The symmetry of electron diffraction zone axis patterns

TLDR

Electron diffraction of fast electrons by thin slabs has been studied using group theory and graphical construction, and convergent beam and bend extinction contour techniques offer richer information than conventional patterns. The study aims to examine the symmetry properties of convergent beam and bend extinction contour diffraction patterns. The authors provide graphical representations and tables linking diffraction groups to specimen and crystal point groups, enabling crystal point group determination from convergent beam or bend contour patterns. The pattern symmetries are described by thirty-one diffraction groups, each isomorphic to a diperiodic plane figure point group and a Shubnikov group, and the method was demonstrated experimentally on germanium and gallium‑arsenide specimens. The tables assume the symmetric Laue condition and neglect irreducible lattice.

Abstract

The convergent beam and bend extinction contour techniques of electron microscopy are capable of providing much more information than can be obtained from conventional diffraction patterns and it is the objective of this work to examine the symmetry properties of each of these patterns. The diffraction of fast electrons by a thin parallelsided slab has been studied by group theory and by a graphical construction. We find that the pattern symmetries may be described by thirty-one diffraction groups and that each of these diffraction groups is isomorphic to one of the point groups of diperiodic plane figures and to one of the thirty-one Shubnikov groups of coloured plane figures. A graphical representation of each diffraction group is given, together with tables showing how the diffraction groups are related to the specimen point groups and under certain assumptions to the crystal point groups. These tables assume the symmetric Laue condition and ignore the presence of irreducible lattice translations normal to the slab. By using the tables, crystal point groups can be obtained from convergent beam or bend contour patterns. The method is demonstrated by experiments on several materials, but particularly on germanium and gallium-arsenide specimens since the similarity of these materials exemplifies the sensitivity of the technique.