X-ray scattering factors for ionic crystals with complete electron shells

Expressions of the X-ray scattering factors were derived for ionic crystals with complete electron shells by using the wave functions of free ions. The non-orthogonality of the atomic wave functions in a crystalline state was taken into account by means of Löwdin’s orthogonalization method when presenting the electron density of crystals. In the case of a small overlap between the wave functions localized at the lattice sites, it was plausible to describe mathematically a crystal ion containing small overlap charge contribution in addition to the free-ion contribution. As an application, the scattering factors for the LiF crystal were computed. The theoretical results obtained agree well with recent experimental data.