scholarly journals Residual lattice strain in quartzites as a potential palaeo-piezometer

2020 ◽  
Vol 222 (2) ◽  
pp. 1363-1378 ◽  
Author(s):  
Hans-Rudolf Wenk ◽  
Brian Chase Chandler ◽  
Kai Chen ◽  
Yao Li ◽  
Nobumichi Tamura ◽  
...  
Keyword(s):  
Lattice Distortion ◽  
Lattice Strain ◽  
Strain Tensor ◽  
Tectonic Deformation ◽  
Laue Diffraction ◽  
X Ray ◽  
Pole Figures ◽  
Strain Axis ◽  
Greenschist Facies Metamorphism ◽  
The Ideal

SUMMARY If a crystal lattice is subjected to a stress, it becomes distorted and no longer represents the ideal crystal symmetry, and if the stress introduces defects such as dislocations, some of this distortion is preserved after the applied stress is removed. In this study, we investigate lattice distortion in quartz at the micron scale with synchrotron X-ray Laue diffraction. From Laue images the local deviatoric strain tensor is derived and corresponding stresses are calculated based on elastic properties. The method is applied to metasedimentary quartzites from the Bergell Alps that were deformed at conditions of greenschist facies metamorphism. The residual palaeostrain is represented in maps of the deviatoric strain tensor components and with deviatoric strain axis pole figures. Data suggest overall shortening perpendicular to the schistosity plane but with considerable asymmetry relative to foliation and lineation, probably attributed to simple shear. Crystallographic pole figures from Laue diffraction agree with neutron diffraction and EBSD measurements and display quartz c-axes girdle distributions with maxima also perpendicular to schistosity. The method shows promise to be used as a palaeo-piezometer to unravel the stress field during tectonic deformation.

Distributions of Domain Size, Lattice Distortion and Dislocation Density in Tubes of Zr-Based Alloys Studied by a Method Combining X-Ray Line Profile Analysis with Texture Measurements

2004 ◽  
Vol 443-444 ◽  
pp. 255-258 ◽  
Author(s):  
Yuriy Perlovich ◽  
Margarita Isaenkova
Keyword(s):  
Dislocation Density ◽  
Lattice Distortion ◽  
Profile Analysis ◽  
Domain Size ◽  
Line Profile Analysis ◽  
Ray Method ◽  
Texture Measurement ◽  
X Ray ◽  
Pole Figures ◽  
Line Analysis

The distributions of substructure parameters for tubes of Zr-based alloys were constructed by use of the X-ray method of Generalized Pole Figures, combining X-ray line analysis and texture measurement. Obtained distributions cover α-Zr crystallites of all orientations and give the fullest description of substructure features of the studied tubes. The interconnection of different substructure parameters are analyzed.

Characterization of SiC Substrates Using X-Ray Rocking Curve Mapping

2006 ◽  
Vol 527-529 ◽  
pp. 729-732 ◽  
Author(s):  
Murugesu Yoganathan ◽  
Ejiro Emorhokpor ◽  
Thomas Kerr ◽  
A. Gupta ◽  
C.D. Tanner ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Lattice Distortion ◽  
Lattice Strain ◽  
Bragg Reflection ◽  
Sharp Change ◽  
Lattice Curvature ◽  
Rocking Curve ◽  
X Ray ◽  
Grain Misorientation

SiC substrates produced at II-VI, Inc. have been characterized using x-ray rocking curve mapping (topography). The rocking curves have been measured in the -scan mode for the (0006) Bragg reflection of 6H and the (0004) reflection of 4H SiC substrates. The maps contain information extracted from the rocking curves, such as the peak angle () and the rocking curve broadening (FWHM). In the case when lattice distortion is present due to the elastic or plastic deformation, the peak angle () changes gradually upon scanning, with the d/dx gradient proportional to the lattice curvature in the plane of diffraction. Multi-peak reflections and/or sharp change in the value of indicate the presence of misoriented grains. X-ray rocking curve mapping of SiC substrates yields excellent measures of crystalline quality that contain important information on the lattice strain and sub-grain misorientation.

scholarly journals Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector

2017 ◽  
Vol 50 (3) ◽  
pp. 901-908 ◽  
Author(s):  
A. Abboud ◽  
C. Kirchlechner ◽  
J. Keckes ◽  
T. Conka Nurdan ◽  
S. Send ◽  
...  
Keyword(s):  
Elastic Strain ◽  
Strain Tensor ◽  
Energy Dispersive ◽  
Single Shot ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Laue Diffraction ◽  
Experimental Procedure ◽  
X Ray ◽  
Diffraction Patterns

The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.

X-ray Micro Laue Diffraction and Neutron Diffraction Analysis of Residual Elastic Strains in a 1% Uniaxial Tensile Tested Nickel Alloy 600 Sample

2008 ◽  
Vol 1137 ◽  
Author(s):  
Jing Chao ◽  
Alison Mark ◽  
Marina Lynn Suominen Fuller ◽  
Rozaliya Barabash ◽  
N. Stewart McIntyre ◽  
...  
Keyword(s):  
Neutron Diffraction ◽  
Nickel Alloy ◽  
Diffraction Data ◽  
Elastic Strain ◽  
Strain Tensor ◽  
Uniaxial Tensile ◽  
Alloy 600 ◽  
Laue Diffraction ◽  
X Ray ◽  
Uniaxial Tensile Stress

AbstractThe magnitude and distribution of elastic strain for a nickel alloy 600 (A600) sample that had been subjected to uniaxial tensile stress were measured by micro Laue diffraction (MLD) and neutron diffraction techniques. For a sample that had been dimensionally strained by 1%, both MLD and neutron diffraction data indicated that the global residual elastic strain was on the order of 10−4, however the micro-diffraction data indicated considerable grain-to-grain variability amongst individual components of the residual strain tensor. A more precise comparison was done by finding those grains in the MLD map that had appropriate <hkl> oriented in the specific directions matching those used in the neutron measurements and the strains were found to agree within the uncertainty. Large variations in strain values across the grains were noted during the MLD measurements which are reflected in the uncertainties. This is a possible explanation for the large uncertainty in the average strains measured from multiple grains during neutron diffraction.

scholarly journals Lattice strain and tilt mapping in stressed Ge microstructures using X-ray Laue micro-diffraction and rainbow filtering

2016 ◽  
Vol 49 (5) ◽  
pp. 1402-1411 ◽  
Author(s):  
Samuel Tardif ◽  
Alban Gassenq ◽  
Kevin Guilloy ◽  
Nicolas Pauc ◽  
Guilherme Osvaldo Dias ◽  
...  
Keyword(s):  
Strain Measurement ◽  
Lattice Strain ◽  
Strain Tensor ◽  
Orientation Distribution ◽  
Numerical Approach ◽  
Biaxial Stress ◽  
Lattice Orientation ◽  
Strain Mapping ◽  
X Ray ◽  
Highly Strained

Laue micro-diffraction and simultaneous rainbow-filtered micro-diffraction were used to measure accurately the full strain tensor and the lattice orientation distribution at the sub-micrometre scale in highly strained, suspended Ge micro-devices. A numerical approach to obtain the full strain tensor from the deviatoric strain measurement alone is also demonstrated and used for faster full strain mapping. The measurements were performed in a series of micro-devices under either uniaxial or biaxial stress and an excellent agreement with numerical simulations was found. This shows the superior potential of Laue micro-diffraction for the investigation of highly strained micro-devices.

scholarly journals Micro-beam Laue alignment of multi-reflection Bragg coherent diffraction imaging measurements

2017 ◽  
Vol 24 (5) ◽  
pp. 1048-1055 ◽  
Author(s):  
Felix Hofmann ◽  
Nicholas W. Phillips ◽  
Ross J. Harder ◽  
Wenjun Liu ◽  
Jesse N. Clark ◽  
...  
Keyword(s):  
Focused Ion Beam ◽  
Lattice Strain ◽  
Ion Beam ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Stress Fields ◽  
X Ray Diffraction ◽  
X Ray ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging

Multi-reflection Bragg coherent diffraction imaging has the potential to allow three-dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here a different approach is demonstrated, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focused ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples.

scholarly journals Influence of Microstructure on Synchrotron X-ray Diffraction Lattice Strain Measurement Uncertainty

Metals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 774
Author(s):  
Chris A. Simpson ◽  
David M. Knowles ◽  
Mahmoud Mostafavi
Keyword(s):  
Measurement Uncertainty ◽  
Strain Measurement ◽  
Lattice Strain ◽  
Strain Tensor ◽  
Measurement Data ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
X Ray ◽  
Lattice Planes ◽  
Sampling Statistics

Accurate residual lattice strain measurements are highly dependent upon the precision of the diffraction peak location and the underlying microstructure suitability. The suitability of the microstructure is related to the requirement for valid powder diffraction sampling statistics and the associated number of appropriately orientated illuminated. In this work, these two sources of uncertainty are separated, and a method given for both the quantification of errors associated with insufficient grain sampling statistics and minimization of the total lattice strain measurement uncertainty. It is possible to reduce the total lattice strain measurement uncertainty by leveraging diffraction peak measurements made at multiple azimuthal angles. Lattice strain measurement data acquired during eight synchrotron X-ray diffraction experiments, monochromatic and energy dispersive, has been assessed as per this approach, with microstructural suitability being seen to dominate total measurement uncertainty when the number of illuminated grains was <106. More than half of the studied experimental data fell into this category, with a severe underestimation of total strain measurement uncertainty being possible when microstructural suitability is not considered. To achieve a strain measurement uncertainty under 10−4, approximately 3×105 grains must be within the sampled gauge volume, with this value varying with the multiplicity of the family of lattice planes under study. Where additional azimuthally arrayed data are available an in-plane lattice strain tensor can be extracted. This improves overall strain measurement accuracy and an uncertainty under 10−4 can then be achieved with just 4×104 grains.

scholarly journals Elastic strain tensor of zirconium hydrides in Zr2.5%Nb pressure tubes by synchrotron X-ray diffraction

2019 ◽  
Vol 52 (5) ◽  
pp. 1128-1143 ◽  
Author(s):  
Miguel Angel Vicente Alvarez ◽  
Javier Santisteban ◽  
Gladys Domizzi ◽  
John Okasinski ◽  
Jonathan Almer
Keyword(s):  
Phase Transformation ◽  
Elastic Strain ◽  
Power Plants ◽  
Strain Tensor ◽  
Axial Direction ◽  
Zirconium Hydride ◽  
X Ray Diffraction ◽  
X Ray ◽  
Pole Figures ◽  
Elastic Strain Tensor

Zirconium alloys are used in fuel cladding and structural components of nuclear power plants. Hydrogen enters the Zr matrix during plant operation and precipitates as hydride particles that degrade the mechanical properties of the alloy, limiting service life. Knowledge of the stress state within hydride precipitates is important to understand stress-induced degradation mechanisms such as delayed hydride cracking, but no direct quantification has yet been reported in the literature. Here, measurements are reported of the average elastic strain tensor within δ zirconium hydride precipitates in Zr2.5%Nb pressure tube material from CANDU power plants. Complete intensity and strain pole figures for the hydride were obtained by synchrotron X-ray diffraction experiments on specimens with hydrogen contents ranging from ∼100 wt p.p.m. hydrogen to nearly 100% δ-hydride. Zirconium hydride precipitates by a process involving a martensitic transformation, with two hydride variants possible from a single α-Zr grain. A synthetic model of the hydride crystallographic texture allowed the interpretation of the measured strain pole figures and quantification of the elastic strain tensor for both texture components. It was found that the two variants appear in nearly equal proportion but with different stress states, differing in the sign of the shear strain components (∼±3000 µ∊). This difference is possibly associated with the shear movement of Zr atoms during the phase transformation. This suggests that hydride clusters are composed of stacks of smaller hydrides in alternating hydride variants. Stresses were estimated from a set of rather uncertain hydride elastic constants. Overall, both variants showed compressive strains along the tube axial direction (∼5000 µ∊). For low hydrogen concentrations, the hydrides' stress tensor is dominated by compressive stresses of ∼300 MPa along the axial direction, probably caused by the elongated morphology of hydride clusters along this direction, and variant-dependent shear stresses of ∼±100 MPa, probably from the shear movement of the Zr atoms involved in the phase transformation.

X-Ray Analysis of Frozen Hydrated Sections:The Unconventional Approach

1982 ◽  
Vol 40 ◽  
pp. 754-757
Author(s):  
R. Beeuwkes ◽  
A. Saubermann ◽  
P. Echlin ◽  
S. Churchill
Keyword(s):  
Ratio Method ◽  
Frozen Sections ◽  
Technical Problems ◽  
Sample Handling ◽  
X Ray ◽  
Common Group ◽  
Ideal Method ◽  
Classic Paper ◽  
Physical Principles ◽  
The Ideal

Fifteen years ago, Hall described clearly the advantages of the thin section approach to biological x-ray microanalysis, and described clearly the ratio method for quantitive analysis in such preparations. In this now classic paper, he also made it clear that the ideal method of sample preparation would involve only freezing and sectioning at low temperature. Subsequently, Hall and his coworkers, as well as others, have applied themselves to the task of direct x-ray microanalysis of frozen sections. To achieve this goal, different methodological approachs have been developed as different groups sought solutions to a common group of technical problems. This report describes some of these problems and indicates the specific approaches and procedures developed by our group in order to overcome them. We acknowledge that the techniques evolved by our group are quite different from earlier approaches to cryomicrotomy and sample handling, hence the title of our paper. However, such departures from tradition have been based upon our attempt to apply basic physical principles to the processes involved. We feel we have demonstrated that such a break with tradition has valuable consequences.

High Resolution Study of Polytypism: Application to SiC and Au3 Mn

1982 ◽  
Vol 40 ◽  
pp. 540-541
Author(s):  
G. Van Tendeloo ◽  
J. Van Landuyt ◽  
S. Amelinckx
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Stacking Sequence ◽  
X Ray ◽  
Powerful Technique ◽  
Resolution Study ◽  
The Ideal

Polytypism has been studied for a number of years and a wide variety of stacking sequences has been detected and analysed. SiC is the prototype material in this respect; see e.g. Electron microscopy under high resolution conditions when combined with x-ray measurements is a very powerful technique to elucidate the correct stacking sequence or to study polytype transformations and deviations from the ideal stacking sequence.

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