Phonon Mode-Resolved Anharmonic Heat Capacity of Solids

We develop and validate a lattice dynamics framework to include anharmonic effects in the calculation of mode-level phonon heat capacities. To capture anharmonicity accurately, we propose a renormalization method based on instantaneous normal modes for obtaining temperature-dependent interatomic force constants. Ground truth total heat capacities are obtained from molecular dynamics simulations. For Lennard-Jones argon (Stillinger-Weber silicon), the deviation of the potential energy contribution to the total heat capacity from the harmonic Dulong-Petit law is -12% (+16%) at the highest modeled temperature of 80 K (1300 K). The mode heat capacities from the lattice dynamics calculations sum to a total heat capacity within 2% of the ground truth values for all temperatures considered. The Lennard-Jones argon mode heat capacities decrease with increasing frequency and are impacted by the effect of anharmonicity on the mode's self energy and its interactions with other modes. In Stillinger-Weber silicon, the acoustic mode heat capacities increase up to 30% relative to the Dulong-Petit law, with the deviations driven by the interactions between modes. The proposed calculation framework will improve high temperature thermal conductivity calculations, where the heat capacity is generally assumed to take on the harmonic value from the Dulong-Petit law.