The Liquid-Solid Two-Phase Coexistence

Abstract

Phase transitions are macroscopic phenomena which one should in principle be able to describe by equilibrium statistical mechanics. Progress has however been very slow in this field over the past decades. This is particularly true for the liquid-solid transition which is nevertheless a very general property of matter. During the present decade some progress has been achieved in the theoretical study of the freezing of simple model systems such as the hard sphere system. Analysis of the experimental ¹ and computer simulation² studies makes it moreover plausible that the freezing of more realistic systems is monitored by the freezing of some underlying hard sphere system so that the theoretical study of the liquid-solid coexistence of more realistic systems may soon also become accessible to equilibrium statistical mechanics. Considerable progress has been realized in recent years in the theory of freezing by reformulating the pioneering (but unsuccessful) work of Kirkwood and Monroe into the more modern language of the density functional theory³. The original work of Kirkwood and Monroe⁴ was formulated on the basis of the Born-Green-Yvon hierarchy which in retrospect is not a good starting point since this hierarchy depends explicitly on the interaction potential whereas freezing is known² to be largely independent of the details of the potential.