Real and imaginary parts of the anisotropic atomic factor near the Fe K-edge: comparison between two theories and experiment for pyrite

The real and imaginary parts of the anisotropy of the iron atomic scattering factor are experimentally determined as functions of the X-ray energy near the iron K-edge in the FeS2 (pyrite) crystal. The anisotropy is a result of a deformation of electronic states induced by local asymmetry of atomic environment of iron atoms in this cubic crystal and provides a quantitative measure of that deformation. Some Bragg reflections, otherwise forbidden by screw-axis or glide-plane symmetry operations, are caused by this anisotropy and their structure factors are proportional to the anisotropy. The energy spectra and azimuthal angle dependence of the anisotropy-induced "forbidden"' reflections is studied and the phase of the anisotropy is determined from an interference of the "forbidden" reflections with different multiple-wave reflections. The energy dependence of the real and imaginary parts of anisotropy is shown to be in good agreement with theoretical curves calculated within two different approaches (the full multiple scattering method employing cluster muffin-tin potential and the pseudopotential ab initio calculations). It is found that the anisotropy is much more sensitive to atomic environment and to the theoretical parameters than the average absorption coefficient.