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Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2018, Volume 10, Issue 2, Pages 57–67 (Mi vyurm375)  

Mechanics

Determining the expression for isobaric coefficient of volume expansion for some molecular crystals of nitro compounds

Yu. M. Kovalev

South Ural State University, Chelyabinsk, Russian Federation

Abstract: A type of equations on the state of molecular crystals of nitro compounds is suggested based on dividing Helmholtz free energy into intramolecular and intermolecular components. It is suggested to approach the thermal part of the internal energy and pressure of a molecular crystal with Debye approximation for intermolecular component, and with Einstein approximation for intramolecular component. This division of Helmholtz energy allowed to obtain clear expressions for all thermodynamic quantities being part of the equations of state. The suggestion that isothermal sound speed of a molecular crystal at the temperature of 0 K is determined solely by elastic characteristics of the crystal made it possible to obtain the dependency of Gruneisen coefficient on volume. The dependencies of thermodynamic quantities on temperature and volume determined in this work were used to build an analog of Gruneisen equation for molecular crystals, and to determine the dependency of isobaric coefficient of crystal volume expansion on temperature. It turned out that to obtain calculated values of volumes of unit cells of triamyno trinitrobenzene (TATB) crystals while integrating Gruneisen equation as per temperature, a high-temperature approximation may be used for Debye specific thermal capacity function. The obtained theoretical dependency of isobaric coefficient of crystal volume expansion on temperature indicates at the automatic meeting the condition of its tending to zero while the temperature tends to zero. The comparative analysis of the calculated and experimental values of volumes of unit cells of molecular crystals of 1,3,5-2,4,6-trinitrobenzene (TATB) depending on the temperature showed that they concur satisfactorily to the accuracy of no more than 3 %.

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

DOI: https://doi.org/10.14529/mmph180206

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UDC: 532.593+536.715
Received: 08.04.2018

Citation: Yu. M. Kovalev, “Determining the expression for isobaric coefficient of volume expansion for some molecular crystals of nitro compounds”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:2 (2018), 57–67

Citation in format AMSBIB
\Bibitem{Kov18}
\by Yu.~M.~Kovalev
\paper Determining the expression for isobaric coefficient of volume expansion for some molecular crystals of nitro compounds
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2018
\vol 10
\issue 2
\pages 57--67
\mathnet{http://mi.mathnet.ru/vyurm375}
\crossref{https://doi.org/10.14529/mmph180206}
\elib{https://elibrary.ru/item.asp?id=32855771}


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