Selection rules for Bloch wave scattering for HREM imaging of imperfect crystals along symmetry axes

Abstract

A Bloch wave analysis is used to investigate high-resolution electron microscope (HREM) imaging of crystals containing atomic displacements due to strain. In the absence of interband scattering, the shifts of peaks and troughs in the image will correspond to the displacements of the atoms in the exit surface. Interband scattering will shift the image peaks away from the actual atom positions and modify the apparent magnitude of the displacement identified by the observed image peak positions. By considering the case of seven-beam imaging of a cubic crystal aligned along a ⟨111⟩ axis, it is shown that the symmetry of the Bloch waves leads to selection rules for the interband scattering, similar to those seen for dipole electron excitations in atoms. It is also shown that, to first order, no intraband scattering can occur.

Acknowledgments

The authors acknowledge useful discussions with Professor K. J. Hemker and Dr B. Mendis. PBH thanks the Head of the Department of Materials, University of Oxford, for provision of facilities. PDN and EC thank the Department of Materials, University of Oxford, for funding.