Effect of the bending of reflecting planes in crystals on the propagation of an anomalous wave in x-ray diffraction

I. A. Smirnova; Смирнова И. А.; E. V. Suvorov; Суворов Э. В.

doi:10.31857/S1028096024010153

Effect of the bending of reflecting planes in crystals on the propagation of an anomalous wave in x-ray diffraction

Authors: Smirnova I.A.¹, Suvorov E.V.¹
Affiliations:
1. Osipyan Institute of Solid State Physics RAS
Issue: No 1 (2024)
Pages: 109–112
Section: Articles
URL: https://journals.rcsi.science/1028-0960/article/view/257070
DOI: https://doi.org/10.31857/S1028096024010153
EDN: https://elibrary.ru/DFTJBY
ID: 257070

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Abstract
About the authors
References
Supplementary files
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Abstract

The effect of bending of reflection planes in crystals on the propagation of an anomalous wave in X-ray diffraction has been studied by numerical simulation methods. The bending sign of the reflection planes was found to affect radically the propagation of the X-ray wave field in the crystal. The Bormann effect was shown to be suppressed at certain bending parameters.

Keywords

diffraction, interference, X-rays, crystal lattice, single crystals, interference fringes, crystal lattice defects, local deformations, bending of reflecting planes, bending sign

About the authors

I. A. Smirnova

Osipyan Institute of Solid State Physics RAS

Author for correspondence.
Email: suvorov@issp.ac.ru
Russian Federation, 142432, Moscow Region, Chernogolovka

E. V. Suvorov

Osipyan Institute of Solid State Physics RAS

Email: suvorov@issp.ac.ru
Russian Federation, 142432, Moscow Region, Chernogolovka

References

Грушко Ю.С., Лапин Е.Г., Сумбаев О.И., Тю- нис А.В. // ЖЭТФ. 1978. Т. 74. Вып. 6. С. 2280.
Суворов Э.В., Смирнова И.А. // Поверхность. Рентген., синхротр. и нейтрон. исслед. 2008. № 10. С. 7.
Смирнова И.А., Суворов Э.В., Шулаков Е.В. // ФТТ. 2007. T. 49. Вып. 6. С. 1050.
Суворов Э.В. Смирнова И.А. // Поверхность. Рентген., синхротр. и нейтрон. исслед. 2021. № 12. С. 23. https://doi.org/10.31857/S1028096021120232
Хирт Дж., Лоте И. Теория дислокаций. М.: Атомиздат, 1972. 599 с.
Takagi S.J. // J. Phys. Soc. Jpn. 1969. V. 26. № 5. P. 1239.
Инденбом В.Л., Чуховский Ф.Н. // Кристаллография. 1971. Т. 16. № 6. С. 1101.
Инденбом В.Л., Чуховский Ф.Н. // УФН. 1972. Т. 107. № 2. С. 229.
Authier A. Dynamical Theory of X-ray Diffraction. Oxford: Oxford University Press, 2002. 674 p.

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2. Fig. 1. Edge dislocation: a is a flat image of the local disorientation field [5] (m is the plane of mirror symmetry, n is the plane of color symmetry); b is the experimentally observed diffraction image [2] (Si single crystal with a thickness of 1810 microns, crystal surface (111), reflection 2_20, CuKa radiation).

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3. Fig. 2. Three–dimensional image of the field of local disorientation of the β edge dislocation (a); two-dimensional sections parallel to the Yß plane at distances from the origin x1 = 35, x2 = -35 microns; b is a section parallel to the Xß plane at x = 0.

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4. Fig. 3. Diagram of the signs of bending of the reflecting planes used in the work: hkl – indices of the reflecting planes; R – radius of bending of the reflecting planes; Khkl – diffraction vector.

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5. Fig. 4. The relative intensity I/Type of the anomalous (Bormann) wave field in the center of the scattering triangle, depending on the bending radius R of the reflecting planes (normalized to the intensity of the ideal crystal Iid).

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6. Fig. 5. Numerical simulation of the wave field in the scattering triangle in the case of a thick crystal with different bending signs of the reflecting planes.

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7. Fig. 6. Fragments of the wave field in the scattering triangles of a thin crystal (150 microns), where normal and abnormal waves are present (numerical simulation).