We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature-dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\times 10$ speedup on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make predictions on the thermodynamics of substoichiometric ${\mathrm{ZrC}}_x$, including vacancy concentration and heat capacity.

• Received 19 December 2018
• Revised 4 April 2019

DOI:https://doi.org/10.1103/PhysRevB.100.024303