The Relationship between Electrical Conductivity and Electromigration in Liquid Metals

Abstract

The phenomena of electrical conductivity and electromigration in metallic systems are related, since in both cases the basic physical process is the scattering of conduction electrons by metal ions. Numerous searches have been made for equations connecting the conductivity with electromigration. In the case of a liquid metal, when using the Drude–Sommerfeld (DS) conductivity equation, it was not possible to obtain a quantitative relationship between these phenomena, which would be correct. Attempts to find such a relationship when taking into account the N. Mott correction (g-factor) in the DS equation were unsuccessful. This article proposes a different correction (b-factor) to the DS equation, which takes into account the possibility of varying the momentum transferred by the conduction electron to a metal ion during the scattering. This correction allows to establish a quantitative relationship between conductivity and electromigration as well as between electromigration in various binary systems with common components, in agreement with the experiment. The proposed theory describes well, in particular, two- and multi-component metal systems of any concentration (the consistency rule for triangles A–B, B–C, C–A). The value of the b-factor smoothly changes depending on the heat of vaporization of the metal, per unit volume.