Resolution of the Ambiguity of Valence States in Spinels Containing Manganese and Iron

The dilemma of whether [${\mathrm{Fe}}^{+3\mathrm{}}$ ${\mathrm{Mn}}^{+2\mathrm{}}$] or [${\mathrm{Fe}}^{+2\mathrm{}}$ ${\mathrm{Mn}}^{+3\mathrm{}}$] are the stably coexisting species on the octahedrally ligated sites of the spinel structure has been resolved by the application of a crystallographic, rather than a magnetic criterion. The solid solution systems ${\left(\mathrm{Zn}\right[{\mathrm{Mn}}_2\left]{\mathrm{O}}_4\right)}_{1-x}·{\left({\mathrm{Zn}}_{0.5}{\mathrm{Ge}}_{0.5}\right[\mathrm{FeMn}\left]{\mathrm{O}}_4\right)}_x$ and ${\left(\mathrm{Zn}\right[\mathrm{FeMn}\left]{\mathrm{O}}_4\right)}_x·{\left({\mathrm{Zn}}_{0.5}{\mathrm{Ge}}_{0.5}\right[{\mathrm{Mn}}_2\left]{\mathrm{O}}_4\right)}_{1-x}$ were synthesized, and their lattice constants were determined. The compositions in these systems for which cooperative tetragonal distortion occurs, due to the Jahn-Teller effect for ${\mathrm{Mn}}^{+3\mathrm{}}$, depend on whether [${\mathrm{Fe}}^{+3\mathrm{}}$ ${\mathrm{Mn}}^{+2\mathrm{}}$] or [${\mathrm{Fe}}^{+2\mathrm{}}$ ${\mathrm{Mn}}^{+3\mathrm{}}$] are stably coexisting species. The crystallographic findings are in complete agreement with the latter valence assignment. Furthermore, the axial ratios are found to be in quantitative agreement with the theory of cooperative distortions advanced by Wojtowicz, provided that the valence assignment [${\mathrm{Fe}}^{+2\mathrm{}}$ ${\mathrm{Mn}}^{+3\mathrm{}}$] is assumed. The valence behavior observed in the systems studied probably obtains for most other spinels in which iron and manganese coexist on the octahedrally ligated sites.