scholarly journals Intragranular strain estimation in far-field scanning X-ray diffraction using a Gaussian process

2021 ◽  
Vol 54 (4) ◽  
Author(s):  
Axel Henningsson ◽  
Johannes Hendriks
Keyword(s):  
Gaussian Process ◽  
Strain Field ◽  
A Priori ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Polycrystalline Specimen ◽  
X Ray ◽  
Reconstruction Methods ◽  
Mean Square Errors

A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction (scanning 3DXRD) data is presented and evaluated. Given an a priori known anisotropic compliance, the regression method enforces the balance of linear and angular momentum in the linear elastic strain field reconstruction. By using a Gaussian process (GP), the presented method can yield a spatial estimate of the uncertainty of the reconstructed strain field. Furthermore, constraints on spatial smoothness can be optimized with respect to measurements through hyperparameter estimation. These three features address weaknesses discussed for previously existing scanning 3DXRD reconstruction methods and, thus, offer a more robust strain field estimation. The method is twofold validated: firstly by reconstruction from synthetic diffraction data, and secondly by reconstruction of a previously studied tin (Sn) grain embedded in a polycrystalline specimen. Comparison against reconstructions achieved by a recently proposed algebraic inversion technique is also presented. It is found that the GP regression consistently produces reconstructions with lower root-mean-square errors, mean absolute errors and maximum absolute errors across all six components of strain.

Three-Dimensional X-Ray Diffraction Microscopy Using High-Energy X-Rays

MRS Bulletin ◽  
2004 ◽  
Vol 29 (3) ◽  
pp. 166-169 ◽  
Author(s):  
Henning F. Poulsen ◽  
Dorte Juul Jensen ◽  
Gavin B.M. Vaughan
Keyword(s):  
Materials Science ◽  
Three Dimensional ◽  
High Energy ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Reconstruction Methods ◽  
The Individual ◽  
Individual Grains

AbstractThree-dimensional x-ray diffraction (3DXRD) microscopy is a tool for fast and nondestructive characterization of the individual grains, subgrains, and domains inside bulk materials. The method is based on diffraction with very penetrating hard x-rays (E ≥ 50 keV), enabling 3D studies of millimeter-to-centimeter-thick specimens.The position, volume, orientation, and elastic and plastic strain can be derived for hundreds of grains simultaneously. Furthermore, by applying novel reconstruction methods, 3D maps of the grain boundaries can be generated. The 3DXRD microscope in use at the European Synchrotron Radiation Facility in Grenoble, France, has a spatial resolution of ∼5 μm and can detect grains as small as 150 nm. The technique enables, for the first time, dynamic studies of the individual grains within polycrystalline materials. In this article, some fundamental materials science applications of 3DXRD are reviewed: studies of nucleation and growth kinetics during recrystallization, recovery, and phase transformations, as well as studies of polycrystal deformation.

scholarly journals Reconstructing intragranular strain fields in polycrystalline materials from scanning 3DXRD data

2020 ◽  
Vol 53 (2) ◽  
pp. 314-325 ◽  
Author(s):  
N. Axel Henningsson ◽  
Stephen A. Hall ◽  
Jonathan P. Wright ◽  
Johan Hektor
Keyword(s):  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Reconstruction Method ◽  
X Ray Diffraction ◽  
Reconstruction Accuracy ◽  
Strain Fields ◽  
Spatial Properties ◽  
Reconstruction Methods ◽  
Reconstruction Quality ◽  
Made In

Two methods for reconstructing intragranular strain fields are developed for scanning three-dimensional X-ray diffraction (3DXRD). The methods are compared with a third approach where voxels are reconstructed independently of their neighbours [Hayashi, Setoyama & Seno (2017). Mater. Sci. Forum, 905, 157–164]. The 3D strain field of a tin grain, located within a sample of approximately 70 grains, is analysed and compared across reconstruction methods. Implicit assumptions of sub-problem independence, made in the independent voxel reconstruction method, are demonstrated to introduce bias and reduce reconstruction accuracy. It is verified that the two proposed methods remedy these problems by taking the spatial properties of the inverse problem into account. Improvements in reconstruction quality achieved by the two proposed methods are further supported by reconstructions using synthetic diffraction data.

High Resolution Synchrotron X-Ray Diffraction Tomography Of Large-Grained Samples

1996 ◽  
Vol 437 ◽  
Author(s):  
D.P. Piotrowski ◽  
S.R. Stock ◽  
A. Guvenilir ◽  
J.D. Haase ◽  
Z.U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Dimensional Distribution

AbstractIn order to understand the macroscopic response of polycrystalline structural materials to loading, it is frequently essential to know the spatial distribution of strain as well as the variation of micro-texture on the scale of 100 μm. The methods must be nondestructive, however, if the three-dimensional evolution of strain is to be studied. This paper describes an approach to high resolution synchrotron x-ray diffraction tomography of polycrystalline materials. Results from model samples of randomly-packed, millimeter-sized pieces of Si wafers and of similarly sized single-crystal Al blocks have been obtained which indicate that polychromatic beams collimated to 30 μm diameter can be used to determine the depth of diffracting volume elements within ± 70 μm. The variation in the two-dimensional distribution of diffracted intensity with changing sample to detector separation is recorded on image storage plates and used to infer the depth of diffracting volume elements.

scholarly journals Maximum a posteriori estimation of crystallographic phases in X-ray diffraction tomography

2015 ◽  
Vol 373 (2043) ◽  
pp. 20140392 ◽  
Author(s):  
Doĝa Gürsoy ◽  
Tekin Biçer ◽  
Jonathan D. Almer ◽  
Raj Kettimuthu ◽  
Stuart R. Stock ◽  
...  
Keyword(s):  
National Laboratory ◽  
Spinous Process ◽  
Argonne National Laboratory ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Reconstruction Method ◽  
Diffraction Tomography ◽  
A Posteriori ◽  
X Ray Diffraction ◽  
X Ray

A maximum a posteriori approach is proposed for X-ray diffraction tomography for reconstructing three-dimensional spatial distribution of crystallographic phases and orientations of polycrystalline materials. The approach maximizes the a posteriori density which includes a Poisson log-likelihood and an a priori term that reinforces expected solution properties such as smoothness or local continuity. The reconstruction method is validated with experimental data acquired from a section of the spinous process of a porcine vertebra collected at the 1-ID-C beamline of the Advanced Photon Source, at Argonne National Laboratory. The reconstruction results show significant improvement in the reduction of aliasing and streaking artefacts, and improved robustness to noise and undersampling compared to conventional analytical inversion approaches. The approach has the potential to reduce data acquisition times, and significantly improve beamtime efficiency.

High Resolution Synchrotron X-Ray Diffraction Tomography of Polycrystalline Samples

1994 ◽  
Vol 375 ◽  
Author(s):  
S. R. Stock ◽  
A. Guvenilir ◽  
D. P. Piotrowski ◽  
Z. U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Compact Tension ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Nondestructive Measurements

AbstractThe macroscopic response of polycrystalline materials to loading depends on both the spatial distribution of strain and the variation of microtexture on the scale of 100 μm. Nondestructive measurements are needed if the three-dimensional evolution of strain is to be studied. This paper describes approaches for high resolution synchrotron polychromatic x-ray diffraction tomography of polycrystalline materials. Preliminary experiments are reported on partially cracked compact tension samples of Al-Li 2090 and on model samples of randomly-packed, millimeter-sized pieces of Si wafers. Polychromatic beams collimated to 100 μm diameter have been used, and the distribution of diffracted intensity has been collected on high resolution x-ray film as well as on image storage plates. The depths of diffracting volume elements are determined from the changes in the spatial distribution of diffracted intensity with varying sample to detector separation.

Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction

2010 ◽  
Vol 43 (3) ◽  
pp. 539-549 ◽  
Author(s):  
Jette Oddershede ◽  
Søren Schmidt ◽  
Henning Friis Poulsen ◽  
Henning Osholm Sørensen ◽  
Jonathan Wright ◽  
...  
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Polycrystalline Sample ◽  
Polycrystalline Materials ◽  
Interstitial Free ◽  
Outlier Rejection ◽  
X Ray Diffraction ◽  
Positional Accuracy ◽  
X Ray ◽  
Elastic Loading

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far-field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near-field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

scholarly journals Formation and annihilation of stressed deformation twins in magnesium

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Karim Louca ◽  
Hamidreza Abdolvand ◽  
Charles Mareau ◽  
Marta Majkut ◽  
Jonathan Wright
Keyword(s):  
Mechanical Response ◽  
Axial Stress ◽  
Three Dimensional ◽  
Service Performance ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Sign Reversal ◽  
X Ray ◽  
Hexagonal Close Packed

AbstractThe mechanical response of polycrystalline materials to an externally applied load and their in-service performance depend on the local load partitioning among the constituent crystals. In hexagonal close-packed polycrystals such load partitioning is significantly affected by deformation twinning. Here we report in-situ compression-tension experiments conducted on magnesium specimens to measure the evolution of grain resolved tensorial stresses and formation and annihilation of twins. More than 13000 grains and 1300 twin-parent pairs are studied individually using three-dimensional synchrotron X-ray diffraction. It is shown that at the early stages of plasticity, the axial stress in twins is higher than that of parents, yet twins relax with further loading. While a sign reversal is observed for the resolved shear stress (RSS) acting on the twin habit plane in the parent, the sign of RSS within the majority of twins stays unchanged until twin annihilation during the load reversal. The variations of measured average stresses across parents and twins are also investigated.

Reconstruction of Grains in Polycrystalline Materials From Incomplete Data Using Laguerre Tessellations

2019 ◽  
Vol 25 (3) ◽  
pp. 743-752 ◽  
Author(s):  
Lukas Petrich ◽  
Jakub Staněk ◽  
Mingyan Wang ◽  
Daniel Westhoff ◽  
Luděk Heller ◽  
...  
Keyword(s):  
Polycrystalline Material ◽  
Three Dimensional ◽  
Morphological Data ◽  
Polycrystalline Materials ◽  
Internal Stresses ◽  
X Ray Diffraction ◽  
X Ray ◽  
Quick Measurement ◽  
Centers Of Mass ◽  
Diffraction Microscopy

AbstractFar-field three-dimensional X-ray diffraction microscopy allows for quick measurement of the centers of mass and volumes of a large number of grains in a polycrystalline material, along with their crystal lattice orientations and internal stresses. However, the grain boundaries—and, therefore, individual grain shapes—are not observed directly. The present paper aims to overcome this shortcoming by reconstructing grain shapes based only on the incomplete morphological data described above. To this end, cross-entropy (CE) optimization is employed to find a Laguerre tessellation that minimizes the discrepancy between its centers of mass and cell sizes and those of the measured grain data. The proposed algorithm is highly parallel and is thus capable of handling many grains (>8,000). The validity and stability of the CE approach are verified on simulated and experimental datasets.

scholarly journals Comparison between a near-field and a far-field indexing approach for characterization of a polycrystalline sample volume containing more than 1500 grains

2014 ◽  
Vol 47 (4) ◽  
pp. 1402-1416 ◽  
Author(s):  
Laura Nervo ◽  
Andrew King ◽  
Jonathan P. Wright ◽  
Wolfgang Ludwig ◽  
Péter Reischig ◽  
...  
Keyword(s):  
Diffraction Data ◽  
Near Field ◽  
Three Dimensional ◽  
Pure Titanium ◽  
Polycrystalline Sample ◽  
Sample Volume ◽  
Polycrystalline Materials ◽  
Far Field ◽  
X Ray Diffraction ◽  
X Ray

A comparison of the performance of X-ray diffraction tomography, a near-field diffraction technique, and a far-field diffraction technique for indexing X-ray diffraction data of polycrystalline materials has been carried out by acquiring two sets of diffraction data from the same polycrystalline sample volume. Both approaches used in this study are variants of the three-dimensional X-ray diffraction (3DXRD) methodology, but they rely on different data-collection and analysis strategies. Previous attempts to assess the quality of 3DXRD indexing results from polycrystalline materials have been restricted to comparisons with two-dimensional electron backscatter diffraction cross sections containing a limited number of grains. In the current work, the relative performance of two frequently used polycrystalline-material indexing algorithms is assessed, comparing the indexing results obtained from a three-dimensional sample volume containing more than 1500 grains. The currently achievable accuracy of three-dimensional grain maps produced with these algorithms has been assessed using a statistical analysis of the measurement of the size, position and orientation of the grains in the sample. The material used for this comparison was a polycrystalline commercially pure titanium grade 2 sample, which has a hexagonal close-packed crystal structure. The comparison of the two techniques shows good agreement for the measurements of the grain position, size and orientation. Cross-validation between the indexing results shows that about 99% of the sample volume has been indexed correctly by either of these indexing approaches. The remaining discrepancies have been analysed and the strengths and limitations of both approaches are discussed.

Energy-dispersive Laue experiments with X-ray tube and PILATUS detector: precise determination of lattice constants

2019 ◽  
Vol 52 (1) ◽  
pp. 72-93
Author(s):  
Fiodar Kurdzesau
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Precise Determination ◽  
Energy Dispersive ◽  
X Ray Diffraction ◽  
Lattice Vector ◽  
X Ray ◽  
Lattice Constants ◽  
Space Pattern ◽  
Measurement Strategies

A PILATUS detector in combination with a conventional sealed X-ray tube was used for the development of the energy-dispersive Laue diffraction technique, which can be applied for precise measurements of single-crystal lattice constants in transmission and reflection modes without moving the sample. Exploiting the ability of PILATUS detectors to suppress counting of X-ray photons below a certain energy threshold allows one to recover the wavelength of diffracted Bragg reflections, reconstruct the three-dimensional reciprocal-space pattern, index X-ray diffraction peaks, and find the orientation and lattice parameters of the crystal without any a priori information about the sample. By making some geometrical assumptions and using a set of fast in situ calibration procedures, it is possible to simultaneously refine lattice constants and hardware correction factors, which simplifies the sample preparation and measurement strategies. Several samples [silicon, quartz, fluorite (CaF2), o′-Al13Co4 quasicrystal approximant, Laves (MgZn2) and Bergman (Mg32(Al,Zn)49) phases] were studied with the developed technique, and 0.01 Å and 0.1° precisions were routinely reached for lattice vector lengths and angles, respectively. The use of the developed methods is only limited by the energy resolution of the PILATUS detector, where lattice vectors with >27 Å length cannot be reliably resolved.

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