A theory of the electrical properties of liquid metals. I: The monovalent metals

Abstract The mean free path of an electron in a liquid metal depends on scattering by the ions. The cross section of each ion depend on its ‘pseudo-potential’, which can be estimated from the band gap in the solid. If the ions scattered independently, the mean free path would be much too short. But there is strong correlation between the positions of the ions in the liquid, giving rise to coherence between waves diffracted by adjacent ions. Using simple perturbation theory, one can show that the resistance should depend on the Fourier transform, a(K), of the radial distribution function, and should be smaller than for independent scatterers. The density fluctuations of the liquid also scatter electrons, through imperfect screening by the ‘other electrons’ of the coulomb fields of the ions. This ‘plasma resistance’ is the main effect in liquid Na, where the band gap is small. When this term has been subtracted, the resistivities of the other monovalent metals come out according to the theory, being approximately proportional to the squares of their pseudo-potentials. The change of resistance on melting is shown to be due to the change in the radial distribution function. Different ratios of ρL/ρS can be explained through differences in the scattering cross sections of ions of different metals -especially the differences in the ion core ‘pseudo-potentials’. The temperature variation of the resistivity follows from the temperature dependence of a(K). The thermoelectric power in the solid, and in the liquid, and its change on melting, all follow qualitatively from the form of a(K) and of the scattering cross section for each type of ion.