A Simplified Theory of Liquid-Solid Transitions. IV

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Abstract
An effective mean free volume is proposed to improve the expandable-lattice theory of liquid-solid transitions developed in previous papers by taking into account the correlation between the intracellular configurations of molecules. In another word, a new approximation called the (l1,l2) approximation is introduced, where l1 and l2 mean that in calculating the mean free volume, l1 and l2 neighboring molecules are fixed at the centers of their cells in the fluid and solid phase, respectively, whereas the other neighboring molecules are treated approximately to move in their cells correlatively with the molecule of the central cell. The freezing and melting points of the hard-core transition are given in the (2,10) approximation by p/tρc=7.700, ρf/ρc=0.6442, ρm/ρc=0.7638, where t=kT/ε, p=Pr03/ε, ρ=Nr03/v and ρc=√2, r0 and ε being the core diameter and the energy parameter, respectively. The critical and triple points of the Lennard-Jones system are also calculated with the improved mean free volumes. The triple point is given in the (2,10) approximation by t=0.7789, p=0.0055, ρg=0.0077, ρl=0.6990, ρm=0.8979, which agree fairly well with experiments on Argon.

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