Crystal chemistry of the MgAl2O4-MgMn2O4-MnMn2O4 system: Analysis of structural distortion in spinel- and hausmannite-type structures

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 octahedral ly 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 (Fd (3) over barm and I4(1)/amd respectively). In contrast to the linear correlation between <lambda(M)> (octahedral quadratic elongation) and sigma(2)(M) (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 <lambda(M)> varies as a function of both sigma(2)(M) and Delta(M) (octahedral bond-length distortion). The degree of octahedral distortion is significant in the spine' 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 Mi(3+) account for the transition from cubic to tetragonal symmetry.