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Exploiting Chemical Short-Range Order (CSRO) is a promising avenue for manipulating the properties of alloys. However, existing modeling frameworks are not sufficient to predict CSRO in multicomponent alloys (>3 components) in an efficient and reliable manner. In this work, we developed a hybrid computational thermodynamics framework by combining unique advantages from Cluster Variation Method (CVM) and CALculation of PHAse Diagram (CALPHAD) method. The key is to decompose the cumbersome cluster variables in CVM into fewer site variables of the basic cluster using the Fowler-Yang-Li (FYL) transform, which considerably reduces the number of variables that must be minimized for multicomponent systems. CSRO is incorporated into CALPHAD with a novel cluster-based solution model called FYL-CVM. This new framework brings more physics into CALPHAD while maintaining its practicality and achieves a good balance between accuracy and computational cost. It leverages statistical mechanics to yield a more physical description of configurational entropy and opens the door to cluster-based CALPHAD database development. The application of the FYL-CVM model in a prototype fcc AB alloy demonstrates its capability to calculate the phase diagram and thermodynamic properties with remarkable accuracy comparable to CVM. The hybrid CVM-CALPHAD framework represents a new methodology for thermodynamic modeling that enables atomic-scale order to be exploited for materials design. 

Abstract Mixed-space cluster expansion (MSCE), a first-principles method to simultaneously model the configuration-dependent short-ranged chemical and long-ranged strain interactions in alloy thermodynamics, has been successfully applied to binary FCC and BCC alloys. However, the previously reported MSCE method is limited to binary alloys with cubic crystal symmetry on a single sublattice. In the current work, MSCE is generalized to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach is then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods.