Thermodynamics of Zn_xMn_3-xO₄ and Mg_1-zCu_zCr₂O₄ spinel solid solutions

The thermodynamic properties of Zn_xMn_3-xO₄ and Mg_1-zCu_zCr₂O₄ spinel solid solutions have been studied using high-temperature oxide melt solution calorimetry. Except for MgCr2O4 spinel, which possesses cubic structure, the other three end-members are tetragonal. The enthalpies of mixing are small endothermic and fit subregular solution behavior. The main contribution to the energetics of mixing of both spinel systems comes from the difference in the crystal structure between the end-members: a change in the tetragonal distortion for Zn_xMn_3-xO₄ solid solutions and a transition from cubic to tetragonal for the Mg_1-zCu_zCr₂O₄ system. If all Mg_1-zCu_zCr₂O₄ spinels possessed the same structure, the mixing enthalpies would be close to zero. Because both series have normal cation distributions, the entropies of mixing are equal to the configurational entropies of mixing of Zn²⁺ and Mn²⁺ and of Mg²⁺ and Cu²⁺ on tetrahedral sites, and the activities would follow Raoult's law. The calculated Gibbs energy of mixing confirms the absence of solvus at any temperature for both systems.