Calculation of the free energy of solids from the energy distribution function

We outline a new methodology for the calculation of the Helmholtz and the Gibbs free energies from a cumulant analysis of the internal-energy and enthalpy distribution functions obtained from a Monte Carlo simulation at a single temperature. It is validated from a comparison of the free energies calculated for a perfect crystal by using this approach with the free energy calculated from a temperature-integration scheme. The new method allows the calculation of the free energy at all temperatures up to melting from a single Monte Carlo simulation at one temperature only. Thus, it is approximately 3--6 times more computationally efficient than a temperature- integration scheme. By comparing the two methods for an inhomogeneous system containing grain boundaries, we investigate the effects of the distribution of local strain on the free energy; for the superlattice of twist grain boundaries studied here, the effects are found to be small