Crystal chemistry of the MgAl (sub 2) O (sub 4) -MgMn (sub 2) O (sub 4) -MnMn (sub 2) O (sub 4) system; analysis of structural distortion in spinel- and hausmannite-type structures

Single crystals of spinel and hausmannite having seven different compositions in the MgAl (sub 2) O (sub 4) -MgMn (sub 2) O (sub 4) -MnMn (sub 2) O (sub 4) 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 Mn (super 2+) for Mg and Mn (super 3+) for Al, respectively. A transition from cubic to tetragonal symmetry occurs at a critical concentration of Mn (super 3+) >1.4 atoms per formula unit as a result of the Jahn-Teller distortion around octahedrally coordinated Mn (super 3+) . 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 (Fd3m and I4 (sub 1) /amd, respectively). In contrast to the linear correlation between <lambda (sub M) > (octahedral quadratic elongation) and sigma (super 2) (sub 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 (sub M) > varies as a function of both sigma (super 2) (sub M) and Delta (sub M) (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 Mn (super 3+) account for the transition from cubic to tetragonal symmetry.