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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Bragg-von Laue diffraction generalized to twisted X-rays.

Dominik Jüstel1, Gero Friesecke1, Richard D James2

  • 1Department of Mathematics, TU Munich, Germany.

Acta Crystallographica. Section A, Foundations and Advances
|February 27, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a novel X-ray method for determining atomic structures without crystallization. The technique shows accuracy comparable to traditional methods for noncrystalline materials like carbon nanotubes.

Keywords:
X-ray diffractionnoncrystalline structuresstructure determinationtwisted X-rays

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Area of Science:

  • Materials Science
  • Crystallography
  • Applied Physics

Background:

  • X-ray crystallography typically requires crystalline samples for atomic structure determination.
  • Obtaining suitable crystals (∼ 10 × 10 × 10 µm) is a significant limitation for many materials.

Purpose of the Study:

  • To propose a new X-ray method for atomic structure determination of noncrystalline materials.
  • To overcome the crystallization requirement inherent in conventional X-ray methods.

Main Methods:

  • Developed a mathematical analog of von Laue's method.
  • Replaced the translation group with a different symmetry group.
  • Utilized exact closed-form solutions of Maxwell's equations instead of plane waves.

Main Results:

  • The proposed method is applicable to noncrystalline structures.
  • Demonstrated effectiveness for helical structures, including carbon nanotubes and filamentous viruses.
  • Computer simulations indicate accuracy comparable to periodic crystalline cases.

Conclusions:

  • The novel X-ray method offers a viable alternative for structure determination of noncrystalline materials.
  • This approach expands the scope of X-ray structural analysis to challenging samples.
  • Potential applications include nanomaterials and biological structures.