Prog. Theor. Phys. Vol. 50 No. 4 (1973) pp. 1248-1264
A Simplified Theory of Liquid-Solid Transitions. IV
— With an Improved Mean Free Volume
Department of Physics, Kyushu University, Fukuoka
*Department of Physics, Fukuoka University, Fukuoka
(Received March 24, 1973)
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.
DOI : 10.1143/PTP.50.1248
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Citing Article(s) :
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Crystal Instability and Premelting Phenomena
Progress of Theoretical Physics Vol. 60 No. 4 (1978) pp. 941-957
Monte Carlo Studies of Lattice Models
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Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1584-1596
A Simple Theory of Hard Disk Transition
Progress of Theoretical Physics Vol. 70 No. 3 (1983) pp. 687-696
Hole Model Approach to Melting