Thermal expansion and kinetic coefficients of crystals

Abstract

Electrical ( ρ) and thermal ( W) resistivities and thermal expansion coefficient ( β) of Cu, Zn, Al, Pb, Ni, β -brass, Al 2O 3, NaCl, Si, SiO 2(∥), and SiO 2(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature ( T D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5–4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ ph / ρ * ≡ β T and W ph / W * ≡ β T (where ρ ph is the phonon electrical resistivity, ρ * = e E ˜ / J c p τ ϕ is the characteristic electrical resistivity, W ph is the phonon thermal resistivity, and W * = k B G / q c p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.