Properties of crystalline solutions were generally dependent not only upon their chemical composition but also upon the configurations of solute atoms and/or point defects. Quantitative knowledge of the configuration-dependent properties was therefore essential for materials design. The cluster expansion method was widely used to describe the configurational properties. Increases in computational power and advances in numerical techniques permitted the performance of a large set of systematic first-principles calculations based upon density functional theory to be combined with cluster expansion calculations. Here, the authors’ procedure of cluster expansion with optimal selections of clusters and density functional theory structures was described. Two examples of such calculations were then shown. One was the cation arrangement in a series of spinel oxides. The other was arrangement of the oxygen vacancy in a series of tin sub-dioxides.

Phase Relationships and Structures of Inorganic Crystals by a Combination of the Cluster Expansion Method and First Principles Calculations. I.Tanaka, A.Seko, A.Togo, Y.Koyama, F.Oba: Journal of Physics - Condensed Matter, 2010, 22[38], 384207