A computational free energy reference for mechanically unstable phases

The CALPHAD (CALculation of PHAse Diagram) framework relies heavily on the availability of a well-defined free energy for all possible phases, including metastable and even mechanically unstable phases. However, for phases that exhibit mechanical instability, the determination of the free energy represents a challenge, both experimentally and computationally. This situation hinders the seamless integration of experimental and ab initio thermodynamic data. A newly developed method, named “inflection-detection”, provides a practical computational solution to this problem with a sound theoretical basis. Extending upon existing energy calculations at absolute zero, we provide further evidence of this method’s effectiveness by computing the temperature-dependent free energy references for 22 elemental structures involving mechanically unstable phases and showing that they are reasonably consistent with the (often wide) range of values determined in earlier experimental assessments. This suggests the feasibility of a reliable computation-based reference free energy standard for mechanically unstable pure elements. • Free energy of mechanically unstable phases can be efficiently determined using inflection-detection approach. • Method enables the use of standard lattice dynamics calculations to obtain the temperature-dependence of free energies. • Calculated free energies show good agreement with prior CALPHAD estimates based on extrapolations from stable regions.