Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions

Abstract

Detailed observations are made of the breakdown of Friedel's law in electron diffraction, using the single-crystal intensity distribution from cadmium sulfide in the [21{\bar 3}0] orientation. It has been found by experiment that no breakdown of Friedel's law occurs in the zero-order beam distribution. An analysis of the problem due to Moodie, using multiple-scattering diagrams, has also led to this result. Multiple-scattering diagrams are used here to illustrate the symmetry properties of the zero-beam distribution. Rules are given for the deduction of the other symmetry elements of the projected structure from the diffraction-pattern symmetry, and from the occurrence of dynamic extinction bands in the kinematically forbidden reflections. These are illustrated by further pictures from cadmium sulfide. This analysis is simplified in the present work by neglecting non-zero-layer interactions. Results obtained by n-beam calculation using the multi-slice method show the possibility of quantitative interpretation, and of absolute orientation determination. The limitations of the systematic dynamic approximation and also of a systematic approximation using corrected scattering potentials are examined for this substance.