Statistical method for molecular dynamics in mixed crystals

We introduce a simple statistical method in molecular dynamics (MD) to study the phase transitions of mixed crystals with arbitrary composition. In the statistical sense, the relation between a mixed crystal and its constituent micro-crystals is analogous to the relation between a system and the samples of its components. Therefore, the features of the mixed crystal can be obtained from the statistical distribution of its micro-crystals. As an example of this method, the analysis of the topologies of all sampling supercells is shown to help reduce the computational work in the study of the perovskite structure RbxK1−xCaF3.