Geodesic
Construction of equations of the state to describe isothermal compression of some molecular crystals of nitro-compounds
Journal of computational and engineering mathematics, Tome 6 (2019) no. 2, pp. 18-31.

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We propose an approach to construct the equations of state of molecular crystals of nitro compounds. The approach allows to describe isothermal compression, and is based on the division of the Helmholtz free energy into thermal and "cold" parts. It turns out that the "cold" part can be divided into the intramolecular and intermolecular components, while the low-frequency and high-frequency vibrations can be distinguished in the thermal part. We propose to approximate the low-frequency component of the thermal part of the internal energy and the pressure of a molecular crystal by the Debye approximation. In order to describe the intermolecular energy of the Van der Waals interaction, we propose a potential that closes on the heat of sublimation of a molecular crystal. The "cold" part of pressure is determined by the change in intramolecular energy. We assume the "cold" part of pressure to be constant, and use the condition that the pressure is equal to 1 atm. under normal conditions in order to determine this part. This division of the Helmholtz energy allows to obtain explicitly the expressions for all thermodynamic values in the equations of state. In this paper, we assume the linear dependence of the Gruneisen coefficient on the volume. The use of a more complex relationship is not necessary, since we consider the isothermal compression, and the thermal component makes an insignificant contribution to the total pressure. We use the obtained dependences of thermodynamic values on temperature and volume in order to find the coefficients related to the known experimental data. A comparative analysis of the calculated and experimental values of the specific volumes of the molecular crystal of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) as a function of pressure shows their coincidence with an accuracy of 1 %.
Keywords: equation of state, molecular crystal, isothermal compression, Helmholtz energy, characteristic Debye temperature, Gruneisen equation, Debye approximation. 
@article{JCEM_2019_6_2_a1,
     author = {Yu. M. Kovalev and K. M. Kalinin},
     title = {Construction of equations of the state to describe isothermal compression of some molecular crystals of nitro-compounds},
     journal = {Journal of computational and engineering mathematics},
     pages = {18--31},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2019_6_2_a1/}
}
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Yu. M. Kovalev; K. M. Kalinin. Construction of equations of the state to describe isothermal compression of some molecular crystals of nitro-compounds. Journal of computational and engineering mathematics, Tome 6 (2019) no. 2, pp. 18-31. http://geodesic.mathdoc.fr/item/JCEM_2019_6_2_a1/