Small Particle X-Ray Scattering by Fibers, Size and Shape of Microcrystallites

Abstract

A theoretical and experimental analysis is given of small particle x-ray scattering by fibers. The scattering by different fibers of high orientation is compared with the theoretical scattering curves derived for independent scattering by an assemblage of parallel cylinders. Under certain conditions of swelling, excellent agreement is obtained between experimental and theoretical curves. From this agreement it is concluded that under these conditions, independent particle scattering is realized and that interparticle interference and multiple scattering do not play a part. Under all other conditions (dry fiber and other conditions of swelling) interparticle interference plays an important role in the scattering by these ``densely packed'' materials as can be concluded from the different distributions of intensity. The swelling method offers a means for separating independent and nonindependent scattering. An analysis of the influence of various conditions of swelling is made, and the correct experimental conditions for obtaining independent scattering are derived from the results. From the scattering under such conditions, the particle size in different fibers is determined on the basis of the theoretical formulas for independent scattering.