Ta-Nb-Mo-W refractory high-entropy alloys: anomalous ordering behavior and its intriguing electronic origin

From electronic-structure-based thermodynamic linear-response, we establish chemical ordering behavior in complex solid solutions versus how Gibbs' space is traversed -- applying it on prototype refractory A2 Ta-Nb-Mo-W high-entropy alloys. Near ideal stoichiometry, this alloy has anomalous, intricate chemical ordering tendencies, with long-ranged chemical interactions that produce competing short-range order (SRO) with a crossover to spinodal segregation. This atypical SRO arises from canonical band behavior that, with alloying, create features near the Fermi-surface (well-defined even with disorder) that change to simple commensurate SRO with (un)filling of these states. Our results reveal how complexity and competing electronic effects control ordering in these alloys.