Infinitesimal lattice-constant treatment of liquid

Abstract

The gas-liquid phase transition of a mono-atomic molecular fluid is studied by placing atoms and vacancies in cubic cells of a simple cubic lattice and by reducing the lattice constant to infinitesimal. The cluster variation method is used to formulate the entropy for three choices of the basic clusters: all shapes and orientations of cell pairs, all cell triplets and all cell quartets. The first two cases fail to derive a stable liquid phase. When we introduce certain approximations to the basic iterative equations of the quartet case, a stable liquid phase appears, although numerical results violate certain thermodynamic relations. The triplet formulation leads to the Persus-Yevick equation as a linearized form, and is also related to the hyper-netted chain equation through a slight modification.