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X-ray Free Electron Lasers pp 253–300Cite as

Structure Determination by Continuous Diffraction from Imperfect Crystals

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Abstract

The coherent diffraction pattern of a non-periodic finite object does not consist of Bragg peaks but is continuously and smoothly varying. Such patterns do not suffer from the well-known phase problem of crystallography. In this case, robust iterative algorithms exist to determine the electron density of the object from the diffraction pattern alone. Continuous diffraction is accessible from ensembles of aligned molecules, including disordered protein crystals. We discuss the application of the concepts of coherent diffractive imaging to such cases and describe the experimental considerations to adequately measure the weak continuous diffraction signals.

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Notes

  1. 1.

    Throughout this chapter we will use the indices abc to uniquely distinguish atom a of rigid body b in unit cell c. When it is not needed to report on which body or cell an atom is part of, we just use the index i.

  2. 2.

    Although \({\mathbf {C}}_{ac\,a'c'}\) runs over four subscripts, this is really two dimensional, since any given atom in the crystal is specified by the indices ac (or a′c′) specifying which atom a in the molecule and which unit cell c in the crystal.

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Acknowledgements

We acknowledge the Gottfried Wilhelm Leibniz Program of the DFG, and the European Research Council under the European Union’s Seventh Framework Programme ERC Synergy Grant 609920 “AXSIS.”

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Authors and Affiliations

  1. Center for Free-Electron Laser Science, DESY, Hamburg, Germany

    Kartik Ayyer, Oleksandr M. Yefanov & Henry N. Chapman

  2. Department of Physics, University of Hamburg, Hamburg, Germany

    Henry N. Chapman

  3. Centre for Ultrafast Imaging, University of Hamburg, Hamburg, Germany

    Henry N. Chapman

Authors
  1. Kartik Ayyer
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  2. Oleksandr M. Yefanov
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  3. Henry N. Chapman
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Correspondence to Henry N. Chapman .

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Editors and Affiliations

  1. SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Sébastien Boutet

  2. School of Molecular Sciences, Arizona State University, Tempe, AZ, USA

    Petra Fromme

  3. SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Mark S. Hunter

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Ayyer, K., Yefanov, O.M., Chapman, H.N. (2018). Structure Determination by Continuous Diffraction from Imperfect Crystals. In: Boutet, S., Fromme, P., Hunter, M. (eds) X-ray Free Electron Lasers. Springer, Cham. https://doi.org/10.1007/978-3-030-00551-1_9

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