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 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.

scholarly journals Modification of structural and dielectric properties of polycrystalline Gd-doped BFO–PZO

2018 ◽  
Vol 08 (05) ◽  
pp. 1850031 ◽  
Author(s):  
Ambika Ray ◽  
Banarji Behera ◽  
Tanmoy Basu ◽  
Saumitra Vajandar ◽  
Santosh Kumar Satpathy ◽  
...  
Keyword(s):  
Dielectric Properties ◽  
Boundary Effect ◽  
Ion Beam ◽  
Ferroelectric Properties ◽  
Compositional Analysis ◽  
Structural Defects ◽  
X Ray ◽  
Dielectric Constant And Loss ◽  
Before And After ◽  
Lcr Meter

[Formula: see text](BiFe[Formula: see text]GdxO3)–y(PbZrO3) composites [Formula: see text], having four different Gd concentrations ([Formula: see text], 0.1, 0.15, and 0.2), were synthesized and their structural, dielectric, and ferroelectric properties have been studied using different characterization techniques. In addition, to investigate the effect of ion implantation on the microstructure and dielectric properties, these composites were exposed to 2[Formula: see text]MeV He[Formula: see text]-ions. Modifications of the structure, surface morphology and electrical properties of the samples before and after ion exposure were demonstrated using powder X-ray diffraction (XRD), scanning electron microscopy (SEM) technique, and LCR meter. The compositional analysis was carried out using energy dispersive X-ray spectrometry (EDS). XRD results demonstrated a decrease in the intensity profile of the dominant peak by a factor of 6 showing a degradation of the crystallinity. Willliamson–Hall (WH) plots reveal reduction in the grain size after irradiation along with an increase in strain and dislocation density. A decrease in the dielectric constant and loss has been recorded after ion beam exposure with reduction in ac conductivity value. The contribution of grain and grain boundary effect in conduction mechanism has been addressed using Nyquist plots. All the samples demonstrate a lossy ferroelectric loop which shows a clear modification upon irradiation. The role of structural defects modifying the physical properties of the composite materials is discussed in this work.

Some Characteristics of Dynamical Diffraction at a Bragg Angle of about π/2

1972 ◽  
Vol 27 (3) ◽  
pp. 484-487 ◽  
Author(s):  
K Köhra ◽  
T Matsushita
Keyword(s):  
Dynamical Theory ◽  
Bragg Angle ◽  
Angular Width ◽  
X Rays ◽  
Dynamical Diffraction ◽  
X Ray ◽  
The One

Abstract The diffraction phenomena of X-rays in the case ΘB≅π/2 are studied on the basis of dynamical theory. The angular width of diffraction for ΘB= π/2, 2√|χh| , is about 103 times as broad as the one for ΘB ⪡π/2, 2|Xh|/sin ΘB . Similar characteristic phenomena are expected for electrons. The π/2 Bragg angle diffraction would be utilized as X-ray resonator.

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.

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