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, creates features near the Fermi surface (well defined even with disorder) that change to simple commensurate SRO with (un)filling of these states. In conclusion, our results reveal how complexity and competing electronic effects control ordering in these alloys.