Relation between pair potentials and radial distribution functions in liquid metals and alloys

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Abstract
It is shown that the pairwise interactions between ions employed in the recent analysis of the radial distribution functions for liquid metals may result from perturbations due to local deviations from a uniform positively charged background of an electron gas in the Hartree description. Such a potential reveals the long-range oscillatory behaviour, as in the current established theories for the shielding of impurities in the electron gas, and it is closely related to the correlation of the ionic positions. The dielectric constant may, as a first approximation, be independent of the relative configuration of ions. It is to be noted that the total potential energy of the liquid metals cannot be expressed as a sum of these potentials in contrast to that of the non-metallic liquids. That is to say, the total potential energy contains the contribution which depends on the average density of ions. Therefore, the equation of the macroscopic quantities of liquid metals represented in terms of the radial distribution functions give reasonable values only when the pair potentials are differentiated with respect to the relative coordinates of ions. If the concept of the pair potentials is valid in such a meaning, the theories due to the radial distribution function of liquids can in principle be applied to liquid alloys as well as pure metals. Simplified procedures are proposed to interpret (i) the interaction of solute atoms in dilute alloys and (ii) the anomalous behaviour of some concentrated alloys, often corresponding to the composition of intermetallic compounds. The treatments based upon the pair potentials are also useful in the non-equilibrium properties of liquid metals such as viscosity.

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