Validity of generalized scattering equations and corresponding inelastic-cross-section expressions for comprehensive electron diffraction conditions

Abstract

Generalized scattering equations for electron diffraction in a crystalline environment have recently been derived with the assumption that the zeroth-order Laue zone (ZOLZ) lies parallel to the crystal surface (or alternatively that the zone axis is parallel to the crystal surface normal) [L. J. Allen and T. W. Josefsson, Phys. Rev. B 52, 3184 (1995)]. The contribution from higher-order Laue zones (HOLZ’s) was not considered. We show that these scattering equations are in fact valid for general orientations of the ZOLZ with respect to the crystal surface, except for the specific case where the ZOLZ lies perpendicular to the surface. Furthermore, a widely applicable expression for the cross s..