Prog. Theor. Phys. Vol. 45 No. 3 (1971) pp. 663-681

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Theory of Melting at High Pressures

— Existence of a Maximum in Melting Curves —

Takeshi Yoshida and Hisao Okamoto

Department of Physics, Faculty of Science, Kyushu University, Fukuoka

(Received September 5, 1970)

Abstract:

A theory of melting is developed in order to study the melting-curve maximum found in recent high-pressure experiments. It is based on the idea that the energy of creating positional disorder in a crystal may have a maximum as a function of volume, if the repulsive interatomic porential at high pressures is properly soft. The melting process is interpreted as an order-disorder transition, which was originally put forward by Lennard-Jones and Devonshire, and a lattice model similar to theirs is introduced. The Bragg-Williams approximation is used in calculations. On the assumption that the repulsive potential between a pair of atoms is effectively represented by an exponential function of the distance, melting curves of rubidium and cesium for which a melting-curve maximum has been found are calculated. They are in fairly good agreement with the observed melting curves near the maximum melting point. However the theory presidcts too small volumes at high pressures. A discussion is given to improve this defect by taking the short-range order in the liquid state into account.

URL : http://ptp.ipap.jp/link?PTP/45/663/
DOI : 10.1143/PTP.45.663

References:

F. P. Bundy, Phys. Rev. 115 (1959), 274[APS].
F. P. Bundy and H. M. Strong, Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press, New York and London), Vol. 13 (1962), p. 81.
H. D. Luedemann and G. C. Kennedy, J. Geophys. Rev. 73 (1968), 2795.
G. C. Kennedy, A. Layaraman and R. C. Newton, Phys. Rev. 126 (1962), 1363[APS].
A. Jayaraman, W. Klement, Jr. and G. C. Kennedy, Phys. Rev. Lett. 10 (1963), 387[APS].
R. A. Stager and H. G. Drickamer, Phys. Rev. 131 (1963), 2524[APS].
G. C. Kennedy and R. C. Newton, Solids under Pressure, edited by W. Paul and D. M. Warschauer (McGraw-Hill, New York, 1963), p. 163.
S. M. Stishov and N. A. Tikhomirova, Zh. Eksp. i Teor. Fiz. 49 (1965), 618 [Sov. Phys. -JETP 22 (1966), 429].
B. C. Deaton and F. A. Blum, Jr., Phys. Rev. 137 (1965), A1131[APS].
P. E. Chaney and S. E. Babb, Jr., J. Chem. Phys. 43 (1965), 1071[CrossRef].
W. Klement, Jr., L. H. Cohen and G. C. Kennedy, J. Phys. Chem. Solids 27 (1966), 171[CrossRef].
A. Jayaraman, Phys. Rev. 135 (1964), A1056[APS].
S. M. Stishov and N. A. Tikhomirova, Zh. Eksp. i Teor. Fiz. 48 (1965), 1216 [Sov. Phys. -JETP 21 (1965), 810].
F. P. Bundy, J. Chem. Phys. 38 (1963), 618[CrossRef].
S. M. Stishov and N. A. Tikhomirova, Sov. Phys. -JETP Lett. 1 (1965), 12.
D. L. Ball, Liquids: Structure, Properties, Solid Interactions, edited by T. J. Hughel (Elsevier, Amsterdam, 1965), pp. 353-369.
S. E. Babb, Jr., P. E. Chaney and B. B. Owens, J. Chem. Phys. 41 (1964), 2210[CrossRef].
E. Rapoport and G. C. Kennedy, J. Phys. Chem. Solids 26 (1965), 1995[CrossRef].
E. Rapoport, J. Chem. Phys. 45 (1966), 2721[CrossRef].
N. Kawai and Y. Inokuti, Jpn. J. Appl. Phys. 7 (1968), 989.
J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. A 169 (1939), 317; ibid. 170 (1939), 464.
R. Sternheimer, Phys. Rev. 78 (1950), 235[APS].
A. Jayaraman, R. C. Newton and J. M. McDonough, Phys. Rev. 159 (1967), 527[APS].
H. Matsuda, Prog. Theor. Phys. 42 (1969), 140[PTP].
S. O. Colgate, J. E. Jordan, I. Amdur and E. A. Mason, J. Chem. Phys. 51 (1969), 968[CrossRef].
I. Amdur and E. A. Mason, J. Chem. Phys. 23 (1955), 2268[CrossRef].
F. A. Lindemann, Z. Phys. 11 (1910), 609.
L. Salter, Phil. Mag. 45 (1954), 369.
L. Cartz, Proc. Phys. Soc. B 68 (1955), 951; ibid. 68 (1955), 957.
J. J. Gilvarry, Phys. Rev. 102 (1956), 308[APS]; ibid. 102 (1956), 317[APS]; ibid. 102 (1956), 325[APS]; ibid. 103 (1956), 1700[APS]; ibid. 104 (1956), 908[APS].
S. N. Vaidya and E. S. R. Gopal, Phys. Rev. Lett. 17 (1966), 635[APS].
M. Ross, Phys. Rev. 184 (1969), 233[APS].
Y. Ida, Phys. Rev. 187 (1969), 951[APS].

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