Heat capacity of matter beyond the Dulong-Petit value

TL;DR

This paper introduces a simple method to evaluate anharmonic effects on heat capacity using only the thermal expansion coefficient, applicable to various states of matter, supported by simulations showing good agreement and novel non-monotonic behavior in liquids.

Contribution

A new approach to assess anharmonic effects on heat capacity using a single parameter, applicable to crystals, glasses, and liquids, validated by molecular dynamics simulations.

Findings

Good agreement between theory and simulations.

Non-monotonic heat capacity behavior in liquids.

Explanation of maximum heat capacity as a competition between anharmonicity and mode reduction.

Abstract

We propose a new simple way to evaluate the effect of anharmonicity on a system's thermodynamic functions such as heat capacity. In this approach, the contribution of all potentially complicated anharmonic effects to constant-volume heat capacity is evaluated by one parameter only, the coefficient of thermal expansion. Importantly, this approach is applicable not only to crystals but also to glasses and viscous liquids. To support this proposal, we perform molecular dynamics simulations of several crystalline and amorphous solids as well as liquids, and find a good agreement between results from theory and simulations. We observe an interesting non-monotonic behavior of liquid heat capacity with a maximum, and explain this effect as a result of competition between anharmonicity at low temperature and decreasing number of transverse modes at high temperature.