The resistance of liquid metals

Abstract

The electrical resistance of most normal metals in the liquid state just above the melting point is about twice as great as that of the solid metal just below the melting point. Certain abnormal metals, however, such as bismuth, gallium and antimony, which are rather poor conductors in the solid state, increase their conductivity on melting. The purpose of this paper is to discuss this change of resistance from the point of view of the modern theory of electronic conduction which is based on the wave mechanics, and to obtain a formula for the change of resistance which is in quantitative agreement with experiment for normal metals. No quantitative theory can as yet be given for the abnormal metals, but we shall show that their behaviour is explicable in a qualitative way. In a solid the atoms vibrate about mean positions which are fixed in the solids in a liquid at temperatures near the melting point, it is now generally recognized that the atoms vibrate about mean positions which, though not fixed, move slowly compared with the velocity, of order of magnitude √( k T/M), with which the atoms vibrate. The most direct evidence for this is afforded by the specific heats of monatomic metals, which have, within the limits of experimental error (~7%), the same values (in the neighbourhood of 3R) for a given metal in the solid and liquid states near the melting point. Further evidence is given by the rates of diffusion of gold in mercury (0·72 sq cm/day) or of thorium B (Pb) in non-radioactive liquid lead (2·2 sq cm/day). If one compares these numbers with the formula for the diffusion coefficient in gases, D = 1/3 lc , where l is the mean free path, and c the mean molecular velocity, one finds, on setting c equal to a quantity of the order of magnitude of √( k T/M), that l must be taken to be about one-hundredth of the interatomic distance.