First-principles study of cation disordering in Mg Al2 O4 spinel with cluster expansion and Monte Carlo simulation

The temperature dependence of cationic disorder in Mg Al2 O4 spinel is investigated using a combination of first-principles total-energy calculations, a cluster expansion, and canonical Monte Carlo simulations. The formation energies of the possible cation-disordered structures within the spinel unit cell are predicted to be all positive, suggesting that the ground state is the normal spinel in consistency with a widely accepted view. The temperature dependence of cationic disorder is well reproduced by considering many effective cluster interactions up to quadruplets. The order-disorder transition temperature is estimated at about 860 K based on the anomaly of specific heat. The cluster expansion of the volume of Mg Al2 O4 indicates that it decreases as more cations exchange.