Size, shape, orientation and crystallinity of cellulose I_β by X-ray powder diffraction using a free spreadsheet program

X-ray powder diffraction is one of the most commonly used methods in cellulose science. This technique is used to identify the cellulose allomorphs, their crystallinity, and the size of their crystallites. In this paper, a novel model is introduced that implicitly takes into account the shape and size of cellulose I_β crystallites in the interpretation of powder diffractograms. Because of the limited amount of data in cellulose powder patterns, this model focuses on a small number of adjustable parameters. The method hypothesizes that cellulose I_β crystallites are straight crystalline rods with superelliptical cross-sections. This superellipse is a parametric curve that can, for example, describe various crystallite shapes as rectangles or ellipses. Additionally, preferred orientation along the (0 0 1) crystallographic planes can be modelled using the March–Dollase approach. The simulated background has a semi-empirical form. An initial model comprised cellulose I_β crystallites and the amorphous background. A second model comprised a biphasic distribution of crystallites and the same amorphous background. In this second model, large cellulose I_β crystallites coexisted with more slender crystallites, usually less than 20 Å in lateral size. Cellulose IV_I nanocrystals were selected as a modeling construct to represent these small and distorted forms of native cellulose. Both models produced simulations in excellent agreement with the experimental measurements.