On the theory of six-beam X-ray spherical-wave diffraction

Khikhlukha

2016

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This paper reports computer simulations of the transmitted-beam intensity distribution for the case of six-beam (000, 220, 242, 044, -224, -202) diffraction of X-rays in a perfect silicon crystal of thickness 1 mm. Both the plane-wave angular dependence and the six-beam section topographs, which are usually obtained in experiments with a restricted beam (two-dimensional slit), are calculated. The angular dependence is calculated in accordance with Ewald's theory. The section topographs are calculated from the angular dependence by means of the fast Fourier transformation procedure. This approach allows one to consider, for the first time, the transformation of the topograph's structure due to the two-dimensional slit sizes and the distance between the slit and the detector. The results are in good agreement with the results of other works and with the experimental data. This method of calculation does not require a supercomputer and it was performed on a standard laptop. A detailed explanation of the main features of the diffraction patterns at different distances between the slit and the detector is presented.

Section: Resultsmentioning

confidence: 99%

“…In the work by Kohn & Toneyan (1986) the theory of the multi-beam diffraction of X-ray spherical waves was presented. It was shown by means of approximate computer calculations that the intensity distribution on the photographic plate in the experimental scheme described above strongly depends on the distance.…”

Section: Introductionmentioning

confidence: 99%

Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. I

Khikhlukha

2016

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“…On the other hand, if the distance L < 10 L f , where L f / t= 0 is the distance of diffraction focusing (Afanas'ev & Kon, 1977b,c), then a slight change of the experimental picture can arise compared to the angular theoretical dependence of intensity, as was shown in the work of Kohn & Toneyan (1986).…”

Section: The Methods Of Computer Simulationsmentioning

confidence: 94%

“…This relation is valid in the geometrical optics approximation for very long distance L. In the real laboratory experiment the slit and the source have a finite size; therefore the picture is smoothed over the slit size and the angular source size. On the other hand, if the distance L < 10 L f , where L f / t= 0 is the distance of diffraction focusing (Afanas'ev & Kon, 1977b,c), then a slight change of the experimental picture can arise compared to the angular theoretical dependence of intensity, as was shown in the work of Kohn & Toneyan (1986).…”

Section: The Methods Of Computer Simulationsmentioning

confidence: 94%

A study of X-ray multiple diffraction by means of section topography

Смирнова

2015

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The results of theoretical and experimental study are presented for the question of how the X-ray multiple diffraction in a silicon single crystal influences the interference fringes of section topography for the 400 reflection in the Laue case. Two different cases of multiple diffraction are discovered for zero and very small values of the azimuthal angle for the sample in the form of a plate with the surface normal to the 001 direction. The cases are seen on the same topogram without rotation of the crystal. Accurate computer simulations of the section topogram for the case of X-ray multiple diffraction are performed for the first time. It is shown that the structure of interference fringes on the section topogram in the region of multiple diffraction becomes more complicated. It has a very sharp dependence on the azimuthal angle. The experiment is carried out using a laboratory source under conditions of low resolution over the azimuthal angle. Nevertheless, the characteristic inclination of the interference fringes on the tails of the multiple diffraction region is easily seen. This phenomenon corresponds completely to the computer simulations.

“…With increasing crystal thickness their visibility will increase. As was shown by Kohn & Toneyan (1986), the stationary phase method allows one to make a correspondence between the intensity of section topograph points and characteristics of plane-wave multiple diffraction such as the shape of the dispersion surface (DS), the amplitude of reflection and absorption coefficient. This correspondence is simpler when many branches of the DS (i.e.…”

Section: Figurementioning

confidence: 99%

Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. II

2017

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This paper reports computer simulations of X-ray six-beam (000, 220, 242, 044, -224, -202) diffraction in a perfect silicon crystal of large thickness where the super-transmission effect prevails, i.e. about 2 cm or more for an X-ray photon energy of 8 keV. Both the plane-wave angular dependence and the six-beam section topographs, which are obtained in experiments with a two-dimensional slit, are calculated. The angular dependence is computed by means of an eigenvalue problem in accordance with Ewald's theory. The section topographs are calculated by means of a fast Fourier transformation procedure from the angular to real space. It is shown that under the effect of X-ray super-transmission the quadrupole part of the photoelectric absorption as well as the Compton scattering give apparent contributions to the minimum absorption coefficient. Comparison of experimental and theoretical results by means of measuring the effective absorption coefficient is proposed. The section topographs for a thick crystal are asymmetric and polarization sensitive. These properties are explained through the angular dependence and the stationary phase method.