Scaling of Low-Temperature Heat Capacity in Cryocrystals

TL;DR

This paper demonstrates a universal scaling law for the low-temperature heat capacity of cryocrystals, linking thermodynamic anomalies to vibrational properties and phonon spectrum features.

Contribution

It introduces a universal scaling function that connects heat capacity anomalies with phonon spectrum characteristics across various cryocrystals.

Findings

Heat capacity scales universally with a characteristic temperature.

The maximum in heat capacity correlates with the van Hove singularity.

Scaling reflects common vibrational origins in lattice dynamics.

Abstract

The low-temperature isochoric heat capacity of cryocrystals was scaled using the universal scaling function. This universality links the magnitude of the anomaly and the characteristic temperature of the hump $T_{\mathrm{max}}$ in heat capacity, which is related to the first van Hove singularity in the phonon spectrum. For atomic, molecular, and quantum cryocrystals, $T_{\mathrm{max}}$ systematically shifts with molar volume, reflecting Brillouin zone scaling and revealing a common vibrational origin. These findings for the scaling function bridge thermodynamics with the vibrational density of states, highlighting fundamental universality in lattice dynamics.