Mode-Resolved High-Temperature Vibrational Heat Capacity

The atomic-scale mechanisms responsible for the thermal properties of condensed matter at high temperatures are poorly understood. We propose and verify an approach using a Taylor effective potential (TEP) and molecular dynamics (MD) simulations to calculate the heat capacity of phonon modes at high temperatures. Existing methods for mode-resolved thermal conductivity calculations rely on harmonic heat capacities (i.e., from Bose-Einstein statistics). Here, we develop a parameter-free first-principles framework to mode-resolved calculate heat capacity at high temperatures, where the harmonic approximation fails. Our model unlocks the ability to study high temperature heat capacity by naturally including anharmonicity and decomposes the bulk heat capacity into contributions from each phonon mode. We study Stillinger-Weber silicon and Lennard-Jones argon and compare heat capacity calculations from the TEP model to those obtained directly from MD simulations. When using zero-temperature phonon modes, the TEP results agree with those from MD at low temperatures, but the error grows as temperature, and thus anharmonicity, increases. This effect is accounted for by using temperature-dependent force constants to parameterize the TEP and by including four-phonon interactions. This approach will contribute to the development of ultrahigh thermal conductivity materials, efficient thermal storage technologies, and practical thermoelectrics.