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arXiv · 2404.19692

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

M. W. C. Dharma-wardana
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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.

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M. W. C. Dharma-wardana. 2024-04-30. The finite-$T$ Lorentz number and the thermal conductivity. Aluminum and carbon conductivities from ambient to millions of degrees Kelvin. https://arxiv.org/abs/2404.19692

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