First-principles study of cation disordering inMgAl2O4spinel with cluster expansion and Monte Carlo simulation

The temperature dependence of cationic disorder in $\mathrm{Mg}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ 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 $860\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ based on the anomaly of specific heat. The cluster expansion of the volume of $\mathrm{Mg}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ indicates that it decreases as more cations exchange.