Towards accurate thermodynamics from random energy sampling

Special Quasi-random Structures (SQSs) are often used to model disordered alloys in small simulation cells. Yet, SQS-based sampling yields chemical potentials (and other thermodynamic properties) that do not match the equilibrium values at some finite temperature, which can for instance be measured in atomic Monte Carlo simulations. This is due to the lack of chemical short-range order in random samples. In this paper, we present a probabilistic analysis of chemical potential calculations based on the distribution of substitution energies and the Widom technique. Performing the analysis by sampling either equilibrium configurations or SQSs, we show that they both yield different results, but that it is possible to correct the results from the random sampling in order to get a result which is much closer to the equilibrium values. The correction is very simple to apply and does not require additional total energy calculations.