The continuous displacement CVM treatment of alloy systems

The continuous displacement (CD) formulation of the CVM allows atoms to be displaced from the reference rigid lattice points. When an atom displaced at r is regarded as a species r, the system is an alloy of an infinite number of species and the CVM entropy can be applied to the system. This paper presents the basic concepts behind the method and its applications. After the method is introduced, applications are presented to 2-dimensional systems including the single component case, surface relaxation and binary alloys of phase separating kind. In the surface studies, the angle dependence of the displacements is plotted in the polar coordinates and a snapshot of the displacements is simulated. In the surface layer, calculations showed inward or outward shift of the layers, For phase separating binary alloys, the change of lattice constant with the composition and the reduction of the transition temperature are shown. Comments are made on future applications.