Cluster variation method in the computational materials science

Cluster Variation Method (CVM) has been very successful in the computations of alloy phase diagrams as well as in many problems of the materials science related to the phase transitions. Originally, CVM was developed in the framework of the so-called rigid lattice approximation, but it has recently been extended to include continuous atomic displacements due to thermal lattice vibration and local atomic distortion due to size mismatch of the constituent atoms. In the present study, we focus our attention on the latter continuous displacement treatment of CVM. The continuous displacement (CD) formulation of the CVM is applied to study the phase stability of the binary alloys. The basic idea is to treat an atom which is displaced by r from its reference lattice point as a species designated by r. The effects of continuous atomic displacement on the thermodynamic quantities and phase transitions of binary alloys are investigated in detail. We also discuss the extension of the CD treatment of CVM to the calculations of solid-liquid and gas liquid phases transitions.