Classification of spinel structures based on first-principles cluster expansion analysis

We examine general trends of the ground-state structure and the order-disorder behavior in spinel oxides. We first determine the cation ordering in the ground state and investigate the temperature dependence of the cation distribution in IV-II spinel oxides by combining calculations based on the density-functional theory with the cluster-expansion method. We predict that Mg₂SnO₄, Zn₂SnO₄, and Zn₂TiO₄ have the inverse configuration while Mg₂TiO₄ has the normal configuration. On the basis of the results for IV-II spinel oxides and those for II-III spinel oxides, the spinels are then classified. The ground-state structure and order-disorder behavior can be classified using the parameters evaluated from the cluster expansion analysis.