Improved cluster-site approximation for the entropy of mixing in multicomponent solid solutions

Although not as soundly based, the cluster-site approximation (CSA) has the considerable advantage of computational simplicity over the cluster variation method (CVM) for the evaluation of mixing entropies in multicomponent solid solutions. The CSA is thus particularly suitable for the calculation of technologically important phase diagrams of multicomponent alloys, a task which necessarily depends on the optimization of the models’ energy parameters with the available experimental data for the constituent binary and ternary systems. Comparison of results obtained by Monte Carlo (MC) simulations for the same energy parameters with those obtained by the CVM and CSA for the tetrahedron approximation for fcc alloy shows them to be of comparable accuracy—the CVM finds the solution to be more random whereas the original CSA (due to Yang and Li) finds the solution to be less random when compared with the MC results. It is shown how the CSA can be improved by the introduction of a single correction parameter. Some CSA-calculated prototype binary phase diagrams which agree very well with those obtained from MC calculations are presented together with two phase diagrams for the Cu-Au system which can be compared with similar diagrams previously calculated using the CVM. It is not suggested that the modified CSA should replace the use of large clusters in the CVM for “first-principles” phase diagram calculations for binary systems.