Temperature dependence of surface and grain boundary energies from first principles

In this study we systematically study the temperature dependence of interface energies in W using first principles. To that purpose, we compute interface free energies and consider different contributions, i.e., from lattice expansion, vibrational contribution from harmonic and quasiharmonic approximation with explicit phonon calculations, and electronic contribution. We find that interface energies decrease with temperature and that in most cases the harmonic approximation to the free energy is sufficient. The relative decrease of the interface energy at 2000 K for the surfaces varies from $\ensuremath{-}20$% to $\ensuremath{-}30$%, while for grain boundaries, the interface energies decrease from $\ensuremath{-}30$% to $\ensuremath{-}55$%. Our results are compared to models on temperature dependence of interface energies available in literature. We find that they are in qualitative agreement also exhibiting a general decrease with higher temperatures. However, most models neglect anisotropy effects and are not in quantitative agreement. The equilibrium crystal shape matches with experimentally observed particle and pore shapes.