An algorithm for calculating diffraction profiles of 2θ scans for multiple diffraction from crystals and thin films

2014 ◽  
Vol 70 (6) ◽  
pp. 572-582
Author(s):  
Hsin-Yi Chen ◽  
Mau-Sen Chiu ◽  
Chia-Hung Chu ◽  
Shih-Lin Chang
Keyword(s):  
Initial Phase ◽  
Atomic Layer ◽  
Dynamical Theory ◽  
Far Field ◽  
X Rays ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
X Ray ◽  
Beam Surface ◽  
Surface Diffraction

An algorithm is developed based on the dynamical theory of X-ray diffraction for calculating the profiles of the diffracted beam,i.e.the diagrams of the intensity distributionversus2θ when a crystal is fixed at an angle of its maximum diffracted intensity. Similar to Fraunhofer (far-field) diffraction for a single-slit case, in the proposed algorithm the diffracted beam from one atomic layer excited by X-rays is described by the composition of (N+ 1) coherent point oscillators in the crystal. The amplitude and the initial phase of the electric field for each oscillator can be calculated based on the dynamical theory with given boundary conditions. This algorithm not only gives diffraction profiles but also provides the contribution of the excitation of modes when extremely asymmetric diffraction is involved in the diffraction process. Examples such as extremely asymmetric two-beam surface diffraction and three-beam surface diffraction are presented and discussed in detail.

Investigation of the phase shift in X-ray forward diffraction using an X-ray interferometer

1998 ◽  
Vol 5 (3) ◽  
pp. 967-968 ◽  
Author(s):  
Keiichi Hirano ◽  
Atsushi Momose
Keyword(s):  
Phase Shift ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bragg Geometry

The phase shift of forward-diffracted X-rays by a perfect crystal is discussed on the basis of the dynamical theory of X-ray diffraction. By means of a triple Laue-case X-ray interferometer, the phase shift of forward-diffracted X-rays by a silicon crystal in the Bragg geometry was investigated.

scholarly journals Experimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs for a silicon crystal

2019 ◽  
Vol 75 (3) ◽  
pp. 483-488 ◽  
Author(s):  
Kouhei Okitsu ◽  
Yasuhiko Imai ◽  
Yoshitaka Yoda
Keyword(s):  
Silicon Crystal ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Good Agreement

Non-coplanar 18-beam X-ray pinhole topographs for a silicon crystal were computer simulated by fast Fourier transforming the X-ray rocking amplitudes that were obtained by solving the n-beam (n = 18) Ewald–Laue dynamical theory (E-L&FFT method). They were in good agreement with the experimentally obtained images captured using synchrotron X-rays. From this result and further consideration based on it, it has been clarified that the X-ray diffraction intensities when n X-ray waves are simultaneously strong in the crystal can be computed for any n by using the E-L&FFT method.

Limits of the X-Ray Collimation by One Asymmetrical Bragg Reflection

1982 ◽  
Vol 37 (6) ◽  
pp. 519-523 ◽  
Author(s):  
◽  
H. R. Höche ◽  
J. Nieber
Keyword(s):  
Bragg Reflection ◽  
Dynamical Theory ◽  
X Rays ◽  
Optimum Conditions ◽  
X Ray Diffraction ◽  
X Ray

Abstract In connection with the production of highly collimated X-rays the study of extremely asymmetrical Bragg reflections became of interest. In this paper the so-called extended dynamical theory of X-ray diffraction will be tested experimentally. As a result of this investigations the optimum conditions for X-ray collimation by means of one asymmetrical Bragg reflection are being discussed.

Laue X-ray diffraction studies of the structural perfection of Al-doped thermomigration channels in silicon

2021 ◽  
Vol 54 (2) ◽  
pp. 588-596
Author(s):  
Andrey A. Lomov ◽  
Vasily I. Punegov ◽  
Boris M. Seredin
Keyword(s):  
Cross Sections ◽  
High Sensitivity ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Structural Perfection ◽  
Laue Diffraction ◽  
X Ray ◽  
Structural Distortions ◽  
Further Development

Si(111) wafers patterned with an array of vertical 100 µm-wide Al-doped (1 × 1019 cm−3) p-channels extending through the whole wafer were studied by X-ray Laue diffraction techniques. The X-ray techniques included projection topography, and measurement of rocking curves and cross sections in the vicinity of the 02\overline 2 reciprocal space node in the double- and triple-crystal geometry, respectively. The channels are uniform along the depth of the wafer, and their structural perfection is comparable to that of the silicon matrix between the channels. Simulation of the rocking curves was performed using the methods of the dynamical theory of X-ray diffraction. The rocking-curve calculations both taking into account and neglecting the effect of the instrumental function were carried out using the Takagi–Taupin equations. The calculated angular dependences of intensities of both diffracted and transmitted X-rays correspond well to the experimentally obtained rocking curves and demonstrate their high sensitivity to the structural distortions in the channel. An unambiguous reconstruction of strain and structural distortions in the Si(Al) channel using the Laue diffraction data requires further development of the theoretical model.

Book Reviews: The gentle pioneer

1996 ◽  
Vol 50 (2) ◽  
pp. 263-264
Keyword(s):  
Modern Science ◽  
Mathematical Physics ◽  
Dynamical Theory ◽  
X Rays ◽  
Experimental Demonstration ◽  
X Ray Diffraction ◽  
International Union ◽  
X Ray ◽  
Oxford University

P.P. Ewald and his Dynamical Theory of X-ray Diffraction . Edited by D.W.J. Cruickshank, H.J. Juretschke & N. Kato. International Union of Crystallography, Oxford University Press, 1992. Pp. x+161, £40.00. ISBN 0-19-855379-X Paul Ewald, who died in 1985 at the age of 97, was one of the greats of modern science. Born in Berlin into a comfortable middle-class academic family, he developed a passion for mathematical physics. When Sommerfeld presented him with a list of possible topics for his Doctoral Thesis he chose one related to crystal optics. This work, presented in 1912, could be applied to the behaviour of X-rays in crystals and it is suggested that it was a conversation between von Laue and Ewald early in 1912 that gave von Laue the idea for his famous experimental demonstration of X-ray diffraction.

X-ray Analysis of Ni/Ti Multilayers

1993 ◽  
Vol 308 ◽  
Author(s):  
J. Chaudhuri ◽  
S.M. Alyan ◽  
A.F. Jankowski
Keyword(s):  
Diffraction Pattern ◽  
Atomic Layer ◽  
Sine Wave ◽  
Dynamical Theory ◽  
X Ray Diffraction ◽  
Rectangular Wave ◽  
X Ray ◽  
Composition Modulation ◽  
Complete Relaxation ◽  
Kinematical Theory

ABSTRACTThe structure, composition and strain in Ni/Ti multilayers are analyzed using x-ray diffraction theories. The repeat period of the multilayers used in this study ranges from 1.3 to 12.8 nm. The composition modulation is obtained by using a kinematical theory of x-ray diffraction. A sine wave for the shorter repeat period and a rectangular wave for the longer repeat period are predicted for the composition modulation. The strain within each atomic layer is found by iteratively fitting the experimental x-ray diffraction pattern with the simulated one from a dynamical theory of x-ray diffraction. The strain at the interface is tensile in Ni and compressive in Ti with a complete relaxation of the strain at a distance away from the interface.

scholarly journals Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory

2018 ◽  
Vol 51 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Hao Feng ◽  
Rana Ashkar ◽  
Nina Steinke ◽  
Robert Dalgliesh ◽  
Nickolay V. Lavrik ◽  
...  
Keyword(s):  
Spin Echo ◽  
Dynamical Theory ◽  
X Rays ◽  
Phase Approximation ◽  
X Ray Diffraction ◽  
Colloidal Structure ◽  
X Ray ◽  
X Ray Scattering ◽  
Weak Phase ◽  
Colloidal Fluids

A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. It is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. While the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.

X-Ray Diffraction Determination of Critical Thickness of InAs and InP on GaAs Grown by Atomic Layer Molecular Beam Epitaxy

1992 ◽  
Vol 263 ◽  
Author(s):  
A. Mazuelas ◽  
L. Gonzalez ◽  
L. Tapfer ◽  
F. Briones
Keyword(s):  
Molecular Beam Epitaxy ◽  
Molecular Beam ◽  
Critical Thickness ◽  
Atomic Layer ◽  
Dynamical Theory ◽  
X Ray Diffraction ◽  
X Ray ◽  
Strained Layer ◽  
Diffraction Determination ◽  
Cap Layer

ABSTRACTTwo series of samples consisting in a strained layer of InAs (InP) of different thickness, InAs N monolayers (ML) with N=1,2,3, and 4, and, InP M ML with M=2,3,4,5,6 and 7, covered by a GaAs cap layer of 200 nm were grown by Atomic Layer Molecular Beam Epitaxy (ALMBE).The samples have been characterized by X-ray diffraction in order to measure the critical thickness of InAs and InP on GaAs.Computer simulation using dynamical theory of X-ray diffraction is used to fit the experimental patterns. In this way we determine the composition, thickness, and strain both in the strained layer of InAs or InP and in the cap layer of GaAs.A disagreement between simulated and experimental curves is reached at a thickness where the beginning of relaxation takes place (i.e. critical thickness). We have found that the critical thickness of InAs on GaAs(001) is 2.3 ML (0.75 nm) and the critical thickness of InP on GaAs(001) is 5.6–5.7 ML (1.71-1.74 nm), both grown by ALMBE.

X-ray diffraction in superabsorbing crystals: absorption intrinsic width

2019 ◽  
Vol 75 (5) ◽  
pp. 772-776
Author(s):  
A. N. C. Lima ◽  
M. A. R. Miranda ◽  
J. M. Sasaki
Keyword(s):  
Diffraction Theory ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Linear Absorption ◽  
New Techniques ◽  
Diffraction Profile ◽  
X Ray ◽  
Kinematical Theory ◽  
Special Case

The several mathematical formulations of X-ray diffraction theory facilitate its understanding and use as a materials characterization technique, since one can opt for the simplest formulation that adequately describes the case being studied. As synchrotrons advance, new techniques are developed and there is a need for simple formulations to describe them. One of these techniques is soft resonant X-ray diffraction, in which the X-rays suffer large attenuation due to absorption. In this work, an expression is derived for the X-ray diffraction profiles of reflections where the linear absorption is far greater than primary extinction; in other words, the crystal is superabsorbing. The case is considered of a parallel plate crystal, for which the diffraction profile of the superabsorbing crystal is computed as a function of crystal size normal to the diffraction planes. For thin crystals or those with negligible absorption, the diffraction profile of a superabsorbing crystal coincides with the result of the kinematical theory. For thick crystals, the absorption intrinsic profile is obtained, described by a Lorentzian function and characterized by the absorption intrinsic width. This absorption intrinsic width is proportional to the linear absorption coefficient and its expression is similar to that for the Darwin width, while the absorption intrinsic profile is a special case of the Laue dynamical theory, and it is similar to the Ornstein–Zernike Lorentzian. The formulation of X-ray diffraction of superabsorbing crystals is simple and provides new perspectives for the soft resonant X-ray diffraction technique.

Generation and Proof of Elliptically Polarized X-Rays

1982 ◽  
Vol 37 (6) ◽  
pp. 524-527
Author(s):  
O. Brümmer ◽  
Ch. Eisenschmidt ◽  
H. R. Höche
Keyword(s):  
Phase Relation ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Wave Fields ◽  
X Ray ◽  
Polarized Waves ◽  
Angle Of Reflection ◽  
Elliptically Polarized

Abstract Using an arrangement being analogous to optics of visible light the phase relation of the mutually perpendicularly polarized wave fields are examined in the Laue case of X-ray diffraction. Bragg reflections at an angle of reflection of about 45° are used as polarizer and analyzer. The different phase relations result from different thicknesses of a wedge-shaped silicon crystal, which is placed between the polarizer and the analyzer and adjusted for the symmetric 220-CuKαl-Laue case. The determined polarization states produced by coherent excitation of both σ-polarized and π-polarized waves in the silicon crystal coincide very well with calculations of the dynamical theory of X-ray diffraction.

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