Mixing and non-stoichiometry in Fe-Ni-Cr-Zn-O spinel compounds: density functional theory calculations.

Density functional theory (DFT) calculations have been performed on A(2+)B2(3+)O4(2-) (where A(2+) = Fe, Ni or Zn, and B(3+) = Fe or Cr) spinel oxides in order to determine some of their thermodynamic properties. Mixing energies were calculated for Fe3O4-NiFe2O4, Fe3O4-ZnFe2O4, Fe3O4-FeCr2O4, NiFe2O4-ZnFe2O4, NiFe2O4-NiCr2O4, FeCr2O4-NiCr2O4, FeCr2O4-ZnCr2O4 and ZnCr2O4-ZnFe2O4 pseudo-binaries based on special quasi random (SQS) structures to account for cationic disorder. The results generally agree with available experimental data and the rule that two normal or two inverse spinel compounds easily form solid solutions, while inverse-normal spinel mixtures exhibit positive deviation from solid solution behavior (i.e. immiscibility). Even though the NiFe2O4-NiCr2O4 and Fe3O4-FeCr2O4 systems obey this rule, they exhibit additional features with implications for the corresponding phase diagrams. In addition to mixing enthalpies, non-stoichiometry was also considered by calculating the energies of the relevant defect reactions resulting in A, B and O excess (or deficiency). The DFT calculations predict close to zero or slightly exothermic reactions for both A and B excess in a number of spinel compounds.