Determination of the form of “elastic” component of the equations of state of molecular crystals

Yu. M. Kovalev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 2, pp. 55-63

Résumé

The paper analyzers the diagram of atom-atom potentials as exemplified by calculation of energy of the molecular crystal lattice of nitro compounds. The performed in the paper calculations of energy of the crystal lattice of a number of nitro compounds have shown that the calculation data coincide with the experiment only when an electrostatic interaction between molecules is taken into account in the diagram of atom-atom potentials. The obtained results allowed us to create a potential for description of an elastic component of the internal energy and pressure in the two-term state equation of the molecular crystal. The accounting of electrostatic energy has lead to the fact the in the Buckingham potential when describing the attraction energy an unknown parameter, i.e. a power coefficient for specific volume of the crystal, appears. On the whole, there are four parameters in the potential for description of the elastic component of the internal energy and pressure. These parameters are determined from experimental data. The analysis of experimental data on thermodynamic measurements has shown that the most adequate description of the elastic component of the internal energy and pressure in the two-term state equation of molecular crystals can be received only when the potential of intermolecular interactions closes on the isothermal compressibility or sound speed at the temperature of the crystal tending to zero. The consecutive passage to the limit in terms of the isothermal sound velocity for the crystal temperature, tending to zero, allowed us to get a rather simple potential for description of the elastic component of the internal energy and pressure, expression of which includes an explicitly isothermal sound speed. This approach enables us to reduce the number of unknown parameters to two, which are specified according to experimental shock adiabats.

Détail

Keywords: state equation, molecular crystal, Helmholtz energy, Lennard–Jones potential, Buckingham potential, Einstein approximation.
Mots-clés : Debye approximation

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