scholarly journals Reconstruction of local orientation in grains using a discrete representation of orientation space

2014 ◽  
Vol 47 (6) ◽  
pp. 1826-1840 ◽  
Author(s):  
Nicola Viganò ◽  
Wolfgang Ludwig ◽  
Kees Joost Batenburg
Keyword(s):  
Dimensional Space ◽  
Near Field ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Reconstruction Algorithm ◽  
Mathematical Framework ◽  
X Ray Diffraction ◽  
Outer Product ◽  
X Ray ◽  
Orientation Space

This work presents a mathematical framework for reconstruction of local orientations in grains based on near-field diffraction data acquired in X-ray diffraction contrast tomography or other variants of the monochromatic beam three-dimensional X-ray diffraction methodology. The problem of orientation reconstruction is formulated in terms of an optimization over a six-dimensional space {\bb X}^6 = {\bb R}^3 \otimes {\bb O}^{3}, constructed from the outer product of real and orientation space, and a strongly convergent first-order algorithm that makes use of modern l_1-minimization techniques is provided, to cope with the increasing number of unknowns introduced by the six-dimensional formulation of the reconstruction problem. The performance of the new reconstruction algorithm is then assessed on synthetic data, for varying degrees of deformation, both in a restricted line-beam illumination and in the more challenging full-beam illumination. Finally, the algorithm's behavior when dealing with different kinds of noise is shown. The proposed framework, along the reconstruction algorithm, looks promising for application to real experimental data from materials exhibiting intra-granular orientation spread of up to a few degrees.

scholarly journals Three-dimensional α colony characterization and prior-β grain reconstruction of a lamellar Ti–6Al–4V specimen using near-field high-energy X-ray diffraction microscopy

2015 ◽  
Vol 48 (4) ◽  
pp. 1165-1171 ◽  
Author(s):  
E. Wielewski ◽  
D. B. Menasche ◽  
P. G. Callahan ◽  
R. M. Suter
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
High Energy ◽  
Grain Structure ◽  
X Ray Diffraction ◽  
Orientation Field ◽  
X Ray ◽  
Hexagonal Close Packed ◽  
Flood Fill ◽  
Diffraction Microscopy

Near-field high-energy X-ray diffraction microscopy has been used to characterize the three-dimensional (3-D) crystallographic orientation field of the hexagonal close-packed α phase in a bulk Ti–6Al–4V specimen with a lamellar (β-annealed) microstructure. These data have been segmented using a 3-D misorientation-based grain finding algorithm, providing unprecedented information about the complex 3-D morphologies and spatial misorientation distributions of the transformed α lamella colonies. A 3-D Burgers orientation relationship-based flood-fill algorithm has been implemented to reconstruct the morphologies and crystallographic orientations of the high-temperature body-centered cubic prior-β grains. The combination of these data has been used to gain an understanding of the role of the prior-β grain structure in the formation of specific morphologies and spatial misorientation distributions observed in the transformed α colony structures. It is hoped that this understanding can be used to develop transformation structures optimized for specific applications and to produce more physically realistic synthetic microstructures for use in simulations.

Three-dimensional grain resolved strain mapping using laboratory X-ray diffraction contrast tomography: theoretical analysis

2022 ◽  
Vol 55 (1) ◽  
Author(s):  
Adam Lindkvist ◽  
Yubin Zhang
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Simulated Data ◽  
Three Dimensions ◽  
X Ray Diffraction ◽  
Strain Mapping ◽  
X Ray ◽  
Microstructural Parameters ◽  
Diffraction Contrast ◽  
Sample Distance

Laboratory diffraction contrast tomography (LabDCT) is a recently developed technique to map crystallographic orientations of polycrystalline samples in three dimensions non-destructively using a laboratory X-ray source. In this work, a new theoretical procedure, named LabXRS, expanding LabDCT to include mapping of the deviatoric strain tensors on the grain scale, is proposed and validated using simulated data. For the validation, the geometries investigated include a typical near-field LabDCT setup utilizing Laue focusing with equal source-to-sample and sample-to-detector distances of 14 mm, a magnified setup where the sample-to-detector distance is increased to 200 mm, a far-field Laue focusing setup where the source-to-sample distance is also increased to 200 mm, and a near-field setup with a source-to-sample distance of 200 mm. The strain resolution is found to be in the range of 1–5 × 10−4, depending on the geometry of the experiment. The effects of other experimental parameters, including pixel binning, number of projections and imaging noise, as well as microstructural parameters, including grain position, grain size and grain orientation, on the strain resolution are examined. The dependencies of these parameters, as well as the implications for practical experiments, are discussed.

X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case

2008 ◽  
Vol 41 (2) ◽  
pp. 302-309 ◽  
Author(s):  
Wolfgang Ludwig ◽  
Søeren Schmidt ◽  
Erik Mejdal Lauridsen ◽  
Henning Friis Poulsen
Keyword(s):  
Three Dimensional ◽  
Reconstruction Technique ◽  
X Ray Diffraction ◽  
X Ray ◽  
Direct Beam ◽  
Novel Technique ◽  
Diffraction Contrast ◽  
Orientation Space ◽  
Grain Orientations ◽  
Projection Images

The principles of a novel technique for nondestructive and simultaneous mapping of the three-dimensional grain and the absorption microstructure of a material are explained. The technique is termed X-ray diffraction contrast tomography, underlining its similarity to conventional X-ray absorption contrast tomography with which it shares a common experimental setup. The grains are imaged using the occasionally occurring diffraction contribution to the X-ray attenuation coefficient each time a grain fulfils the diffraction condition. The three-dimensional grain shapes are reconstructed from a limited number of projections using an algebraic reconstruction technique. An algorithm based on scanning orientation space and aiming at determining the corresponding crystallographic grain orientations is proposed. The potential and limitations of a first approach, based on the acquisition of the direct beam projection images only, are discussed in this first part of the paper. An extension is presented in the second part of the paper [Johnson, King, Honnicke, Marrow & Ludwig (2008).J. Appl. Cryst.41, 310–318], addressing the case of combined direct and diffracted beam acquisition.

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.

Adaptive reconstruction method for three-dimensional orientation imaging

2013 ◽  
Vol 46 (2) ◽  
pp. 512-524 ◽  
Author(s):  
S. F. Li ◽  
R. M. Suter
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Real Data ◽  
Reconstruction Algorithm ◽  
High Energy ◽  
Real Space ◽  
Reconstruction Method ◽  
Orientation Imaging ◽  
Orientation Space ◽  
Spatially Adaptive

An adaptive orientation reconstruction algorithm is developed for near-field high-energy X-ray diffraction microscopy. When combined with a spatially adaptive extension the algorithm results in a factor of 10–1000 speed-up over the existing forward modeling reconstruction method while preserving most of the spatial and orientation resolution characteristics. Tests of the reconstruction code based on simulated structures and real data on a complex microstructure are presented. Simulated structures include intra-granular orientation gradients and noisy detector images. It is shown that resolution in both real space and orientation space degrades gracefully as complexity and detector noise increase.

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.

Novel Near Field Detector for Three-Dimensional X-Ray Diffraction Microscopy

MRS Advances ◽  
2018 ◽  
Vol 3 (39) ◽  
pp. 2341-2346 ◽  
Author(s):  
Scott Annett ◽  
Sergio Morelhao ◽  
Darren Dale ◽  
Stefan Kycia
Keyword(s):  
New Technologies ◽  
Spatial Information ◽  
Near Field ◽  
Three Dimensional ◽  
High Energy ◽  
Field Of View ◽  
Large Field ◽  
X Ray Diffraction ◽  
Synchrotron Source ◽  
X Ray

AbstractThree dimensional X-ray diffraction (3DXRD) microscopy is a powerful technique that provides crystallographic and spatial information of a large number, of the order of thousands, of crystalline grains in a sample simultaneously. A key component of every 3DXRD microscopy experiment is the near field detector that provides high resolution spatial information of the grains. In this work we present a novel design for a semi-transparent, 16 megapixel near field detector. As opposed to a typical single scintillator phosphor detector, this design, we call the Quad Near Field Detector, uses four quadrants. It has a total field of view is 5.3 mm x 5.3 mm with an effective pixel size of 1.3 µm x 1.3 µm. The detector’s relatively large field of view can be used to obtain higher order diffraction spots which we anticipate will lead to improved spatial resolution in grain reconstructions. The large field of view can also enable the detector to be positioned further from the sample, in this way increasing the working distance and enabling larger environmental cells for in-situ studies. Many alignment parameters can be resolved by careful mechanical design. For this reason a novel translation stage for focusing the microscopes was developed, tested, and implemented. The near field detector was calibrated and characterized at the Cornell High Energy Synchrotron Source. The operational feasibility of such a multi-plate detector demonstrated in this work paves the way for new technologies in instrumentation of 3DXRD microscopy.

scholarly journals Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements

2018 ◽  
Vol 74 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Marianne Liebi ◽  
Marios Georgiadis ◽  
Joachim Kohlbrecher ◽  
Mirko Holler ◽  
Jörg Raabe ◽  
...  
Keyword(s):  
Small Angle ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Reciprocal Space ◽  
Mathematical Framework ◽  
X Ray ◽  
Tensor Tomography ◽  
X Ray Scattering ◽  
Degree Of Orientation ◽  
Ray Scattering

Small-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebiet al.[Nature(2015),527, 349–352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transferqrange. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges ofq. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.

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