Adaptation of Wallace's Approach to the Specific Heat of Elemental Solids with Significant Intrinsic Anharmonicity, Particularly the Light Actinide Metals

TL;DR

This paper introduces the elastic softening approximation, an alternative to the quasiharmonic model, to better capture intrinsic anharmonic effects in the specific heat of elemental solids, especially light actinide metals.

Contribution

We extend Wallace's thermodynamic framework with the elastic softening approximation to model anharmonicity, revealing correlations with Poisson's ratio and applying it to actinides.

Findings

Poisson's ratio correlates with phonon softening rates.

Elemental solids follow the phonon softening trend across Poisson's ratios.

Actinides show large anharmonic phonon contributions at high temperatures.

Abstract

The quasiharmonic approximation is the most common method for modeling the specific heat of solids; however, it fails to capture the effects of intrinsic anharmonicity. In this study, we introduce the "elastic softening approximation," an alternative approach to modeling intrinsic anharmonic effects on thermodynamic quantities, which is grounded in Wallace's thermodynamic framework that tracks entropy changes resulting from the continuous change (e.g., softening) of phonons as a function of temperature. A key finding of our study is a direct correlation between Poisson's ratio and the differential rate of phonon softening at finite frequencies, compared to lower frequencies relevant to elastic moduli measurements. We observe that elemental solids such as $\alpha$-Be, diamond, Al, Cu, In, W, Au, and Pb, which span a wide range of Poisson's ratios and exhibit varying degrees of intrinsic anharmonicity, consistently follow this trend. When applied to $\alpha$-U, $\alpha$-Pu, and $\delta$-Pu, our method reveals unusually large anharmonic phonon contributions at elevated temperatures across all three light actinide metals. These findings are attributed to the unique combination of enhanced covalency and softer elastic moduli inherent in the actinides, potentially influenced by their 5f-electron bonding.