Space is continuous-continuous-displacement treatment of phase-separating diagrams

The conventional crystal statistics treats permutation of species placed at lattice points of a fixed lattice. The present work removes the fixed lattice restriction and allows displacement of atoms from lattice points of a fixed reference lattice, This extension responds to the need of taking into account local lattice distortion caused by size differences of species in alloys, Because the continuous displacement concept had not been studied before in the cluster variation method formulation, the current series started with the two-dimensional lattices. This work is the first in the series to venture into the three-dimensional lattices, We use the pair approximation for fcc and work out phase diagrams of phase-separating systems. The step-by-step formulation of the theory is presented. Numerical computations on a number of model systems show asymmetrical phase diagrams, Various future applications are discussed.