Quantitative evaluation of orientation in cellulose fibres from the X‐ray fibre diagram

Abstract The theory of fibre diagrams as given by Polanyi and first applied to cellulose fibres by Sisson and Kratky enables one to derive the orientation in a fibre from the intensity distribution in the diatropic interferences. Since these interferences are usually too weak in the X‐ray diagrams of cellulose fibres, we must resort to the paratropic reflexions. The present paper shows how these paratropic reflexions must be evaluated to obtain the orientation factor f r as a rational measure of average orientation. It is shown on experimental grounds that the proximity of the A 4 interference does not invalidate the evaluation of the A 3 sickle. A special procedure must be applied to fibres in which the orientation is not very pronounced, since here the interferences of the (021) planes partly overlap those of the paratropic A 3 planes. It is assumed throughout this article that in all experiments the Bragg angle is negligible. The correction required when dealing with finite Bragg angles is discussed in section 6. The relation between orientation and optical constants is set forth in section 5. Finally, section 8 gives an illustration along with a short summary of the method.