Abstract
We have performed first-principles density functional theory calculations to investigate the possible physical origins of the discrepancies between the existing theoretical and experimental studies on cation distribution in Mg${X}_{2}$O${}_{4}$ ($X$ $=$ Al, Ga, In) spinel oxides. We show that for MgGa${}_{2}$O${}_{4}$ and MgIn${}_{2}$O${}_{4}$, it is crucial to consider the effects of lattice vibrations to achieve agreement between theory and experiment. For MgAl${}_{2}$O${}_{4}$, we find that neglecting short-range order effects in thermodynamic modeling can lead to significant underestimation of the degree of inversion. Furthermore, we demonstrate that the common practice of representing disordered structures by randomly exchanging atoms within a small periodic supercell can incur large computational error due to either insufficient statistical sampling or finite supercell size effects.
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