Spinel single crystals of 19 compositions along the magnetite-ulvöspinel join were synthesized by use of a flux-growth method. To obtain quantitative site populations, the crystals were analyzed by single-crystal X-ray diffraction, electron-microprobe techniques, and Mössbauer spectroscopy. All results were processed by using an optimization model.
The unit-cell parameter, oxygen fractional coordinate, and tetrahedral bond length increase with increasing ulvöspinel component, whereas the octahedral bond length decreases marginally. These changes result in sigmoidal crystal-chemical relationships consistent with cation substitutions in fully occupied sites. As a first approximation, the Akimoto model T(Fe1−X3+FeX2+)M(Fe2+Fe1−X3+TiX)O4 describes the cation substitutions. Deviations from this model can be explained by an electron exchange reaction TFe2+ + MFe3+ = TFe3+ + MFe2+, which causes MFe2+ ≠ 1 and TFe2+/Ti ≠ 1. The resultant S-shaped trends may be related to a directional change in the electron exchange reaction at Ti ≈ 0.7 apfu. In general, variations in structural parameters over the whole compositional range can be split into two contributions: (1) a linear variation due to the TFe3+ + MFe3+ = TFe2+ + MTi4+ chemical substitution and (2) non-linear variations caused by the internal electron exchange reaction.
In accordance with bond-valence theory, strained bonds ascribable to steric effects characterize the structure of magnetite-ulvöspinel crystals. To relax the bonds and thereby minimize the internal strain under retained spinel space group symmetry, the electron exchange reaction occurs.