Equivalence of the Percus-Yevick Collective Coordinate Theoru of liquids with the Self Consistent Field Theory of Melting

Abstract

In this paper we compare the recent description of melting via the self consistent field scheme of Johannsson¹ with the Percus-Yevick² collective coordinate approach to the theory of liquids, as applied to the melting phenomenon and the liquid structure factor of liquid metals by omini³. We show that the formalism used to extract a self consistent order parameter naturally leads to the concept of a liquid phonon analogous to a paramagnon in the theory of ferromagnetic-paramagnetic or antiferromagnetic-paramagnetic phase transitions, which can readily be identified with Percus-Yevick² technique of decribing the liquid in terms of 3N collective coordinates. This description has been used very successfully by Omini³ to relate the entropy of melting to the long wavelength limit of the liquid structure factor for a variety of simple metals, so that a relation can be demonstrated between the self consistent field parameter and melting via another route, the Percus-Yevick² theory. Lastly, we relate both the self consistent field (order) parameter and the energy of formation of a vacancy-interstitial pair, via the Percus-Yevick dispersion relation, tpo the Lindemann melting criterion parameter, the root mean square lattice displacemene of the atoms critical to melting.