Electron and lattice conduction in metals

Abstract

The theory of the transport phenomena in metals is re-examined, the departure from equilibrium of both the electron and the lattice distribution functions being simultaneously taken into account in a consistent fashion. Simple expressions are derived for the conduction magnitudes which are exact at sufficiently high and sufficiently low temperatures and which are assumed to be approximately valid for all temperatures. The behaviour of the terms which arise from the non-equilibrium of the lattice depends upon the relative importance of the various causes responsible for scattering the lattice vibrations. In the case of the electrical conductivity these terms are estimated to be small in general, but they may have a bearing on some of the observed resistance anomalies at very low temperatures. Further, while the present theory gives nothing new in the case of the thermal conductivity, which is given by the sum of the usual electronic and lattice conductivities, the behaviour of the thermo-electric power is found to be profoundly modified, the non-equilibrium of the lattice leading in general to a considerably increased value which may show a complex temperature variation. The theory can account for the observed thermo-electric power of sodium at low temperatures and it suggests reasons for the complex character of the thermo-electric behaviour of metals in general, although in the present form the theory is not sufficiently general to account for all the observed anomalies even in the monovalent metals.