Анализ некоторых приближений для описания тепловой части уравнений состояния молекулярных кристаллов

Abstract

Приводится анализ существующих приближений для описания зависимости теплоемкости при постоянном объеме от температуры молекулярного кристалла. Показано, что рассмотренные приближения не позволяют адекватно описывать зависимость теплоемкости при постоянном объеме от температуры молекулярных кристаллов нитросоединений. Данное заключение требует разработки специальных приближений, описывающих как низкочастотную, так и высокочастотную части колебательных спектров молекулярных кристаллов. The paper deals with the analysis of available approximations to describe the dependence of heat capacity at constant volume on the temperature of a molecular crystal. The information on the dependence of heat capacity at constant volume on the molecular crystal’s temperature plays an important role in construction of molecular crystal state equations. Molecular crystals are closing relations of mathematical models, which describe shock wave propagation, initiation of detonation in molecular crystals, etc. It is shown that the examined in the paper Debye and Einstein approximations, widely used for description of thermodynamic properties of monoatomic crystals, do not enable us to sufficiently describe the dependence of heat capacity at constant volume on the temperature of molecular crystals of nitro compounds. The suggestion by A.I. Kitaygorosky to divide crystal vibration frequency into intramolecular and vibration of a molecule as a whole (three vibrations of the molecule’s center of gravity and three vibrations of Euler angles), well-proven when calculating thermodynamic functions of a number of organic molecular crystals with planar molecules, doesn’t make it possible to adequately describe the dependence of heat capacity at constant volume on the temperature of molecular crystals of nitro compounds. The obtained in this work results highlight the necessity for development of special approximations, which provide an opportunity to adequately describe both low-frequency and high-frequency parts of a vibration spectrum of molecular crystals of nitro compounds, the dependence of heat capacity at constant volume on the crystal’s temperature and the Gruneisen function, which is a link between heat and cold components of the molecular crystal state equation.