Ion-ion oscillatory potentials in liquid metals

Abstract

Radial distribution functions obtained by X-ray and neutron measurements have been analyzed for eight liquid metals, Li, Na, K, Rb, Cs, Hg, Al and Pb, and for the liquid insulator Ar. It is shown that pair potentials between the ions in liquid metals can be obtained from the data, and that the general features of these curves are similar on the basis of various approximate theories of liquids. In particular, the Born-Green theory and the method of Percus & Yevick have been used in all cases. For the eight liquid metals, and for two different temperatures in each case, long-range oscillatory interactions are always found in the ion-ion potentials. While these general features of the pair potentials are the same in Born-Green and Percus-Yevick theories, in the important region round the first minimum and the following maximum the results are quantitatively different. The potentials, however, are only weakly temperature-dependent in the Born-Green approach, and the approximate validity of this method for liquid metals appears to receive further confirmation from calculations of viscosity and surface tension, which are in quite surprisingly good agreement with experiment. The Percus-Yevick approach seems distinctly less good for metals, but may perhaps be more appropriate to deal with liquid insulators. However, many body forces may also be important in argon. The long-range oscillations are interpreted as conduction electron screening of the ions, though the amplitude of the oscillations is substantially greater than a Hartree point-ion model predicts. It is pointed out that core sizes and/or electron interactions will have to be incorporated carefully into the screening theory in order to understand the present findings in a fully quantitative way. The long-range oscillations afford striking evidence that the Fermi surface is quite sharp even in a liquid metal like mercury, where the mean free path is short. Some evidence of the damping of the oscillations is found, and rough values thereby obtained for the blurring of the Fermi distribution. Sodium remains a somewhat puzzling case, as the oscillations appear to fall off rather more slowly than theory would predict. By means of the Ornstein-Zernike direct correlation function f, it is pointed out that, solely from radial distribution function data which appears at first sight rather similar for insulating and conducting liquids, the two types may be distinguished. For insulators, f has no nodes, whereas for metals it has marked oscillations. This suggests that f is closely connected with the pair interaction $\phi$(r), and by analysis of the equations of the Born-Green, Percus-Yevick and hyperchain methods, it is shown that they all yield f(r) = -$\phi$(r)/kT for sufficiently large r. It is inferred therefore that this is a general result, and does not depend on the use of approximate theories.