Finite-temperature bulk moduli from an EOS-based Gr\"uneisen function

Abstract

An equation-of-state (EOS)-based construction of the Gr\"uneisen function is developed and assessed through predictions of finite-temperature bulk moduli. In this approach, the volume dependence of the Gr\"uneisen function is expressed analytically in terms of static EOS information, anchored by Debye temperatures obtained from elastic data sampled near equilibrium, and constrained by the infinite-compression limit. The resulting form requires as material-specific input only static energy-volume data and near-equilibrium elastic properties, with no parameters adjusted to thermal data. Within a Mie--Gr\"uneisen--Debye framework, the approach is examined for diamond, magnesium oxide, silicon, and sodium chloride, chosen to span a broad range of stiffness, using machine-learning interatomic potentials from the Universal Models for Atoms (UMA) and Universal Point Edge Transformer (UPET) families, together with a dispersion-corrected variant of UMA. The calculated bulk moduli reproduce the expected experimental softening trends and capture the overall scale of the bulk-modulus temperature derivatives, although the level of quantitative agreement depends on the material, the underlying interatomic potential, and the selected analytic EOS form. These results show that an EOS-based construction of the Gr\"uneisen function can capture the leading thermal-softening behavior of bulk moduli without fitting to thermal data. The observed sensitivity to the underlying static description further suggests that the framework may help identify deficiencies relevant to thermoelastic transferability and thereby inform future training and validation strategies for universal machine-learning interatomic potentials.