Determining the parameters of the equation of the state of molecular crystals based on diffractometric studies

M. A. Biryukova   ; Yu. M. Kovalev   ; D. V. Petrov   ; A. V. Stankevich   ; M. A. Shestakov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 3, pp. 70-78

Résumé

The paper presents the results of determining the crystal structure of PETN, hexogen, and HMX samples by X-ray diffractometry and calculations of the unit cell parameters of molecular crystals associated with the processing of X-ray diffractometry results, and experimental relationships between the unit cell volumes of molecular crystals on temperature. The obtained experimental data on the isobaric compression and expansion of the studied molecular crystals allowed us to specify the thermal component of the equations of the state of molecular crystals and obtain an expression for the isobaric thermal expansion coefficient associated with the mathematical model of the thermal component of the equations of state of molecular crystals. The obtained analytical dependence of the isobaric coefficient of thermal expansion on the temperature of the considered samples correctly describes the limiting transition to low temperatures. We propose a method of approximation for the obtained experimental relationships between temperature and the unit cell volume of the studied substances under isobaric compression/expansion based on a mathematical model of the semi-empirical equations of state of molecular crystals. This approach allowed us to obtain analytical relationships between the crystal unit cell volume and temperature, which describes the results of X-ray diffractometry of the molecular crystal samples considered in the work with an accuracy of up to 3 %.

Détail

Keywords: equation of state, molecular crystal, diffractometry
Mots-clés : isobar, Debye approximation.

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