Universal Electrostatic Origin of Cation Ordering in A2BO4 Spinel Oxides

The crystal structures of A(2)BO(4) spinet oxides are classified as either normal or inverse, representing different distributions of the A and B cations over the tetrahedrally and octahedrally coordinated cation sites. These structures undergo characteristic structural changes as a function of temperature: (i) the nominally disordered inverse structure orders crystallographically at low T, and (ii) at finite temperatures, both inverse and normal develop characteristic distributions of cations associated with order disorder structural changes. We show here that all of these universal features emerge naturally from a simple point-ion electrostatic (PIE) model with a single adjustable parameter. Monte Carlo simulations of the PIE Hamiltonian provide quantitative order disorder characteristic temperatures. We show that, with the help of the PIE model, the magnitude of the temperatures can be inferred from the nominal charges of the atomic species in the spinet. Indeed, we show that characteristic order-disorder temperatures in 3-2 spinets (nominal charges Z(A) = 3 and Z(B) = 2) are approximately an order of magnitude lower than in 2-4 spinets, thus explaining why typical 3-2 samples exhibit much larger degrees of disorder than those belonging to the 2-4 class.