Contribution of the vibrational free energy to phase stability in substitutional alloys: Methods and trends

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Abstract
Recent studies show that the effect of the lattice vibrations on predictions of phase stability can be important. Because complete computations of the phonon density of states from first principles are difficult, simpler models for the vibrational free energy have been used to incorporate these effects into phase diagram calculations. In this paper, we systematically investigate the accuracy of these approximations by studying model systems for which the vibrational free energy can be computed exactly in the harmonic approximation. We found that the Debye approximation, usually used in first-principles studies, fails to capture the configuration dependence of the vibrational free energy. We explain the reason for this failure. With the same model systems, we analyzed the effect of the lattice vibrations on the predicted phase diagrams as a function of size mismatch and chemical affinity. By fitting our results to the available experimental information, we find that the effect of vibrations on phase transition temperatures may be significant.