A Rigorous and Self-contained Algorithm for Evaluating Free Energy of Liquid and Solid Phases of an Alloy System*

In this work, 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 pure solid phase is calculated with thermodynamic integration using the Einstein crystal as the reference system. The free energy of pure liquid can be obtained by integrating ΔH/T² with temperature, where ΔH is the latent heat during melting. The central part of our method is the construction of a reversible path from pure liquid to 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 liquids and the melting curve for fcc-Al and Al₃Sm are also calculated.