Short-range order and compositional phase stability in refractory high-entropy alloys via first-principles theory and atomistic modeling: NbMoTa, NbMoTaW, and VNbMoTaW

Using an all-electron, first-principles, Landau-type theory, we study the nature of short-range order and compositional phase stability in equiatomic refractory high-entropy alloys, NbMoTa, NbMoTaW, and VNbMoTaW. We also investigate selected binary subsystems to provide insight into the physical mechanisms driving order. Our approach examines the short-range order of the solid solutions directly, infers disorder/order transitions, and also extracts parameters suitable for atomistic modeling of diffusional phase transformations. We find a hierarchy of relationships between the chemical species in these materials which promote ordering tendencies. The most dominant is a relative atomic size difference between the $3d$ element, V, and the other $4d$ and $5d$ elements which drives a $B32$-like order. For systems where V is not present, ordering is dominated by the difference in filling of valence states; pairs of elements that are isoelectronic remain weakly correlated to low temperatures, while pairs with a valence difference present $B2$-like order. Our estimated order-disorder transition temperature in VNbMoTaW is sufficiently high for us to suggest that SRO in this material may be experimentally observable.