Site occupancy of Fe²⁺, Fe³⁺ and Ti⁴⁺ in titanomagnetite determined by valence-difference contrast in synchrotron X-ray resonant scattering

A synchrotron X-ray diffraction study of a single crystal of titanomagnetite shows that the cation distribution of Fe²⁺, Fe³⁺ and Ti⁴⁺ is of the inverse-spinel type. The valence-difference contrast (VDC) method of resonant scattering was applied at a wavelength of λ = 1.7441 Å (E = 7.1085 keV) within the pre-edge of the Fe K absorption spectrum, utilizing the large difference in the real part of anomalous scattering factors, between −7.45 and −6.50, for Fe²⁺ and Fe³⁺, respectively. The most plausible atomic arrangement in Ti_0.31Fe_2.69O₄ obtained from our analysis is [Fe³⁺_1.00]^A[Fe³⁺_0.38Fe²⁺_1.31Ti⁴⁺_0.31]^BO₄, where A and B in an AB₂O₄-type structure correspond to the tetrahedral and octahedral sites, respectively. This result suggests that titanomagnetite has the complete inverse-spinel structure continuously from the end-member of magnetite, even in the case of relatively high Ti content. The physical properties may be described by the Néel model, which claims that Fe³⁺ preferentially occupies the tetrahedral site, within a Ti-poor half-region of the solid solution. Based on the ordering scheme the magnetic structure of titanomagnetite is considered to be analogous to that of magnetite. The combination of circularly polarized X-rays and a horizontal-type four-circle diffractometer used in this VDC technique has the advantage of increasing the experimental accuracy and freedom with the simultaneous reduction of experimental noise.