  We describe implementation and analysis of a first-principles theory, derived
in an earlier work, for the leading terms in an expansion of a Gibbs free
energy of a multi-component alloy in terms of order parameters that
characterize potential, compositional phases. The theory includes effects of
rearranging charge and other electronics from changing atomic occupancies on
lattice sites. As well as the rigorous description of atomic short-range order
in the homogeneously disordered phase, pairwise interaction parameters suited
for atomistic modelling in a multicomponent setting can be calculated. From our
study of an indicative series of the Cantor-Wu alloys, NiCo, NiCoCr, NiCoFeCr,
and NiCoFeMnCr, we find that the interactions are not approximated well either
as pseudobinary or restricted to nearest neighbour range. Our computed
order-disorder transition temperatures are low, consistent with experimental
observations, and the nature of the ordering is dominated by correlations
between Ni, Co, and Cr, while Fe and Mn interact weakly. Further atomistic
modelling suggests that there is no true single-phase low-temperature ground
state for these multicomponent systems. Instead the single-phase solid solution
is kept stable to low temperatures by the large configurational entropy and the
Fe, Mn dilution effects. The computationally cost-effectiveness of our method
makes it a good candidate for further exploration of the space of
multicomponent alloys.
