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.

In commercial practice, two-step ageing is commonly used in Al-Zn-Mg alloys to produce a fine dispersion of η′ precipitates to accentuate the mechanical properties and resistance to stress corrosion cracking. While this is true in Al-Zn-Mg alloys, two-step ageing leads to inferior properties in Al-Mg-Si alloys. This controversial behaviour in different alloys can be explained by Pashley’s Kinetic model. Pashley’s model addresses the stability of clusters after two-step ageing. In the development of the model, the surface energy term between cluster and matrix is taken into account while the coherency strains between the cluster and matrix are not considered. In the present work, a model is developed which takes into account the coherency strains between cluster and matrix and defines a new stability criterion, inclusive of strain energy term. Experiments were done on AA 7010 aluminium alloy by carrying out a two-step ageing treatment and the results fit the new stability criterion. Thus it is found that the new model for two-step ageing is verified in the case of Al-Zn-Mg alloy.

The thermodynamic origin of various types of phase diagrams in simple binary systems exhibiting two phases (e.g. a liquid and a solid phase) has been examined using the regular solution model. The necessary conditions for the occurrence of each of these types are identified in terms of the appropriate intersections of the miscibility gap boundaries (in solid/liquid phases) and the liquidus/solidus/iso-𝐺 curves. Thus, the regions of occurrence of the different types of possible phase diagrams in the space of the regular solution interchange energy parameters (𝑊^𝛼, 𝑊^𝛽) are clearly delineated. This analysis makes it easier to make intelligent initial selections of model (energy) parameters for their optimization in the calculation of phase diagrams using thermodynamic models such as CALPHAD/CVM.

The powerful framework of cluster expansion–cluster variation methods (CE–CVM) expresses alloy free energy in terms of energy (model) parameters, macroscopic variables (composition and temperature) and microscopic variables (correlation functions). A simultaneous optimization of thermodynamic and phase equilibria data using CE–CVM is critically dependent on giving good initial values of energy parameters, macroscopic and microscopic variables, respectively. No standard method for obtaining the initial values of the energy parameters is available in literature. As a starting point, a method has been devised to estimate the values of energy parameters from consolute point (miscibility gap maximum) data. Empirical relations among energy parameters, temperature (𝑇_c), composition (𝑥_c) and 𝑑²}𝑇/𝑑𝑥² at the consolute point, have been developed using CE–CVM free energy functions for bcc and fcc structures in the tetrahedron and tetrahedron–octahedron approximations, respectively. Thus from the observed data of 𝑇_c, 𝑥_c and 𝑑²}𝑇/𝑑𝑥² in the above relations, good initial values of energy parameters can be obtained. Further, a necessary modification to the classical NR method for solving simultaneous nonlinear/transcendental equations with a double root in one variable and a simple root in the other has been presented.