer, Université du Québec à Rimouski, Rimouski, QC, Canada LA PHYSIQUE AU CANADA septembre / octobre 2006 329 Sept06-FF.qxd 11/7/2006 2:07 PM Page 330 BOOK REVIEWS WHISTLER-MODE WAVES IN A HOT PLASMA, Sergei Sazhin, Cambridge University Press, 1993, pp: 257, ISBN 0521401658 (hc); Price: US$70 An idea of the content and theme of this book can be gained from a list of the chapters, including their length. Chapters: 1. Basic equations (35 pp.); 2. Propagation in a cold plasma (25 pp.); 3. Parallel propagation (weakly relativistic approximation) (15 pp.); 4. Parallel propagation (non-relativistic approximation) (45 pp.); 5. Quasi-longitudinal approximation (27 pp.); 6. Quasi-electrostatic approximation (23 pp.); 7. Growth and damping of the waves (41 pp.); 8. Non-linear effects (15 pp.); 9. Application to the Earth’s magnetosphere (26 pp.). This review is structured in the form of a response to the publisher’s description (which is given below in italics): The book provides an extensive theoretical treatment of whistler-mode propagation, instabilities and damping in a collisionless plasma. This is true enough, in that there is presented a massive development of whistler wave behaviour in a uniform Vlasov plasma and the results of making various simplifying approximations. Unfortunately, in spite of the publicity outline (see below), there is little beyond that. The reader interested in deciding whether it would be worthwhile to wade through this large mass of detailed analysis is given little guidance as to what will be gained thereby. In particular, no connection is made to any actual data except for the first part of the discussion of whistler sonogram “noses” such as shown (one supposes to whet the reader’s appetite) on p. 1 in Fig. 1. The first part of the discussion of data at the very end of the book (in Sec. 9.1, pp. 210-214) uses very elementary cold-plasma analysis, based on whistler behaviour near the magnetosphere equator. The actual application of the approximations developed in the previous 200 pages is to be seen in the subsequent part of Chapter 9 (Sec. 9.1(b, c) pp. 214224). There the conclusion is reached that “before the method can be recommended for practical applications we need to be able to specify more accurately the model of the electron density and temperature distribution in the ionosphere, have a better estimate for the effect of ducted ray paths and increase the precision of determining the whistler parameters.” Put in the opposite way, it seems that the generally modest corrections that this analysis gives in the context of the magnetosphere are usually less than the other uncertainties. In effect, we have a painstakingly developed methodology which appears to be rather far in advance of the state of knowledge of the magnetosphere. (By the way, considering the importance of whistler wave ducting to observed whistlers, the total lack of discussion of ducting with a cold plasma and of the effects on ducting and ducting analysis of the temperature terms the author discusses at such length make the work much less useful than it might be, even for devoted whistler specialists.) This book fills a gap between oversimplified analytical studies of these waves, based on the cold plasma approximation, and studies based on numerical methods. The principal preoccupation of this work is the derivation of many variations of the equations for wave propagation in uniform plasmas, usually quickly specialized to the whistler wave context. The link to numerical work is not made with useful clarity. Also, whether the adjective “oversimplified” is justified is unclear. In other words, it is up to the author to make the case that the whistler enthusiast needs to follow all this work and that the more complete theory is necessary for adequate understanding of whistler waves. My impression is that it would take very high-quality whistler data indeed to necessitate even first-order-temperature theory. 330 PHYSICS IN CANADA Although the book is primarily addressed to space plasma physicists and radio physicists, it will also prove useful to laboratory plasma physicists. “Laboratory plasma physics” would appear to mean electron-ion laboratory near-Vlasov plasma physics (i.e., excluding pure-electron plasmas). This should not include magnetic confinement fusion physics (already well developed by the specialists in this field) and apart from the industrial plasma applications where collisions usually cause dominant warm or Vlasov plasma effects (apart from sheaths). This leaves pretty well the usually low-density plasma experiments addressing issues of space plasmas; however, the author does not discuss this aspect at all. The experimental results and conclusions of such “stars” in the field as Reiner Stenzel or Walter Gekkelmann (let alone the earlier work of Roy Gould) pass completely without mention. The statement on laboratory utility would thus seem to be more of a pious hope than a realistic opinion. Mathematical methods described in the book can be applied in a straightforward way to the analysis of other types of plasma waves. With no actual examples given, it is not clear just what the author has in mind here, beyond the presentation of the various approximations. Problems included in this book, along with their solutions, allow it to be used as a textbook for postgraduate students. If a course were to be taught along the lines of the material given here, this book could well be useful as an associated reference. However, as implied above, the application of this work is so limited that such a use by anyone other than the author would seem to be an unlikely occurrence. In another textbook aspect, that of accessibility, a serious drawback is that the author seems either unwilling or unable to indicate or highlight the plasma physics significance of any of the work. In particular, the lack of any use of constant-frequency contours in wavevector space to illuminate the basic aspects of anisotropic propagation seems to border on the perverse. In addition, the reader is constantly forced to refer back to equations given in earlier chapters; if the intention is to use the book for a course, it is much better to repeat the relevant equations for convenience as needed. To sum up, while the author has succeeded in getting into print, in this very specialized monograph, much of the work to which he has devoted his life, the specialization is such that it is hard to think of any customers for the work as presented. There may well be an interesting and exciting book on whistler waves including their kinetics to be written, but this is not it. In addition to the general comments just given, while no actual errors leapt off the page, some few points which are at best confusing and at worst misleading are given below. (1) On p. 20 at the end of Sec. 1.4, the notation is introduced for a normalized parallel component of phase velocity pph = ωmα /kz , (“z” here means component parallel to the magnetic field, the symbol “parallel” not being available for this review). The point is that since the (n = 0) resonance is ω – kAv = 0, the quantity ωmα /kz is to be compared with mανz and not with pz = mανz(1 - (ν 2/c 2))-1/2 = Mανz, the z-component mα momentum corresponding to the z-directed phase velocity ω/kz. (For instance, in a phase space (z, pz) plot, it is pzph = Mανz that is needed to make sense of the orbits, and not mανzph.) My preference would be to use mανzph for the quantity now termed pph. (2) On p. 48, with reference to the Storey angle (in any case more easily seen as arcsin(1/3)), here is a case where any September / October 2006 Sept06-FF.qxd 11/7/2006 2:07 PM Page 331 CRITIQUES DE LIVRES snapshot of the constant-frequency contour in wavevector space (similar to that shown by Helliwell) would show clearly what is being discussed. To be more specific, the group velocity (Mw/Mk) is in the direction normal to the frequency contour in k-space. The whistler contours (with electrostatic effects ignored) are bell- or Gaussian-shaped, with axis along the magnetic field. The largest angle from parallel to the magnetic field the normal makes is at the inflection site of the contours and this is the Storey angle, giving the propagation zone angular width. This is readily seen graphically. Similarly, when the effect of electrostatics is included the curves become W-shaped (the contour edges tending now to slope away from a right angle). The so-called Gendrin angle (Sec. 2.2, Eq. (2.45) p. 45) is then simply associated with the bottoms of the W’s. (3) On p. 95 there is a particularly flagrant example of complicated referencing to follow a change of notation. One sees, after Eq. (5.5) “ … and P = 1 – νY 2 is the same as in (1.79).” Now on p. 21, after Eq. (1.79), we were given “P = 1 –X”. It is after this until after Eq. (1.89) on p. 22, that one learns that X = Π 2/ω2, where Π α was earlier defined at the top of p.20. Also on p.22 one is told that Y = Ω/ω. So far so good. What about ν? After a bit of a search one finds in Chapter 2, on p. 38, after Eq. (2.10) that (as one might hope) ν = Π 2/Y 2, so that νY 2 = X, and all is well. The reader should not have to follow such a tortuous path. This sort of opacity is not what one would recommend in a text. CANADIAN INSTITUTE FOR THEORETICAL ASTROPHYSICS/ INSTITUT CANADIEN D’ASTROPHYSIQUE THÉORIQUE SENIOR RESEARCH ASSOCIATE POSITIONS CITA is a national centre for theoretical astrophysics located at the University of Toronto. The Institute expects to offer one or more senior research associate positions of three to five years duration. The starting date will be 1 September, 2007. Applicants should have an excellent research record in astrophysics and postdoctoral experience. Funds will be available for travel and other research expenses. The primary duty is to carry out original research in theoretical astrophysics, but senior research associates are also expected to work with postdoctoral fellows and to assist with administration of the Institute. All applicants for senior research associate positions will also be considered automatically for postdoctoral fellowships. HOW TO APPLY: We would prefer electronic submissions. Please check http://www.cita.utoronto.ca under “Working at CITA” for instructions. Applicants unable to access the web should mail: a curriculum vitae; statement of research interests; and arrange for three letters of recommendation to be sent to: Professor N. Murray, Director Canadian Institute for Theoretical Astrophysics University of Toronto, 60 St. George Street Toronto, Ontario Canada M5S 3H8 DEADLINE FOR APPLICATIONS AND ALL LETTERS OF RECOMMENDATION IS 1, DECEMBER 2006. All qualified candidates are encouraged to apply; however, Canadians and permanent residents will be given priority. In accordance with its Employment Equity Policy, the University of Toronto encourages applications from qualified women and men, members of visible minorities, aboriginal peoples and persons with disabilities. Tudor Wyatt Johnston INRS-EMT (Université du Québec) Varennes, Québec, Canada Faculty Positions, Department of Physics Astrophysics, Condensed Matter Theory, Particle Physics and Geophysics The Department of Physics, University of Alberta (www.phys.ualberta.ca ) invites applications for five tenure-track faculty positions. We plan to hire in each of the following areas: observational astrophysics, condensed matter theory, experimental particle physics, theoretical particle physics and geophysics. We primarily seek candidates at the Assistant Professor level, but exceptional candidates at a more senior level will be considered. The start date for these positions is July 1, 2007. Applicants must possess a PhD, have outstanding promise in research and be committed to teaching. The successful candidates will be expected to build strong research programs, supervise graduate students and teach at the undergraduate and graduate levels. The Department of Physics has approximately 35 faculty and 115 graduate students, with research interests in astrophysics, subatomic physics, condensed matter physics, geophysics and medical physics. The Department has excellent electronics, machine shop and computational facilities and staff, as well as access to high performance computational infrastructure (see www.westgrid.ca ). Initiatives by the Governments of Alberta and Canada provide exceptional opportunities for additional funding to establish new research programs at the University of Alberta. See, for example, www.albertaingenuity.ca, www.gov.ab.ca/sra, www.icore.ca, and www.innovation.ca for further information. The application should include a curriculum vitae, a research plan, and a description of teaching experience and interests. The applicant must also arrange to have at least three confidential letters of reference sent to the relevant selection committee. For details about the positions and application procedures please see www.careers.ualberta.ca or www.phys.ualberta.ca/jobs/; or contact the Department of Physics by e-mail at: [email protected]. All qualified candidates are encouraged to apply; however, Canadians and permanent residents will be given priority. If suitable Canadian citizens and permanent residents cannot be found, other individuals will be considered. The University of Alberta hires on the basis of merit. We are committed to the principle of equity in employment. We welcome diversity and encourage applications from all qualified women and men, including persons with disabilities, members of visible minorities, and Aboriginal persons. LA PHYSIQUE AU CANADA septembre / octobre 2006 331 Sept06-FF.qxd 11/7/2006 EMPLOYMENT 2:17 PM Page 332 OPPORTUNITIES TENURE TRACK FACULTY POSITION (S) Department of Physics and Astronomy The University of British Columbia Competition 2006 - 05 — Planetary Astronomy The Department of Physics & Astronomy at the University of British Columbia seeks applications for one or more tenure track faculty positions in Planetary Astronomy / Science. These positions are primarily intended to be at the Assistant Professor level, but applications from senior candidates will also be considered. Applicants must have a PhD. Degree or equivalent, relevant postdoctoral experience, an outstanding research record and a strong interest in teaching at the undergraduate and graduate level. UBC is expanding into the area of planetary sciences, led by the Physics and Astronomy and Earth and Ocean Sciences departments. Candidates are sought whose research addresses issues related to the formation and evolution of planetary systems. The Department of Physics and Astronomy has expertise in solar system dynamics, small-body observations, searches for and studies of planets in globular clusters, and transit studies of extrasolar planets. The deadline for receipt of all application materials is November 15, 2006. Applicants should complete the online application form at http://www.physics.ubc.ca/cgi-bin/Job_Appl_Info.cgi, making sure to select the Planetary Astronomy competition. A CV, publications list, and statements of research and teaching interests are required and can be uploaded directly. Three letters of reference may be submitted electronically to [email protected] , or sent by mail to: Chair, Planetary Astronomy Search Committee Department of Physics and Astronomy University of British Columbia 6224 Agricultural Road Vancouver, B.C. V6T 1Z1 Canada The University of British Columbia hires on the basis of merit and is committed to employment equity. We encourage all qualified persons to apply - however, Canadian citizens and permanent residents will be given priority. PHYSICS UNDERGRADUATE LABORATORY TECHNOLOGIST Classification: Salary: Education: Continuing non-academic starting at $52,000 per annum plus benefits Bachelor degree in Physics or closely related fields; Masters/PhD degree with experience in experimental physics is desirable. Qualifications: Teaching: - Demonstrated excellence in teaching undergraduate labs, including the ability to assess students’ performance. - Excellent writing and communication skills and ability to interact with graduate and undergraduate students from diverse backgrounds. - Ability to instruct and supervise graduate teaching assistants (TA’s). - Experience with web development, spreadsheets and other software for laboratory teaching. Technology: - Strong background in experimental physics. - Experience in a range of experimental techniques, such as optics, electronics, instrumentation, and computer based data acquisition. Duties: - Provide technical support for senior labs: setup, troubleshooting, teaching, TA training, consultation and supervision. - Develop and produce lab manuals for senior labs. - Develop and maintain new experiments for senior labs. - Coordinate and teach laboratories for junior level courses: equipment setup, TA meetings, develop manuals, administer marks. Deadline for applications: Expected starting date: 30 September, 2006 01 December, 2006 Send a cover letter and a CV including the names and contact information of three references via email to: [email protected] For information regarding the Department of Physics at the University of Alberta go to www.phys.ualberta.ca The University of Alberta hires on the basis of merit. We are committed to the principle of equity in employment. We welcome diversity and encourage applications from all qualified women and men, including persons with disabilities, members of visible minorities, and Aboriginal persons. TENURE TRACK FACULTY POSITION (S) Department of Physics and Astronomy The University of British Columbia Competition 2006 - 06 — Biological Physics The Department of Physics & Astronomy at the University of British Columbia seeks applications for one or more tenure track faculty positions in Biological Physics. These positions are primarily intended to be at the Assistant Professor level, but applications from senior candidates will also be considered. Applicants must have a PhD. degree or equivalent, relevant postdoctoral experience, an outstanding research record and a strong interest in teaching at the undergraduate and graduate level. Candidates are sought who will lead a vigorous research program in theoretical, experimental or computational biophysics, inspired by fundamental questions in biology. The University of British Columbia offers a rich collaborative research environment that in biophysics includes members of the Faculties of Science, Applied Science and Medicine, many of whom are affiliated with the Michael Smith Laboratories and the British Columbia Cancer Agency. The University of British Columbia hires on the basis of merit and is committed to employment equity. We encourage all qualified persons to apply - however, Canadian citizens and permanent residents will be given priority. Applicants should complete the online application form at http://www.physics.ubc.ca/cgi-bin/Job_Appl_Info.cgi, making sure to select the Biological Physics competition. A CV, publications list, and statements of research and teaching interests are required and can be uploaded directly. Three letters of reference may be submitted electronically to [email protected], or sent by mail to: Chair, Biological Physics Search Committee Department of Physics and Astronomy University of British Columbia 6224 Agricultural Road Vancouver, B.C. V6T 1Z1 Canada The deadline for receipt of all application materials is December 15, 2006. 332 PHYSICS IN CANADA September / October 2006 Sept06-FF.qxd 11/7/2006 2:17 PM Page IBC1 L’ART DE LA PHYSIQUE ART OF PHYSICS EXHIBITION There are currently 38 photographs and captions in the CAP's Art of Physics Exhibition. It is available for loan to any group or organization wishing to display it. The cost for insurance of the exhibition is $50 per loan. The CAP will arrange for shipping to you; you will be responsible for the shipping costs to either return the exhibit to the CAP or else forward it on to the next exhibitor. Interested? Simply download the booking form found at https://www.cap.ca/art/artex.html and return it with your fee to the CAP office. Sept06-FF.qxd 11/7/2006 3:52 PM Page BC2 ALL UNDELIVERABLE COPIES IN CANADA / TOUTE CORRESPONDANCE NE POUVANT ETRE LIVREE AU CANADA should be returned to / devra être retournée à : Canadian Association of Physicists/l’Association canadienne des physiciens et physiciennes Suite/bur. 112 Imm. McDonald Bldg. Univ. of/d’Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5