Simple Point-Ion Electrostatic Model Explains the Cation Distribution in Spinel Oxides

The A2BO4 spinel oxides are distinguished by having either a normal (N) or an inverse (I) distribution of the A, B cations on their sublattices. A point-ion electrostatic model parametrized by the oxygen displacement parameter u and by the relative cation valencies Z{A} vs Z{B} provides a simple rule for the structural preference for N or I: if Z{A}>Z{B} the structure is normal for u>0.2592 and inverse for u<0.2578, while if Z{A}<Z{B} the structure is normal for u<0.2550 and inverse for u>0.2578. This rule is illustrated for the known spinel oxides, proving to be ∼98% successful.