The electron transport properties of pure liquid metals

Progress in the theory of the electrical conductivity and other ordinary transport properties of liquid metals since 1961 is reviewed. After a brief account of the basic nearly-free-electron diffraction formula, the quantitative comparison of this formula with experiment is discussed.

For the alkali metals, the agreement is adequate, given the uncertainty of the pseudopotentials, although there is controversy about the calculation of the temperature coefficient of ρ _L. To explain the observed volume dependence of ρ _L, and the thermoelectric power, it also seems necessary to allow for the variation of the pseudopotential with the positions of the Fermi level and the core levels relative to the bottom of the conduction band.

Quantitative results for the noble and polyvalent metals are meagre, and although calculations of ρ _L for Al and Zn are in excellent agreement with experiment there may be other cases where the basic formula is not adequate. The general question of the structure and convergence of the perturbation series for ρ _L is discussed, and it is suggested that corrections for higher order terms can be minimized by making the pseudopotential as near as possible to the t-matrix of an ion.

The anomalous properties of Hg are then discussed, in the light of the work of Mott (1966). In this connection it is shown that Edwards' formula (1962) for ρ _L, in which the Fermi velocity, v _F, is taken to be that of a free electron, ?k _F/m, despite deviations from the free-electron curve for ?(k), can be derived by using the expectation value of the current operator in place of e v _F in the Boltzmann equation. This modification of the elementary theory allows the Hall constant of a liquid metal to deviate from 1/nec, as found experimentally.