Single crystals of spinel and hausmannite having seven different compositions in the MgAl2O4-MgMn2O4-MnMn2O4 system were synthesized and structurally and chemically characterized by X-ray diffraction and electron microprobe techniques. As predicted, tetrahedral and octahedral bond lengths increase with increasing substitutions of Mn2+ for Mg and Mn3+ for Al, respectively. A transition from cubic to tetragonal symmetry occurs at a critical concentration of Mn3+ > 1.4 atoms per formula unit as a result of the Jahn-Teller distortion around octahedrally coordinated Mn3+.

The present data in conjunction with data from the literature provide a basis for quantitative analyses of the cation polyhedral-distortion parameters and their variations in spinel- and hausmannite-type structures (Fdm and I41/amd, respectively). In contrast to the linear correlation between <λM> (octahedral quadratic elongation) and σ2M (octahedral bond-angle variance) observed for many silicates and isomorphic structures, these two distortion parameters are not correlated in multiple oxides with spinel- and hausmannite-type structures. By using a model of multiple linear regression, it is demonstrated that <λM> varies as a function of both σ2M and ΔM (octahedral bond-length distortion). The degree of octahedral distortion is significant in the spinel structures and is in fact comparable with that calculated for the hausmannite-type structures. The degree of octahedral distortion is related to steric effects in both spinel- and hausmannite-type structures, whereas the electronic effects caused by Mn3+ account for the transition from cubic to tetragonal symmetry.

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