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X-ray Crystallography02:18

X-ray Crystallography

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Origin and application of the Lorentz factor in X-ray diffraction.

Fabian Gasser1, Josef Simbrunner2, Guillaume Freychet3

  • 1Institute of Solid State Physics, Graz University of Technology, Petersgasse 16, Graz, 8010, Austria.

Acta Crystallographica. Section A, Foundations and Advances
|July 7, 2026
PubMed
Summary

The Lorentz factor is crucial for X-ray diffraction analysis, relating measured intensities to structure factors. This review unifies its understanding and application across diverse diffraction methods for accurate data interpretation.

Keywords:
Lorentz factorgrazing-incidence diffractionintegrated intensitiesintensity correctionspowder diffractionsingle-crystal diffractionsmall-angle scattering

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Area of Science:

  • Crystallography
  • Materials Science
  • Physics

Background:

  • The Lorentz factor is essential for quantitative X-ray diffraction (XRD) analysis.
  • It connects measured integrated peak intensities to calculated structure factors.
  • Accurate application of the Lorentz factor is vital for reliable XRD data interpretation.

Purpose of the Study:

  • To present a unified approach to the Lorentz factor's physical origin, derivation, and implementation.
  • To clarify its trigonometric and wavelength-dependent contributions.
  • To provide a comprehensive overview for various modern XRD techniques.

Main Methods:

  • Unified approach treating the Lorentz factor as a Jacobian.
  • Systematic derivation of equations for diverse XRD geometries.
  • Analysis of angular-velocity formulation for rotational measurements.

Main Results:

  • Demonstration that the Lorentz factor depends on experimental geometry and sample type.
  • Clarification of trigonometric and wavelength dependencies.
  • Equations derived for single-crystal, powder, grazing-incidence diffraction, and small-angle X-ray scattering.

Conclusions:

  • A unified understanding of the Lorentz factor supports consistent intensity evaluation in XRD.
  • The Lorentz factor's dependence on geometry and sample type is highlighted.
  • Discussion on avoiding Lorentz correction via direct reciprocal-space integration and its limitations.