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

Abstract

Density functional theory (DFT) calculations have been performed on A²⁺B₂³⁺O₄²⁻ (where A²⁺ = Fe, Ni or Zn, and B³⁺ = 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.