  The theory of phase stability in the Ni-Au alloy system is a popular topic
due to the large size mismatch between Ni and Au, which makes the effects of
atomic relaxation critical, and also the fact that Ni-Au exhibits a phase
separation tendency at low temperatures, but measurements at high-temperature
show an ordering-type short-range order. We have clarified the wide disparity
which exists in the previously calculated values of mixing energies and
thermodynamic properties by computing ``state-of-the-art'' energetics
(full-potential, fully-relaxed LDA total energies) combined with
``state-of-the-art'' statistics (k-space cluster expansion with Monte Carlo
simulations) for the Ni-Au system. We find: (i) LDA provides accurate mixing
energies of disordered Ni_{1-x}Au_x alloys (\Delta H_{mix} < +100 meV/atom)
provided that both atomic relaxation (a ~100 meV/atom effect) and short-range
order (~25 meV/atom) are taken into account properly. (ii) Previous studies
using empirical potentials or approximated LDA methods often underestimate the
formation energy of ordered compounds, and hence also underestimate the mixing
energy of random alloys. (iii) Measured values of the total entropy of mixing
combined with calculated values of the configurational entropy demonstrate that
the non-configurational entropy in Ni-Au is large, and leads to a significant
reduction in miscibillity gap temperature. (iv) The calculated short-range
order agrees well with measurements, and both predict ordering in the
disordered phase. (v) Consequently, using inverse Monte Carlo to extract
interaction energies from the measured/calculated short-range order in Ni-Au
would result in interactions which would produce ordering-type mixing energies,
in contradiction with both experimental measurements and precise LDA energies.
