Exploring Structures and Phase Relationships of Ceramics from First Principles

Statistical thermodynamics plays a crucial role in modern materials science. The free energy of compounds is indispensable for discussing the phase stability. In general, a number of phenomena contribute to the temperature dependence of the free energy. In multicomponent systems, an important contribution to the free energy arises from the atomic configuration. The configurational effects have been estimated by density functional theory (DFT) calculations and the cluster expansion (CE) method. In this article, methodologies for computing the configurational properties based on DFT calculations and the CE method are reviewed. Several applications of the methodologies to the configurational behaviors in ceramic systems are then discussed. We have constructed a phase diagram for a pseudobinary ZnO-MgO system using a combination of the CE method and the cluster variation method (CVM). Instead of the CVM, Monte Carlo (MC) simulations can be adopted to take account of the configurational contribution. Using a combination of DFT calculations and the canonical MC simulations via the CE method, we have investigated the temperature dependence of the cation distribution in MgAl2O4 spinel. A similar combined approach has been applied to elucidate the stable cation ordering in spinel oxides and the structure and phase stability of a series of nonstoichiometric SnO2-x compounds.