Continuous Displacement Cluster Variation Method for the Study of Local Lattice Distortion in an Alloy

Systematic studies on the lattice expansion and order-disorder phase equilibria are attempted for the A-B binary alloy on the two-dimensional square lattice. The atomic pair potentials are described by the Morse potential and the configurational entropy is formulated within the pair approximation of the Cluster Variation Method (CVM). The lattice expansion of the uniformly deformable lattice is enhanced by introducing lattice vibration effects through the Debye–Grüneisen model. The introduction of the local lattice distortion by continuous displacement CVM (CDCVM) further increases the lattice expansion. The transition temperature obtained for a uniformly deformable lattice is reduced by the thermal vibration effects, which is interpreted as the curvature effects of atomic pair potentials. The local lattice relaxation further reduced the transition temperature, which is ascribed to the additional freedom of distributing atomic pairs over a wide range of distances.