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

The A(2)BO(4) 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 similar to 98% successful.