Microbeam X-ray diffraction from twisted lamellar crystals: theory and computer simulation

The diffraction peak position, width and intensity distribution are calculated for the case of a helicoidally twisted crystalline lamella, both analytically and numerically. It is shown that the diffraction peak broadening depends on the orientation of the corresponding reciprocal-space vector with respect to the helicoid axis and the normal to the lamellar basal plane. The equatorial peaks, which are close to the normal direction to the lamellar basal plane, are characterized by the highest azimuthal width. By contrast, the reflections positioned close to the lamellar surface have the smallest azimuthal width. For non-equatorial peaks in the proximity of the twisting axis the intensity has an unusual asymmetric shape. The shape of the microbeam, as well as its position and direction with respect to the lamella, influences the shape of the diffraction peaks in reciprocal space and their appearance in two-dimensional diffractograms. The proposed approach can be useful, for example, for the interpretation of microbeam diffractograms of banded polymer spherulites.