What question did this study set out to answer?

To explore how bending of reflecting planes in a crystal affects diffraction image formation using numerical methods.

April 4, 2026

X-ray Diffraction in a Crystal under the Bending of Reflecting Planes

ISI. A. SmirnovaOsipyan Institute of Solid State Physics RAS ESE. V. SuvorovOsipyan Institute of Solid State Physics RAS

Key Points

To explore how bending of reflecting planes in a crystal affects diffraction image formation using numerical methods.
Studied the bending effect on crystal lattice using numerical integration of Takagi equations.
Analyzed diffraction intensity for small absorption conditions in a real experimental setup.
Examined intensity variations based on the divergence of the incident beam.
Intensity of the reflected wave depended on the bending sign, violating Friedel's law.
Integrated intensity of diffracted waves increased linearly at high beam divergence.
At lower divergence, intensity approached saturation, linked to wave field propagation along scattering edges.

Abstract

The effect of bending of reflecting planes of the crystal lattice on the formation of a diffraction image in section topography was studied by numerical integration of the Takagi equations. All calculations were performed for the case of small absorption and a real experiment. The intensity of the reflected wave exhibited a dependence on the sign of bending (violation of Friedel’s law). The integrated intensity of the diffracted wave increased linearly at large divergence of the incident beam (much larger than the angular region of reflection of an ideal crystal). In contrast, at a small divergence, it tended to saturation rather than increasing linearly. The decrease in the integrated intensity was associated with the part of the wave field propagating along the edge of the scattering triangle.

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