**A self-contained algorithm for determination of solid-liquid equilibria
in an alloy system**

L Yang and Y Sun and Z Ye and F Zhang and MI Mendelev and CZ Wang and KM Ho, COMPUTATIONAL MATERIALS SCIENCE, 150, 353-357 (2018).

DOI: 10.1016/j.commatsci.2018.04.028

We describe a self-contained procedure to evaluate the free energy of liquid and solid phases of an alloy system. The free energy of a single- element solid phase is calculated with thermodynamic integration using the Einstein crystal as the reference system. Then, free energy difference between the solid and liquid phases is calculated by Gibbs- Duhem integration. The central part of our method is the construction of a reversible alchemical path connecting a pure liquid and a liquid alloy to calculate the mixing enthalpy and entropy. We have applied the method to calculate the free energy of solid and liquid phases in the Al-Sm system. The driving force for fcc-Al nucleation in Al-Sm liquid and the melting curve for fcc-Al and Al3Sm are also calculated.

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