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.

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.

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.

The Scherrer equation and the dynamical theory of X-ray diffraction

2016 ◽  
Vol 72 (3) ◽  
pp. 385-390 ◽  
Author(s):  
Francisco Tiago Leitão Muniz ◽  
Marcus Aurélio Ribeiro Miranda ◽  
Cássio Morilla dos Santos ◽  
José Marcos Sasaki
Keyword(s):  
Crystallite Size ◽  
Dynamical Theory ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Linear Absorption ◽  
X Ray ◽  
Crystallite Sizes ◽  
Scherrer Equation ◽  
High Degree ◽  
Kinematical Theory

The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm−1the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.

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.

A study on the limit of application of kinematical theory of X-ray diffraction

2020 ◽  
Vol 235 (11) ◽  
pp. 523-531
Author(s):  
Diego Felix Dias ◽  
José Marcos Sasaki
Keyword(s):  
Critical Thickness ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
Bragg Angle ◽  
Crystal Thickness ◽  
X Ray Diffraction ◽  
Linear Absorption ◽  
X Ray ◽  
Integrated Intensities ◽  
Kinematical Theory

AbstractIn this work, the limit of application of the kinematical theory of X-ray diffraction was calculate integrated intensities was evaluated as a function of perfect crystal thickness, when compared with the Ewald–Laue dynamical theory. The percentual difference between the dynamical and kinematical integrated intensities was calculated as a function of unit cell volume, Bragg angle, wavelength, module, and phase of structure factor and linear absorption coefficient. A critical thickness was defined to be the value for which the intensities differ 5%. We show that this critical thickness is 13.7% of the extinction length, which a specific combination of the parameters mentioned before. Also, we find a general expression, for any percentage of the difference between both theories, to determine the validity of the application of the kinematical theory. Finally, we also showed that the linear absorption decreases this critical thickness.

Electron Microscopy of Shock Loaded Polycrystalline Beryllium

1974 ◽  
Vol 32 ◽  
pp. 506-507 ◽  
Author(s):  
J. M. Galbraith ◽  
L. E. Murr ◽  
A. L. Stevens
Keyword(s):  
Electron Microscopy ◽  
Wave Propagation ◽  
Structural Change ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Shock Loading ◽  
Slip Systems ◽  
Compression Tests ◽  
X Ray Diffraction ◽  
X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

Cytomembrane Preservation in Tissue Dehydrated Only With Glutaraldehyde and Epon 812 Resin

1973 ◽  
Vol 31 ◽  
pp. 320-321
Author(s):  
Daniel C. Pease
Keyword(s):  
Diffraction Pattern ◽  
X Ray Diffraction ◽  
High Concentration ◽  
Unpublished Study ◽  
X Ray ◽  
Sectioned Material

A previous study demonstrated that tissue could be successfully infiltrated with 50% glutaraldehyde, and then subsequently polymerized with urea to create an embedment which retained cytomembrane lipids in sectioned material. As a result, the 180-190 Å periodicity characteristic of fresh, mammalian myelin was preserved in sections, as was a brilliant birefringence, and the capacity to bind OsO4 vapor in the hydrophobic bilayers. An associated (unpublished) study, carried out in co-operation with Drs. C.K. Akers and D.F. Parsons, demonstrated that the high concentration of glutaraldehyde (and urea) did not significantly alter the X-ray diffraction pattern of aldehyde-fixed, myelin. Thus, by itself, 50% glutaraldehyde has little effect upon cytomembrane systems and can be used with confidence for the first stages of dehydration.

scholarly journals Efficient methods of X-ray diffraction pattern inversion

2019 ◽  
Vol 15 ◽  
pp. 102605
Author(s):  
Ian Gregory Shuttleworth
Keyword(s):  
Diffraction Pattern ◽  
X Ray Diffraction ◽  
X Ray

scholarly journals X-ray diffraction analysis of matter taking into account the second harmonic in the scattering of powerful ultrashort pulses of an electromagnetic field

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. K. Eseev ◽  
A. A. Goshev ◽  
K. A. Makarova ◽  
D. N. Makarov
Keyword(s):  
Electromagnetic Field ◽  
Diffraction Analysis ◽  
Diffraction Pattern ◽  
Second Harmonic ◽  
Ultrashort Pulses ◽  
X Ray Diffraction ◽  
X Ray ◽  
Scattering Spectra ◽  
Technical Possibility ◽  
2D And 3D

AbstractIt is well known that the scattering of ultrashort pulses (USPs) of an electromagnetic field in the X-ray frequency range can be used in diffraction analysis. When such USPs are scattered by various polyatomic objects, a diffraction pattern appears from which the structure of the object can be determined. Today, there is a technical possibility of creating powerful USP sources and the analysis of the scattering spectra of such pulses is a high-precision instrument for studying the structure of matter. As a rule, such scattering occurs at a frequency close to the carrier frequency of the incident USP. In this work, it is shown that for high-power USPs, where the magnetic component of USPs cannot be neglected, scattering at the second harmonic appears. The scattering of USPs by the second harmonic has a characteristic diffraction pattern which can be used to judge the structure of the scattering object; combining the scattering spectra at the first and second harmonics therefore greatly enhances the diffraction analysis of matter. Scattering spectra at the first and second harmonics are shown for various polyatomic objects: examples considered are 2D and 3D materials such as graphene, carbon nanotubes, and hybrid structures consisting of nanotubes. The theory developed in this work can be applied to various multivolume objects and is quite simple for X-ray structural analysis, because it is based on analytical expressions.

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