Thermal and electrical conductivities of the alkali metals at low temperatures

Abstract

Measurements of the thermal and electrical conductivities of very pure lithium, sodium, potassium, rubidium and caesium have been made down to temperatures as low as 2°K. The respective resistivities,Wandρ, may be written as the sum of an impurity resistance (W0,ρ0) and a so-called ‘ideal’ component (Wi,ρi) due to scattering by the thermal vibrations of the lattice. The terms in the thermal resistivity may be represented byW0=A/TandW1=BTnforT≤θ/10, wheren≃ 2 andA= (ρ0/2⋅45) x 108cm deg.2W-1. Current theory predicts thatt he quantityC≡Bθ2/W∞N⅔should be constant, whereNis the number of free electrons per atom andWis the measured high-temperature resistivity. TakingN= 1, the present experiments yieldC≃ 18 ± 4. The electrical resistance may be writtenρ=ρ0+βTmforT<θ/10withm≃ 5 except for sodium, where, below 8°K ,mis found to increase to 6. The theoretical relationships which exist between the low-temperature ‘ideal’ resistivities and those at higher temperatures are discussed in conjunction with the measured values. It is concluded that with the existing theories, no common adjustment ofθcan give satisfactory agreement of theory with experiment. A new simple semi-empirical expression is put forward forWiwhich provides rather good agreement with experiment.