Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain

2021 ◽  
Vol 77 (4) ◽  
Author(s):  
Anatoly G. Shabalin ◽  
Oleg G. Shpyrko
Keyword(s):  
Structure Factor ◽  
Scattering Amplitude ◽  
Atomic Displacement ◽  
Ferroelectric Material ◽  
Unit Cell ◽  
Lattice Deformation ◽  
X Ray Diffraction ◽  
Diffractive Imaging ◽  
X Ray ◽  
Cell Configuration

The X-ray Bragg coherent diffractive imaging (CDI) technique assumes that the structure factor holds constant over the measured crystal. This approximation breaks down for materials exhibiting variations in the unit-cell configuration, such as piezo- and ferroelectrics. In that case, the strain field cannot be reliably determined from the reconstruction because the lattice deformation and the structure factor contribute concomitantly. Proposed here is a solution to this problem achieved by combining Bragg CDI and the multiwavelength anomalous diffraction approach that measures a Friedel pair of reflections at two different photon energies near an absorption edge. Comparing the obtained reconstructions with a parametric model that includes calculating the scattering amplitude as a function of wavelength and the unit-cell configuration, the contributions of the lattice deformation and the structure factor are separated. Simulations of the ferroelectric material BaTiO3 demonstrate the possibility of simultaneous probing of the strain and displacement of the Ti atoms. The proposed method opens up an opportunity to apply coherent X-ray diffraction for nanoscale-resolved 3D mapping of polarization domains in micro- and nanocrystals.

A method of material design for systematic absence of X-ray diffraction

2010 ◽  
Vol 25 (S1) ◽  
pp. S48-S51
Author(s):  
Huan-hua Wang
Keyword(s):  
Solid Solution ◽  
Structure Factor ◽  
Material Design ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Time Resolved ◽  
Xrd Pattern ◽  
X Ray ◽  
X Ray Scattering ◽  
Calculation Process

Materials with systematic absence of X-ray diffraction (XRD) peaks are desirable for conducting some special researches using X-ray diffraction or time-resolved X-ray scattering. This paper proposes a method for designing this kind of materials. It utilizes solid solution to reduce the structure factor of a selected reflection to zero by choosing proper components and their contents to let the reflection amplitudes from different atomic layers in a unit cell of the solid solution cancel each other completely. This method on how to select a solid solvent and how to calculate its content was illustrated using SrTiO3 as an example. A solid solution Sr1−xCaxTiO3 with a systematic absence of the (001) diffraction can be designed, and the value of x can be determined to be x=0.54 using an iteration calculation process. This result was verified by the experimental XRD pattern of a Sr0.46Ca0.54TiO3 sample.

Fabrication and study the effect of the laser on the properties of the compound Tl2-xHgxBa2-ySryCa2Cu3O10+δ superconductor

2018 ◽  
pp. 168
Author(s):  
A. Kareem Dahash Ali ◽  
Nihad Ali Shafeek
Keyword(s):  
Transition Temperature ◽  
Solid State ◽  
Hydrostatic Pressure ◽  
Electrical Properties ◽  
Co2 Laser ◽  
Temperature Shift ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structural And Electrical Properties

This study included the fabrication of    compound (Tl2-xHgxBa2-ySryCa2Cu3O10+δ) in a manner solid state and under hydrostatic pressure ( 8 ton/cm2) and temperature annealing(850°C), and determine the effect of the laser on the structural and electrical properties elements in the compound, and various concentrations of x where (x= 0.1,0.2,0.3 ). Observed by testing the XRD The best ratio of compensation for x is 0.2 as the value of a = b = 5.3899 (A °), c = 36.21 (A °) show that the installation of four-wheel-based type and that the best temperature shift is TC= 142 K  .When you shine a CO2 laser on the models in order to recognize the effect of the laser on these models showed the study of X-ray diffraction of these samples when preparing models with different concentrations of the values ​​of x, the best ratio of compensation is 0.2 which showed an increase in the values ​​of the dimensions of the unit cell a=b = 5.3929 (A °), c = 36.238 (A°). And the best transition temperature after shedding laser is TC=144 K. 

scholarly journals Crystal Structure of Moganite and Its Anisotropic Atomic Displacement Parameters Determined by Synchrotron X-ray Diffraction and X-ray/Neutron Pair Distribution Function Analyses

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Seungyeol Lee ◽  
Huifang Xu ◽  
Hongwu Xu ◽  
Joerg Neuefeind
Keyword(s):  
Crystal Structure ◽  
Distribution Function ◽  
Single Crystal ◽  
Pair Distribution Function ◽  
Atomic Displacement ◽  
Single Crystal Xrd ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutron Pair ◽  
Atomic Displacement Parameters

The crystal structure of moganite from the Mogán formation on Gran Canaria has been re-investigated using high-resolution synchrotron X-ray diffraction (XRD) and X-ray/neutron pair distribution function (PDF) analyses. Our study for the first time reports the anisotropic atomic displacement parameters (ADPs) of a natural moganite. Rietveld analysis of synchrotron XRD data determined the crystal structure of moganite with the space group I2/a. The refined unit-cell parameters are a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4)°. The ADPs of Si and O in moganite were obtained from X-ray and neutron PDF analyses. The shapes and orientations of the anisotropic ellipsoids determined from X-ray and neutron measurements are similar. The anisotropic ellipsoids for O extend along planes perpendicular to the Si-Si axis of corner-sharing SiO4 tetrahedra, suggesting precession-like movement. Neutron PDF result confirms the occurrence of OH over some of the tetrahedral sites. We postulate that moganite nanomineral is stable with respect to quartz in hypersaline water. The ADPs of moganite show a similar trend as those of quartz determined by single-crystal XRD. In short, the combined methods can provide high-quality structural parameters of moganite nanomineral, including its ADPs and extra OH position at the surface. This approach can be used as an alternative means for solving the structures of crystals that are not large enough for single-crystal XRD measurements, such as fine-grained and nanocrystalline minerals formed in various geological environments.

scholarly journals X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2949
Author(s):  
Marzieh Rabiei ◽  
Arvydas Palevicius ◽  
Amir Dashti ◽  
Sohrab Nasiri ◽  
Ahmad Monshi ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Ultrasonic Pulse ◽  
High Accuracy ◽  
Unit Cell ◽  
Deformation Model ◽  
X Ray Diffraction ◽  
Uniform Deformation ◽  
X Ray ◽  
Pulse Echo

Taking into account X-ray diffraction, one of the well-known methods for calculating the stress-strain of crystals is Williamson-Hall (W–H). The W-H method has three models, namely (1) Uniform deformation model (UDM); (2) Uniform stress deformation model (USDM); and (3) Uniform deformation energy density model (UDEDM). The USDM and UDEDM models are directly related to the modulus of elasticity (E). Young’s modulus is a key parameter in engineering design and materials development. Young’s modulus is considered in USDM and UDEDM models, but in all previous studies, researchers used the average values of Young’s modulus or they calculated Young’s modulus only for a sharp peak of an XRD pattern or they extracted Young’s modulus from the literature. Therefore, these values are not representative of all peaks derived from X-ray diffraction; as a result, these values are not estimated with high accuracy. Nevertheless, in the current study, the W-H method is used considering the all diffracted planes of the unit cell and super cells (2 × 2 × 2) of Hydroxyapatite (HA), and a new method with the high accuracy of the W-H method in the USDM model is presented to calculate stress (σ) and strain (ε). The accounting for the planar density of atoms is the novelty of this work. Furthermore, the ultrasonic pulse-echo test is performed for the validation of the novelty assumptions.

scholarly journals Study of Structural, Magnetic, and Mossbauer Properties of Dy2Fe16Ga1−xNbx (0.0 ≤ x ≤ 1.0) Prepared via Arc Melting Process

2021 ◽  
Vol 7 (3) ◽  
pp. 42
Author(s):  
Jiba N. Dahal ◽  
Kalangala Sikkanther Syed Ali ◽  
Sanjay R. Mishra
Keyword(s):  
Isomer Shift ◽  
Cell Volume ◽  
Intermetallic Compounds ◽  
Unit Cell Volume ◽  
Rietveld Analysis ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
X Ray ◽  
Arc Melting ◽  
Nb Content

Intermetallic compounds of Dy2Fe16Ga1−xNbx (x = 0.0 to 1.00) were synthesized by arc melting. Samples were investigated for structural, magnetic, and hyperfine properties using X-ray diffraction, vibration sample magnetometer, and Mossbauer spectrometer, respectively. The Rietveld analysis of room temperature X-ray diffraction data shows that all the samples were crystallized in Th2Fe17 structure. The unit cell volume of alloys increased linearly with an increase in Nb content. The maximum Curie temperature Tc ~523 K for x = 0.6 sample is higher than Tc = 153 K of Dy2Fe17. The saturation magnetization decreased linearly with increasing Nb content from 61.57 emu/g for x = 0.0 to 42.46 emu/g for x = 1.0. The Mössbauer spectra and Rietveld analysis showed a small amount of DyFe3 and NbFe2 secondary phases at x = 1.0. The hyperfine field of Dy2Fe16Ga1−xNbx decreased while the isomer shift values increased with the Nb content. The observed increase in isomer shift may have resulted from the decrease in s electron density due to the unit cell volume expansion. The substantial increase in Tc of thus prepared intermetallic compounds is expected to have implications in magnets used for high-temperature applications.

scholarly journals Crystal Structure Refinements of Four Monazite Samples from Different Localities

Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1028 ◽  
Author(s):  
M. Mashrur Zaman ◽  
Sytle M. Antao
Keyword(s):  
Crystal Structure ◽  
Electron Probe ◽  
Unit Cell Volume ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Large Unit Cell ◽  
A Site

This study investigates the crystal chemistry of monazite (APO4, where A = Lanthanides = Ln, as well as Y, Th, U, Ca, and Pb) based on four samples from different localities using single-crystal X-ray diffraction and electron-probe microanalysis. The crystal structure of all four samples are well refined, as indicated by their refinement statistics. Relatively large unit-cell parameters (a = 6.7640(5), b = 6.9850(4), c = 6.4500(3) Å, β = 103.584(2)°, and V = 296.22(3) Å3) are obtained for a detrital monazite-Ce from Cox’s Bazar, Bangladesh. Sm-rich monazite from Gunnison County, Colorado, USA, has smaller unit-cell parameters (a = 6.7010(4), b = 6.9080(4), c = 6.4300(4) Å, β = 103.817(3)°, and V = 289.04(3) Å3). The a, b, and c unit-cell parameters vary linearly with the unit-cell volume, V. The change in the a parameter is large (0.2 Å) and is related to the type of cations occupying the A site. The average <A-O> distances vary linearly with V, whereas the average <P-O> distances are nearly constant because the PO4 group is a rigid tetrahedron.

Compressibility of β-As4S4: an in situ high-pressure single-crystal X-ray study

2012 ◽  
Vol 76 (4) ◽  
pp. 963-973 ◽  
Author(s):  
G. O. Lepore ◽  
T. Boffa Ballaran ◽  
F. Nestola ◽  
L. Bindi ◽  
D. Pasqual ◽  
...  
Keyword(s):  
Pressure Range ◽  
Substantial Reduction ◽  
Structural Data ◽  
Unit Cell ◽  
Van Der Waals Interactions ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Intermolecular Distances

AbstractAmbient temperature X-ray diffraction data were collected at different pressures from two crystals of β-As4S4, which were made by heating realgar under vacuum at 295ºC for 24 h. These data were used to calculate the unit-cell parameters at pressures up to 6.86 GPa. Above 2.86 GPa, it was only possible to make an approximate measurement of the unit-cell parameters. As expected for a crystal structure that contains molecular units held together by weak van der Waals interactions, β-As4S4 has an exceptionally high compressibility. The compressibility data were fitted to a third-order Birch–Murnaghan equation of state with a resulting volume V0 = 808.2(2) Å3, bulk modulus K0 = 10.9(2) GPa and K' = 8.9(3). These values are extremely close to those reported for the low-temperature polymorph of As4S4, realgar, which contains the same As4S4 cage-molecule. Structural analysis showed that the unit-cell contraction is due mainly to the reduction in intermolecular distances, which causes a substantial reduction in the unit-cell volume (∼21% at 6.86 GPa). The cage-like As4S4 molecules are only slightly affected. No phase transitions occur in the pressure range investigated.Micro-Raman spectra, collected across the entire pressure range, show that the peaks associated with As–As stretching have the greatest pressure dependence; the S–As–S bending frequency and the As–S stretching have a much weaker dependence or no variation at all as the pressure increases; this is in excellent agreement with the structural data.

Low-temperature powder X-ray diffraction measurements in vacuum: analysis of the thermal displacement of copper

2016 ◽  
Vol 49 (1) ◽  
pp. 110-119 ◽  
Author(s):  
Nanna Wahlberg ◽  
Niels Bindzus ◽  
Sebastian Christensen ◽  
Jacob Becker ◽  
Ann-Christin Dippel ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution Function ◽  
Cell Parameter ◽  
Atomic Displacement ◽  
Cryogenic Temperatures ◽  
X Ray Diffraction ◽  
Atomic Displacement Parameter ◽  
Thermal Displacement ◽  
X Ray ◽  
Helium Gas

A serious limitation of the all-in-vacuum diffractometer reported by Straasø, Dippel, Becker & Als-Nielsen [J. Synchrotron Rad.(2014),21, 119–126] has so far been the inability to cool samples to near-cryogenic temperatures during measurement. The problem is solved by placing the sample in a jet of helium gas cooled by liquid nitrogen. The resulting temperature change is quantified by determining the change in unit-cell parameter and atomic displacement parameter of copper. The cooling proved successful, with a resulting temperature of ∼95 (3) K. The measured powder X-ray diffraction data are of superb quality and high resolution [up to sinθ/λ = 2.2 Å−1], permitting an extensive modelling of the thermal displacement. The anharmonic displacement of copper was modelled by a Gram–Charlier expansion of the temperature factor. As expected, the corresponding probability distribution function shows an increased probability away from neighbouring atoms and a decreased probability towards them.

scholarly journals Linear Structural Trends and Multi-Phase Intergrowths in Helvine-Group Minerals, (Zn,Fe,Mn)8[Be6Si6O24]S2

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 325
Author(s):  
Sytle Antao
Keyword(s):  
Cell Parameter ◽  
Structural Parameters ◽  
Unit Cell ◽  
Fluid Composition ◽  
Ternary Solid Solution ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Difference ◽  
Multi Phase ◽  
And Diffusion

Synchrotron high-resolution powder X-ray diffraction (HRPXRD) and Rietveld structure refinements were used to examine the crystal structure of single phases and intergrowths (either two or three phases) in 13 samples of the helvine-group minerals, (Zn,Fe,Mn)8[Be6Si6O24]S2. The helvine structure was refined in the cubic space group P4¯3n. For the intergrowths, simultaneous refinements were carried out for each phase. The structural parameters for each phase in an intergrowth are only slightly different from each other. Each phase in an intergrowth has well-defined unit-cell and structural parameters that are significantly different from the three endmembers and these do not represent exsolution or immiscibility gaps in the ternary solid-solution series. The reason for the intergrowths in the helvine-group minerals is not clear considering the similar radii, identical charge, and diffusion among the interstitial M cations (Zn2+, Fe2+, and Mn2+) that are characteristic of elongated tetrahedral coordination. The difference between the radii of Zn2+ and Mn2+ cations is 10%. Depending on the availability of the M cations, intergrowths may occur as the temperature, pressure, fugacity fS2, and fluid composition change on crystallization. The Be–Si atoms are fully ordered. The Be–O and Si–O distances are nearly constant. Several structural parameters (Be–O–Si bridging angle, M–O, M–S, average <M–O/S>[4] distances, and TO4 rotational angles) vary linearly with the a unit-cell parameter across the series because of the size of the M cation.

scholarly journals Li3Al2, eine neue Phase im System Li/Al / Li3Al2, a New Phase in the System Li/Al

1973 ◽  
Vol 28 (9-10) ◽  
pp. 600-605 ◽  
Author(s):  
Karl-Friedrich Tebbe ◽  
Hans Georg Schnering ◽  
Barbara Rüter ◽  
Gisela Rabeneck
Keyword(s):  
Unit Cell ◽  
The Body ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structural Relation ◽  
New Phase

Besides ‘Li2Al’ which was recently shown to be the phase Li9Al4 there exists the phase Li3Al2 characterized by preparation and X-ray diffraction methods. It cristallizes with a rhomboedric unit cell, R3̄m, a = 4.508 Å, c = 14.26 Å and z = 3 formula units (hexagonal setting). The structure can be looked at as a variant of the body centred cubic packing with Αl-atom layers of puckered six membered rings. The structural relation of the phases LiAl, Li3Al2, Li9Al4, Li is discussed.

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