Calculation of phase diagrams of binary fcc and ideal hcp alloys undergoing ordering transitions

The tetrahedron approximation of the cluster variation method (CVM) has been employed to investigate phase diagrams having fcc-based ordered and disordered phases. This approximation is also applicable to the binary hcp ordered structures with ideal axial ratio. The CVM developed by Kikuchi consists of calculating approximate expressions for the number of configurations and hence entropy of a crystal lattice having definite distribution of clusters (points, pairs, triangles, tetrahedra, etc.) of lattice points which in general may be occupied by one of a given set of atomic species. Tetrahedral multi-atom interactions denoted by α and β are utilized for expressing the configurational energy. The equilibrium cluster distribution is then found by minimizing the free energy by utilizing the natural iteration method developed by Kikuchi. The effect of α and β parameters on the topology of the resulting phase diagrams is observed by assigning several negative and positive values to them. The invariant reactions were also determined in each case. Finally a study was made on the Cd-Mg diagram.