What is the way to determine the fit of a grain set?

Based on the relatively high number of pairs per grain, outliers can be rejected on a purely statistical basis by determining whether they fit in the observed distributions.

How can the authors measure diffraction angles in grain-by-grain samples?

By optimizing the experimental conditions, it is possible to achieve sufficient accuracy in the determination of the diffraction angles to measure elastic lattice strains on a grain-by-grain basis in an in situ loaded sample.

What is the advantage of 3D scanning?

Since the 3D scanning procedure isolates the signal from small volume elements, this method can be applied to plastically deformed specimen and provides access to local orientation and deviatoric components of the elastic strain tensor.

How many grains were recovered by the heat treatment?

The heat treatment allowed recovery of any residual stresses or plastic deformation introduced during sample manufacture and increased the average beta grain size to 55 m.

How many diffraction spots can be produced?

each set of lattice planes can give rise to a maximum of four diffraction spots, which make up two pairs, each separated by a 180° rotation of the sample.

How does the algorithm find diffraction spots?

This uses all spatial and crystallographic cri-teria simultaneously to form consistent sets, in a reliable and computationally efficient manner, of diffraction spot pairs belonging to the same grain.

How can the accuracy of the DCT map be assessed?

The accuracy with which diffraction data are observed can be assessed using the redundant measurements of the scattering vectors from which two Friedel pairs are observed.

What is the way to reconstruct grain maps?

As opposed to the inverse reconstruction approach presented in the current paper, one may envisage reconstruction of grain maps by forward simulation approaches.

What is the angle between a given grain and the incident beam?

During the rotation of the sample, the angle between a given crystal plane of a grain and the incident beam varies sinusoidally between zero and some maximum value.

Open AccessJournal Article10.1063/1.3100200

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

Wolfgang Ludwig, +7 more

- 19 Mar 2009

- Review of Scientific Instruments

- Vol. 80, Iss: 3, pp 033905-033905

291

TL;DR: A modified DCT data acquisition strategy is described which permits the incorporation of an innovative Friedel pair method for analyzing diffraction data, resulting in an increase in the accuracy with which the diffraction vectors are determined.

Abstract: X-ray diffraction contrast tomography (DCT) is a technique for mapping grain shape and orientation in plastically undeformed polycrystals. In this paper, we describe a modified DCT data acquisition strategy which permits the incorporation of an innovative Friedel pair method for analyzing diffraction data. Diffraction spots are acquired during a 360 degrees rotation of the sample and are analyzed in terms of the Friedel pairs ((hkl) and (hkl) reflections, observed 180 degrees apart in rotation). The resulting increase in the accuracy with which the diffraction vectors are determined allows the use of improved algorithms for grain indexing (assigning diffraction spots to the grains from which they arise) and reconstruction. The accuracy of the resulting grain maps is quantified with reference to synchrotron microtomography data for a specimen made from a beta titanium system in which a second phase can be precipitated at grain boundaries, thereby revealing the grain shapes. The simple changes introduced to the DCT methodology are equally applicable to other variants of grain mapping.

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Most frequently asked questions

1. What have the authors contributed in "Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of friedel pairs in diffraction data analysis" ?

The DCT methodology presented in this paper represents significant progress over previous versions of the DCT and can be more readily automated than previously.

2. What future works have the authors mentioned in the paper "Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of friedel pairs in diffraction data analysis" ?

The improved determination of diffraction angles using Friedel pairs opens the possibility of achieving sensitivity to elastic strain at the level of individual grains.

3. What is the way to measure the grain structure in polycrystalline materials?

Polychromatic x-ray diffraction in combination with differential aperture x-ray microscopy13,14 is a powerful tool for probing the 3D grain structure in polycrystalline materials at the submicrometer length scale.

4. Why was the acquisition of the DCT scan performed in the initial state before heat treatment?

Since precipitation may entail an increase of the local effective misorientation inside grains, the acquisition of the DCT scan was performed in the initial state before heat treatment.

FIG. 1. Schematic of the DCT setup. The detector is placed close behind the sample so that both transmitted and diffracted beams are caught.

FIG. 2. Representation of a Friedel pair in the reference fixed to the sample. Diffraction spot A appears at . Its pair, spot B, is shown on the opposite imaginary detector plane at +180°. The diffraction path connecting both passes through the grain of origin.

FIG. 5. Color online Rendition of the 3D grain structure in a cylindrical beta-Ti specimen containing 1008 grains, as obtained by the DCT processing route described in this paper.

FIG. 6. Cross section through the PCT reconstruction. The -phase appears dark. It precipitated during a heat treatment for 24 h at 790 °C performed after acquisition of the DCT scan. The rectangle marks the area on which the image processing for the completion of grain boundaries is illustrated Fig. 7 .

FIG. 7. Image processing steps for the completion of the grain boundaries not visible in PCT. a Shows the original PCT image after median filtering and contrast enhancement. One grain boundary is not visible and shall be completed. First, the grain boundaries are labeled semiautomatically as far as visible b . The overlay of the slimmed labeled grain boundaries with the DCT image c shows that some DCT grains extend over the grain boundaries. Those parts have to be removed d before the DCT image can be used as marker image for the watershed algorithm. e The missing grain boundary was completed. Note that the originally labeled grain boundaries remain unaffected by the algorithm. The accuracy of DCT was determined from the completed network of grain boundaries and the DCT data f . The average error for the grain shown in this figure is 4.1 voxels or 2.3 m .

FIG. 4. Flow chart of the iterative indexing procedure

Citations

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Quantitative X-ray tomography

Eric Maire, +1 more

- 09 Jan 2014

- International Materials Reviews

TL;DR: In this paper, the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight than conventional attenuation based tomography.

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In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics

Jean-Yves Buffiere, +4 more

- 28 Jan 2010

- Experimental Mechanics

TL;DR: In this article, the potential of X-ray tomography for studying the mechanical behavior of materials through in situ experiments is illustrated; typical experimental tomography set ups which use laboratory and synchrotron X ray sources are described; advantages and limitations of both types of sources are presented.

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469

•Journal Article•10.1038/S41524-019-0267-Z

Machine learning enabled autonomous microstructural characterization in 3D samples

Henry Chan, +6 more

- 06 Jan 2020

TL;DR: This work introduces an unsupervised machine learning (ML) based technique for the identification and characterization of microstructures in three-dimensional samples obtained from molecular dynamics simulations, particle tracking data, or experiments that combines topology classification, image processing, and clustering algorithms.

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422

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Dark-field X-ray microscopy for multiscale structural characterization

Hugh Simons, +8 more

- 14 Jan 2015

- Nature Communications

TL;DR: Dark-field X-ray microscopy; a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses on lengths scales from 100 nm to 1 mm within embedded sampling volumes is presented.

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Book•10.1002/9783527631483

Crystal Plasticity Finite Element Methods: In Materials Science and Engineering

Franz Roters, +3 more

- 13 Oct 2010

TL;DR: In the field of CPFE Experimental Validation Stability and Grain Fragmentation in Aluminum under Plane Strain Deformation Texture and Dislocation Density Evolution in a Bent Single-Crystalline Copper-Nanowire Texture and Microstructure underneath a Nanoindent in a Copper Single Crystal Application of a Non-local Dislocations Model including Geometrically Necessary Dislocating to Simple Shear Tests of Aluminum Single Crystals application of a Grain Boundary Constitutive Model to Simple shear tests of Aluminum Bicrystals with different Misorient

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References

Journal Article•10.1038/415887A

Three-dimensional X-ray structural microscopy with submicrometre resolution

Bennett C. Larson, +4 more

- 21 Feb 2002

- Nature

TL;DR: A three-dimensional X-ray microscopy technique that uses polychromatic synchrotron X-rays to probe local crystal structure, orientation and strain tensors with submicrometre spatial resolution is described, applicable to single-crystal, polycrystalline, composite and functionally graded materials.

...read moreread less

757

Journal Article•10.1063/1.364374

Observation of microstructure and damage in materials by phase sensitive radiography and tomography

Peter Cloetens, +6 more

- 01 May 1997

- Journal of Applied Physics

TL;DR: In this paper, phase jumps related to the interface between the matrix and the reinforcing phases of the composites are detected even when these phases show very similar x-ray attenuation, illustrating the potential of the technique for assessing damage in materials with improved resolution and sensitivity.

...read moreread less

568

•Journal Article•10.1126/SCIENCE.1156211

Observations of intergranular stress corrosion cracking in a grain-mapped polycrystal.

Andrew T. King, +6 more

- 18 Jul 2008

- Science

TL;DR: Several sensitization-resistant crack-bridging boundaries were identified, and although they have special geometric properties, they are not the twin variant boundaries usually maximized during grain boundary engineering.

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505

Book•10.1007/B97884

Three-Dimensional X-Ray Diffraction Microscopy

Henning Friis Poulsen

- 01 Jan 2004

417

Journal Article•10.1063/1.2783112

Invited article: The fast readout low noise camera as a versatile x-ray detector for time resolved dispersive extended x-ray absorption fine structure and diffraction studies of dynamic problems in materials science, chemistry, and catalysis

Jean-Claude Labiche, +8 more

- 17 Sep 2007

- Review of Scientific Instruments

TL;DR: It is demonstrated that in this mode the FReLoN can be applied equally to the investigation of rapid changes in long range order and local order and in situations of x-ray hardness and flux beyond the capacity of other detectors.

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411

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

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Most frequently asked questions

1. What have the authors contributed in "Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of friedel pairs in diffraction data analysis" ?

2. What future works have the authors mentioned in the paper "Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of friedel pairs in diffraction data analysis" ?

3. What is the way to measure the grain structure in polycrystalline materials?

4. Why was the acquisition of the DCT scan performed in the initial state before heat treatment?

5. What is the way to determine the fit of a grain set?

6. How can the authors measure diffraction angles in grain-by-grain samples?

7. What is the advantage of 3D scanning?

8. How many grains were recovered by the heat treatment?

9. How many diffraction spots can be produced?

10. How does the algorithm find diffraction spots?

11. How can the accuracy of the DCT map be assessed?

12. What is the way to reconstruct grain maps?

13. What is the angle between a given grain and the incident beam?

Figures

Citations

Quantitative X-ray tomography

In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics

Machine learning enabled autonomous microstructural characterization in 3D samples

Dark-field X-ray microscopy for multiscale structural characterization

Crystal Plasticity Finite Element Methods: In Materials Science and Engineering

References

Three-dimensional X-ray structural microscopy with submicrometre resolution

Observation of microstructure and damage in materials by phase sensitive radiography and tomography

Observations of intergranular stress corrosion cracking in a grain-mapped polycrystal.

Three-Dimensional X-Ray Diffraction Microscopy

Invited article: The fast readout low noise camera as a versatile x-ray detector for time resolved dispersive extended x-ray absorption fine structure and diffraction studies of dynamic problems in materials science, chemistry, and catalysis

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