Diffraction indicates varied cellulose Iβ unit cell dimensions. Reasons include relatively weak van der Waals forces along the unit cell a-axis and varying crystallite dimensions. Although a crystal structure is available for large-crystal tunicate cellulose , there is less information about commercial cellulose structures with smaller crystallites. This is a problem for application of the Rietveld method for analyzing the diffraction patterns for the details of crystallinity, size, and structure.For cellulose, the Rietveld method reports what changes to the model tunicate structure are needed to make its calculated diffraction pattern match the observed pattern. The model is modified by refining the important variables: background, crystallite size and size anisotropy, unit cell dimensions, amorphous content and non-random orientation of the crystallites in the sample holder. Rietveld could determine individual atomic positions, but the limited data from cellulose powders is already overtaxed by these important variables. When the MAUD Rietveld software changes the unit cell dimensions, it compresses or stretches molecular structures without rotation. Such refinements could lead to structures with high calculated energy, in part because the tunicate structure might be distant from the correct structure. To gain insight, we used Quantum Espresso software to vary the a- and b-axis lengths and theγ angle. Results for unit cells with the shortest axes were about 36 kJ above the minimum energy structure.
References: Nishiyama Y, Langan P, Chanzy H (2002) Crystal structure hydrogen-bonding system in cellulose Iβ from X-ray and neutron fiber diffraction. J Am Chem Soc 124(31):9074–9082. https://doi:10.1021/ja0257319
Young, R A (ed.), The Rietveld Method (Oxford, 1993; online edn, Oxford Academic, 31 Oct. 2023), https://doi.org/10.1093/oso/9780198555773.001.0001,
MAUD is free, open source software developed mainly by Luca Lutterotti. https://luttero.github.io/maud/
Quantum Espresso is free, open-source for electronic-structure and materials modeling. https://www.quantum-espresso.org/