On the effect of thermal expansion on the intensity of diffraction from molecules

Abstract

A number of polymers have been discovered recently for which the intensity of some Bragg reflections with d > 10 A considerably increases with temperature. Thermal expansion may be the reason for this anomalous phenomena. In sufficiently large molecules electron density distribution should change at the molecular boundaries upon thermal expansion. In the middle part of a molecule, owing to the rigidity of interatomic bonds, an increase in temperature will not cause appreciable changes. As a result, thermal expansion may lead to a re-distribution of the electron density and an increase in the intensity of Bragg reflections with temperature. The scattering from model systems of particles was calculated. The calculations show that the rate of the growth of the Bragg reflection intensity with maximum d increases when a relative size of the central part of particle with constant density increases. The larger the molecule, the faster the Bragg reflection intensity increases with temperature rise. Thermal expansion should lead to an increase in the intensity of Bragg reflections with largest d and thermal expansion should not affect the intensity of Bragg reflections at all if d values are small. The temperature factor of the intensity associated with thermal expansion should not depend on the Debye-Waller factor. The Debye-Waller factor characterizes the effect of thermal vibrations on the intensity of Bragg reflections in the harmonic approximation, while thermal expansion is related to anharmonic effects.