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Ab initio phasing of X-ray powder diffraction patterns by charge flipping

Abstract

Determining crystal structures from powder X-ray diffraction data remains a challenging problem in materials science. By embedding a Le-Bail-like procedure within the recently discovered charge-flipping phasing algorithm, an extremely simple, fast and effective ab initio method has been developed to determine phases directly from indexed powder diffraction patterns. The algorithm solves the degeneracy problem by applying spherical averaging for overlapping Bragg reflections, while solving the phase problem by using the Oszlányi–Sütő charge-flipping algorithm. The processes of peak decomposition and phasing are integrated within the same iteration, and a dynamic support is used. The Fienup hybrid input–output algorithm is also incorporated to minimize stagnation. The ability of the algorithm to find structure-factor phases rapidly is found to assist with the fundamental problem of degeneracy (overlapping reflections) which is intrinsic to powder diffraction data. Space-group and chemical-composition information are not needed as inputs, and can be determined from the result. The method is illustrated using several experimental powder patterns of indifferent quality.

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Figure 1: Solving the phase problem of pyrite from a laboratory X-ray powder diffraction pattern using the charge-flipping algorithm.
Figure 2: Solving the phase problem of perovskite CaTiO3 from laboratory X-ray powder data using the charge-flipping algorithm.
Figure 3: Solving the phase problem of olivine from laboratory X-ray powder data using the charge-flipping algorithm.
Figure 4: Solving the phase problem of TTB structures from laboratory X-ray powder pattern using the charge-flipping algorithm.

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Acknowledgements

This work is supported by ARO award W911NF-05-1-0152 (to J.C.H.S.) and NSF grant DMR 0451443 (to M.O.K.).

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Correspondence to Jinsong Wu.

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Supplementary tables S1 - S10 and figure S1 (PDF 201 kb)

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Wu, J., Leinenweber, K., Spence, J. et al. Ab initio phasing of X-ray powder diffraction patterns by charge flipping. Nature Mater 5, 647–652 (2006). https://doi.org/10.1038/nmat1687

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