Asymmetric cation nonstoichiometry in spinels: Site occupancy in Co2ZnO4 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(ATd) and B atom ΔH(BOh) 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 Rh2ZnO4. These results show that Co2ZnO4 is heavily Co nonstoichiometric above 500 deg. C, whereas Rh2ZnO4 is slightly Zn nonstoichiometric. We found that, in general, the calculated ΔH(ATd) is smaller than ΔH(BOh), 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.