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We propose an approach to calculate the anharmonic part of thevolumetric-strain and temperature dependent free energy of a crystal. Themethod strikes an effective balance between accuracy and computationalefficiency, showing a $\times10$ speed-up on comparable free energy approachesat the level of density functional theory, with average errors less than 1meV/atom. As a demonstration we make new predictions on the thermodynamics ofsubstoichiometric ZrC$_x$, including vacancy concentration and heat capacity.

A fast anharmonic free energy method with an application to vacancies in ZrC