Analysis of some approximation for the description of thermal side of the equation states of molecular crystals

Yu. M. Kovalev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 1, pp. 49-56

Résumé

The paper deals with the analysis of available approximations to describe the dependence of heat capacity at constant volume on the temperature of a molecular crystal. The information on the dependence of heat capacity at constant volume on the molecular crystal's temperature plays an important role in construction of molecular crystal state equations. Molecular crystals are closing relations of mathematical models, which describe shock wave propagation, initiation of detonation in molecular crystals, etc. It is shown that the examined in the paper Debye and Einstein approximations, widely used for description of thermodynamic properties of monoatomic crystals, do not enable us to sufficiently describe the dependence of heat capacity at constant volume on the temperature of molecular crystals of nitro compounds. The suggestion by A.I. Kitaygorosky to divide crystal vibration frequency into intramolecular and vibration of a molecule as a whole (three vibrations of the molecule's center of gravity and three vibrations of Euler angles), well-proven when calculating thermodynamic functions of a number of organic molecular crystals with planar molecules, doesn't make it possible to adequately describe the dependence of heat capacity at constant volume on the temperature of molecular crystals of nitro compounds. The obtained in this work results highlight the necessity for development of special approximations, which provide an opportunity to adequately describe both low-frequency and high-frequency parts of a vibration spectrum of molecular crystals of nitro compounds, the dependence of heat capacity at constant volume on the crystal's temperature and the Gruneisen function, which is a link between heat and cold components of the molecular crystal state equation.

Détail

Keywords: equation of state, molecular crystal, energy of Helmholtz, Boltzmann's constant, Einstein's approach.
Mots-clés : Planck's constant, Debye approximation

Bibliographie

[1] Zharkov V. N., Kalinin V. A., Equations of state at high temperature and pressure, Nauka Publ., M., 1968, 311 pp. (in Russ.)

[2] Kovalev Yu. M., “Mathematical Modelling of the Thermal Component of the Equation of State of Molecular Crystals”, Bulletin of the South Ural State University. Series Mathematical Modelling, Programming Computer Software, 6:1 (2013), 34–42 (in Russ.)

[3] Zhirifal'ko L., Statistical physics of solid body, Mir Publ., M., 1975, 382 pp. (in Russ.)

[4] Kitaygorodskiy A. I., Molecular crystals, Nauka Publ., M., 1971, 424 pp. (in Russ.)

[5] B. M. Dobratz, P. C. Crawford, LLNL Explosives Handbook. Properties of Chemical Explosives and Explosive Simulants, Lawrence Livermore National Laboratory Report UCRL-52997, 1985

[6] T. R. Gibbs, A. Popolato, Last explosive property data, Los Alamos series on dynamic material properties, University of California Press, Berkeley–Los Angeles–London, 1980

[7] Kovalev Yu. M., Belik A. V., Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2013, no. 9(300), 5–10 (in Russ.)

[8] Klark T., Computer chemistry, Mir Publ., M., 1990, 384 pp. (in Russ.)