Abstract
Atomistic and statistical mechanical methods are combined to determine the vacancy formation free energy in binary solid solutions. The first-shell grey model is based on the assumption that all the atoms are effective or mean-field atoms, but with the concentration of the first shell different from the bulk. Comparison of the vacancy formation free energy and the average local concentration profile around the vacancy obtained from the first-shell grey model and the more accurate but much less computationally efficient first-shell black-white model (where the mean-field approximation is not used) suggest that only the composition of the first atomic shell adjacent to the vacancy must be determined. The temperature dependence of the vacancy formation free energy for a Cu-Ni system can be efficiently determined using the first-shell grey atom approximation. Our results show that the vacancy has a strong tendency to form in Cu-rich regions of the Cu-Ni alloy at low temperatures and low Cu bulk concentrations. This preference of vacancies to form in regions of composition fluctuations (of one sign) is the most important effect to include that goes beyond the standard mean-field theories of vacancy formation thermodynamics in solid-solution alloys.