  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.
