Empirical Formulae of Electrical and Thermal Conductivities of Elemental Metals at Room Temperature Ranges

TL;DR

This paper develops empirical formulas for electrical and thermal conductivities of elemental metals at room temperature, using a simplified relaxation time and electron configuration-based parameters, achieving ~20% accuracy.

Contribution

It introduces a novel empirical approach linking conductivity to atomic number density and electron configuration, improving predictive accuracy for elemental metals.

Findings

Empirical formulas match experimental data within ~20%.

The approach applies to various elemental metals including semimetals.

Using electron configuration sums as parameters enhances model accuracy.

Abstract

We propose empirical formulae of the electrical conductivity sigma and thermal conductivity for elemental metals such as Na, Cu or Fe at room temperature ranges. Assuming the relaxation time is given by the Planck constant divided by pai and further divided by the thermal energy kT for all metals, we propose that sigma is given by the Drude form with the number density of atoms instead of the electron number density, and further divided by a single free integer parameter G. If we adopt that G is the sum of outer electron numbers in electron configuration such as G=1 for Cu(4s^{1}),G=1+2=3 for In(5s^{2}4p^{1}) and G=5 for Nb(3d^{4}4s^{1}), the `absolute values' of sigma and a similar one for the thermal conductivity agree with experiments within ~20% for the majority of metals even including semimetals.