Heat capacity estimation of complex materials for energy technologies

Heat capacity, which directly relates to free energy changes and thermal transport, is fundamental to modern engineering design. Even though current computational technology provides a detailed picture of atomic vibrations, the Debye and Dulong-Petit models are still widely utilized despite being prone to lower accuracy. Modern considerations of vibrational states, anharmonicity, electronic carriers, and phase transformations could improve estimates. Herein, the physics-based vibrational + dilation + electronic (VDE) model incorporates a user-provided phonon density of states, a phonon pressure-based dilation term, and an electronic component. Phonon density of states from analytical, machine-learned, and first-principles methods are compared, thus highlighting the advantages of machine-learned technology. Heat capacity estimates for 38 diverse materials are often within 5% of experimental values between 200 and 600 K. Detailed temperature-dependent investigations are carried out for several materials, including $\text{LiCo}{O}_2$ , ZIF-8, ${\text{Mg}}_{\text{3}}{\text{Sb}}_{\text{2}}$ , polyvinyl chloride (PVC), and amorphous silicon. $C{u}_2$ Se is modeled through its phase transition, which further demonstrates the model's capabilities to enable engineering design and sophisticated analysis.