Systematic Absences and the X-Ray Diagram of Cellulose

Abstract

ON many X-ray diffraction photographs from high polymers only even-order meridional reflexions are observed. It is therefore assumed that there is a two-fold screw axis in the structure. In general this is valid, but there are special circumstances when such absences occur for a different reason. Thus, in a unit cell containing an asymmetric unit composed of two sub-units, the condition for the observed absences can be satisfied within the asymmetric unit itself if the sub-units have identical distributions of diffracting power along the y-axis (the fibre axis) and are separated by half a cell dimension in the y-direction. The structure can then be regarded as built up of two interlinked lattices, the absent reflexions being associated with the identity of the two lattice units along the y-axis. With polymers where the asymmetric units consist of parts of more than one chain, this condition can be attained by displacing half the chains by half a cell dimension relative to the rest, in the direction of the chain axis, at the same time allowing them to rotate through arbitrary angles about their chain axes. When this rotation is zero, conditions arise similar to those in a centred cell; when it is π the conditions for a two-fold screw axis occur. However, for all degrees of rotation the y co-ordinates remain the same, and the same systematic absences will occur on the meridian.