Recursive alloy Hamiltonian construction and its application to the Ni-Al-Cr system

Abstract Navigating the high dimensional composition spaces of multi-principle element alloys, also referred to as high entropy alloys, will require new methods to construct first-principles alloy Hamiltonians. We introduce a recursive approach to parameterizing multi-component alloy Hamiltonians using interaction parameters from simpler subsystems as Bayesian informative priors. We applied this approach to perform a first-principles statistical mechanics study of the Ni-Al-Cr system. Ternary cluster expansions for the Ni-Al-Cr alloy were constructed by building on optimized Ni-Al and Ni-Cr binary cluster expansions. Monte Carlo simulations predict a sizable Cr solubility in the Ni-rich FCC based γ and γ ′ phases. The L 1 2 -ordered γ ′ phase is predicted to dissolve Cr primarily on its Al-sublattice. We also identify a family of hierarchical long-period super structure orderings as groundstates in the Ni-Cr and Al-Cr binaries. The recursive approach to parameterizing alloy Hamiltonians opens the door to rigorous first-principles treatments of the elevated temperature thermodynamics of alloys in high dimensional composition spaces.