In-situ neutron diffraction study of non-convergent cation ordering in the(Fe3O4)(1-x)(MgAl2O4)(x) spinel solid solution

Non-convergent cation ordering in the (Fe3O4)(1-x)(MgAl2O4)(x) solid soluti on was investigated using in-situ time-of-flight neutron powder diffraction . The approach to equilibrium in a sample with x = 0.75 was observed at 923 K by performing in situ structure refinements at intervals of 5 min, and t he ordering behavior was traced through the time-dependence of the lattice parameter, the cation-oxygen bond lengths, and the cation-site scattering l engths. The data are consistent with a two-stage kinetic process in which r elatively rapid exchange of Fe3+ with Mg and Fe2+ between tetrahedral and o ctahedral sites was followed by slower exchange of Mg with Al. The Fe3+ cat ions are shown to order onto tetrahedral sites, contrary to the predictions of thermodynamic models for the solid solution. Equilibrium cation distributions in samples with x = 0.4, 0.5, and 0.75 wer e determined between 1073 and 1273 K by combining the structure refinements with measurements of saturation magnetization in quenched material. The ad opted cation distribution was a compromise between the normal and inverse d istributions observed in the end-members. The conflict of site preference b etween these two ordering schemes resulted in a simple behavior in the midd le of the solid solution in which Al occurred predominantly on octahedral s ites and the Mg, Fe2+, and Fe3+ cations were distributed randomly over the remaining sites. The ordering scheme adopted away from the middle of the so lid solution was obtained by combining this pseudo-random scheme with a tet rahedral site preference of Fe3+ relative to Mg and Fe2+. Comparison of the structure refinements with published thermodynamic models demonstrates tha t quantitative agreement was poor between calculated and observed behavior in this system. Qualitative agreement with the O'Neill-Navrotsky thermodyna mic model was found near the middle of the solid solution.