Prog. Theor. Phys. Vol. 48 No. 3 (1972) pp. 731-751
A Simplified Theory of Liquid-Solid Transitions. II
— Lennard-Jones and 1/r12 System
Department of Physics, Kyushu University, Fukuoka
(Received February 1, 1972)
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/t5/4 = 2.759, ρf/t1/4 = 0.5320, ρm/t1/4 = 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.
DOI : 10.1143/PTP.48.731
- H. Mori, H. Okamoto and S. Isa, Prog. Theor. Phys. 47 (1972), 1087[PTP]. This is referred to as I.
H. M. Peek and T. L. Hill, J. Chem. Phys. 18 (1950), 1252[CrossRef].
- J. E. Lennard-Jones and A. F. Devonshire, Proc. Roy. Soc. A 169 (1939), 317; ibid. 170 (1939), 464.
T. Morita, J. Phys. Soc. Jpn. 12 (19657), 1195[JPSJ];
ibid. 14 (1959), 570[JPSJ].
A. Bellemans and R. K. Nigam, J. Chem. Phys. 46 (1967), 2922[CrossRef].
D. S. Gaunt, J. Chem. Phys. 46 (1967), 3237[CrossRef].
J. Orban and A. Bellemans, J. Chem. Phys. 49 (1968), 363[CrossRef].
J. Orban, J. Van Craen and A. Bellemans, J. Chem. Phys. 49 (1968), 1778[CrossRef].
J.-P. Hansen and L. Verlet, Phys. Rev. 184 (1969), 151[APS].
G. A. Mansoori and F. B. Canfield, J. Chem. Phys. 51 (1969), 4967[CrossRef].
J.-P. Hansen, Phys. Rev. A 2 (1970), 221[APS].
W. G. Hoover, M. Ross, K. W. Johnson, D. Henderson, J. A. Barker and B. C. Brown, J. Chem. Phys. 52 (1970), 4931[CrossRef].
- Y. Hiwatari and H. Matsuda, Prog. Theor. Phys. 47 (1972), 741[PTP].
W. G. Hoover, S. G. Gray and K. W. Johnson, J. Chem. Phys. 55 (1971), 1128[CrossRef].
G. C. Kennedy, A. Jayaraman and R. C. Newton, Phys. Rev. 126 (1962), 1363[APS].
N. Kawai and Y. Inokuti, Jpn. J. Appl. Phys. 7 (1968), 989.
- T. Yoshida and H. Okamoto, Prog. Theor. Phys. 45 (1971), 663[PTP].
Y. Kuramoto and H. Furukawa, Prog. Theor. Phys. 47 (1972), 1069[PTP].
T. Yoshida and S. Kamakura, Prog. Theor. Phys. 47 (1972), 1801[PTP].
- H. Matsuda, Prog. Theor. Phys. 42 (1969), 414[PTP].
M. Plischke and D. Mattis, preprint.
- W. G. Hoover and M. Ross, Contemporary Phys. (1971).
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
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