Inelastic scattering of electrons by crystals. I. The theory of small-angle in elastic scattering

TLDR

The study investigates the theory of inelastic scattering for fast electrons transmitted through crystals, incorporating Bloch wave descriptions and Bragg reflection. Fast electrons are modeled as Bloch waves to account for Bragg reflection during crystal transmission. Solutions for small‑angle inelastic scattering show that interband transitions are forbidden for long‑range potentials, explain recent electron‑microscope diffraction contrast observations, predict a Poisson distribution of peak intensities, and reveal an asymmetric angular distribution in thick crystals consistent with experiments.

Abstract

The theory of inelastic scattering is studied for the transmission of fast electrons through crystals when the fast electrons are described by Bloch waves so that Bragg reflexion is also considered. Solutions for the wave amplitudes are obtained for the case of small-angle inelastic scattering and it is shown that interband inelastic scattering transitions of the fast electron are forbidden when the interaction potential is of the long range type which might arise in the excitation of Plasmon’s. This result would explain recent electron microscope observations of similar diffraction contrast effects obtained using elastically scattered or inelastically scattered electrons, and also shows that such inelastic scattering need not be considered in theories of diffraction contrast. The theory also predicts a Poisson distribution for the intensities of the various peaks observed in the energy spectrum of the transmitted electrons. In thick crystals, where anomalous absorption effects are important, the angular distribution of the scattered intensity round the Bragg diffraction spots is found to contain an asymmetry in qualitative agreement with the experimental observations.