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.

Three-Dimensional Electron Density Mapping of Shape-Controlled Nanoparticle by Focused Hard X-ray Diffraction Microscopy

Nano Letters ◽  
2010 ◽  
Vol 10 (5) ◽  
pp. 1922-1926 ◽  
Author(s):  
Yukio Takahashi ◽  
Nobuyuki Zettsu ◽  
Yoshinori Nishino ◽  
Ryosuke Tsutsumi ◽  
Eiichiro Matsubara ◽  
...  
Keyword(s):  
Electron Density ◽  
Three Dimensional ◽  
Dimensional Electron ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Mapping ◽  
Shape Controlled ◽  
Diffraction Microscopy

D068 Three-Dimensional X-ray Diffraction Microscopy of Grain Boundaries

2003 ◽  
Vol 18 (2) ◽  
pp. 172-172
Author(s):  
W. Liu ◽  
G. E. Ice ◽  
W. Yang ◽  
J. Z. Tischler ◽  
B. C. Larson
Keyword(s):  
Grain Boundaries ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Microscopy

Second Order Stresses Distribution in Textured Copper

2006 ◽  
Vol 524-525 ◽  
pp. 859-864
Author(s):  
Neila Hfaiedh ◽  
Manuel François ◽  
Khemais Saanouni
Keyword(s):  
Peak Position ◽  
Second Order ◽  
Polycrystalline Materials ◽  
Internal Stresses ◽  
Plastic Strains ◽  
Sensitive Detector ◽  
X Ray Diffraction ◽  
X Ray ◽  
Position Sensitive ◽  
Specific Correction

Internal stresses are an important factor in understanding the work hardening behaviour of polycrystalline materials. The goal of the present paper is to study the development of second order stresses in textured copper sheets at large plastic strains, up to fracture by X-ray diffraction. Second order stresses manifest themselves as peak displacements and width changes as azimuth and tilt angles are varied. As the acquisition is performed with a position sensitive detector, a specific correction of intensities is required in order to take into account texture influence on peak shape and consequently on peak position and width.

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.

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