The theory of the transport phenomena in metals

Abstract

Exact expressions, valid for all temperatures, are obtained in the form of infinite determinants for the electrical conductivity, the thermal conductivity and the thermo-electric power of a degenerate gas of quasi-free electrons interacting with the ionic lattice of a metal. It is shown that the values of the electrical and thermal conductivities, in general, exceed the values given by the approximate interpolation formulae due to Bloch (1930), Wilson (1937) and others, and, in particular, that the Grüneisen-Bloch formula for the ideal electrical resistance is appreciably in error in the region close to the Debye temperature. It is further shown that the residual and ideal resistances of an impure metal are not strictly additive in the region where the two are of the same order of magnitude. The behaviour of the thermal conductivity is shown to agree qualitatively with the discussion based on Wilson’s formula given by Makinson (1938); the numerical values of the thermal conductivity, however, are increased appreciably, particularly for an ideal metal at low temperatures. The thermo-electric power is also discussed, but no simple results can be given for the intermediate temperature range.