The finite-$T$ Lorentz number and the thermal conductivity. Aluminum and carbon conductivities from ambient to millions of degrees Kelvin

TL;DR

This paper introduces a universal finite-temperature Lorentz number function for electron-ion systems, enabling simplified predictions of thermal conductivity across a wide temperature range, with applications in astrophysics and materials science.

Contribution

It provides a new finite-temperature Lorentz number formulation expressed via elementary Fermi integrals, applicable to diverse densities and temperatures, and includes practical fitting parameters for ease of use.

Findings

Derived a universal function for $L_N(T)$ based on Fermi integrals.

Calculated thermal conductivities for aluminum and carbon up to millions of Kelvin.

Compared theoretical predictions with experimental and simulation data for validation.

Abstract

Theoretical prediction of the thermal conductivity $\kappa$ of metal-like electron-ion systems would be greatly simplified if a convenient generalization of the Lorentz number $L_N$ for arbitrary temperatures ($T$) and densities were available. Such calculations are needed in astrophysics, high-energy-density physics, semiconductor physics as well as in materials science. We present a finite-$T$ form of $L_N(T)$, expressed in terms of elementary Fermi integrals. It is a universal function of $t=T/E_F$, where $E_F$ is the Fermi energy of the electrons. A convenient four-parameter fit to $L_N(t)$ for $t=0-\infty$ further simplifies the applications. The effect of electron-electron interactions is also briefly discussed. Calculations for $L_N(t)$ and thermal conductivities $\kappa$ for Al and C are presented at several compressions and into the million-Kelvin range. Experimental isobaric conductivities for Al just above the meting point, and isochoric conductivities for Al and C from available density-functional theory simulations and average-atom calculations are used as comparisons.