Materials theory


Cluster Expansion of Alloy Theory: A Review of Historical Development and Modern Innovations

The parameterization of a physical or empirical model from a set of highly accurate but expensive calculations or measurements to generate less precise but cheaper predictions is common in many disciplines. In computational materials science and informatics-enabled design of materials, the cluster expansion (CE) method provides a direct approximation of the free energy of a lattice, or any other thermodynamic variable, in terms of a discrete cluster function, making it one of the most widely used approaches for phase diagram calculations, including order–disorder phase transitions. In this article, we review the theoretical developments that culminated in the formulation of the CE method, numerous statistical techniques currently used to fit and optimize the parameters of the CE model, the convergence of the CE method with modern machine learning and data science techniques, and recent developments that push the field beyond the conventional CE, including for structural alloy design.

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Sara Kadkhodaei and Jorge A. Muñoz, JOM 73, 3326 (2021)