Theory of diffraction in disordered crystals formed by linear asymmetric molecules

Abstract

Using the general principles of Krivoglaz’s theory of diffraction for irregular crystals as well as the expansion of scattering structure amplitudes in spherical harmonics, a kinematic theory of diffraction has been developed for crystals, which consist of asymmetric linear molecules characterized by a “head-tail” disorder. The random variables that determine the statistics of deviations of molecular centers of mass and orientations of molecular axes from their average values are supposed to be independent. Detailed analysis is carried out for the N2O and CO cryocrystals, the structure of which is described on average by space group symmetry Pa3. The final formulas for integrated intensities of Bragg lines allow reconstruction of all parameters, which characterize the statistics of deviations of the relevant geometric parameters from their crystal averages.