X-Ray Diffraction

2021 ◽  
pp. 408-480
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Point Group ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Symmetry Point Group ◽  
X Ray ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Diffraction Patterns ◽  
Lattice Planes

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

scholarly journals Simultaneous Multi-Bragg Peak Coherent X-ray Diffraction Imaging

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 312
Author(s):  
Florian Lauraux ◽  
Stéphane Labat ◽  
Sarah Yehya ◽  
Marie-Ingrid Richard ◽  
Steven J. Leake ◽  
...  
Keyword(s):  
Bragg Reflection ◽  
Volume Ratio ◽  
X Ray Diffraction ◽  
X Ray ◽  
Crystal Substrate ◽  
In Series ◽  
Diffraction Imaging ◽  
Diffraction Patterns ◽  
Lattice Planes ◽  
Oriented Parallel

The simultaneous measurement of two Bragg reflections by Bragg coherent X-ray diffraction is demonstrated on a twinned Au crystal, which was prepared by the solid-state dewetting of a 30 nm thin gold film on a sapphire substrate. The crystal was oriented on a goniometer so that two lattice planes fulfill the Bragg condition at the same time. The Au 111 and Au 200 Bragg peaks were measured simultaneously by scanning the energy of the incident X-ray beam and recording the diffraction patterns with two two-dimensional detectors. While the former Bragg reflection is not sensitive to the twin boundary, which is oriented parallel to the crystal–substrate interface, the latter reflection is only sensitive to one part of the crystal. The volume ratio between the two parts of the twinned crystal is about 1:9, which is also confirmed by Laue microdiffraction of the same crystal. The parallel measurement of multiple Bragg reflections is essential for future in situ and operando studies, which are so far limited to either a single Bragg reflection or several in series, to facilitate the precise monitoring of both the strain field and defects during the application of external stimuli.

Micro Diffraction Imaging of Bulk Polycrystalline Materials

2006 ◽  
Vol 524-525 ◽  
pp. 273-278
Author(s):  
Thomas Wroblewski ◽  
A. Bjeoumikhov ◽  
Bernd Hasse
Keyword(s):  
High Spatial Resolution ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Short Sample ◽  
X Ray ◽  
Detector Distance ◽  
Transmission Geometry ◽  
Diffraction Imaging ◽  
Position Sensitive

X-ray diffraction imaging applies an array of parallel capillaries in front of a position sensitive detector. Conventional micro channel plates of a few millimetre thickness have successfully been used as collimator arrays but require short sample to detector distances to achieve high spatial resolution. Furthermore, their limited absorption restricts their applications to low energy X-rays of around 10 keV. Progress in the fabrication of long polycapillaries allows an increase in the sample to detector distance without decreasing resolution and the use of high X-ray energies enables bulk investigations in transmission geometry.

2D real space visualization of d values in polycrystalline bulk materials of different hardness

2021 ◽  
Vol 54 (2) ◽  
pp. 597-603
Author(s):  
Mari Mizusawa ◽  
Kenji Sakurai
Keyword(s):  
Lattice Distortion ◽  
Structural Information ◽  
Hardness Test ◽  
Real Space ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Imaging ◽  
D Values

Conventional X-ray diffraction measurements provide some average structural information, mainly on the crystal structure of the whole area of the given specimen, which might not be very uniform and may include different crystal structures, such as co-existing crystal phases and/or lattice distortion. The way in which the lattice plane changes due to strain also might depend on the position in the sample, and the average information might have some limits. Therefore, it is important to analyse the sample with good lateral spatial resolution in real space. Although various techniques for diffraction topography have been developed for single crystals, it has not always been easy to image polycrystalline materials. Since the late 1990s, imaging technology for fluorescent X-rays and X-ray absorption fine structure has been developed via a method that does not scan either a sample or an X-ray beam. X-ray diffraction imaging can be performed when this technique is applied to a synchrotron radiation beamline with a variable wavelength. The present paper reports the application of X-ray diffraction imaging to bulk steel materials with varying hardness. In this study, the distribution of lattice distortion of hardness test blocks with different hardness was examined. Via this 2D visualization method, the grains of the crystals with low hardness are large enough to be observed by X-ray diffraction contrast in real space. The change of the d value in the vicinity of the Vickers mark has also been quantitatively evaluated.

The Use of 2-D Detector Utilizing Laser-Stimulated Luminescence for X-ray Diffraction Studies on Mechanical Behaviour of Materials

1989 ◽  
Vol 33 ◽  
pp. 389-396 ◽  
Author(s):  
Y. Yoshioka ◽  
T. Shinkai ◽  
S. Ohya
Keyword(s):  
Fracture Analysis ◽  
X Rays ◽  
Large Reduction ◽  
X Ray Diffraction ◽  
Crystalline Materials ◽  
X Ray ◽  
Material Evaluation ◽  
Position Sensitive ◽  
Diffraction Patterns ◽  
Position Sensitive Detectors

The development of linear position-sensitive detectors (PSD) has resulted in a large reduction of data acquisition times in the field of x-ray stress analysis. However, we also require two-dimensional (2-D) diffraction patterns for material evaluation. Especially, the microbeam x-ray diffraction technique gives valuable information on the structure of crystalline materials and this technique has been applied to fracture analysis by x-rays. Many kinds of 2-D PSD have been developed that have insufficient spatial resolution. So x-ray film has still been used as a 2-D detector, but it requires relatively long exposure times and then the process after exposure is very troublesome.

Electrochemical Deposition and Characterization of Cd-Fe-Se Thin Films

2009 ◽  
Vol 68 ◽  
pp. 69-76 ◽  
Author(s):  
S. Thanikaikarasan ◽  
T. Mahalingam ◽  
K. Sundaram ◽  
Tae Kyu Kim ◽  
Yong Deak Kim ◽  
...  
Keyword(s):  
Thin Films ◽  
Hexagonal Structure ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Iron Selenide ◽  
Glass Substrates ◽  
Diffraction Patterns ◽  
Cadmium Iron Selenide ◽  
Deposited Films

Cadmium iron selenide (Cd-Fe-Se) thin films were deposited onto tin oxide (SnO2) coated conducting glass substrates from an aqueous electrolytic bath containing CdSO4, FeSO4 and SeO2 by potentiostatic electrodeposition. The deposition potentials of Cadmium (Cd), Iron (Fe), Selenium (Se) and Cadmium-Iron-Selenide (Cd-Fe-Se) were determined from linear cathodic polarization curves. The deposited films were characterized by x-ray diffraction (XRD), scanning electron microscope (SEM), energy dispersive analysis by x-rays (EDX) and optical absorption techniques, respectively. X-ray diffraction patterns shows that the deposited films are found to be hexagonal structure with preferential orientation along (100) plane. The effect of FeSO4 concentration on structural, morphological, compositional and optical properties of the films are studied and discussed in detail.

Developments in Analytical Diffraction Using Isotopic X-Ray Sources

1970 ◽  
Vol 14 ◽  
pp. 139-145
Author(s):  
W. S. Toothacker ◽  
L. E. Preuss
Keyword(s):  
Exposure Time ◽  
Specific Activity ◽  
X Rays ◽  
X Ray Diffraction ◽  
Glass Capillary ◽  
X Ray ◽  
Oak Ridge ◽  
Position Sensitive ◽  
Diffraction Patterns ◽  
Intense Source

AbstractLobov et al., in Leningrad, and workers at this laboratory have been working on the idea of using x rays from radioactive sources for x ray diffraction analysis. The Russians have been using iron-55 produced by the (n, Y) reaction in their work with a small focusing camera which operates in the back reflection region. We have been using iron-55 produced by the (p,n) reaction in conjunction with a small Debye-Scherrer camera. The preliminary work of this laboratory was reported at this conference two years ago. At that time a 13 mCi iron-55 source was used in a two inch diameter Debye-Scherrer camera to obtain x-ray diffraction patterns of LiF. The exposure times were of the order of 120 hours and the reflection from the 200 plane was about 3 degrees wide. Since that time a new and more intense source has been constructed at Oak Ridge National Laboratories. With the new source it was possible to produce LiF diffraction patterns of the same density and resolution as before in a period of less than ten hours.The above mentioned diffraction patterns were made with the LiF powder placed in a 1.0 mm diameter glass capillary. After reduction of the glass capillary diameter to 0.5 mm and appropriate reduction of the collimator width, we were able to improve the resolution considerably with no accompanying reduction in line density. The LiF patterns obtained in this way required an exposure time of about 20 hours and the width of the reflection from the 200 plane has been reduced to about 1.5 degrees.Hence we are able to report a reduction in exposure time from 116 hours to 20 hours and an increase in resolution by a factor of two over the data reported here two years ago. Thus the concept of using x rays from an isotope for powder diffraction has changed from a laboratory curiosity into a technique with practical possibilities. Both sources mentioned above were produced by the (p, n) reaction. The 135 mCi source had a specific activity of about 400 Ci/gm. Since iron-55 sources have been made with specific activities of about 1000 Ci/gm, a considerable decrease in exposure time could be accomplished by using such a source. The application to this work of a position sensitive proportional counter as developed by Semmler will also be discussed.

Strain Measurement of Pure Titanium Covered With Soft Tissue Using X-Ray Diffraction

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Kazuhiro Fujisaki ◽  
Shigeru Tadano
Keyword(s):  
Pure Titanium ◽  
Physiological Saline ◽  
Skin Tissue ◽  
Bragg Angle ◽  
X Rays ◽  
X Ray Diffraction ◽  
Diffraction Profile ◽  
X Ray ◽  
Bending Loads ◽  
Lattice Planes

Measurement of the stress and strain applied to implants and bone tissue in the human body are important for fracture prediction and evaluations of implant adaptation. The strain of titanium (Ti) materials can be measuring by X-ray diffraction techniques. This study applied X-ray diffraction to the skin tissue-covered Ti. Characteristic X-rays of Mo Kα were used and the X-rays diffracted from the Ti were detected through the covering skin tissue. The X-ray absorption by skin tissue is large under the diffracted X-rays detected in low angles because the length of penetration depends on the angle of inclination, equal to the Bragg angle. The effects of skin tissue to detect the diffracted X-rays were investigated in the experiments. And the strain measurements were conducted under bending loads applied to the Ti specimen. The effect of skin tissue was absorption of X-rays as well as the X-rays scattered from the physiological saline contained in the tissue. The X-rays scattered by the physiological saline creates a specific background pattern near the peaks from the (002) and (011) lattice planes of Ti in the X-ray diffraction profile. Diffracted X-rays from the Ti were detected after being transmitted through 1 mm thick skin tissue by Mo Kα. Individual peaks such as (010), (002), (011), and (110) were clearly established by using a parallel beam arrangement. The strains of (110) lattice planes were measured with or without the tissue cover were very similar. The strain of the (110) lattice planes of Ti could be measured by Mo Kα when the Ti specimen was located under the skin tissue.

scholarly journals Time-resolved X-ray diffraction at NERL

2001 ◽  
Vol 19 (1) ◽  
pp. 125-131 ◽  
Author(s):  
KENICHI KINOSHITA ◽  
HIDEKI HARANO ◽  
KOJI YOSHII ◽  
TAKERU OHKUBO ◽  
ATSUSHI FUKASAWA ◽  
...  
Keyword(s):  
Research Laboratory ◽  
Experimental Results ◽  
X Rays ◽  
Nuclear Engineering ◽  
X Ray Diffraction ◽  
Time Resolved ◽  
X Ray ◽  
Engineering Research ◽  
Fs Laser ◽  
Diffraction Patterns

For ultrafast material analyses, we constructed the time-resolved X-ray diffraction system utilizing ultrashort X-rays from laser-produced plasma generated by the 12-TW–50-fs laser at the Nuclear Engineering Research Laboratory. Ultrafast transient changes in laser-irradiated GaAs crystals were observed as X-ray diffraction patterns. Experimental results were compared with numerical analyses.

scholarly journals The atomic scattering factor for X-rays in the region of anomalous dispersion

1933 ◽  
Vol 139 (838) ◽  
pp. 459-466 ◽  
Keyword(s):  
Free Electron ◽  
Scattered Radiation ◽  
Wave Length ◽  
Anomalous Dispersion ◽  
X Rays ◽  
Characteristic Frequencies ◽  
X Ray ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

The atomic scattering factor ( f -factor) for X-rays is the ratio of the amplitude of the X-rays scattered by a given atom and that scattered according to the classical theory by one single free electron. It is given as a function of sin ϑ/λ, λ being the wave-length of the X-rays, 2ϑ the angle between the primary and the scattered radiation. It is assumed to be independent of the wave-length so long as sin ϑ/λ remains constant. Recently, however, it has been shown both theoretically and experimentally that the last assumption is no longer valid, when the scattered frequency is in the neighbourhood of one of the characteristic frequencies of the scattering element. The first to show the influence of the anomalous dispersion on the f factor were Mark and Szilard, who reflected strontium and bromine radiations by a rubidium bromide crystal. Theoretically the problem was dealt with by Coster, Knol and Prins in their investigation of the influence of the polarity of zincblende on the intensity of X-ray reflection and later on once more by Gloeker and Schäfer.

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