Volume 6, no. 1Pages 34 - 42

Mathematical Modelling of the Thermal Component of the Equation of State of Molecular Crystals

Yu.M. Kovalev
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 Gr'uneisen and parameters for the thermal component of the equation of state of molecular crystal.
Full text
equation of state, pressure, temperature, energy, Gr'u
1. Zharkov V.N., Kalinin V.A. Equation of State at High Temperatures and Pressures. Moscow, Nauka, 1968. (in Russian)
2. Kovalev Yu.M. Equation of State and Temperature of Shock Compression of Crystalline Explosives. Combustion, Explosion, and Shock Waves, 1984, vol. 20, no. 2, pp. 102-107. (in Russian)
3. Molodets A.M. Gruneisen Function and Zero Isotherm Three Metals to Pressures of 10 GPa. J. of Experimental and Theoretical Physics, 1995, vol. 107, no. 3, pp. 824-831.(in Russian)
4. Zhirifal'ko L. Statistical Physics of Solids. Moscow, Mir, 1975. (in Russian)
5. Kitaygorodskiy A.I. Molecular Crystals. Moscow, Nauka, 1971.(in Russian)
6. Molodets A.M. Gruneisen Function, Defined on the Basis of the Laws of Shock Compression of Solid Material. Doklady RAN, 1995, vol. 341, no. 6, pp.753-754. (in Russian)
7. Clark T. Computer Chemistry. Moscow, Mir, 1990. (in Russian)
8. Dobrats B.M., Crawford P.C LLNL Explosives Handbook. Properties of Chemical Explosives and Explosive Simulants. Livermore, California, University of California, 1985.