A theory of the electrical properties of liquid metals II. Polyvalent metals

Abstract

The electronic properties of liquid polyvalent metals are discussed in relation to the nearly-free-electron model. The observed Hall effect (including some new measurements on Hg, In and Sn) is consistent in most cases with a spherical Fermi surface for the valence electrons. The optical properties fit a simple Drude formula, with the same density of states as for free electrons. The evidence from the magnetic susceptibility and its change at the melting point is only qualitative, but is consistent with a free-electron sphere in the liquid. Only the observed small change in the Knight shift on melting is difficult to interpret in our model. As in I (Ziman 1961) the electrical resistivity is assumed to be represented, in first approximation, by an integral over the angle of scattering of a conduction electron, where the integrand contains the x-ray scattering function of the liquid and the Fourier transform of a ‘pseudo-potential’ for each ion. The formula adequately describes the data, with a pseudo-potential which seems to depend systematically on the place of the element in the periodic table. It appears to be smaller than the equivalent quantity in the solid, where it determines the energy gaps between electron bands. The thermoelectric power has been measured for Zn, Cd, Hg, In, Sn, Pb, Bi, and can be made to fit the theory if it is assumed that in a few metals (especially Hg) the scattering cross section of each atom depends on the energy of the electron. This dependence may also be apparent in the effect of pressure on the resistivity, which is observed to be empirically correlated with the magnitude of the thermoelectric power. Finally, it is shown that the temperature-dependence of resistivity (especially the negative coefficient in the divalent metals) can be qualitatively explained, still within the framework of the nearly-free-electron model, in terms of thermal expansion and changes in the x-ray scattering function.