VALIDITY OF GENERALIZED SCATTERING EQUATIONS AND CORRESPONDING INELASTIC-CROSS-SECTION EXPRESSIONS FOR COMPREHENSIVE ELECTRON-DIFFRACTION CONDITIONS

Generalized scattering equations for electron diffraction in a crystal line environment have recently been derived with the assumption that t he zeroth-order Laue zone (ZOLZ) lies parallel to the crystal surface (or alternatively that the zone axis is parallel to the crystal surfac e normal) [L. J. Alien and T. W. Josefsson, Phys. Rev. B 52, 3184 (199 5)]. The contribution from higher-order Laue zones (HOLZ's) was not co nsidered. We show that these scattering equations are in fact valid fo r general orientations of the ZOLZ with respect to the crystal surface , except for the specific case where the ZOLZ lies perpendicular to th e surface. Furthermore, a widely applicable expression for the cross s ection for any type of inelastic scattering in a crystal is shown to b e valid for any orientation of the ZOLZ and allows the inclusion of re flections in the HOLZ's.