Theory of Imaging a Perfect Crystal under the Conditions of X-Ray Spherical Wave Dynamical Diffraction

2000 ◽  
Vol 222 (2) ◽  
pp. 407-423 ◽  
Author(s):  
V.G. Kohn ◽  
I. Snigireva ◽  
A. Snigirev
Keyword(s):  
Spherical Wave ◽  
Perfect Crystal ◽  
Dynamical Diffraction ◽  
X Ray

X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal

2015 ◽  
Vol 22 (6) ◽  
pp. 1410-1418 ◽  
Author(s):  
Minas K. Balyan
Keyword(s):  
Analytical Solution ◽  
Perfect Crystal ◽  
Total Reflection ◽  
Numerical Calculations ◽  
Third Order ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Infinite Crystal ◽  
Nonlinear Plane ◽  
Diffraction Effects

Two-wave symmetric Bragg-case dynamical diffraction of a plane X-ray wave in a crystal with third-order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non-absorbing perfect semi-infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi-infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.

Pendellösungfringes for X-ray spherical-wave diffraction in a perfect crystal

1980 ◽  
Vol 36 (6) ◽  
pp. 1002-1013 ◽  
Author(s):  
V. V. Aristov ◽  
V. I. Polovinkina ◽  
A. M. Afanas'ev ◽  
V. G. Kohn
Keyword(s):  
Wave Diffraction ◽  
Spherical Wave ◽  
Perfect Crystal ◽  
X Ray

X-Ray Dynamical Diffraction Process Inside a Distorted Crystal

1982 ◽  
Vol 37 (5) ◽  
pp. 460-464
Author(s):  
S. Takagi
Keyword(s):  
Wave Field ◽  
Perfect Crystal ◽  
Primary Wave ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Exit Surface ◽  
Wave Induced ◽  
The Waves ◽  
Resultant Wave

It is shown that the dynamical diffraction process inside a distorted crystal consists of ordinary dynamical progression inside perfect portions of the crystal and scattering at distortions. The scattered waves proceed as in the perfect crystal and can be multiply scattered. The sum of the primary wave induced at the entrance surface and the waves scattered at distorted parts inside the “inverted Borrmann triangle” gives the resultant wave field at the exit surface.

scholarly journals X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal. Erratum

2016 ◽  
Vol 23 (5) ◽  
pp. 1272-1272
Author(s):  
Minas K. Balyan
Keyword(s):  
Plane Wave ◽  
Perfect Crystal ◽  
Third Order ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Nonlinear Plane ◽  
Diffraction Effects

Formulae in the paper by Balyan (2015) [J. Synchrotron Rad.22, 1410–1418] are corrected.

scholarly journals Spherical-wave X-ray dynamical diffraction Talbot effect inside a crystal

2020 ◽  
Vol 76 (4) ◽  
pp. 494-502
Author(s):  
Minas K. Balyan ◽  
Levon V. Levonyan ◽  
Karapet G. Trouni
Keyword(s):  
Spherical Wave ◽  
Transmission Function ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Focusing Effect ◽  
Wave Effects ◽  
Focus Point ◽  
Amplitude Transmission

Two-wave dynamical diffraction of an X-ray spherical wave in a crystal, when the wave passes through an object with a periodic amplitude transmission function, is considered. The behavior of the diffracted wave (spherical-wave Talbot effect) in the crystal is investigated. The Talbot effect inside the crystal is accompanied by the focusing effect and the pendulum effect. Peculiarities of the effect before the focus point, in the focusing plane and in the region after the focus point inside the crystal are revealed. An expression is found for the Talbot depth and the spherical-wave Talbot effect in these three regions is investigated. The spherical-wave dynamical diffraction Talbot effect in a crystal is compared with the classical spherical-wave Talbot effect and also with spherical-wave effects inside the crystal without a periodic object.

Computer simulations of X-ray spherical wave dynamical diffraction in one and two crystals in the Laue case

2018 ◽  
Vol 74 (6) ◽  
pp. 699-704 ◽  
Author(s):  
V. G. Kohn ◽  
I. A. Smirnova
Keyword(s):  
Single Crystals ◽  
Computer Simulations ◽  
Integral Intensity ◽  
Spherical Wave ◽  
Secondary Source ◽  
Weak Absorption ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Spherical Waves ◽  
Energy Spectrometer

This article reports computer simulations of X-ray spherical wave dynamical diffraction in one and two single crystals in the Laue case. An X-ray compound refractive lens (CRL) as a secondary radiation source of spherical waves was considered for the first time and in contrast to previous simulations with the assumption of the use of a slit. The main properties of the CRL as a secondary source are discussed and two focusing phenomena are analysed. The first one is the diffraction focusing effect for one single crystal in the reflected beam and in the case of a large source-to-detector distance. The second one is the same but for two single crystals and for the twice-reflected beam in the case of a short distance between the source and detector. The first effect is well pronounced in the case of strong absorption. However, it may also be used as an element of an energy spectrometer in the medium and even weak absorption case. The second effect will appear in the case of weak absorption. It is shown that it is not effective to use it in an energy spectrometer. In the case of weak absorption the transverse size of the diffraction focused beam will oscillate together with the reflected beam integral intensity. The oscillation period is close to the extinction length.

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

2019 ◽  
Vol 26 (5) ◽  
pp. 1650-1659 ◽  
Author(s):  
Minas K. Balyan
Keyword(s):  
Perfect Crystal ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Dispersion Branch ◽  
Talbot Distance ◽  
Rational Multiple ◽  
Talbot Effects ◽  
First Time ◽  
Initial Distributions

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization-sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.

Phase of Pendellösung oscillations in X-ray dynamical diffraction for perfect crystals

2020 ◽  
Vol 76 (2) ◽  
pp. 132-136
Author(s):  
Takashi Saka
Keyword(s):  
Phase Shift ◽  
Perfect Crystal ◽  
Dynamical Diffraction ◽  
X Ray ◽  
The Real ◽  
Diffracted Waves

Formulations are given for the intensities of transmitted and diffracted waves in the Laue case of a perfect crystal. This is applicable irrespective of the magnitudes of both the real and imaginary parts of the Fourier components of the crystal polarizability. The phase shift of the Pendellösung oscillations of the transmitted and diffracted waves is analyzed in detail for a symmetrical Laue case. The phase is determined to shift continuously from out of phase to in phase for absorbing crystals.

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