Asymmetric cation nonstoichiometry in spinels: Site occupancy in Co ₂ZnO₄ and Rh₂ZnO₄

Two cations A and B in A₂BO₄ spinels appear in precise 2:1 Daltonian ratio ("line compounds") only at very low temperature. More typically, at finite temperature, they tend to become either A rich or B rich. Here we survey the experimentally observed stoichiometry asymmetries and describe the first-principles framework for calculating these. Defect calculations based on first principles are used to calculate the enthalpies of substitution of A atom ΔH(AT_d) and B atom ΔH(BO_h) and determine their site occupancies leading to (non)-stoichiometry. In Co₂ZnO₄, the result of the calculation for site occupancy compares well with that measured via anomalous x-ray diffraction. Further, the calculated phase boundary also compares well with that measured via Rietveld refinement of x-ray diffraction data on bulk ceramic sintered samples of Co₂ZnO₄ and Rh ₂ZnO₄. These results show that Co₂ZnO ₄ is heavily Co nonstoichiometric above 500C, whereas Rh ₂ZnO₄ is slightly Zn nonstoichiometric. We found that, in general, the calculated ΔH(AT_d) is smaller than ΔH(BO_h), if the A-rich competing phase is isostructural with the A₂BO₄ host, for example, A₂AO₄, whereas B-rich competing phase is not, for example, BO. This observation is used to qualitatively explain nonstoichiometry and solid solutions observed in other spinels.