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Crystal bending in triple-Laue X-ray interferometry. Part I. Theory.

C P Sasso1, G Mana1,2, E Massa1

  • 1INRIM, Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy.

Journal of Applied Crystallography
|June 7, 2023
PubMed
Summary

The measured silicon lattice spacing may not represent the bulk crystal value, potentially impacting the new kilogram definition. This study models X-ray interferometry with bent crystals to clarify lattice spacing measurements.

Keywords:
Laue diffractionbent crystalscrystal X-ray interferometrydynamical theory of X-ray diffraction

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Area of Science:

  • Materials Science
  • Metrology
  • Crystallography

Background:

  • Accurate measurement of silicon 28 lattice-plane spacing is crucial for realizing the kilogram via atom counting.
  • Current methods assume measured spacing reflects the bulk, unstrained crystal value.

Purpose of the Study:

  • To investigate whether X-ray interferometry in bent crystals measures bulk or surface lattice spacing.
  • To provide an analytical model supporting experimental phase-contrast topography studies.

Main Methods:

  • Development of a comprehensive analytical model for X-ray propagation in bent crystals.
  • Modeling the operation of a triple-Laue interferometer with bent splitting/recombining crystals.

Main Results:

  • Analytical and numerical studies suggest measured lattice spacing may correspond to the crystal surface, not the bulk.
  • The model accounts for X-ray propagation effects in bent crystal interferometers.

Conclusions:

  • The assumption of bulk lattice spacing in X-ray interferometry may be invalid for bent crystals.
  • Further experimental validation using phase-contrast topography is supported by this model.