A Cluster-Based Computational Thermodynamics Framework with Intrinsic Short-Range Order

CALPHAD is a leading method for modeling and calculations of phase equilibria in materials. However, the prevailing solution model used in CALPHAD, the sublattice model, is an empirical mean-field model based on the Bragg-Williams (ideal entropy of mixing) approximation. This makes CALPHAD inadequate for properly describing order-disorder transformations or chemical short-range order (SRO) in alloys. First-principles calculations of phase diagrams, using the cluster variation method (CVM) or the cluster expansion method, can describe SRO but are generally limited to binary or ternary systems due to the large number of configuration variables. In the current work, we develop a hybrid framework by marrying unique advantages from CVM and CALPHAD through incorporating chemical SRO into CALPHAD with a novel cluster-based solution model. The key is to use the Fowler-Yang-Li transform to decompose the cumbersome cluster probabilities in CVM into fewer site/point probabilities of the basis cluster, thereby considerably reducing the number of variables that must be minimized for multicomponent systems. We have put more physics, primarily intrinsic SRO, into CALPHAD, while maintaining its practicality and efficiency. The novel cluster-based modeling framework leverages statistical mechanics to yield a more physical description of configurational entropy and opens the door to cluster-based CALPHAD database development. The configurational and non-configurational (vibrational, elastic, electronic) contributions to free energy are modeled separately, gaining insights into their respective effects on phase stability. Phase diagrams of representative alloy systems are calculated using the novel framework, showing great comparison with experiments. This hybrid CVM-CALPHAD framework represents a new methodology for thermodynamic modeling that enables atomic-scale order to be exploited as a dimension for materials design, which potentially leads to novel complex concentrated alloys.