CYLINDRICALLY AVERAGED DIFFRACTION BY DISTORTED LATTICES

Theory is developed for calculating cylindrically averaged diffraction from an ensemble of finite two-dimensional distorted lattices. The tw o-dimensional lattices are distorted in three dimensions, and the corr elations between displacements of different lattice sites are describe d by an imposed correlation field. Expressions for diffraction by latt ices with circularly symmetric statistics are derived that permit effi cient numerical calculation of cylindrically averaged intensities. The motivation for this investigation is to develop a model for describin g disorder in, and diffraction by: polycrystalline fibres in which the constituent crystallites are randomly rotated about the fibre axis, a nd the molecules in the crystallites are subject to correlated displac ements. The approach adopted, however, is also applicable to systems w ithout rotational disorder. The diffraction properties of distorted la ttices are investigated by numerical calculation. The profiles and dis tribution of sharp 'Bragg' reflections throughout reciprocal space are examined as functions of site variances, correlation lengths and crys tallite size. The results show that certain distinct combinations of t hese parameters (different crystallite sizes and kinds of disorder) ca n lead to diffraction patterns that are almost identical. The results have implications for the analysis of disorder and molecular structure s in polycrystalline fibres using X-ray diffraction analysis.