The Unsymmetrized Self-Consistent Field Method (USCFM) has applied to a linear infinite chain consisting of two different particles. Expanding the self-consistent potential in power series of the lattice displacement, and taking the anharmonicity up to the fifth order, we show that all thermodynamic properties can be found in terms of two universal functions M1(α)M1(β), which can be implicitly expressed in terms of parabolic cylinder functions. We have applied this approach to study one dimensional system of KCl crystal using Born-Mayer-Huggins pair potential, and have determined some thermoelastic properties of this system.
References
[1]
Diu, B., Guthman, C., Lederer, D. and Roulet B. (1989) Elements De Physique Statistique. Hermann, Paris. (in French)
[2]
Akhiezer, A.I. and Peletminskii, S.V. (1981) Methods of Statistical Physics. Translated from Russian by M. Schukin, Pergamon Press, Oxford.
[3]
Akhiezer, A.I. (1974) Electrodynamics of Plasma. Nauka, Moscow. (in Russian)
[4]
Bazarov, I.P. (1971) Statistical Theory of Crystalline State. Moscow State University, Moscow. (in Russian).
[5]
Zubov, V.I. (2003) Unsymmetrized Distribution Functions and the Self-Consistent Theory of Strongly Anharmonic Crystals. Vestnik RUDN, Seria Physica, No. 11, 119-141. (in Russian)
[6]
Bateman, H. and Erdelyi, A. (1953) Higher Transcendental Functions: Vol. II. McGraw-Hill Book Company, Inc., New York.
Molhem, A. (2021) Interionics in Alkali Halide Crystals. (in Print)
[9]
Mayer, J.E. (1933) Dispersion and Polarizability and the van der Waals Potential in the Alkali Halides. The Journal of Chemical Physics, 1, 270.
https://doi.org/10.1063/1.1749283
[10]
Born, M. and Huang, K. (1954) Dynamical Theory of Crystal Lattices. Clarendon Press, Oxford.
[11]
Anderson, O.L. (1995) Equation of State of Solids for Geophysics and Ceramic Science. Oxford University Press, Oxford.
[12]
Sirdeshmukh, D.B., Sirdeshmukh, L. and Subhadra, K.G. (2001) Alkali Halides: A Handbook of Physical Properties. Springer-Verlag, Berlin.
https://doi.org/10.1007/978-3-662-04341-7
[13]
Salim？ki, K.E. (1960) The Thermal Expansion Coefficients of KCl and KBr, and Their Solid Solutions in the Temperature Range -180° to 400°C. Annales Academiae Scientiarum Fennicae. Series A. VI, Physica, 56, 1-40. (in German).
[14]
Bogoliubov, N.N. (1946) The Problems of Dynamical Theory in Statistical Physics. GosTekhIzdat, Moscow-Leningrad. (in Russian).
