Ni-Au: A testing ground for theories of phase stability

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 to 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 Ni1− xAux alloys (Hmix ≤ + 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 miscibility 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 calculations.