Cluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculations

The cluster expansion (CE) method has been used to evaluate configurational properties in multicomponent systems based on the density-functional theory (DFT) calculations. Appropriate selections of not only clusters but also structures for DFT calculations (DFT structures) are crucial for the accuracy and the efficiency of the CE. In a conventional procedure to construct the CE, the CE error is reduced mainly through an appropriate selection of clusters. In the present paper, we propose an improved procedure that systematically leads to optimal selections of both clusters and DFT structures. DFT structures are chosen to cover as much of the configurational space as possible. During the iterative process, the predictive power of the out-of-sample structures can be increased up to the accuracy that is required to describe alloy thermodynamics. We apply the procedure to configurational behaviors in a simple MgO-ZnO pseudobinary system and in a complex MgAl₂O₄ system. The CE error is reduced in both systems, in particular, in the complex system, thereby significantly improving configurational properties at high temperatures compared with the conventional CE procedure.