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.
Cite this paper
Assef, M. (2021). Statistical Theory of Two-Component Crystal I-Case of One Dimensional Crystal. Open Access Library Journal, 8, e7433. doi: http://dx.doi.org/10.4236/oalib.1107433.
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)
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
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
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).
