Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.5, p. 286

Section Zone-axis patterns from CBED

P. Goodmanb Zone-axis patterns from CBED

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Symmetry analysis is necessarily tied to examination of patterns near relevant zone axes, since the most intense N-beam interaction occurs amongst the zero-layer zone-axis reflections, with in addition a limited degree of upper-layer (higher-order Laue zone) interaction. There will generally be several useful zone axes accessible for a given parallel-sided single crystal, with the regions between axes being of little use for symmetry analysis. Only one such zone axis can be parallel to a crystal surface normal, and a microcrystal is usually chosen at least initially to have this as the principal symmetry axis. Other zone axes from that crystal may suffer mild symmetry degradation because the N-beam lattice component (`excitation error' extension) will not have the symmetry of the structure (Goodman, 1974[link]; Eades et al., 1983[link]).

Upper-layer interactions, responsible for imparting three-dimensional information to the zero layer, are of two types: the first arising from `overlap' of dynamic shape transforms and causing smoothly varying modulations of the zero-layer reflections, and the second, caused by direct interactions with the upper-layer, or higher-order Laue zone lines, leading to a sharply defined fine-line structure. These latter interactions are especially useful in increasing the accuracy of space-group determination (Tanaka et al., 1983[link]), and may be enhanced by the use of low-temperature specimen stages. The presence of these defect lines in convergent-beam discs, occurring especially in low-symmetry zone-axis patterns, allows symmetry elements to be related to the three-dimensional structure (Section[link]; Fig.[link]).

To the extent that such three-dimensional effects can be ignored or are absent in the zero-layer pattern the projection approximation (Chapter 5.2[link] ) can be applied. This situation most commonly occurs in zone-axis patterns taken from relatively thin crystals and provides a useful starting point for many analyses, by identifying the projected symmetry.


First citation Eades, J. A., Shannon, M. D. & Buxton, B. F. (1983). Crystal symmetry from electron diffraction. In Scanning electron microscopy, 1983/III, pp. 1051–1060. Chicago: SEM Inc.Google Scholar
First citation Goodman, P. (1974). The role of upper layer interactions in electron diffraction. Nature (London), 251, 698–701.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

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