Prog. Theor. Phys. Vol. 48 No. 3 (1972) pp. 731-751

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A Simplified Theory of Liquid-Solid Transitions. II

— Lennard-Jones and 1/r¹² System —

Hisao Okamoto, Shiro Isa and Hazime Mori

Department of Physics, Kyushu University, Fukuoka

(Received February 1, 1972)

Abstract:

In the first paper, a new lattice theory of liquid-solid transitions was proposed and the phase transitions in the Lennard-Jones system was studied with the use of a new approximation. In the present paper, the same problem is explored by using a different but self-consistent approximation which takes into account the short-range correlation between the first-nearest neighbors. It is confirmed that the fluid and solid phases are represented by different, separate branches in the free-energy versus density diagram.
The fluid-solid transition in the system of molecules interacting with the inverse-power repulsive potential 4ε(r₀/r)¹² is also treated and its freezing and melting point are determined as p/t^5/4 = 2.759, ρ_f/t^1/4 = 0.5320, ρ_m/t^1/4 = 0.6059, where p = Pr₀³/ε, t = kT/ε, ρ= Nr₀³/V. Freezing and melting phenomena in the Lennard-Jones system at high pressures are thus clarified.

URL : http://ptp.ipap.jp/link?PTP/48/731/
DOI : 10.1143/PTP.48.731

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Citing Article(s) :

Progress of Theoretical Physics Vol. 48 No. 5 (1972) pp. 1474-1492 :
A Simplified Theory of Liquid-Solid Transitions. III

Hazime Mori, Shiro Isa, Hisao Okamoto and Hiroshi Furukawa
Progress of Theoretical Physics Vol. 50 No. 4 (1973) pp. 1248-1264 :
A Simplified Theory of Liquid-Solid Transitions. IV

Hisao Okamoto, Shiro Isa, Naganori Hijikuro and Hazime Mori
Progress of Theoretical Physics Vol. 52 No. 2 (1974) pp. 385-396 :
Crystal Instability and Premelting Phenomena

Katsuya Honda
Progress of Theoretical Physics Vol. 60 No. 4 (1978) pp. 941-957 :
Monte Carlo Studies of Lattice Models

Takao Ichimura, Tadahiko Shiotani and Akira Ueda
Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1584-1596 :
A Simple Theory of Hard Disk Transition

Hikaru Kawamura

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