Cluster Expansions for Thermodynamics and Kinetics of Multicomponent Alloys

Cluster expansions have proven a very useful tool to model thermodynamics and kinetics of substitutional alloys in metallic, ionic, and even covalently bonded systems. Cluster expansions are usually obtained with the structure inversion method in which the energies, or other relevant property, of a set of structures are used to obtain expansion coefficients. The expansion coefficients are multipliers of correlation functions which pertain to clusters of sites on the parent lattice. There are significant practical issues associated with obtaining a cluster expansion, such as selecting which structures and especially which correlation functions are required for an adequate description of the energy. While these issues are significant for binary alloys, they become much more daunting when dealing with multicomponent alloys. Moreover, oftentimes interest is not limited to the energetics of the thermodynamic equilibrium state, but the evolution of quenched alloys with time is just as important. The treatment of diffusion within the context of cluster expansions is then another challenge. The article describes a formal method for utilizing cluster expansions for transition states as occur during vacancy mediated diffusion in substitutional alloys. The methods are illustrated with some applications to the prediction of initial coherent precipitates in Al-Cu and Al-Mg-Si alloys.