Three-Dimensional X-Ray Diffraction Microscopy Using High-Energy X-Rays

MRS Bulletin ◽  
2004 ◽  
Vol 29 (3) ◽  
pp. 166-169 ◽  
Author(s):  
Henning F. Poulsen ◽  
Dorte Juul Jensen ◽  
Gavin B.M. Vaughan
Keyword(s):  
Materials Science ◽  
Three Dimensional ◽  
High Energy ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Reconstruction Methods ◽  
The Individual ◽  
Individual Grains

AbstractThree-dimensional x-ray diffraction (3DXRD) microscopy is a tool for fast and nondestructive characterization of the individual grains, subgrains, and domains inside bulk materials. The method is based on diffraction with very penetrating hard x-rays (E ≥ 50 keV), enabling 3D studies of millimeter-to-centimeter-thick specimens.The position, volume, orientation, and elastic and plastic strain can be derived for hundreds of grains simultaneously. Furthermore, by applying novel reconstruction methods, 3D maps of the grain boundaries can be generated. The 3DXRD microscope in use at the European Synchrotron Radiation Facility in Grenoble, France, has a spatial resolution of ∼5 μm and can detect grains as small as 150 nm. The technique enables, for the first time, dynamic studies of the individual grains within polycrystalline materials. In this article, some fundamental materials science applications of 3DXRD are reviewed: studies of nucleation and growth kinetics during recrystallization, recovery, and phase transformations, as well as studies of polycrystal deformation.

3DXRD – Mapping Grains and Their Dynamics in 3 Dimensions

2004 ◽  
Vol 467-470 ◽  
pp. 1363-1372 ◽  
Author(s):  
Henning Friis Poulsen ◽  
Xing Fu ◽  
Erik Knudsen ◽  
Erik M. Lauridsen ◽  
L. Margulies ◽  
...  
Keyword(s):  
European Synchrotron Radiation Facility ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Time Dynamic ◽  
3 Dimensional ◽  
Reconstruction Methods ◽  
Set Up ◽  
The Individual ◽  
Individual Grains

3-Dimensional X-Ray Diffraction (3DXRD) microscopy is a tool for fast and non-destructive characterization of the individual grains, sub-grains and domains inside bulk materials. The method is based on diffraction with highly penetrating hard x-rays, enabling 3D studies of millimeter - centimeter thick specimens. The position, volume, orientation, elastic and plastic strain can be derived for hundreds of grains simultaneously. Furthermore, by applying novel reconstruction methods 3D maps of the grain boundaries can be generated. With the present 3DXRD microscope set-up at the European Synchrotron Radiation Facility, the spatial resolution is ~ 5 µm, while grains of size 100 nm can be detected. 3DXRD microscopy enables, for the first time, dynamic studies of the individual grains and sub-grains within polycrystalline materials. The methodology is reviewed with emphasis on recent advances in grain mapping. Based on this a series of general 3DXRD approaches are identified for studies of nucleation and growth phenomena such as recovery, recrystallisation and grain growth in metals.

An introduction to three-dimensional X-ray diffraction microscopy

2012 ◽  
Vol 45 (6) ◽  
pp. 1084-1097 ◽  
Author(s):  
Henning Friis Poulsen
Keyword(s):  
Materials Science ◽  
Strain Tensor ◽  
Three Dimensional ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
X Ray Diffraction ◽  
Synchrotron Source ◽  
X Ray ◽  
The Individual ◽  
Diffraction Microscopy

Three-dimensional X-ray diffraction microscopy is a fast and nondestructive structural characterization technique aimed at studies of the individual crystalline elements (grains or subgrains) within millimetre-sized polycrystalline specimens. It is based on two principles: the use of highly penetrating hard X-rays from a synchrotron source and the application of `tomographic' reconstruction algorithms for the analysis of the diffraction data. In favourable cases, the position, morphology, phase and crystallographic orientation can be derived for up to 1000 elements simultaneously. For each grain its average strain tensor may also be derived, from which the type II stresses can be inferred. Furthermore, the dynamics of the individual elements can be monitored during typical processes such as deformation or annealing. A review of the field is provided, with a viewpoint from materials science.

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.

scholarly journals Utilizing broadband X-rays in a Bragg coherent X-ray diffraction imaging experiment

2016 ◽  
Vol 23 (5) ◽  
pp. 1241-1244 ◽  
Author(s):  
Wonsuk Cha ◽  
Wenjun Liu ◽  
Ross Harder ◽  
Ruqing Xu ◽  
Paul H. Fuoss ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Individual Crystal ◽  
Sample Motion ◽  
Diffraction Imaging ◽  
Individual Grains

A method is presented to simplify Bragg coherent X-ray diffraction imaging studies of complex heterogeneous crystalline materials with a two-stage screening/imaging process that utilizes polychromatic and monochromatic coherent X-rays and is compatible within situsample environments. Coherent white-beam diffraction is used to identify an individual crystal particle or grain that displays desired properties within a larger population. A three-dimensional reciprocal-space map suitable for diffraction imaging is then measured for the Bragg peak of interest using a monochromatic beam energy scan that requires no sample motion, thus simplifyingin situchamber design. This approach was demonstrated with Au nanoparticles and will enable, for example, individual grains in a polycrystalline material of specific orientation to be selected, then imaged in three dimensions while under load.

scholarly journals Intragranular strain estimation in far-field scanning X-ray diffraction using a Gaussian process

2021 ◽  
Vol 54 (4) ◽  
Author(s):  
Axel Henningsson ◽  
Johannes Hendriks
Keyword(s):  
Gaussian Process ◽  
Strain Field ◽  
A Priori ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Polycrystalline Specimen ◽  
X Ray ◽  
Reconstruction Methods ◽  
Mean Square Errors

A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction (scanning 3DXRD) data is presented and evaluated. Given an a priori known anisotropic compliance, the regression method enforces the balance of linear and angular momentum in the linear elastic strain field reconstruction. By using a Gaussian process (GP), the presented method can yield a spatial estimate of the uncertainty of the reconstructed strain field. Furthermore, constraints on spatial smoothness can be optimized with respect to measurements through hyperparameter estimation. These three features address weaknesses discussed for previously existing scanning 3DXRD reconstruction methods and, thus, offer a more robust strain field estimation. The method is twofold validated: firstly by reconstruction from synthetic diffraction data, and secondly by reconstruction of a previously studied tin (Sn) grain embedded in a polycrystalline specimen. Comparison against reconstructions achieved by a recently proposed algebraic inversion technique is also presented. It is found that the GP regression consistently produces reconstructions with lower root-mean-square errors, mean absolute errors and maximum absolute errors across all six components of strain.

Metal Microstructures in Four Dimensions

2004 ◽  
Author(s):  
S. F. Nielsen ◽  
C. Gundlach ◽  
E. M. Lauridsen ◽  
R. V. Martins ◽  
H. F. Poulsen ◽  
...  
Keyword(s):  
Grain Growth ◽  
Three Dimensional ◽  
High Energy ◽  
Third Generation ◽  
Plastic Strains ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Four Dimensions

By Three Dimensional X-ray Diffraction (3DXRD) microscopy it is possible to characterize microstructures non-destructively in 3 dimensions. The measurements are furthermore typically so fast that dynamics may be monitored in-situ, giving also the 4th dimension, namely the time. The 3DXRD technique is based on diffraction of high energy x-rays from third generation synchrotron sources. In the present paper the 3DXRD technique is described and it’s potentials are illustrated by examples relating to elastic and plastic strains, recovery, recrystallization and grain growth.

scholarly journals High-Energy X-Ray Diffraction Microscopy in Materials Science

2020 ◽  
Vol 50 (1) ◽  
pp. 395-436 ◽  
Author(s):  
Joel V. Bernier ◽  
Robert M. Suter ◽  
Anthony D. Rollett ◽  
Jonathan D. Almer
Keyword(s):  
Materials Science ◽  
Three Dimensional ◽  
High Energy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Grain Boundary Character ◽  
Orientation Fields ◽  
Orientation Distributions ◽  
Development Orientation ◽  
Diffraction Microscopy

High-energy diffraction microscopy (HEDM) is an implementation of three-dimensional X-ray diffraction microscopy. HEDM yields maps of internal crystal orientation fields, strain states, grain shapes and locations as well as intragranular orientation distributions, and grain boundary character. Because it is nondestructive in hard materials, notably metals and ceramics, HEDM has been used to study responses of these materials to external fields including high temperature and mechanical loading. Currently available sources and detectors lead to a spatial resolution of ∼1 μm and an orientation resolution of <0.1○. With the penetration characteristic of high energies ( E ≥ 50 keV), sample cross-section dimensions of ∼1 mm can be studied in materials containing elements across much of the Periodic Table. This review describes hardware and software associated with HEDM as well as examples of applications. These applications include studies of grain growth, recrystallization, texture development, orientation gradients, deformation twinning, annealing twinning, plastic deformation, and additive manufacturing. We also describe relationships to other X-ray-based methods as well as prospects for further development.

Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders

2001 ◽  
Vol 34 (6) ◽  
pp. 751-756 ◽  
Author(s):  
H. F. Poulsen ◽  
S. F. Nielsen ◽  
E. M. Lauridsen ◽  
S. Schmidt ◽  
R. M. Suter ◽  
...  
Keyword(s):  
Stress State ◽  
Grain Boundaries ◽  
Tensile Deformation ◽  
Strain Tensor ◽  
Three Dimensional ◽  
High Energy ◽  
European Synchrotron Radiation Facility ◽  
X Rays ◽  
The Individual ◽  
Individual Grains

A fast and non-destructive method for generating three-dimensional maps of the grain boundaries in undeformed polycrystals is presented. The method relies on tracking of micro-focused high-energy X-rays. It is verified by comparing an electron microscopy map of the orientations on the 2.5 × 2.5 mm surface of an aluminium polycrystal with tracking data produced at the 3DXRD microscope at the European Synchrotron Radiation Facility. The average difference in grain boundary position between the two techniques is 26 µm, comparable with the spatial resolution of the 3DXRD microscope. As another extension of the tracking concept, algorithms for determining the stress state of the individual grains are derived. As a case study, 3DXRD results are presented for the tensile deformation of a copper specimen. The strain tensor for one embedded grain is determined as a function of load. The accuracy on the strain is Δ∊ ≃ 10−4.

Recent Developments In Monochromatic Microprobe X-Ray Fluorescence (MMXRF)

1998 ◽  
Vol 4 (S2) ◽  
pp. 378-379
Author(s):  
Z. W. Chen ◽  
D. B. Wittry
Keyword(s):  
Materials Science ◽  
High Vacuum ◽  
Three Dimensional ◽  
High Sensitivity ◽  
X Rays ◽  
Fluorescence Excitation ◽  
X Ray ◽  
Quantitative Microanalysis ◽  
Recent Developments ◽  
Fifth Order

A monochromatic x-ray microprobe based on a laboratory source has recently been developed in our laboratory and used for fluorescence excitation. This technique provides high sensitivity (ppm to ppb), nondestructive, quantitative microanalysis with minimum sample preparation and does not require a high vacuum specimen chamber. It is expected that this technique (MMXRF) will have important applications in materials science, geological sciences and biological science.Three-dimensional focusing of x-rays can be obtained by using diffraction from doubly curved crystals. In our MMXRF setup, a small x-ray source was produced by the bombardment of a selected target with a focused electron beam and a toroidal mica diffractor with Johann pointfocusing geometry was used to focus characteristic x-rays from the source. In the previous work ∼ 108 photons/s were obtained in a Cu Kα probe of 75 μm × 43 μm in the specimen plane using the fifth order reflection of the (002) planes of mica.

scholarly journals Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

2013 ◽  
Vol 05 (01) ◽  
pp. 1350002 ◽  
Author(s):  
I. Benedetti ◽  
F. Barbe
Keyword(s):  
Three Dimensional ◽  
Constitutive Modelling ◽  
Polycrystalline Materials ◽  
High Fidelity ◽  
Computational Capability ◽  
Mechanical Models ◽  
Three Dimensional Models ◽  
The Individual ◽  
Individual Grains ◽  
Micro Structures

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material micro-structures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to two-dimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.

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