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.

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.

scholarly journals A flexible and standalone forward simulation model for laboratory X-ray diffraction contrast tomography

2020 ◽  
Vol 76 (6) ◽  
pp. 652-663 ◽  
Author(s):  
H. Fang ◽  
D. Juul Jensen ◽  
Y. Zhang
Keyword(s):  
Crystal Structure ◽  
Simulation Model ◽  
Forward Simulation ◽  
X Ray Diffraction ◽  
Bulk Materials ◽  
X Ray ◽  
Diffraction Contrast ◽  
Input Structure ◽  
Grain Orientations ◽  
Non Destructive

Laboratory X-ray diffraction contrast tomography (LabDCT) has recently been developed as a powerful technique for non-destructive mapping of grain microstructures in bulk materials. As the grain reconstruction relies on segmentation of diffraction spots, it is essential to understand the physics of the diffraction process and resolve all the spot features in detail. To this aim, a flexible and standalone forward simulation model has been developed to compute the diffraction projections from polycrystalline samples with any crystal structure. The accuracy of the forward simulation model is demonstrated by good agreements in grain orientations, boundary positions and shapes between a virtual input structure and that reconstructed based on the forward simulated diffraction projections of the input structure. Further experimental verification is made by comparisons of diffraction spots between simulations and experiments for a partially recrystallized Al sample, where a satisfactory agreement is found for the spot positions, sizes and intensities. Finally, applications of this model to analyze specific spot features are presented.

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.

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.

scholarly journals Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

2009 ◽  
Vol 80 (3) ◽  
pp. 033905 ◽  
Author(s):  
W. Ludwig ◽  
P. Reischig ◽  
A. King ◽  
M. Herbig ◽  
E. M. Lauridsen ◽  
...  
Keyword(s):  
Data Analysis ◽  
Diffraction Data ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Contrast

scholarly journals 3D grain reconstruction from laboratory diffraction contrast tomography

2019 ◽  
Vol 52 (3) ◽  
pp. 643-651 ◽  
Author(s):  
Florian Bachmann ◽  
Hrishikesh Bale ◽  
Nicolas Gueninchault ◽  
Christian Holzner ◽  
Erik Mejdal Lauridsen
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Grain Structure ◽  
X Ray Diffraction ◽  
Shape Information ◽  
X Ray ◽  
Reconstruction Scheme ◽  
Diffraction Contrast ◽  
Tomography System ◽  
Diffraction Geometry

A method for reconstructing the three-dimensional grain structure from data collected with a recently introduced laboratory-based X-ray diffraction contrast tomography system is presented. Diffraction contrast patterns are recorded in Laue-focusing geometry. The diffraction geometry exposes shape information within recorded diffraction spots. In order to yield the three-dimensional crystallographic microstructure, diffraction spots are extracted and fed into a reconstruction scheme. The scheme successively traverses and refines solution space until a reasonable reconstruction is reached. This unique reconstruction approach produces results efficiently and fast for well suited samples.

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 grain structure of sintered bulk strontium titanate from X-ray diffraction contrast tomography

2012 ◽  
Vol 66 (1) ◽  
pp. 1-4 ◽  
Author(s):  
M. Syha ◽  
W. Rheinheimer ◽  
M. Bäurer ◽  
E.M. Lauridsen ◽  
W. Ludwig ◽  
...  
Keyword(s):  
Strontium Titanate ◽  
Three Dimensional ◽  
Grain Structure ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Contrast
Sign in / Sign up

Export Citation Format

Share Document