The finite-$T$ Lorentz number and the thermal conductivity. Aluminum and carbon conductivities from ambient to millions of degrees Kelvin
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914777812434944 |
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| author | Dharma-wardana, M. W. C. |
| author_facet | Dharma-wardana, M. W. C. |
| contents | Theoretical prediction of the thermal conductivity $κ$ 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 $κ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_19692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The finite-$T$ Lorentz number and the thermal conductivity. Aluminum and carbon conductivities from ambient to millions of degrees Kelvin Dharma-wardana, M. W. C. Materials Science Plasma Physics Theoretical prediction of the thermal conductivity $κ$ 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 $κ$ 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. |
| title | The finite-$T$ Lorentz number and the thermal conductivity. Aluminum and carbon conductivities from ambient to millions of degrees Kelvin |
| topic | Materials Science Plasma Physics |
| url | https://arxiv.org/abs/2404.19692 |