Solid-liquid phase equilibria from free-energy perturbation calculations

S Angioletti-Uberti and M Asta and MW Finnis and PD Lee, PHYSICAL REVIEW B, 78, 134203 (2008).

DOI: 10.1103/PhysRevB.78.134203

A method for calculating free-energy differences based on a free-energy perturbation (FEP) formalism in an alloy system described by two different Hamiltonians is reported. The intended application is the calculation of solid-liquid phase equilibria in alloys with the accuracy of first-principles electronic density-functional theory (DFT). For this purpose free energies are derived with a classical interatomic potential, and FEP calculations are used to compute corrections to these reference values. For practical applications of this approach, due to the relatively high computational cost of DFT calculations, it is critical that the FEP calculations converge rapidly in terms of the number of samples used to estimate relevant ensemble averages. This issue is investigated in the current study employing two classical interatomic-potential models for Ni-Cu. These models yield differences in predicted phase-boundary temperatures of approximately 100 K, comparable to those that might be expected between a DFT Hamiltonian and a well-fit classical potential. We show that for pure elements the FEP calculations converge rapidly with the number of samples, yielding free- energy differences converged to within a fraction of a meV/atom in a few dozen energy calculations. For a concentrated equiatomic alloy similar precision requires roughly a hundred samples. The results suggest that the proposed methodology could provide a computationally tractable framework for calculating solid-liquid phase equilibria in concentrated alloys with DFT accuracy.

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