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Convergent Beam Electron Diffraction (CBED) Poster Group Z: Martin Moran John Roche David Tims Nikki Truss Group Coordinator: Prof. Hongzhou Zhang I. Basics II. History CBED is a technique of electron microscopy using a convergent beam of electrons directed at a specimen to produce a diffraction pattern to investigate the structure of a specimen. The convergence of electrons is acquired in a transmission electron microscope, TEM, by using an electrical or magnetic lens. The convergence semiangle, α, can be adjusted by changing the C2 aperture. The size of the diffraction disk depends on α. Depending on α different patterns are produced. For small α, a Kossel-Möllenstedt pattern is produced. For large α, a Kossel pattern is produced. In general, a Kossel-Möllenstedt pattern contains more useful information than a Kossel pattern. The diffraction pattern in CBED is produced by the electron beam interacting with the atoms in the specimen. There are two kinds of scattering from crystalline specimen: inelastic scattering which can go in any direction and elastic scattering which can go in only one direction. Scattering is given by Braggs Law: 2dsinθ=nλ where n is an integer, λ is the wavelength of the incident electrons, θ is the spacing between the planes of the atomic lattice, is the angle between the incident beam and the scattering planes. An electron after scattering is going in a direction which is 2θ away from the direction it had before the scattering. At the specimen in CBED, the electrons are travelling in a range of directions inside a cone. Electrons are scattered in all directions in the convergent conical illumination. Each point in the direct beam disc is one direction of illumination so each point in the disc can be scattered by the same 2θ. Therefore the diffracted electrons also form discs, one for each Bragg reflection. Fig1.1 Ray diagram showing CBED pattern formation At a zone axis reflection, the diffraction pattern consists of a regular net of discs. In this orientation, the reflections in the diffraction pattern break up into zones called Laue zones. The central zone is called the zero-order Laue zone, ZOLZ. The first ring is called the firstorder Laue zone, FOLZ, and so on. The first-order, second-order, third-order etc. are known collectively as the higher-order Laue zones, HOLZ. Because the narrow, dark, straight lines in the bright field disc are associated with diffraction into a HOLZ reflection, they are known as HOLZ lines. Fig 1.2 CBED pattern from[111] Si Ernst Abbe originally proposed that the ability to resolve detail in an object was limited by the wavelength of the light used in imaging, thus limiting the useful obtainable magnification from an optical microscope to a few micrometers. Developments into ultraviolet (UV) microscopes, led by Köhler and Rohr, allowed for an increase in resolving power of about a factor of two, but required more expensive quartz optical components. At this point it was believed that obtaining an image with sub-micrometer information was simply impossible due to this wavelength constraint. In 1891 it was recognized by that cathode rays could be focused with magnetic f ields, allowing for simple lens designs. In 1928, Max Knoll and a team of researchers at the Technological University of Berlin created a device that used two magnetic lenses to achieve higher magnifications, arguably the first electron microscope. The wave nature of electrons, which were considered charged matter particles, had not been fully realised until the publication of the De Broglie hypothesis in 1927. The group was unaware of this publication until 1932, where it was quickly realized that the De Broglie wavelength of electrons was many orders of magnitude smaller than that for light, theoretically allowing for imaging at atomic scales. After these discoveries, in the early 1930’s, Hungarian physicist Leo Szilárd invented and patented the modern electron microscope, however a prototype was not constructed until 1931, when an apparatus capable of 400 times magnification was built. Two years later, in 1933, Ernst Ruska, a German physicist, built an electron microscope that exceeded the resolution attainable with an optical lens microscope, a major milestone in the evolution of electron microscopy. The first practical electron microscope was constructed in 1938, at the University of Toronto, by Eli Franklin Burton and his students. By 1939 Ruska was working for Siemens, and together they produced the first commercial transmission electron microscope (TEM). It was then installed in the Physics department of I. G Farben-Werke. Further work on the electron microscope was held back by the destruction of a new laboratory constructed at Siemens by an air-raid, as well as the death of two of the researchers, during World War II. Fig 2.1 Ernst Ruska, one of the fathers of electron microscopy After the war, Ruska resumed work at Siemens, where he continued to develop the electron microscope, producing the first microscope with 100k magnification. The fundamental structure of this microscope design, with multi-stage beam preparation optics, is still used in modern microscopes. Once the electron microscope had been developed, a variety of techniques were invented to examine samples. With the invention of the TEM, it was realised that diffraction of the electron beam through the sample gave more detail when it came to analysing the sample, thus came the dawn of electron diffraction microscopy, and the foundations of CBED. If the specimen is thick enough, a large number of scattered electrons will be generated which travel in all directions. They are incoherently scattered but not necessarily inelastically scattered. These diffusely scattered electrons can then be Bragg diffracted by the planes. The resultant pattern, the Kikuchi lines, is explained by geometry. The Kikuchi lines consist of an excess line and a deficient line. In the diffraction pattern, the excess is further from the direct beam than the deficient line. The Kikuchi lines are fixed to the crystal so they can be used to determine the orientation of the crystals accurately. IV. Advantages/Disadvantages X-ray/Neutron microscopy: CBED has become the most prominent method in microscopy due to its benefits over other methods like x-ray microscopy. The main problems of x-ray and even neutron microscopy is the lack of an interaction between the particles of the sample and the x-rays/neutrons themselves. Some problems arising from this include a minimum thickness necessary from the sample. Without the thickness of ~100nm, the x-rays/neutrons will simply pass through the sheets. Electron diffraction in general covers this problem due to the much stronger interaction between electrons and atoms, as discussed in greater detail later in the poster. Fig 1.3 Diagram showing lines formed in CBED pattern III. Evolution SAD None of these problems appear when using SAD, as expected due to its use of electrons. However there are still many notable problems of this technique. There exists the engineering aspect of manufacturing the aperture. There is much difficulty in manufacturing these to compete with converging . While it is easy to make apertures of ~1μm, it is currently difficult to reduce this size to ~1nm. The use of CBED does not require an aperture of this size due to the convergence of the beam. With the development of TEM, the associated technique of scanning transmission electron microscopy (STEM) was re-investigated, but no real progress was made until the 1970s, when the field emission gun was developed, and a high quality objective lens was added to create the modern STEM. Using this design, Albert Crewe of the University of Chicago demonstrated the ability to image atoms using annular dark-field imaging. Since then many modifications have been added, and a wide range of more sophisticated techniques have been developed. Disadvantages One of the main disadvantages of CBED is the fact that the focused beam gives a very high current density. This can cause atoms to be stripped from the surface of the sample. Ways of counteracting this include cooling the specimen itself using a cooling rod and liquid nitrogen. Following the invention of the TEM, research began into the field of electron diffraction. The first effort was selected area electron diffraction (SAED) where a parallel beam of electrons is incident on the sample. This technique proved excellent for analysis of the surface of a material, however it did not provide in-depth crystallographic information that researchers still needed. In search of better imaging techniques, convergent beam electron diffraction (CBED) was developed, first being used in the commercial microscope developed by Ruska in 1939. It was found that if a convergent beam of electrons, essentially beams of many angles of incidence, was passed through a sample, then diffraction occurred at many angles, giving a 3D representation of the material being examined. This was a revolution in electron microscopy, allowing crystallographers and solid state physicists access to more data than ever before. Fig 3.1 A transmission electron microscope constructed in 1928 Although CBED is a highly advanced technique, it is still evolving, recent researchers have been experimenting with a technique called large angle electron diffraction (LACBED). As a larger angle (about 2°-5° in modern TEM’s) of the convergent beam of electrons is used, more deficiency lines become visible on the images obtained, offering more accurate measurements and interpretations of results. The thickness of the specimen under investigation in CBED has a major effect on the diffraction pattern produced. Thin specimens produce kinematical-diffraction conditions, where the diffraction discs are uniformly bright and devoid of contrast. Thicker specimen produce diffraction patterns of strong dynamic contrast, producing ZOLZ, HOLZ, HOLZ lines and Kikuchi lines as well as other characteristic patterns. These patterns give more information than those of kinematical-diffraction, so in general, when using the CBED technique, thicker specimens are better. When specimens are too thick, however, certain lines from the diffraction pattern disappear. Kikuchi lines disappear in very thick specimens because inelastic scattering of the electrons dominates over elastic scattering. V. Applications Nanodiffraction: Uses CBED to obtain diffraction patterns from regions of a specimen ~[1nm] or less in diameter. The electron beam is perfectly coherent with diameters as small as 0.2nm, which allows one to obtain crystallographic information on a near atomic scale. Specifically, the study of defects and disorder in very small particles, structure of individual defects in thin crystal foils and determination of local symmetry within particular parts of a defect or a unit cell of a crystal. Strain / Lattice Parameter Measurements Strain occurs from changes in the lattice spacing’s of a material which may arise from the presence of defects such as dislocations or through local changes in the chemistry. Making use of certain fine features of the HOLZ lines pattern, CBED can be used to measure the lattice parameter from microscopic regions. The lines appear as a pair called "deficiency" and "excess" lines. The angular position of these lines is sensitive to the accelerating voltage. If the accelerating voltage of the incident electrons is maintained constant, the changes in the angular position of these HOLZ lines can be directly correlated to the variations in the lattice parameter. By measuring the HOlZ line positions we can measure changes in lattice parameters and in particular changes due to strain. VI. Thickness Measurement Fig 6.1 Parallel Kossel-Möllenstedt fringes in a ZOLZ CBED pattern from pure Al taken under two-beam conditions with (200) strongly excited Thickness determination is a useful application of CBED patterns. The 000 disk usually contains concentric diffuse fringes known as KosselMöllenstedt, K-M, fringes. The number of these fringes in the 000 disk increases by one every time the thickness of the specimen increases by one extinction distance, ξg. When the specimen thickness is less than the extinction distance, the 000 disk is uniformly bright and no K-M fringes appear. Extinction distance can be found using the equation: where Vc is the volume of a unit cell, θB is the Braggs angle, λ is the wavelength of the electrons and Fg is the structure factor of the unit cell for reflection g. Fig 5.1 High-resolution TEM of atomic arrangement in a crystal lattice. Lattice Imaging Using coherent nano probes with a large convergence angle, the discs in CBED patterns which form are allowed to overlap. Lattice fringes are revealed in this overlapping region of the pattern, which leads to STEM lattice imaging. It is possible to locate the probe accurately by this method at various regions within the unit cell. The CBED patterns obtained from these areas show different site symmetries and atomic positions. A coherent CBED pattern recorded with a very large objective aperture or without the objective aperture, so that a gross overlap of CBED discs occurs is called a ‘ronchigram’. References ‘CBED Basics 2006’ – J.A. Eades ‘Transmission Electron Microscopy – D. B. Williams and C. B. Carter ‘LACBED’ – Morniroli www.wikipedia.org www.ammrf.org.au ‘Impact of Electron and Scanning Probe Microscopy on Materials Research’ – David G. Rickerby A more practical way of using this method is to tilt the specimen to two beam conditions with only one strongly excited hkl reflection. Under these conditions, the CBED disks contain parallel rather than concentric intensity oscillations as shown in Fig 6.1. The central bright fringe is at the exact Bragg condition where s=0. The deviation for the ith fringe can be obtained from the equation: where is the angle corresponding to the fringe spacing, is the Bragg angle for the diffracting hkl plane and d is the hkl interplanar spacing. The specimen thickness, t, can then be calculated using the equation: Fig 6.2 Diagram of diffraction pattern with two beam conditions with only one strongly excited hkl reflection where nk is an integer. Thickness determination has become the most popular use for CBED patterns, because the specimen thickness can be measured precisely at the point of diffraction and because the method can be computerized. This method is limited to crystalline specimens and is a bit tedious, but it is one of the best and most accurate method of thickness determination © School of Physics, Trinity College Dublin