A Simplified Theory of Liquid-Solid Transitions. I

Abstract

A new lattice theory of liquid-solid transitions is developed to clarify the statistical­ mechanical mechanism of freezing and melting processes. This is done by employing the expandable-lattice model in which the cell size is determined as a function of temperature and density by minimizing the free energy, and by introducing a simple approximation which takes into account the short-range correlation between molecules locating within the force range. In the pressure versus density diagram, the fluid and solid phase are represented by different, separate branches which have different cell sizes and molecular fractions. The branch which yields the fluid phase is disordered all over, while another consists of disor­ dered and ordered subbranches, the ordered subbranch leading to the solid phase. This result differs from those of Lennard-Jones and Devonshire's theory and the rigid-lattice theo­ ries, in which the fluid and solid phase are described by one branch which consists of dis­ ordered and ordered subbranches. Thus the fluid-solid transition turris out to have no critical point above which the transition ceases to be of the first order. It also turns out that although the solid state meets a thermodynamic instability below the melting density, the liquid metastable state remains stable far beyond the freezing density. We assume the Lennard-Jones potential and take up to the second-nearest-neighbor interaction. Then we obtain the usual shape of the phase diagram with the liquid range Tcr1t!Ttrip=l.38. Various constants of the critical and triple point are in fairly good agree­ ment with experiments except the pressure at the triple point. It is shown that the liquid states near the critical and triple point have adequate numbers of holes.