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Wave optic and basics of TEM Etienne SNOECK CEMES - Toulouse CEMES -CNRS 29, rue Jeanne Marvig 31055 Toulouse email: [email protected] http://www.cemes.fr Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Wave optic and basics of TEM • Wave - particles dualism • Electron – matter interactions • • • single atom electron scattering • electron diffraction Electron optics • TEM column • Magnetic lenses Image formation and aberration Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 1 The beginning… 1897: J. J. Thomson discovered the electrons by studying the «cathodic beams » Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse The beginning… 1925: Louis de Broglie introduced the matter and wave-particle duality Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 2 The beginning… 1927: C. Davisson and L. Germer showed the wave behaviour of electrons Electron wave lengths vs acceleration voltage Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse The beginning… Electrons are particles • Mass me and kinetic energy: 1/2 mev2 • Electric charge -e and electrostatic energy: eV • Submited to electrostatic force : F = -e.E • Submited to magnetic force : F = -eVB • Interact with the electrons cloud and nucleus of atoms • Can be localized Electrons are waves • Wave lenght : = h/mv • Interferences • Cannot be localized • Diffraction by periodical lattices Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 3 Waves Spherical wave Plane wave k=1/ Wave front S Wave front k S k Ponctual source « Extented » source ( r , t ) Ar exp i t k r ( r ) Wave function Amplitude Propagation Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Interferences Plane wave Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 4 Interferences Electrons are particles and waves Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Wave optic and basics of TEM • Wave - particles dualism • Electron – matter interactions • • • single atom electron scattering • electron diffraction Electron optics • TEM column • Magnetic lenses Image formation and aberration Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 5 Electrons are particles What do an electron see when entering a crystal ? atom k0 nucleus k’ Electron cloud screening 2 4π with 4π 2 Atoms = Scattering centers : essentialy the nucleus positively charged Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse What do an electron see when entering a crystal Mean inner potential Electrons are particles Vi Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 6 What do an electron see when entering a crystal Electrons are particles An highly localised positive potential Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse What do an electron see when entering a crystal Electrons are waves Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 7 Electrons are waves What do an electron see when entering a crystal Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Electrons are waves What do an electron see when entering a crystal S1 S2 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 8 Electrons are waves What do an electron see when entering a crystal Electron wave Pure « Amplitude » object Pure « Phase » object I ( x ) * a 2 2 Measured intensity : Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Huygens-Fresnel principle Huygens contribution (1678) The light propagates step by step. Every element of surface diffuses and behaves as a secondary source of spherical waves. Fresnel contribution (1818) The complex amplitude of the wave at a specific point is the sum of the complex amplitudes of the vibrations produced by all the secondary sources. These vibrations interfere to form the vibration in the considered point. • wave at point « M »: M 0 exp it with 0 complex amplitude and = 2 the wave frequency S r M dS n P wave at point « P »: exp i 2 k r ( P ) M Q dS r S with • • • • r = MP k = 1/ dS surface element @M Q a diffusion coefficient Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 9 Rutherford diffusion Electrons are particles Rutherford diffusion : X rays (single Si atom) : Electrons s (nm-1) s (nm-1) f i X ( s ) A j exp( B j s 2 ) C me 2 2 f ei ( ) 2 ( ) ( Zi fi X ) 2h sin Doyle-Turner coefficient Huge electron –matter Interaction 4 j 1 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Waves and rays Electrons are waves Incident plane wave on a single atom Incident plane wave on a 1D periodic array of atoms atom k0 k’ k0 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 10 Rutherford diffusion Electrons are particles + interference a s (nm-1) s (nm-1) f ei ( ) me 2 2 ( ) ( Zi fi X ) 2h 2 sin Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Rutherford diffusion Electrons are particles + interference a' s (nm-1) s (nm-1) 1/a’ me 2 2 ) ( Zi fi X ) f ei ( ) 2 ( 2h sin Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 11 Waves and rays Electrons are waves Incident plane wave on a periodic 3D array of atoms k0 kB Path difference : 2 = 2d.sin d Constructive interferences : = n. d.sin 2d.sin n. k0 d ~ 10-10 m ~ 10-12 m ~ 10-3 rad (sinB= B ) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Atomic diffusion The crystal contains n atoms. Each atom j in as only elastic diffusion is considered rj creates an elastic diffusion of the wave k0 k Incident beam k 0 • phase shift relative to the original wave • fj atomic diffusion factor k Diffused beam Atom • The diffused wave function by the atom j is: : k rj j ( r , t ) 0 exp i t r . f j Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 12 Atomic diffusion Total phase shift of the diffused wave in « r » P r o r ri k k0 2 rj 1 2 contributions : 2 2 k r rj r j : phase shift 1 of the incident wave relative to the origin: Phase shift 2 of the diffused wave between the atom in r j and the point r 1 2 k0 rj • 0 • Total phase shift: r 1 2 2 k0 rj k r rj 2 k k0 rj k r Diffraction vector: Difference between the diffused wave vector k and the incident wave vector k0 K k k0 P r k0 k K k0 o 1 k rj 2 r ri Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Atomic diffusion K k k0 Wave function in « r » due to the diffusion of the atom in rj i 2 K r j j ( r , t ) 0 exp i t 2 k r . f j exp o k0 1 P r K k rj r ri 2 • For the cristal (n atoms): the diffracted beam tot is the sum of the diffused waves by the n atoms. ( r , t ) j ( r , t ) 0 exp i t 2 k r . f j exp n j 1 n i 2 K r j j 1 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 13 Diffraction Electrons are particles and waves ( r , t ) j ( r , t ) 0 exp i t 2 k r . f j exp n j 1 n i 2 K r j j 1 Diffraction by the crystal with n atoms located on the « j » position :r j FK f e j ( ) exp( B j 2 ) exp( 2iK .rj ) j B j 8 2 u 2 r j ru Rm,n , p Periodic crystal ru u2 Debye-Waller due to the atom vibration xu , yu , zu 0,1 R m a n b p c vector of the lattice: m ,n , p vector of the unit cell: ru xu a yu b zu c with O (m, n, p integers) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Diffraction FK Electrons are particles and waves exp i 2 K R m ,n , p m ,n , p S(K ) . f eu ( ) exp( Bu 2 ) exp i 2 K ru u exp i 2 K R m ,n , p m ,n , p F ( K ) f eu ( ) exp( Bu 2 ) exp i 2 K ru u Structure Factor (unit cell) Form Factor (whole crystal) The total diffracted intensity in a direction « K » is given by 2 I ( r , t )*. ( r , t ) ( r , t ) => I F K 2 S K 2 Yes in x-ray diffraction BUT… generally not in TEM Maximal when K corresponds to a node of the reciprocal lattice K K hkl h a k b l c Laue conditions Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 14 Wave optic and basics of TEM • Wave - particles dualism • Electron – matter interactions • • single atom electron scattering • electron diffraction Electron optics • TEM column • Magnetic lenses • Diffraction pattern formation • Image formation and aberration Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Why microscopy with electrons ? Diffraction through a circular aperture • First minimum at sin 1, 22 a « a » being the aperture diameter Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 15 Why microscopy with electrons ? Resolution Two ponctual sources could be separated if their diffraction figures do not overlap Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Why microscopy with electrons ? Rayleigh criterium • The two images are just separated when the central maximum of one diffraction figure overlap with the first minimum of the other • The angular switching between the two sources corresponding to Rayleigh criteria is : c 1, 22 a Lord Rayleigh (1842-1919) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 16 Why microscopy with electrons ? c 1, 22 a Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Why microscopy with electrons ? c 1, 22 a Increase the resolution decrease the wavelength of the radiation (X-Ray : 10-10 - 10-12 m but no lenses !!) h mv Use « fast » electrons Gun, electromagnetic lenses, etc… microscope Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 17 How to focalize electrons ? Wehnelt and Gabor: using electric and magnetic fields 1927: Beginning of electron optic: by Hans Busch « an electromagnetic field has the same effect on an electron than an optic lens on a light beam » Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse TEM : the beginning… Ernst Ruska et Max Knoll worked at TH Berlin, early 30es Oscilloscope with a small intense spot and a fast scan 1931: Ruska get a first X14.4 magnified image. Ruska E (translated by Mulvey T). The early development of electron lenses and electron microscopy. Stuttgart: Hirzel, 1980. Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 18 TEM : the beginning… D’après Knoll et Ruska, Ann. Phys. 12, 607, 1932 1932: Vertical microscope Higher magnification than an optical (12000 X ) • • • • • Cold cathod (glow discharge) 65kV Condenser Objective Projector Fluorescent screen Ruska, E, Z. Physik 87, 580-602 (1934) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse TEM Optical microscope TEM Def Gun Source Def Beam Sample Def Image Diff Optical column Def Proj Gun + High tension Condensor Part C1+C2 Condensor aperture Objective Part Objective aperture Diffraction Part Diff + inter SAED aperture Shutter Projector Part P1+P2 Detector Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 19 TEM Increasing the resolution … h mv v Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 20 The TEM column A TEM = 6 parts + deflectors to align each part each other Def Gun Gun + High tension Part of the column Bloc Line tube Condensor Part C1+C2 Def Beam Condensor aperture + Def Image Diff = + Objective Part Polar piece Objective aperture Diffraction Part Diff + inter Def Proj SAED aperture Projector Part P1+P2 Shutter Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse The electron source Def Gun Def Beam Gun + High tension Condensor Part C1+C2 Condensor aperture Def Image Diff Objective Part Objective aperture Def Proj Diffraction Part Diff + inter SAED aperture Projector Part P1+P2 Shutter Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 21 Thermoionic source Electron acceleration Schematic representation Metallic filament heating Filament Vacuum Increase the T°K Exit work = f E Fermi Level Fermi-Dirac distribution change with T°K Real design Filament Whenelt 8mm W filament T 2800 K 4,5eV Cross over LaB6 filament T 2000 K 2,5eV Anode 10 7 Torr Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Cold Field Emission Gun (CFEG) Real design Supressor Tip Emission process : Schottky effect Fermi-Dirac distribution at 300K Tunneling effect Extractor 10 11Torr Fowler-Nordheim law jFN 4me 2 b d exp h3 d d b c2 c1 F f ( F , ) 3/ 2 F g ( F , ) W <310> Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 22 CFEG issues I-a I-b-c-d II II Arc I Solution : flash to heat the tip with a current during some seconds Technology more difficult Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Comparison between sources Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 23 Electromagnetic lenses Def Gun Def Beam Gun + High tension Condensor Part C1+C2 Condensor aperture Def Image Diff Objective Part Objective aperture Def Proj Diffraction Part Diff + inter SAED aperture Projector Part P1+P2 Shutter Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Principle of electromagnetic lenses Electrons rotation + focalisation e Real design of a lens coil + plugs + cooling + polar piece Power supply Water Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 24 Basic geometrical optic Magnetic lens = thin convergent optical lens Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Magnetic lens focalisation Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 25 Magnetic lens focalisation Main advantage of electromagnetic lenses : the focal length is tunable with the lens current !! Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Illumination system of the column Def Gun Def Beam Def Image Diff Def Proj Gun + High tension Condensor Part C1+C2 Condensor aperture Objective Part Objective aperture Diffraction Part Diff + inter SAED aperture Shutter Projector Part P1+P2 Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 26 Illumination system of the column 1. Spot Size : Condensor 1 C1 Strength Spot size 2. Intensity: Condensor 2 C2 Strength change the illumination area and the convergence angle Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Illumination system of the column Sample illumination and convergence angle of the electron beam change Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 27 Objective lens Def Gun Def Beam Def Image Diff Def Proj Gun + High tension Condensor Part C1+C2 Condensor aperture Objective Part Objective aperture Diffraction Part Diff + inter SAED aperture Shutter Projector Part P1+P2 Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Objective lens The objective lens transfers two informations: • image in the image plane • Fraunhofer diffraction in the focal plane Object plane Object Conjugated planes f Focal plane Fourier Transform (FT) of the object : diffraction pattern Image plane Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 28 The diffraction lens and the projection system Def Gun Gun + High tension Condensor Part C1+C2 Def Beam Condensor aperture Def Image Diff Objective Part Objective aperture Diffraction Part Diff + inter Def Proj SAED aperture Projector Part P1+P2 Shutter Detector Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse The diffraction lens and the projection system « diffraction » mode « imaging » mode 1/p1 + 1/p2 = 1/f objective Focal plane p’1 Image plane Diffraction lens p1 f f’ p2 Adjusting the focal lenght of the diffraction lens, one can get either the image plane or the focal plane (diffraction) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 29 The diffraction lens and the projection system • Diffraction lens : select the image or the diffraction plane (Diffraction control) • Intermediate lens + Projector 1 and Projector 2 change the magnification or the camera length Cross over of the Gun Condensor 1 Spot size Condensor 2 Intensity Minilens Objective Condensor Focus Objective Image Diffraction lens Diffraction and image mode Intermediate Projector 1 Magnification Projector 2 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Wave optic and basics of TEM • Wave - particles dualism • Electron – matter interactions • • • single atom electron scattering • electron diffraction Electron optics • TEM column • Magnetic lenses Image formation and aberration Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 30 High Resolution Imaging e– Incident Electron wave Crystal Crystal 2q Lens Exit Wave function e– Screen Depends on • Aberrations • Atomic potential • Defocalization • Diffusion • Beam incoherences • Diffraction • Phase shift Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse High Resolution Imaging : electron wave within the object e– (r , z ) e iKz (r) e– (r, z ) (r )eiKz exit (r ) Exit Wave function Diffracted beams ~ ( k ) exit (r ) k ~( k ) exp( 2ik.r ) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 31 High Resolution Imaging : electron wave in the column o exp(iK.r ) Object obj ao (r) expi( K .r o (r)) Objective s As( r )exp i ( K .r s( r )) Focal plane Intermediate lenses & projector I(x,y) s As2(r) 2 s (r ) is lost Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse High Resolution Imaging ~ s (r) gexp{2ig.r} g Wave function on the detector Diffracted beams I (r) s (r) 2 ~ ~ gg*exp{2i(g g).r} Measured intensity g g • The contrast is due to the interferences between the g and g’ diffracted beams Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 32 Single crystal in zone axis 0 g2 0 g1 0 g3 g1 g3 0 g2 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse High Resolution Imaging: interferences + TEM aberrations exit(r) ~gexp{2ig.r} g Exit wave function Diffracted beams (r) ~gei (g)exp{2ig.r} g Image wave function on the detector Tranfert function I(r) (r) 2 Image intensity • The objective lens aberrations modifies the phase of the exit wave phase plate Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 33 Lens Aberration Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Spherical Aberration Disk of least confusion Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 34 Spherical Aberration In optical microscopy: Convergent lens + divergente lens Divergent lens in TEM ??? Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Spherical Aberration Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 35 Spherical Aberration delocalisation Pb with surface and interface Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Chromatic Aberration Slow electrons Fast electrons Lack of resolution Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 36 Axial Coma and First order Astigmatism C2 The coma (off-axial aberration) C2’ I C1’ C1 O Astigmatism and field curvature (On and Off axial aberrations) : Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Anisotropic aberrations Anisotropic coma, anisotropic astigmatism, anisotropic distorsion Due to the helicoïdal trajectories of the electrons inside the lenses Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 37 Aberrations : wavefront description • Focalisation (first order effect) C1 C1 • Spherical aberration C3 (Cs), C5, etc … and • Chromatic aberration (Cc) C3=Cs and … A1 • Off-axial aberrations • Astignatism and field curvature (A1, A2, etc ..) • Coma (B2, B4, etc …) B2 A2 A3 • High order aberrations (S3,D3, …) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse The first order astigmatism correction: the stigmator Quadrupole lenses : Huge elliptic beam Round beam Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 38 The first order astigmatism correction: the stigmator Size of the line tube 2 quadrupoles stigmator (correction of A1) Uncorrected spot Corrected spot Qpol X Qpol Y Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Spherical aberration correction: see Max Haider lecture Non cylindrical lenses : Quadrupoles, Octopoles Hexapoles Dodecapoles Two major effects • Negative C3 • Huge A2 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 39 High Resolution Imaging: interferences + TEM aberrations (r) ~gei (g)exp{2ig.r} g C1 C3=Cs B2 A1 C1 + C3 A2 A3 + A1(astigmatism) (g ) + B1 (coma) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Phase plate (g ) Scherzer focus Zero focus Cs = 1.34mm C1 = 0 Cs = 1.34mm C1 = -60nm (@300kV) Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 40 Contraste transfert function sin g C1 = 0 nm C1 = – 60 nm 1 (1.8Å)–1 –1 g g Scherzer focus Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Exple : CdSe crystal C = 0 nm C = – 60 nm Cd S • Complicated and non trivial contrast at Gaussian focus • The HREM image at Scherzer focus is the negative of the projected potential Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 41 Phase plate: astigmatism C1 = – 60nm A1 = 0 + A1 = 80nm Scherzer focus + A1 = 80nm (g) Cd Cd Cd S S S The effect of the objective lens is not symetric Looks like a bad sample alignement…. Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Phase plate: Coma C1 = – 60nm B2 = 0 + B2 = 1000nm Scherzer focus + B2 = 1000nm (g ) Cd Cd S S incident beam The central beam is not aligned along the optic axis crystal The g and –g diffracted beam have not the same phase lens The symetry is broken Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 42 Cs Aberration corrector Cs = 1.34 mm - C1 = 0 Cs = 0 nm - C1 = 0 0.5 nm 0.5 nm 5 nm Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Cs Aberration corrector HubbleTelescope Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 43 Advanced TEMs Gun Cond Biprism 1 Condensor aperture 1 Stigm Cond Condensor 1 Condensor 2 Probe Cs corrector Condensor aperture 2 Condensor 3 Condensor Objective Large pole piece gap for in situ (10 mm) Contrast aperture Obj Objective Image Stigm obj Transfert lens doublet 1 Short hexapole 1 Transfert lens doublet 2 Image Cs corrector Long hexapole Transfert lens doublet 3 Short hexapole 2 Transfert lens doublet 4 Diff Stigm diff Biprism 2 SA aperture Intermediate lens 1 Biprism 3 Proj Intermediate lens 2 Biprism 4 Intermediate lens 3 Detector Projector 1 Projector 2 Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse Advanced TEMs Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 44 Wave optic and basics of TEM The end email: [email protected] http://www.cemes.fr Dr. Etienne SNOECK - CEMES - Toulouse CEMES - Toulouse 45
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