Theory of the Low-Temperature Thermal Resistivity in Simple Metals

Abstract

A variational calculation of the low-temperature thermal resistivity, valid for arbitrary relative strength of phonon and elastic scattering, has been carried out. The trial electron distribution function chosen is linear combination of the usual one appropriate to elastic scattering and a step-function approximation to the distribution function obtained by Klemens appropriate for phonon scattering. The relative magnitude of these two terms is the parameter that is adjusted to minimize the thermal resistivity, and is itself a function of the relative importance of elastic and inelastic scattering. The result obtained agrees with current theories where elastic scattering dominates and is within 5% of the Klemens's result when phonon scattering dominates as well as providing a prediction of behavior between these two limiting cases. The theory also suggests a manner of experimentally comparing thermal resistivities of different samples in a way somewhat analogous to Matthiessen's rule.