Powder diffraction

Abstract: SUPERFLIP is a computer program that can solve crystal structures from diffraction data using the recently developed charge-flipping algorithm. It can solve periodic structures, incommensurately modulated structures and quasicrystals from X-ray and neutron diffraction data. Structure solution from powder diffraction data is supported by combining the charge-flipping algorithm with a histogram-matching procedure. SUPERFLIP is written in Fortran90 and is distributed as a source code and as precompiled binaries. It has been successfully compiled and tested on a variety of operating systems.

Abstract: Introduction to the Rietveld Method 1. The early days: a retrospective view 2. Mathematical aspects of Rietveld refinement 3. The flow of radiation in a polycrystalline material 4. Data collection strategies: fitting the experiment to the need 5. Background modelling in Rietveld analysis 6. Analytical profile fitting of X-ray powder diffraction profiles in Rietveld analysis 7. Crystal imperfection broadening and peak shape in the Rietveld method 8. Bragg reflection profile shape in X-ray powder diffraction patterns 9. Restraints and constraints in Rietveld refinement 10. Rietveld refinement with time-of-flight powder diffraction data from pulsed neutron sources 11. Combined X-ray and neutron Rietveld refinement 12. Rietveld analysis programs Rietan and Premos and special applications 13. Position - constrained and unconstrained powder-pattern-decomposition methods 14. Ab initio structure solutions with powder diffraction data

Abstract: Cellulose samples are routinely analyzed by X-ray diffraction to determine their crystal type (polymorph) and crystallinity. However, the connection is seldom made between those efforts and the crystal structures of cellulose that have been proposed with synchrotron X-radiation and neutron diffraction over the past decade or so. In part, this desirable connection is thwarted by the use of different conventions for description of the unit cells of the crystal structures. In the present work, powder diffraction patterns from cellulose Iα, Iβ, II, IIII, and IIIII were calculated based on the published atomic coordinates and unit cell dimensions contained in modified “crystal information files” (.cif) that are supplied in the Supplementary Information. The calculations used peak widths at half maximum height of both 0.1 and 1.5° 2θ, providing both highly resolved indications of the contributions of each contributing reflection to the observable diffraction peaks as well as intensity profiles that more closely resemble those from practical cellulose samples. Miller indices are shown for each contributing peak that conform to the convention with c as the fiber axis, a right-handed relationship among the axes and the length of a < b. Adoption of this convention, already used for crystal structure determinations, is also urged for routine studies of polymorph and crystallinity. The calculated patterns are shown with and without preferred orientation along the fiber axis. Diffraction intensities, output by the Mercury program from the Cambridge Crystallographic Data Centre, have several uses including comparisons with experimental data. Calculated intensities from different polymorphs can be added in varying proportions using a spreadsheet program to simulate patterns such as those from partially mercerized cellulose or various composites.