Bragg-von Laue diffraction generalized to twisted X-rays

Dominik Jüstel, Gero Friesecke, Richard D. James

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


A pervasive limitation of nearly all practical X-ray methods for the determination of the atomic scale structure of matter is the need to crystallize the molecule, compound or alloy in a sufficiently large (∼10 x 10 x 10 μm) periodic array. In this paper an X-ray method applicable to structure determination of some important noncrystalline structures is proposed. It is designed according to a strict mathematical analog of von Laue's method, but replacing the translation group by another symmetry group, and simultaneously replacing plane waves by different exact closed-form solutions of Maxwell's equations. Details are presented for helical structures like carbon nanotubes or filamentous viruses. In computer simulations the accuracy of the determination of structure is shown to be comparable to the periodic case.

Original languageEnglish (US)
Pages (from-to)190-196
Number of pages7
JournalActa Crystallographica Section A: Foundations and Advances
StatePublished - 2016

Bibliographical note

Funding Information:
GF was partially supported by DFG through SFB-TR 109. RDJ was supported by AFOSR (FA9550-15-1-0207) and partially supported by ONR (N00014-14-0714), NSF/PIRE (OISE-0967140), the MURI program (FA9550-12-1-0458), and a John Von Neumann visiting professorship at TU Munich. DJ was partially supported by a stipend from Universitä t Bayern e.V. GF and RDJ thank Dominik Schryvers for helpful information on vortex beams and GF thanks Robin Santra for providing advice on the derivation of X-ray diffraction intensities from quantum electrodynamics.

Publisher Copyright:
© International Union of Crystallography 2016.


  • X-ray diffraction
  • noncrystalline structures
  • structure determination
  • twisted X-rays


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