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.

X-ray dynamical diffraction Talbot effect behind a crystal in free space

2021 ◽  
Vol 77 (2) ◽  
pp. 149-159
Author(s):  
Minas Balyan ◽  
Levon Levonyan ◽  
Karapet Trouni
Keyword(s):  
Plane Wave ◽  
Free Space ◽  
Fourier Spectrum ◽  
Structural Defects ◽  
Bragg Angle ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Talbot Distance ◽  
Before And After

The dynamical diffraction Talbot effect takes place inside a crystal, when a periodic object is illuminated by a plane or spherical X-ray wave which then falls on the crystal at an angle close to the Bragg angle for some reflection. Both theoretical consideration and numerical calculations show that the dynamical diffraction Talbot effect also takes place behind the crystal. The effect is accompanied by the dynamical diffraction pendulum effect and wave focusing. Expressions are found for the dynamical diffraction Talbot distance for areas before and after focusing. The spatial Fourier spectrum of the periodic object is obtained on the focusing plane. Detailed analysis when the periodic object is illuminated by a plane wave has shown new features of this effect. The dynamical diffraction Talbot effect in free space can be used to determine the structure of a periodic object, to determine the structure of an arbitrary object placed before or after the periodic object, and to determine structural defects and deformations of the crystal.

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.

Preparation of Tetragonal and Hexagonal Calcium Zincate

2011 ◽  
Vol 130-134 ◽  
pp. 1454-1457 ◽  
Author(s):  
Song Li ◽  
Yuan Yuan Zhou
Keyword(s):  
Infrared Spectroscopy ◽  
Crystal Size ◽  
Active Material ◽  
Transformation Method ◽  
Perfect Crystal ◽  
Crystal Shape ◽  
X Ray ◽  
Secondary Battery ◽  
Base Solution ◽  
First Time

Tetragonal and hexagonal calcium zincate as an active material in Zn/Ni secondary battery has been successfully prepared with precipitation transformation method by isothermal in the reasonable concentration of KOH as base solution for the first time. The chemical composition of Ca [Zn (OH)3]2•2H2O was confirmed by X-ray powder diffraction pattern 、TG-DSC and infrared spectroscopy. These results all show that perfect crystal shape of either regular tetragonal or hexagonal calcium zincate (regardless of crystal size) should always have the same chemical expression of Ca [Zn (OH)3]2•2H2O as its form; and incomplete crystal shape of calcium zincate prepared in different conditions , their chemical expression may be the form of Ca [Zn (OH)3]2•nH2O(n=1~2).

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.

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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