Residual-density mapping and site-selective determination of anomalous scattering factors to examine the origin of the Fe K pre-edge peak of magnetite

The electron-density distribution and the contribution to anomalous scattering factors for Fe ions in magnetite have been analyzed by X-ray resonant scattering at the pre-edge of Fe K absorption. Synchrotron X-ray experiments were carried out using a conventional four-circle diffractometer in the right-handed circular polarization. Difference-Fourier synthesis was applied with a difference in structure factors measured on and off the pre-edge (E_on = 7.1082 keV, E_off = 7.1051 keV). Electron-density peaks due to X-ray resonant scattering were clearly observed for both A and B sites. The real part of the anomalous scattering factor f' has been determined site-independently, based on the crystal-structure refinements, to minimize the squared residuals at the Fe K pre-edge. The f' values obtained at E_on and E_off are -7.063 and -6.682 for the A site and -6.971 and -6.709 for the B site, which are significantly smaller than the values of -6.206 and -5.844, respectively, estimated from the Kramers-Kronig transform. The f' values at E_on are reasonably smaller than those at E_off. Our results using a symmetry-based consideration suggest that the origin of the pre-edge peak is Fe ions occupying both A and B sites, where p-d mixing is needed with hybridized electrons of Fe in both sites overlapping the neighbouring O atoms.