The simple theory of resistivity originally applied to pure liquid metals (Ziman 1961, Bradley et al. 1962) is formally extended to liquid alloys. In dilute solutions, size difference between solute and solvent ions can be allowed for, approximately, by a modification of the pseudo-potential of the solute, in a manner reminiscent of the modification of solute valency suggested by Harrison and Blatt (1957) in dealing with the resistance of solid alloys. The theory explains qualitatively a number of interesting features of the behaviour of liquid binary alloys, e.g. the failure of liquid solutions in polyvalent metals to obey the familiar rules of Nordheim and Linde. Some speculations on the anomalous behaviour of mercury amalgams are included. A bibliography of experimental results for both resistivity and density in liquid alloys is collected in Appendix II.

A theory of the electrical properties of liquid metals

REVIEW ARTICLE: Glassy metals

(1967). Electrons in disordered structures. Advances in Physics: Vol. 16, No. 61, pp. 49-144.

Electrons in disordered structures

An electron conductivity model for dense plasmas is described which gives a consistent and complete set of transport coefficients including not only electrical conductivity and thermal conductivity, but also thermoelectric power, and Hall, Nernst, Ettinghausen, and Leduc–Righi coefficients. The model is useful for simulating plasma experiments with strong magnetic fields. The coefficients apply over a wide range of plasma temperature and density and are expressed in a computationally simple form. Different formulas are used for the electron relaxation time in plasma, liquid, and solid phases. Comparisons with recent calculations and available experimental measurement show the model gives results which are sufficiently accurate for many practical applications.

An electron conductivity model for dense plasmas

Electrons in transition metals

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 pse...

J. M. Ziman

Papers

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