Direct coupling of first-principles calculations with replica exchange Monte Carlo sampling of ion disorder in solids.

We demonstrate the feasibility of performing sufficient configurational sampling of disordered oxides directly from first-principles without resorting to the use of fitted models such as cluster expansion. This is achieved by harnessing the power of modern-day cluster supercomputers using the replica exchange Monte Carlo method coupled directly with structural relaxation and energy calculation performed by density functional codes. The idea is applied successfully to the calculation of the temperature-dependence of the degree of inversion in the cation sublattice of MgAl