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.

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.

X-Ray Dynamical Diffraction in Powder Samples with Time-Dependent Particle Size Distributions

MRS Advances ◽  
2019 ◽  
Vol 5 (29-30) ◽  
pp. 1585-1591 ◽  
Author(s):  
Adriana Valério ◽  
Sérgio L. Morelhão ◽  
Alex J. Freitas Cabral ◽  
Márcio M. Soares ◽  
Cláudio M. R. Remédios
Keyword(s):  
Particle Size ◽  
Single Phase ◽  
Diffraction Peak ◽  
Time Dependent ◽  
Peak Width ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Integrated Intensity ◽  
Diffraction Effects

ABSTRACTIn situ X-ray diffraction is one of the most useful tools for studying a variety of processes, among which crystallization of nanoparticles where phase purity and size control are desired. Growth kinetics of a single phase can be completely resolved by proper analysis of the diffraction peaks as a function of time. The peak width provides a parameter for monitoring the time evolution of the particle size distribution (PSD), while the peak area (integrated intensity) is directly related to the whole diffracting volume of crystallized material in the sample. However, to precisely describe the growth kinetics in terms of nucleation and coarsening, the correlation between PSD parameters and diffraction peak widths has to be established in each particular study. Corrections in integrated intensity values for physical phenomena such as variation in atomic thermal vibrations and dynamical diffraction effects have also to be considered in certain cases. In this work, a general correlation between PSD median value and diffraction peak width is deduced, and a systematic procedure to resolve time-dependent lognormal PSDs from in situ XRD experiments is described in details. A procedure to correct the integrated intensities for dynamical diffraction effects is proposed. As a practical demonstration, this analytical procedure has been applied to the single-phase crystallization process of bismuth ferrite nanoparticles.

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.

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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