Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.5, pp. 285-286

Section CBED

P. Goodmanb CBED

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Convergent-beam electron diffraction, originating in the experiments of Kossel and Möllenstedt (Kossel & Möllenstedt, 1938[link]) has been established over the past two decades as a powerful technique for the determination of space group in inorganic materials, with particular application when only microscopic samples are available. Relatively recently, with the introduction of the analytical electron microscope, this technique – abbreviated as CBED – has become available as a routine, so that there is now a considerable accumulation of data from a wide range of materials. A significant extension of the technique in recent times has been the introduction of LACBED (large-angle CBED) by Tanaka & Terauchi (1985[link]). This technique allows an extensive angular range of single diffraction orders to be recorded and, although this method cannot be used for microdiffraction (since it requires an extensive single-crystal area), new LACBED applications appear regularly, particularly in the field of semiconductor research (see Section[link]).

The CBED method relies essentially on two basic properties of transmission electron diffraction, namely the radical departure from Friedel's law and the formation of characteristic extinction bands within space-group-forbidden reflections. Departure from Friedel's law in electron diffraction was first noted experimentally by Miyake & Uyeda (1950)[link]. The prediction of space-group-forbidden bands (within space-group-forbidden reflections) by Cowley & Moodie (1959)[link], on the other hand, was one of the first successes of N-beam theory. A detailed explanation was later given by Gjønnes & Moodie (1965)[link]. These are known variously as `GM' bands (Tanaka et al., 1983[link]), or more simply and definitively as `GS' (glide–screw) bands (this section). These extinctions have a close parallel with space-group extinctions in X-ray diffraction, with the reservation that only screw axes of order two are accurately extinctive under N-beam conditions. This arises from the property that only those operations which lead to identical projections of the asymmetric unit can have N-beam dynamical symmetries (Cowley et al., 1961[link]).

Additionally, CBED from perfect crystals produces high-order defect lines in the zero-order pattern, analogous to the defect Kikuchi lines of inelastic scattering, which provide a sensitive measurement of unit-cell parameters (Jones et al., 1977[link]; Fraser et al., 1985[link]; Tanaka & Terauchi, 1985[link]).

The significant differences between X-ray and electron diffraction, which may be exploited in analysis, arise as a consequence of a much stronger interaction in the case of electrons (Section 2.5.2[link]). Hence, thin, approximately parallel-sided crystal regions must be used in high-energy (100 kV–1 MV) electron transmission work, so that diffraction is produced from crystals effectively infinitely periodic in only two dimensions, leading to the relaxation of three-dimensional diffraction conditions known as `excitation error' (Chapter 5.2[link] ). Also, there is the ability in CBED to obtain data from microscopic crystal regions of around 50 Å in diameter, with corresponding exposure times of several seconds, allowing a survey of a material to be carried out in a relatively short time.

In contrast, single-crystal X-ray diffraction provides much more limited symmetry information in a direct fashion [although statistical analysis of intensities (Wilson, 1949[link]) will considerably supplement this information], but correspondingly gives much more direct three-dimensional geometric data, including the determination of unit-cell parameters and three-dimensional extinctions.

The relative strengths and weaknesses of the two techniques make it useful where possible to collect both convergent-beam and X-ray single-crystal data in a combined study. However, all parameters can be obtained from convergent-beam and electron-diffraction data, even if in a somewhat less direct form, making possible space-group determination from microscopic crystals and microscopic regions of polygranular material. Several reviews of the subject are available (Tanaka, 1994[link]; Steeds & Vincent, 1983[link]; Steeds, 1979[link]). In addition, an atlas of characteristic CBED patterns for direct phase identification of metal alloys has been published (Mansfield, 1984[link]), and it is likely that this type of procedure, allowing N-beam analysis by comparison with standard simulations, will be expanded in the near future.


First citation Cowley, J. M. & Moodie, A. F. (1959). The scattering of electrons by atoms and crystals. III. Single-crystal diffraction patterns. Acta Cryst. 12, 360–367.Google Scholar
First citation Cowley, J. M., Moodie, A. F., Miyake, S., Takagi, S. & Fujimoto, F. (1961). The extinction rules for reflections in symmetrical electron diffraction spot patterns. Acta Cryst. 14, 87–88.Google Scholar
First citation Fraser, H. L., Maher, D. M., Humphreys, C. J., Hetherington, C. J. D., Knoell, R. V. & Bean, J. C. (1985). The detection of local strains in strained superlattices. In Microscopy of semiconducting materials, pp. 1–5. London: Institute of Physics.Google Scholar
First citation Gjønnes, J. & Moodie, A. F. (1965). Extinction conditions in dynamic theory of electron diffraction patterns. Acta Cryst. 19, 65–67.Google Scholar
First citation Jones, P. M., Rackham, G. M. & Steeds, J. W. (1977). Higher order Laue zone effects in electron diffraction and their use in lattice parameter determination. Proc. R. Soc. London Ser. A, 354, 197–222.Google Scholar
First citation Kossel, W. & Möllenstedt, G. (1938). Electron interference in a convergent beam. Nature (London), 26, 660.Google Scholar
First citation Mansfield, J. (1984). Convergent beam electron diffraction of alloy phases by the Bristol Group under the direction of John Steeds. Bristol: Adam Hilger.Google Scholar
First citation Miyake, S. & Uyeda, R. (1950). An exception to Friedel's law in electron diffraction. Acta Cryst. 3, 314.Google Scholar
First citation Steeds, J. W. (1979). Convergent beam electron diffraction. In Introduction to analytical electron microscopy, edited by J. J. Hren, J. I. Goldstein & D. C. Joy, pp. 387–422. New York: Plenum.Google Scholar
First citation Steeds, J. W. & Vincent, R. (1983). Use of high symmetry zone axes in electron diffraction in determining crystal point and space groups. J. Appl. Cryst. 16, 317–324.Google Scholar
First citation Tanaka, M. (1994). Convergent-beam electron diffraction. Acta Cryst. A50, 261–286.Google Scholar
First citation Tanaka, M., Sekii, H. & Nagasawa, T. (1983). Space group determination by dynamic extinction in convergent beam electron diffraction. Acta Cryst. A39, 825–837.Google Scholar
First citation Tanaka, M. & Terauchi, M. (1985). Convergent-beam electron diffraction. Tokyo: JEOL Ltd.Google Scholar
First citation Wilson, A. J. C. (1949). The probability distribution of X-ray intensities. Acta Cryst. 2, 318–321.Google Scholar

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