Characteristics of Friedel pairs and diffraction contrast tomography with non-perpendicular rotation axis

2015 ◽  
Vol 22 (4) ◽  
pp. 1062-1071 ◽  
Author(s):  
Qiru Yi ◽  
Gang Li ◽  
Jie Zhang ◽  
Sheng-Nian Luo ◽  
Duan Fan ◽  
...  
Keyword(s):  
Rotation Axis ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Polycrystalline Sample ◽  
Reconstruction Technique ◽  
Pure Aluminium ◽  
Axis Orientation ◽  
X Ray ◽  
Diffraction Contrast ◽  
Detector Distance

The characteristics of Friedel pairs in diffraction contrast tomography (DCT) are studied in the condition that the rotation axis of the sample is not exactly perpendicular to the incident X-ray direction. For the rotation axis approximately aligned along the vertical direction, the Friedel pairs close to the horizontal plane are insensitive to the non-perpendicularity of the rotation axis, and can be used to refine the sample-to-detector distance and X-ray energy, while the Friedel pairs close to the vertical direction are sensitive to the non-perpendicularity of the rotation axis, and can be used to determine the rotation axis orientation. The correct matching proportion of Friedel pairs decreases with increasing non-perpendicularity of the rotation axis. A method of data processing considering rotation axis misalignment is proposed, which significantly increases the correct matching and indexing proportions of the diffraction spots. A pure aluminium polycrystalline sample is investigated using DCT at beamline 4W1A of Beijing Synchrotron Radiation Facility. Based on the analysis of Friedel pairs, the sample-to-detector distance and X-ray energy are refined to be 8.67 mm and 20.04 keV, respectively. The non-perpendicular angle of the rotation axis is calculated to be 0.10°. With these refined geometric parameters, the matching proportion of the spatial position of diffraction spots is 90.62%. Three-dimensional reconstruction of the sample with 13 grains is realised using the algebraic reconstruction technique. It is demonstrated that the precise correction of the orientation of the sample rotation axis is effective in DCT suffering from rotation axis misalignment, and the higher accuracy in determining the rotation axis is expected to improve the reconstruction precision of grains.

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.

A modified discrete tomography for improving the reconstruction of unknown multi-gray-level material in the `missing wedge' situation

2018 ◽  
Vol 25 (6) ◽  
pp. 1847-1859 ◽  
Author(s):  
Jianhong Liu ◽  
Zhiting Liang ◽  
Yong Guan ◽  
Wenbin Wei ◽  
Haobo Bai ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Iteration Process ◽  
Reconstruction Technique ◽  
Morphological Operations ◽  
Algebraic Reconstruction Technique ◽  
Discrete Tomography ◽  
Boundary Extraction ◽  
X Ray ◽  
Dimensional Reconstruction

Full angular rotational projections cannot always be acquired in tomographic reconstructions because of the limited space in the experimental setup, leading to the `missing wedge' situation. In this paper, a recovering `missing wedge' discrete algebraic reconstruction technique algorithm (rmwDART) has been proposed to solve the `missing wedge' problem and improve the quality of the three-dimensional reconstruction without prior knowledge of the material component's number or the material's values. By using oversegmentation, boundary extraction and mathematical morphological operations, `missing wedge' artifact areas can be located. Then, in the iteration process, by updating the located areas and regions, high-quality reconstructions can be obtained from the simulations, and the reconstructed images based on the rmwDART algorithm can be obtained from soft X-ray nano-computed tomography experiments. The results showed that there is the potential for discrete tomography.

X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. II. The combined case

2008 ◽  
Vol 41 (2) ◽  
pp. 310-318 ◽  
Author(s):  
Greg Johnson ◽  
Andrew King ◽  
Marcelo Goncalves Honnicke ◽  
J. Marrow ◽  
Wolfgang Ludwig
Keyword(s):  
Electron Backscatter Diffraction ◽  
Three Dimensional ◽  
Real Data ◽  
X Ray Diffraction ◽  
Data Set ◽  
Transmitted Beam ◽  
X Ray ◽  
Diffraction Contrast ◽  
Simultaneous Acquisition ◽  
Backscatter Diffraction

By simultaneous acquisition of the transmitted and the diffracted beams, the applicability of the previously introduced diffraction contrast tomography technique [Ludwig, Schmidt, Lauridsen & Poulsen (2008).J. Appl. Cryst.41, 302–309] can be extended to the case of undeformed polycrystalline samples containing more than 100 grains per cross section. The grains are still imaged using the occasionally occurring diffraction contribution to the X-ray attenuation coefficient, which can be observed as a reduction in the intensity of the transmitted beam when a grain fulfils the diffraction condition. Automating the segmentation of the extinction spot images is possible with the additional diffracted beam information, even in the presence of significant spot overlap. By pairing the corresponding direct (`extinction') and diffracted beam spots a robust sorting and indexing approach has been implemented. The analysis procedure is illustrated on a real data set and the result is validated by comparison with a two-dimensional grain map obtained by electron backscatter diffraction.

Scanning texture analysis of lamellar bone using microbeam synchrotron X-ray radiation

2007 ◽  
Vol 40 (1) ◽  
pp. 115-120 ◽  
Author(s):  
Wolfgang Wagermaier ◽  
Himadri S. Gupta ◽  
Aurélien Gourrier ◽  
Oskar Paris ◽  
Paul Roschger ◽  
...  
Keyword(s):  
Texture Analysis ◽  
Three Dimensional ◽  
Compact Bone ◽  
Axis Orientation ◽  
Thin Sections ◽  
X Ray ◽  
Synthetic Materials ◽  
Mineralized Tissues ◽  
Lamellar Texture ◽  
Dimensional Distribution

Texture analysis with microbeam scanning diffraction enables the local mapping of three-dimensional crystallite orientation in heterogeneous natural and synthetic materials. Cortical (compact) bone is an example of a hierarchically structured biocomposite, which is built mainly of cylindrical osteons, having a lamellar texture at the micrometre level. In this work, a combination of microbeam synchrotron X-ray texture analysis with thin sections of osteonal bone is used to measure the three-dimensional distribution of thec-axis orientation of the mineral apatite in bone with positional resolution of 1 µm. The data reduction procedure needed to go from the stereographic projection of X-ray intensity to the determination of the local orientation of mineralized collagen fibrils is described. The procedure can be applied to other mineralized tissues (such as trabecular bone and chitin) with micrometre scale and biologically controlled fibrillar texture.

Evaluation of grain-average stress tensor in a tensile-deformed Al–Mn polycrystal by high-energy X-ray diffraction

2017 ◽  
Vol 50 (4) ◽  
pp. 1144-1157 ◽  
Author(s):  
Loïc Renversade ◽  
András Borbély
Keyword(s):  
Rotation Axis ◽  
Three Dimensional ◽  
Calibration Method ◽  
High Energy ◽  
Normal Strain ◽  
X Ray Diffraction ◽  
Synchrotron Source ◽  
X Ray ◽  
Strain Stress ◽  
Individual Grains

Three-dimensional X-ray diffraction was applied to characterize the strain/stress evolution in individual grains of an Al–0.3 wt% Mn polycrystal deformedin situat a synchrotron source. Methodological aspects concerning the calibration of the geometrical setup and the evaluation of the strain/stress tensors are discussed. A two-step calibration method separately treating the detector and the rotation axis allows one to determine the centre-of-mass position and crystallographic orientation of grains with standard errors of about 1.5 µm and 0.02°, respectively. Numerical simulations indicate that the error of normal strain components (about 1 × 10−4) is mainly caused by calibration errors, while the error of shear components (about 0.5 × 10−4) is largely influenced by counting statistics and random spot-centre errors due to detector distortion. The importance of monitoring the beam energy is emphasized.

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.

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 Synthesis and crystal structure of (1,4,7,10-tetraazacyclododecane-κ4 N)(tetrasulfido-κ2 S 1,S 4)manganese(II)

2020 ◽  
Vol 76 (3) ◽  
pp. 456-460
Author(s):  
Felix Danker ◽  
Christian Näther ◽  
Wolfgang Bensch
Keyword(s):  
Hydrogen Bonding ◽  
Title Compound ◽  
Hydrothermal Reaction ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Synthesis And Crystal Structure ◽  
X Ray ◽  
Dimensional Network ◽  
Using Data ◽  
Similar Complex

The title compound, [Mn(S4)(C8H20N4)], was accidentally obtained by the hydrothermal reaction of Mn(ClO4)2·6H2O, cyclen (cyclen = 1,4,7,10-tetraazacyclododecane) and Na3SbS4·9H2O in water at 413 K, indicating that polysulfide anions might represent intermediates in the synthesis of thiometallate compounds using Na3SbS4·9H2O as a reactant. X-ray powder diffraction proves that the sample is slightly contaminated with NaSb(OH)6 and an unknown crystalline phase. The crystal investigated was twinned with a twofold rotation axis as the twin element, and therefore a twin refinement using data in HKLF-5 format was performed. The asymmetric unit of the title compound consists of one MnII cation, one [S4]2− anion and one cyclen ligand in general positions. The MnII cation is sixfold coordinated by two cis-S atoms of the [S4]2− anions, as well as four N atoms of the cyclen ligand within an irregular coordination. The complexes are linked via pairs of N—H...S hydrogen bonds into chains, which are further linked into layers by additional N—H...S hydrogen bonding. These layers are connected into a three-dimensional network by intermolecular N—H...S and C—H...S hydrogen bonding. It is noted that only one similar complex with MnII is reported in the literature.

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