Geodesic
Mathematical Modelling of the Thermal Component of the Equation of State of Molecular Crystals
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 1, pp. 34-42 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This work is devoted to the construction of mathematical models of the equation of state of molecular crystals. Its practical value lies in the fact that all the solid explosives are molecular crystals. Therefore, after developing a mathematical model of the equation of state of molecular crystals, it will be possible to predict the behavior of explosives at high pressures and temperatures. The difficulty of the construction of the equation of state molecular crystals is that a large number of degrees of freedom of the molecules in the crystal structure does not allow the use of direct calculations. In this paper, we proposed an approach that allowed the use of all that is best in the Debye and Einstein models to describe the thermodynamics of crystals. Frequency separation of the normal vibrations in the crystal at high-frequency and low-frequency fluctuations allowed to getan analytical expression for the Grüneisen and parameters for the thermal component of the equation of state of molecular crystal.
Keywords: equation of state, pressure, temperature, energy
Mots-clés : Grüneisen coefficient. 
@article{VYURU_2013_6_1_a3,
     author = {Yu. M. Kovalev},
     title = {Mathematical {Modelling} of the {Thermal} {Component} of the {Equation} of {State} of {Molecular} {Crystals}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {34--42},
     year = {2013},
     volume = {6},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_1_a3/}
}
TY  - JOUR
AU  - Yu. M. Kovalev
TI  - Mathematical Modelling of the Thermal Component of the Equation of State of Molecular Crystals
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2013
SP  - 34
EP  - 42
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VYURU_2013_6_1_a3/
LA  - ru
ID  - VYURU_2013_6_1_a3
ER  - 
%0 Journal Article
%A Yu. M. Kovalev
%T Mathematical Modelling of the Thermal Component of the Equation of State of Molecular Crystals
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2013
%P 34-42
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/VYURU_2013_6_1_a3/
%G ru
%F VYURU_2013_6_1_a3
Yu. M. Kovalev. Mathematical Modelling of the Thermal Component of the Equation of State of Molecular Crystals. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 1, pp. 34-42. http://geodesic.mathdoc.fr/item/VYURU_2013_6_1_a3/

[1] Zharkov V. N., Kalinin V. A., Equation of State at High Temperatures and Pressures, Nauka, M., 1968 (in Russian)

[2] Kovalev Yu. M., “Equation of State and Temperature of Shock Compression of Crystalline Explosives”, Combustion, Explosion, and Shock Waves, 20:2 (1984), 102–107 (in Russian) | MR

[3] Molodets A. M., “Gruneisen Function and Zero Isotherm Three Metals to Pressures of 10 GPa”, J. of Experimental and Theoretical Physics, 107:3 (1995), 824–831 (in Russian)

[4] Zhirifal'ko L., Statistical Physics of Solids, Mir, M., 1975 (in Russian)

[5] Kitaygorodskiy A. I., Molecular Crystals, Nauka, M., 1971 (in Russian)

[6] Molodets A. M., “Gruneisen Function, Defined on the Basis of the Laws of Shock Compression of Solid Material”, Doklady RAN, 341:6 (1995), 753–754 (in Russian)

[7] Clark T., Computer Chemistry, Mir, M., 1990 (in Russian)

[8] B. M. Dobrats, P. C. Crawford, LLNL Explosives Handbook. Properties of Chemical Explosives and Explosive Simulants, University of California, Livermore, California, 1985