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

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 LN 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 LN(T), expressed in terms of elementary Fermi integrals. It is a universal function of t=T/EF, where EF is the Fermi energy of the electrons. A convenient four-parameter fit to LN(t) for t=0-∞ further simplifies the applications. The effect of electron-electron interactions is also briefly discussed. Calculations for LN(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.