Direct Correlation Function Properties of Liquid Metals Near Freezing

Abstract

Motivated by the prediction of the Percus-Yevick hard sphere solution that, for dense liquids, the ratio R = c(r = 0)/c(q = 0) is very near to unity, c(r) being the direct correlation function and c(q) its Fourier transform, this ratio has been calculated from diffraction plus thermodynamic data for some fifteen liquid metals near their freezing points. It is found that 0.2 < R < 1.3, but for the liquid alkalis, the noble metals and the first row transition metals chosen, R is near to unity. This is to be contrasted with R ≈ 2 for liquid argon near the triple point.

The polyvalent metals Ga, Pb and Sn, with the smallest values of R, are plainly totally at variance with the hard sphere prediction. However, R is near to unity for Na, K and Rb and yet it is known fron neutron inelastic scattering that Rb exhibits a collective mode and is therefore quite different from a hard sphere liquid also. In fact, by examining long-range damping in c(q) for Na and Pb, we conclude that Pb has the harder core of these two metals.

Finally it is argued that for Pb, c(r) remains negative and non-zero just outside the ‘core’ diameter and this then accounts immediately for the low value of R, as also in the cases of Ga and Sn. In contrast, for argon c(r) has passed through a node before or at the core diameter, leading to R much greater than unity.