Short-range order and compositional phase stability in refractory high-entropy alloys via first principles theory and atomistic modelling: 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 modelling 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 which 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.