Nature Commun. 6, 7559 (2015)

Credit: NATURE PUBLISHING GROUP

Free energies are only strictly defined for equilibrium states, yet it is common to assume that the free energy of unstable phases can be extrapolated from the free-energy functional derived or computed for equilibrium states. However, extrapolation schemes do not always agree, and it can occur that extrapolated free energies for an unstable phase result in values lower than that of a stable phase. Now, A. van de Walle and colleagues describe a simple computational method to smoothly extend the free energy of stable solid phases into mechanically unstable ones without any need for extrapolation. The method relies on partitioning the phase space into 'neighbourhoods' on the basis of a criterion based on local curvature, and is shown to yield smoothly varying free energies that agree with those of known extrapolation schemes (for a benchmark ternary alloy system displaying three common cubic lattices). Computational-thermodynamic frameworks should benefit from the approach.