General method for incorporating CALPHAD free energies of mixing into phase field models: Application to the α-zirconium/δ-hydride system

This paper presents a general method of incorporating CALPHAD-based free energies into a phase field model. While CALPHAD-based free energy descriptions provide realistic energetics of alloys, their formulations may pose numerical difficulties for phase field simulations. Specifically, the free energies of mixing for different phases may not necessarily be defined over the same concentration ranges, and their derivatives may exhibit highly nonlinear behavior. The method presented approximates the free energies of mixing using piecewise functions to eliminate the aforementioned characteristics while largely retaining the free energy values and the first and second derivative information, which affect the thermodynamic and kinetic behavior of the system. The method is verified by planar interface simulations of the α-zirconium/δ-hydride system. The phase fractions and compositions obtained from the phase field simulations are compared to the values calculated from the common tangent construction on the original free energies. The results indicate a high degree of accuracy.