Theoretical explanation of the uniform compressibility behavior observed in oxide spinels

Simple algebraic equations show that the bulk compressibility in spinel-type compounds can be expressed by means of cation oxide polyhedral compressibilities and a term that accounts for the pressure effect on the internal oxygen position in the unit cell. The equations explain (i) the difference of compressibilities at octahedral and tetrahedral sites, (ii) why the macroscopic bulk modulus can be estimated as the average of these polyhedral bulk moduli, and (iii) the uniform behavior found in oxide spinels under hydrostatic pressure. Quantum-mechanical ab initio perturbed ion results on MgAl₂O₄, ZnAl₂O₄, ZnGa₂O₄, and MgGa₂O₄ direct spinels and on MgGa₂O₄ inverse spinel are reported to illustrate the interpretative capabilities of the proposed equations.