The thermal conductivity of metals

Source abstract

The methods used to measure separately the electronic and lattice heat conductivities κ e and κ g in a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κ e and for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratio L e = κ e /σ T as a function of T , both for the monovalent metals and for a model metal with 1·8 × 10 −2 conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κ e and κ g as functions of T are given in both cases, and these, together with a comparison of the observed Lorentz ratio and L e , show that in the monovalent metals κ g is unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth. Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls. The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.