Vacancy formation free energy in concentrated alloys: Equilibrium vs. random sampling

Special Quasi-random Structures (SQSs) are often used to model disordered alloys in small simulation cells. Yet, SQS-based sampling yields defect formation energies that do not match the equilibrium values, for instance measured in atomic Monte Carlo simulations, due to the lack of chemical short-range order in random samples. In this paper, our approach to computing chemical potentials in alloys through random sampling techniques is extended to the computation of vacancy formation free energies. By rigorous thermodynamic derivation, we show that vacancy formation free energies computed from randomly sampled local chemical environments must be corrected to ensure its consistency between various available calculations. Indeed, irrespective of the choice of the species being replaced by a vacancy, we should arrive at the same value of the vacancy formation free energy. We propose a simple way to compute this correction term, and compare the outcome with equilibrium Monte Carlo results and with approximations found in the literature.