A statistical approach for atomistic calculations of vacancy formation energy and chemical potentials in concentrated solid-solution alloys

This article presents a statistical approach for atomistic calculations of vacancy formation energy, which is expected to exhibit a probability distribution in concentrated solid-solution alloys, due to the variation in atomic environment. Demonstrated using a random FeCrNi ternary alloy, a general formulation is given for applications in random, concentrated alloys with any number of components. The proposed approach calculates the mean vacancy formation energy, based on the total energies of the reference and defected supercells—each with a vacancy—without separate calculations for chemical potentials, thus avoiding the additional computational cost and the associated uncertainty. The chemical potential of each component can be back-derived in a self-consistent manner to give the distribution of vacancy formation energy. This is opposed to most current studies, in which the individual chemical potentials are calculated separately prior to calculating the vacancy formation energy. It is also found that, with the same mean vacancy formation energy, a broader distribution may lead to a higher equilibrium vacancy concentration at a given temperature, indicating the critical importance of statistically obtaining the full distribution of vacancy formation energy.