Phase diagram calculations : Contribution of AB intio and cluster variation methods

The possibility now exists of deriving phase diagrams at a high level of accuracy by combining both quantum mechanical and statistical thermodynamic contributions. These calculations have to take into account the local chemical environment, which is important in determining both the internal energy and the configurational entropy. The statistical treatment of short- and long-range order in solid solutions, and of order-disorder transformations needs to use the cluster variation method (CVM) or Monte Carlo simulations. The input of these methods is tile interaction parameters between the atoms called the cluster interactions. These parameters may be fitted using either thermodynamic and phase diagram data, such as enthalpies of formation or order-disorder temperatures, or stuctural data, such as long and short range order or site occupancies. However, this procedure is ambiguous since the nature of the most important cluster interactions (pairs, triplets, quadruplets etc), their range, and their composition dependence are a priori unknown. During the last decade, several attempts have been made to deduce the cluster interactions from first principle calculations. Two approaches are available for such calculations. In the first one, the energy of the completely disordered solid solution is calculated by the coherent-potential approximation, the effective cluster interactions are obtained from the embedded-cluster Method or from the generalized perturbation method. The second approach, that is now extensively used, consists in performing ab initio total energy calculations of perfectly ordered compounds in order to estimate the values of the cluster interactions. A review of the phase diagrams obtained using these methods is presented. This review is restricted to metallic systems.