Theory of the electrical conductivity in the liquid–vapor interface of a simple metal

Abstract

We report an analysis of the electrical conductivity in an inhomogeneous liquid metal. The particular problem addressed is the assessment of the influence of a liquid–vapor transition zone, with nonzero width and internal structure, on the components of the conductivity perpendicular to and parallel to the surface. Our analysis is developed from a generalization of the Ziman theory of conductivity of a homogeneous liquid metal. It is based on the nearly free electron-pseudopotential model of liquid metal, and is valid in the domain for which the penetration depth is large relative to the mean free path, which in turn is large relative to the nearest neighbor spacing in the liquid. We show that the parallel component of the conductivity, as a function of distance along the normal to the surface, increases continuously from the bulk value to a maximum somewhere in the liquid–vapor transition zone, then decays to zero in the vapor. The predicted anisotropy of the conductivity at the surface, σ∥≳σ⊥, is in agreement with the model conductivity profile proposed by Rice and co-workers to reconcile the optical constants of liquid Hg determined separately from reflectivity and ellipsometric data.