SYMMETRIES IN REAL AND RECIPROCAL SPACE IN DYNAMICAL ELECTRON DIFFRACTION: A BLOCH-WAVE DESCRIPTION INCLUDING HIGHER LAUE ZONES
J. Gjonnes and V. Hansen
University of Oslo, Center for Materials Science, Gaustadallen 21, 0371 OSLO, Norway
Symmetry relations under dynamical scattering conditions deviate from those that apply to the kinematical case, by the explicit dependence on incident beam direction, in addition to the symmetry of the unit cell. This is exploited in the well-known convergent-beam electron diffraction procedures for determination of point group and space group symmetries [1,2].
A Bloch wave description of symmetry relations in dynamical electron diffraction was presented previously for centrosymmetrical projections [3]. This has now been extended to include higher-order Laue zones and non-centrosymmmetrical cases. Symmetries in real and reciprocal space are represented by extending the point group and space group notations used by International Tables of Crystallography to apply to Bloch waves. In the centrosymmetrical case this can be done in terms of the two-coloured symmetry groups introduced by Cochran [4]. Tables and figures for the 63 two-coloured space groups will be shown on the poster. Higher Laue zones can be included either by transition matrix elements with selection rules, or by a two-dimensional point groups of lower symmetry than the projection. Symmetry determination in connection with recent structures solved by electron diffraction will be discussed.