Journal of Applied CrystallographyCrystallography JournalsOnline

X-ray diffraction microscopy special issue (March 2013)

Guest Editor: A. Borbély


cover image
Cover illustration: Structures of polycrystals and of a Schizosaccharomyces pombe spore at different length scales. Courtesy of Reischig et al. [J. Appl. Cryst. (2013), 46, 297-311], Larson & Levine [J. Appl. Cryst. (2013), 46, 153-164] and Rodriguez et al. [J. Appl. Cryst. (2013), 46, 312-318].

editorial


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J. Appl. Cryst. (2013). 46, 295-296    [doi:10.1107/S0021889813004160]

X-ray diffraction microscopy: emerging imaging techniques for nondestructive analysis of crystalline materials from the millimetre down to the nanometre scale

A. Borbély and A. R. Kaysser-Pyzalla

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In anticipation of the International Year of Crystallography in 2014, Journal of Applied Crystallography presents a virtual issue on recent developments in X-ray diffraction microscopy. This issue collects together a series of articles originally published in the journal between August 2012 and April 2013, which focus on novel diffraction methods that enable visualization of the internal structure of crystalline materials from the millimetre down to the nanometre scale.


X-ray diffraction microscopy


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J. Appl. Cryst. (2012). 45, 1084-1097    [doi:10.1107/S0021889812039143]

An introduction to three-dimensional X-ray diffraction microscopy

H. F. Poulsen

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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.

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J. Appl. Cryst. (2013). 46, 297-311    [doi:10.1107/S0021889813002604]

Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss and W. Ludwig

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Diffraction contrast tomography is a near-field diffraction-based imaging technique that provides high-resolution grain maps of polycrystalline materials simultaneously with the orientation and average elastic strain tensor components of the individual grains with an accuracy of a few times 10-4. Recent improvements that have been introduced into the data analysis are described. The ability to process data from arbitrary detector positions allows for optimization of the experimental setup for higher spatial or strain resolution, including high Bragg angles (0 < 2[theta] < 180°). The geometry refinement, grain indexing and strain analysis are based on Friedel pairs of diffraction spots and can handle thousands of grains in single- or multiphase materials. The grain reconstruction is performed with a simultaneous iterative reconstruction technique using three-dimensional oblique angle projections and GPU acceleration. The improvements are demonstrated with the following experimental examples: (1) uranium oxide mapped at high spatial resolution (300 nm voxel size); (2) combined grain mapping and section topography at high Bragg angles of an Al-Li alloy; (3) ferrite and austenite crystals in a dual-phase steel; (4) grain mapping and elastic strains of a commercially pure titanium sample containing 1755 grains.

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J. Appl. Cryst. (2012). 45, 1098-1108    [doi:10.1107/S0021889812039519]

Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy

S. F. Li, J. Lind, C. M. Hefferan, R. Pokharel, U. Lienert, A. D. Rollett and R. M. Suter

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The evolution of the crystallographic orientation field in a polycrystalline sample of copper is mapped in three dimensions as tensile strain is applied. Using forward-modeling analysis of high-energy X-ray diffraction microscopy data collected at the Advanced Photon Source, the ability to track intragranular orientation variations is demonstrated on an ~2 µm length scale with ~0.1° orientation precision. Lattice rotations within grains are tracked between states with ~1° precision. Detailed analysis is presented for a sample cross section before and after ~6% strain. The voxel-based (0.625 µm triangular mesh) reconstructed structure is used to calculate kernel-averaged misorientation maps, which exhibit complex patterns. Simulated scattering from the reconstructed orientation field is shown to reproduce complex scattering patterns generated by the defected microstructure. Spatial variation of a goodness-of-fit or confidence metric associated with the optimized orientation field indicates regions of relatively high or low orientational disorder. An alignment procedure is used to match sample cross sections in the different strain states. The data and analysis methods point toward the ability to perform detailed comparisons between polycrystal plasticity computational model predictions and experimental observations of macroscopic volumes of material.

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J. Appl. Cryst. (2013). 46, 153-164    [doi:10.1107/S0021889812043737]

Submicrometre-resolution polychromatic three-dimensional X-ray microscopy

B. C. Larson and L. E. Levine

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The ability to study the structure, microstructure and evolution of materials with increasing spatial resolution is fundamental to achieving a full understanding of the underlying science of materials. Polychromatic three-dimensional X-ray microscopy (3DXM) is a recently developed nondestructive diffraction technique that enables crystallographic phase identification, determination of local crystal orientations, grain morphologies, grain interface types and orientations, and in favorable cases direct determination of the deviatoric elastic strain tensor with submicrometre spatial resolution in all three dimensions. With the added capability of an energy-scanning incident beam monochromator, the determination of absolute lattice parameters is enabled, allowing specification of the complete elastic strain tensor with three-dimensional spatial resolution. The methods associated with 3DXM are described and key applications of 3DXM are discussed, including studies of deformation in single-crystal and polycrystalline metals and semiconductors, indentation deformation, thermal grain growth in polycrystalline aluminium, the metal-insulator transition in nanoplatelet VO2, interface strengths in metal-matrix composites, high-pressure science, Sn whisker growth, and electromigration processes. Finally, the outlook for future developments associated with this technique is described.

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J. Appl. Cryst. (2012). 45, 1109-1124    [doi:10.1107/S0021889812041039]

Diffraction/scattering computed tomography for three-dimensional characterization of multi-phase crystalline and amorphous materials

M. Álvarez-Murga, P. Bleuet and J.-L. Hodeau

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The three-dimensional characterization method described herein is based on diffraction and scattering techniques combined with tomography and uses the variation of these signals to reconstruct a two-dimensional/three-dimensional structural image. To emphasize the capability of the method in discriminating between different poorly ordered phases, it is named diffraction/scattering computed tomography (DSCT). This combination not only allows structural imaging but also yields an enhancement of the weak signals coming from minor phases, thereby increasing the sensitivity of structural probes. This article reports the suitability of the method for discrimination of polycrystalline and amorphous phases and for extraction of their selective local patterns with a contrast sensitivity of about 0.1% in weight of minor phases relative to the matrix. The required background in tomography is given and then the selectivity of scattering signal, the efficiency of the method, reconstruction artefacts and limitations are addressed. The approach is illustrated through different examples covering a large range of applications based on recent literature, showing the potential of DSCT in crystallography and materials science, particularly when functional and/or precious samples with sub-micrometre features have to be investigated in a nondestructive way.

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J. Appl. Cryst. (2012). 45, 1077-1083    [doi:10.1107/S0021889812039131]

Diffraction microcomputed tomography of an Al-matrix SiC-monofilament composite

S. R. Stock and J. D. Almer

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The structure of an SiC-monofilament-reinforced Al-matrix composite was reconstructed using diffraction rings from these two phases. A 65 keV X-ray beam with 15 µm width (horizontal) and 150 µm length (vertical) was scanned across the specimen in 15 µm steps. A 2° rotation about the vertical rotation axis was used between projections, and filtered back projection reconstructions were created with 15 × 15 µm in-plane and 150 µm out-of-plane volume elements (voxels). The integrated intensities of the 11.0, 10.1 and 10.2 SiC and the 111, 200 and 220 Al diffraction rings were used to produce six independent reconstructions. The transmitted-intensity reconstruction agreed with that of higher resolution, absorption-contrast synchrotron microcomputed tomography. The Al reconstructions showed the effect of large grains, and the SiC reconstructions revealed the two microstructural zones in the fibers.

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J. Appl. Cryst. (2013). 46, 312-318    [doi:10.1107/S0021889813002471]

Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities

J. A. Rodriguez, R. Xu, C.-C. Chen, Y. Zou and J. Miao

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Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free-electron lasers, high harmonic generation, soft X-ray lasers and electrons. Despite recent rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities is presented. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stages of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. It is expected that OSS will find application in the rapidly growing CDI field, as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed. The MATLAB (The MathWorks Inc., Natick, MA, USA) source code of the OSS algorithm is freely available from http://www.physics.ucla.edu/research/imaging.

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J. Appl. Cryst. (2012). 45, 778-784    [doi:10.1107/S0021889812018900]

Three-dimensional Bragg coherent diffraction imaging of an extended ZnO crystal

X. Huang, R. Harder, S. Leake, J. Clark and I. Robinson

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A complex three-dimensional quantitative image of an extended zinc oxide (ZnO) crystal has been obtained using Bragg coherent diffraction imaging integrated with ptychography. By scanning a 2.5 µm-long arm of a ZnO tetrapod across a 1.3 µm X-ray beam with fine step sizes while measuring a three-dimensional diffraction pattern at each scan spot, the three-dimensional electron density and projected displacement field of the entire crystal were recovered. The simultaneously reconstructed complex wavefront of the illumination combined with its coherence properties determined by a partial coherence analysis implemented in the reconstruction process provide a comprehensive characterization of the incident X-ray beam.

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