Theory of geometrical broadening of diffraction peaks from twisted lamellar crystals for interpretation of X-ray microbeam and selected-area electron diffraction experiments

Abstract

A simple theory of angular broadening of diffraction peaks is presented for the X-ray and electron diffraction from twisted crystalline lamellae. The diffraction peak position, width and asymmetry are computed in the limit of a small natural reflection width. The 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. It is found that the equatorial peaks, which are close to the normal direction to the lamellar basal plane, are characterized by the highest azimuthal width. The theory also describes the azimuthal drift of the non-equatorial reflections on a flat two-dimensional detector as the incident beam scans along the main helicoid axis. The proposed approach can be useful for interpretation of microbeam diffractograms measured on banded polymer spherulites. It can be easily generalized to describe diffraction from crystals of any arbitrary shape obtained by deformation of a flat lamella, under the condition that upon the deformation all the in-plane angles and distances are preserved in the linear approximation.