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Free energies play a central role in many descriptions of equilibrium andnon-equilibrium properties of solids. Continuum partial differential equations(PDEs) of atomic transport, phase transformations and mechanics often rely onfirst and second derivatives of a free energy function. The stability, accuracyand robustness of numerical methods to solve these PDEs are sensitive to theparticular functional representations of the free energy. In this communicationwe investigate the influence of different representations of thermodynamic dataon phase field computations of diffusion and two-phase reactions in the solidstate. First-principles statistical mechanics methods were used to generaterealistic free energy data for HCP titanium with interstitially dissolvedoxygen. While Redlich-Kister polynomials have formed the mainstay ofthermodynamic descriptions of multi-component solids, they require high orderterms to fit oscillations in chemical potentials around phase transitions. Herewe demonstrate that high fidelity fits to rapidly fluctuating free energyfunctions are obtained with spline functions. Spline functions that are manydegrees lower than Redlich-Kister polynomials provide equal or superior fits tochemical potential data and, when used in phase field computations, result insolution times approaching an order of magnitude speed up relative to the useof Redlich-Kister polynomials.

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations