First-principles study of cation distribution in eighteen closed-shell AIIB2IIIO4 and AIVB2IIO4 spinel oxides

Using a first-principles band-structure method, we have systematically studied the cation distribution in closed-shell $A^{\mathrm{II}}{B}_2^{\mathrm{III}}{\mathrm{O}}_4$ and $A^{\mathrm{IV}}{B}_2^{\mathrm{II}}{\mathrm{O}}_4$ spinels where the group-II atoms are Mg, Zn, and Cd, the group-III atoms are Al, Ga, and In, and the group-IV atoms are Si, Ge, and Sn. The total energies, the structural parameters, and the band gaps of these compounds in both normal and inverse spinel structures are calculated. Compared with previous model studies, we show that an atomistic method is crucial to correctly identify the stability of the spinels and to calculate the anion displacement parameter u. The preference of cations with delocalized valence d states (e.g., Zn) to form covalent tetrahedral bonds also plays a significant role in determining the cation distribution in the spinels. Furthermore, the electronic structures of these spinel compounds depend strongly on the cation distribution. For most of the spinels studied here, the calculated band gaps for the inverse spinels are smaller than the corresponding normal spinels except for $\mathrm{Sn}{B}_2^{\mathrm{II}}{\mathrm{O}}_4.$