Bloch wave symmetry in electron diffraction

Abstract

The symmetry of Bloch waves in high energy electron diffraction is described in two dimensions (zero Laue zone) with the aid of two-coloured symmetry elements, in reciprocal and real space. At symmetrical positions in the Brillouin zone the Bloch wave amplitude in real space can be referred to 63 two-coloured, two-dimensional space groups. The symmetry of Bloch wave coefficients about these positions can be described in terms of the 21 two-coloured point groups. The notation follows a scheme analogous to the International Tables for Crystallography. Extinctions of the kinematically forbidden reflections in the space group pmg and Friedels law deviation in the non-centrosymmetric p3 are shown as examples.