Atomic Short-Range Order and Phase Stability of the Refractory High-Entropy Alloys

We apply our perturbative, DFT-based approach for analysing emergent atomic short- and long-range order in multicomponent alloys to the refractory high-entropy alloys (HEAs). This is a family of HEAs forming on the bcc lattice and containing the elements V, Nb, Mo, Ta, and W, which are of interest for applications where materials are subjected to high temperatures and levels of radiation. We choose to study the prototypical refractory HEAs, VNbMoTaW and NbMoTaW, as well as selected subsystems. Our modelling approach predicts a B2 ordering in the NbMoTaW system while, in the VNbMoTaW system, the addition of V drives a competing, B32 ordering. These ordering tendencies are interpreted physically as originating in electronic mechanisms including atomic size and bandwidth differences, charge transfer between elements, and valence differences between chemical species. Lattice-based Monte Carlo simulations using an effective pair interaction enable the nature of atomic ordering below the initial disorder-order transition to be studied in detail. The results are shown to compare favourably with alternative modelling approaches, and with experimental data. We also examine the failure of the band-only approximation to describe these systems, as well as discuss the importance of the Onsager correction.