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

Multi-scale analysis of the mechanism of microbially induced calcium carbonate precipitation consolidation loess

Microbial-induced calcium carbonate precipitation (MICP) treatment of consolidated loess has the advantages of high efficiency and environmental protection. In this study, changes in the microscopic pore structure of loess before and after MICP treatment were compared and quantified, combined with test results at different scales, to better understand the mechanisms of MICP-consolidated loess. The unconfined compressive strength (UCS) of MICP-consolidated loess is significantly increased, and the stress-strain curve indicates improved strength and stability of the loess. X-ray diffraction (XRD) test results show that the signal strength of calcium carbonate crystals is significantly enhanced after loess consolidation. The microstructure of the loess was determined by scanning electron microscopy (SEM). The loess SEM microstructure images are quantitatively analyzed using comprehensive image processing methods (including gamma adjustment, grayscale threshold selection, median processing). The changes in microscopic pore area and average pore sizes (Feret diameter) of the loess before and after consolidation are described. More than 95% of the pores consist of pores with a pore area of less than 100 μm² and an average pore size of less than 20 μm. The total percentage of pore numbers with pore areas of 100-200 and 200-1000 μm² decreased by 1.15% after MICP consolidation, while those with 0-1 and 1-100 μm² increased. The percentage of pore numbers with an average pore size greater than 20 μm decreased by 0.93%, while the 0-1, 1-10, and 10-20 μm increased. Particle size distributions revealed a significant increase in particle size after MICP consolidation, with an increase of 89 μm in D₅₀.

Study of GaN coalescence by dark-field X-ray microscopy at the nanoscale

This work illustrates the potential of dark-field X-ray microscopy (DFXM), a 3D imaging technique of nanostructures, in characterizing novel epitaxial structures of gallium nitride (GaN) on top of GaN/AlN/Si/SiO₂ nano-pillars for optoelectronic applications. The nano-pillars are intended to allow independent GaN nanostructures to coalesce into a highly oriented film due to the SiO₂ layer becoming soft at the GaN growth temperature. DFXM is demonstrated on different types of samples at the nanoscale and the results show that extremely well oriented lines of GaN (standard deviation of 0.04°) as well as highly oriented material for zones up to 10 × 10 µm² in area are achieved with this growth approach. At a macroscale, high-intensity X-ray diffraction is used to show that the coalescence of GaN pyramids causes misorientation of the silicon in the nano-pillars, implying that the growth occurs as intended (i.e. that pillars rotate during coalescence). These two diffraction methods demonstrate the great promise of this growth approach for micro-displays and micro-LEDs, which require small islands of high-quality GaN material, and offer a new way to enrich the fundamental understanding of optoelectronically relevant materials at the highest spatial resolution.

Implementation of grain mapping by diffraction contrast tomography on a conventional laboratory tomography setup with various detectors

Laboratory-based diffraction contrast tomography (LabDCT) is a novel technique used to resolve grain orientations and shapes in three dimensions at the micrometre scale using laboratory X-ray sources, allowing the user to overcome the constraint of limited access to synchrotron facilities. To foster the development of this technique, the implementation of LabDCT is illustrated in detail using a conventional laboratory-based X-ray tomography setup, and it is shown that such implementation is possible with the two most common types of detectors: CCD and flat panel. As a benchmark, LabDCT projections were acquired on an AlCu alloy sample using the two types of detectors at different exposure times. Grain maps were subsequently reconstructed using the open-source grain reconstruction method reported in the authors' previous work. To characterize the detection limit and the spatial resolution for the current implementation, the reconstructed LabDCT grain maps were compared with the map obtained from a synchrotron measurement, which is considered as ground truth. The results show that the final grain maps from measurements by the CCD and flat panel detector are similar and show comparable quality, while the CCD gives a much better contrast-to-noise ratio than the flat panel. The analysis of the grain maps reconstructed from measurements with different exposure times suggests that a grain map of comparable quality could be obtained in less than 1 h total acquisition time without a significant loss of grain reconstruction quality and indicates a clear potential for time-lapse LabDCT experiments. The current implementation is suggested to promote the generic use of the LabDCT technique for grain mapping on conventional tomography setups.

Characterization of Pharmaceutical Tablets by X-ray Tomography

Solid dosage forms such as tablets are extensively used in drug administration for their simplicity and large-scale manufacturing capabilities. High-resolution X-ray tomography is one of the most valuable non-destructive techniques to investigate the internal structure of the tablets for drug product development as well as for a cost effective production process. In this work, we review the recent developments in high-resolution X-ray microtomography and its application towards different tablet characterizations. The increased availability of powerful laboratory instrumentation, as well as the advent of high brilliance and coherent 3rd generation synchrotron light sources, combined with advanced data processing techniques, are driving the application of X-ray microtomography forward as an indispensable tool in the pharmaceutical industry.

In situ synchrotron X-ray multimodal experiment to study polycrystal plasticity

The microstructure of polycrystals is known to govern the performance of structural materials. This drives the need for mechanical characterization methods capable of probing large representative volumes at the grain and sub-grain scales. In this paper, the use of in situ diffraction contrast tomography (DCT) along with far-field 3D X-ray diffraction (ff-3DXRD) at the Psiché beamline of Soleil is presented and applied to study crystal plasticity in commercially pure titanium. A tensile stress rig was modified to comply with the DCT acquisition geometry and used for in situ testing. DCT and ff-3DXRD measurements were carried out during a tensile test of a tomographic Ti specimen up to 1.1% strain. The evolution of the microstructure was analyzed in a central region of interest comprising about 2000 grains. Using the 6DTV algorithm, DCT reconstructions were successfully obtained and allowed the characterization of the evolution of lattice rotation in the entire microstructure. The results are backed up by comparisons with EBSD and DCT maps acquired at ESRF-ID11 that allowed the validation of the orientation field measurements in the bulk. Difficulties at the grain boundaries are highlighted and discussed in line with increasing plastic strain during the tensile test. Finally, a new outlook is provided on the potential of ff-3DXRD to enrich the present dataset with access to average lattice elastic strain data per grain, on the possibility of performing crystal plasticity simulations from DCT reconstructions, and ultimately on comparisons between experiments and simulations at the scale of the grain.

xrd_simulator: 3D X-ray diffraction simulation software supporting 3D polycrystalline microstructure morphology descriptions

An open source Python package named xrd_simulator, capable of simulating geometrical interactions between a monochromatic X-ray beam and a polycrystalline microstructure, is described and demonstrated. The software can simulate arbitrary intragranular lattice variations of single crystals embedded within a multiphase 3D aggregate by making use of a tetrahedral mesh representation where each element holds an independent lattice. By approximating the X-ray beam as an arbitrary convex polyhedral region in space and letting the sample be moved continuously through arbitrary rigid motions, data from standard and non-standard measurement sequences can be simulated. This implementation is made possible through analytical solutions to a modified, time-dependent version of the Laue equations. The software, which primarily targets three-dimensional X-ray diffraction microscopy (high-energy X-ray diffraction microscopy) type experiments, enables the numerical exploration of which sample quantities can and cannot be reconstructed for a given acquisition scheme. Similarly, xrd_simulator targets investigations of different measurement sequences in relation to optimizing both experimental run times and sampling.

Reconstruction algorithms for grain mapping by laboratory X-ray diffraction contrast tomography

X-ray-based non-destructive 3D grain mapping techniques are well established at synchrotron facilities. To facilitate everyday access to grain mapping instruments, laboratory diffraction contrast tomography (LabDCT), using a laboratory-based conical polychromatic X-ray beam, has been developed and commercialized. Yet the currently available LabDCT grain reconstruction methods are either ill-suited for handling a large number of grains or require a commercial licence bound to a specific instrument. To promote the availability of LabDCT, grain reconstruction methods have been developed with multiple reconstruction algorithms based on both forward and back calculations. The different algorithms are presented in detail and their efficient implementation using parallel computing is described. The performance of different reconstruction methods is assessed on synthetic data. The code to implement all the described algorithms has been made publicly accessible with the intention of fostering the development of grain mapping techniques on widely available laboratory instruments.

Development of a new, fully automated system for electron backscatter diffraction (EBSD)-based large volume three-dimensional microstructure mapping using serial sectioning by mechanical polishing, and its application to the analysis of special boundaries in 316L stainless steel

We report the development of a fully automatic large-volume 3D electron backscatter diffraction (EBSD) system (ELAVO 3D), consisting of a scanning electron microscope (ZEISS crossbeam XB 1540) with a dedicated sample holder, an adapted polishing automaton (Saphir X-change, QATM), a collaborative robotic arm (Universal Robots UR5), and several in-house built devices. The whole system is orchestrated by an in-house designed software, which is also able to track the process and report errors. Except for the case of error, the system runs without any user interference. For the measurement of removal thickness, the samples are featured with markers put on the perpendicular lateral surface, cut by plasma focused ion beam (PFIB) milling. The individual effects of both 1 μm diamond suspension and oxide polishing suspension polishing were studied in detail. Coherent twin grain boundaries (GBs) were used as an internal standard to check the removal rates measured by the side markers. The two methods for Z-spacing measurements disagreed by about 10%, and the inaccurate calibration of the PFIB system was found to be the most probable reason for this discrepancy. The angular accuracy of the system was determined to be ∼2.5°, which can be significantly improved with more accurate Z-spacing measurements. When reconstructed grain boundary meshes are sufficiently smoothed, an angular resolution of ±4° is achieved. In a 3D EBSD dataset of a size of 587 × 476 × 72 μm³, we focused on the investigation of coincidence site lattice ∑9 GBs. While bearing predominantly a pure tilt character, ∑9 GBs can be categorized into three groups based on correlative 3D morphologies and crystallography.

Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures

Ultrasonic testing of polycrystalline media relies heavily on simulation of the expected signals in order to detect and correctly interpret deviations due to defects. Many effects disturb ultrasonic waves propagating in polycrystalline media. One of them is scattering due to the granular microstructure of the polycrystal. The thus arising so-called microstructural noise changes with grain size distribution and testing frequency. Here, a method for simulating this noise is introduced. We geometrically model the granular microstructure to determine its influence on the backscattered ultrasonic signal. To this end, we utilize Laguerre tessellations generated by random sphere packings dividing space into convex polytopes—the cells. The cells represent grains in a real polycrystal. Cells are characterized by their volume and act as single scatterers. We compute scattering coefficients cellwise by the Born approximation. We then combine the Generalized Point Source Superposition technique with the backscattered contributions resulting from the cell structure to compute the backscattered ultrasonic signal. Applying this new methodology, we compute the backscattered signals in a pulse-echo experiment for a coarse grain cubic crystallized Inconel-617 and a fine grain hexagonal crystallized titanium. Fitting random Laguerre tessellations to the observed grain structure allows for simulating within multiple realizations of the proposed model and thus to study the variation of the backscattered signal due to microstructural variation.

Deep learning for improving non-destructive grain mapping in 3D

Laboratory X-ray diffraction contrast tomography (LabDCT) is a novel imaging technique for non-destructive 3D characterization of grain structures. An accurate grain reconstruction critically relies on precise segmentation of diffraction spots in the LabDCT images. The conventional method utilizing various filters generally satisfies segmentation of sharp spots in the images, thereby serving as a standard routine, but it also very often leads to over or under segmentation of spots, especially those with low signal-to-noise ratios and/or small sizes. The standard routine also requires a fine tuning of the filtering parameters. To overcome these challenges, a deep learning neural network is presented to efficiently and accurately clean the background noise, thereby easing the spot segmentation. The deep learning network is first trained with input images, synthesized using a forward simulation model for LabDCT in combination with a generic approach to extract features of experimental backgrounds. Then, the network is applied to remove the background noise from experimental images measured under different geometrical conditions for different samples. Comparisons of both processed images and grain reconstructions show that the deep learning method outperforms the standard routine, demonstrating significantly better grain mapping.

Crystallographic tomography and molecular modelling of structured organic polycrystalline powders

Novel combination of crystallographic tomography and molecular modelling is used to examine the powder packing behaviour and crystal interactions for an organic polycrystalline powder bed.

Molecular to Macroscale Energy Absorption Mechanisms in Biological Body Armour Illuminated by Scanning X-ray Diffraction with In Situ Compression

Determining multiscale, concurrent strain, and deformation mechanisms in hierarchical biological materials is a crucial engineering goal, to understand structural optimization strategies in Nature. However, experimentally characterizing complex strain and displacement fields within a 3D hierarchical composite, in a multiscale full-field manner, is challenging. Here, we determined the in situ strains at the macro-, meso-, and molecular-levels in stomatopod cuticle simultaneously, by exploiting the anisotropy of the 3D fiber diffraction coupled with sample rotation. The results demonstrate the method, using the mineralized 3D α-chitin fiber networks as strain sensors, can capture submicrometer deformation of a single lamella (mesoscale), can extract strain information on multiple constituents concurrently, and shows that α-chitin fiber networks deform elastically while the surrounding matrix deforms plastically before systematic failure under compression. Further, the results demonstrate a molecular-level prestrain gradient in chitin fibers, resulting from different mineralization degrees in the exo- and endo cuticle.

Nondestructive evaluation of 3D microstructure evolution in strontium titanate

Nondestructive X-ray diffraction contrast tomography imaging was used to characterize the microstructure evolution in a polycrystalline bulk strontium titanate specimen. Simultaneous acquisition of diffraction and absorption information allows for the reconstruction of shape and orientation of more than 800 grains in the specimen as well as porosity. Three-dimensional microstructure reconstructions of two coarsening states of the same specimen are presented alongside a detailed exploration of the crystallographic, topological and morphological characteristics of the evolving microstructure. The overall analysis of the 3D structure shows a clear signature of the grain boundary anisotropy, which can be correlated to surface energy anisotropy: the grain boundary plane distribution function shows an excess of 〈100〉-oriented interfaces with respect to a random structure. The results are discussed in the context of interface property anisotropy effects.

Intragranular three-dimensional stress tensor fields in plastically deformed polycrystals

The failure of polycrystalline materials used in infrastructure and transportation can be catastrophic. Multiscale modeling, which requires multiscale measurements of internal stress fields, is the key to predicting the deformation and failure of alloys. We determined the three-dimensional intragranular stress tensor fields in plastically deformed bulk steel using a high-energy x-ray microbeam. We observed intragranular local stresses that deviated greatly from the grain-averaged stresses and exceeded the macroscopic tensile strength. Even under deformation smaller than the uniform elongation, the intragranular stress fields were in highly triaxial stress states, which cannot be determined from the grain-averaged stresses. The ability to determine intragranular stress tensor fields can facilitate the understanding and prediction of the deformation and failure of materials through multiscale modeling.

3D grain reconstruction from laboratory diffraction contrast tomography

A novel reconstruction method to retrieve grain structure from laboratory diffraction contrast tomography is presented and evaluated.

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.

Mapping of individual dislocations with dark-field X-ray microscopy

This article presents an X-ray microscopy approach for mapping deeply embedded dislocations in three dimensions using a monochromatic beam with a low divergence. Magnified images are acquired by inserting an X-ray objective lens in the diffracted beam. The strain fields close to the core of dislocations give rise to scattering at angles where weak beam conditions are obtained. Analytical expressions are derived for the image contrast. While the use of the objective implies an integration over two directions in reciprocal space, scanning an aperture in the back focal plane of the microscope allows a reciprocal-space resolution of ΔQ/Q < 5 × 10−5 in all directions, ultimately enabling high-precision mapping of lattice strain and tilt. The approach is demonstrated on three types of samples: a multi-scale study of a large diamond crystal in transmission, magnified section topography on a 140 µm-thick SrTiO3 sample and a reflection study of misfit dislocations in a 120 nm-thick BiFeO3 film epitaxially grown on a thick substrate. With optimal contrast, the half-widths at half-maximum of the dislocation lines are 200 nm.

Reciprocal space mapping and strain scanning using X-ray diffraction microscopy

Dark-field X-ray microscopy is a new full-field imaging technique for nondestructively mapping the structure of deeply embedded crystalline elements in three dimensions. Placing an objective in the diffracted beam generates a magnified projection image of a local volume. By placing a detector in the back focal plane, high-resolution reciprocal space maps are generated for the local volume. Geometrical optics is used to provide analytical expressions for the resolution and range of the reciprocal space maps and the associated field of view in the sample plane. To understand the effects of coherence a comparison is made with wavefront simulations using the fractional Fourier transform. Reciprocal space mapping is demonstrated experimentally at an X-ray energy of 15.6 keV. The resolution function exhibits suppressed streaks and an FWHM resolution in all directions of ΔQ/Q = 4 × 10−5 or better. It is demonstrated by simulations that scanning a square aperture in the back focal plane enables strain mapping with no loss in resolution to be combined with a spatial resolution of 100 nm.

Percolative core formation in planetesimals enabled by hysteresis in metal connectivity

The segregation of dense core-forming melts by porous flow is a natural mechanism for core formation in early planetesimals. However, experimental observations show that texturally equilibrated metallic melt does not wet the silicate grain boundaries and tends to reside in isolated pockets that prevent percolation. Here we use pore-scale simulations to determine the minimum melt fraction required to induce porous flow, the percolation threshold. The composition of terrestrial planets suggests that typical planetesimals contain enough metal to overcome this threshold. Nevertheless, it is currently thought that melt segregation is prevented by a pinch-off at melt fractions slightly below the percolation threshold. In contrast to previous work, our simulations on irregular grain geometries reveal that a texturally equilibrated melt network remains connected down to melt fractions of only 1 to 2%. This hysteresis in melt connectivity allows percolative core formation in planetesimals that contain enough metal to exceed the percolation threshold. Evidence for the percolation of metallic melt is provided by X-ray microtomography of primitive achondrite Northwest Africa (NWA) 2993. Microstructural analysis shows that the metal-silicate interface has characteristics expected for a texturally equilibrated pore network with a dihedral angle of ∼85°. The melt network therefore remained close to textural equilibrium despite a complex history. This suggests that the hysteresis in melt connectivity is a viable process for percolative core formation in the parent bodies of primitive achondrites.

X-ray diffraction microscopy based on refractive optics

A formalism is presented for dark-field X-ray microscopy using refractive optics. The new technique can produce three-dimensional maps of lattice orientation and axial strain within millimetre-sized sampling volumes and is particularly suited toin situstudies of materials at hard X-ray energies. An objective lens in the diffracted beam magnifies the image and acts as a very efficient filter in reciprocal space, enabling the imaging of individual domains of interest with a resolution of 100 nm. Analytical expressions for optical parameters such as numerical aperture, vignetting, and the resolution in both direct and reciprocal spaces are provided. It is shown that the resolution function in reciprocal space can be highly anisotropic and varies as a function of position in the field of view. Inserting a square aperture in front of the objective lens facilitates disjunct and space-filling sampling, which is key for three-dimensional reconstruction and analysis procedures based on the conservation of integrated intensity. A procedure for strain scanning is presented. Finally the formalism is validated experimentally at an X-ray energy of 17 keV.

Integrated Three-Dimensional Microanalysis Combining X-Ray Microtomography and X-Ray Fluorescence Methodologies

A novel 3D elemental and morphological analysis approach is presented combining X-ray computed tomography (μCT), X-ray fluorescence (XRF) tomography, and confocal XRF analysis in a single laboratory instrument (Herakles). Each end station of Herakles (μCT, XRF-CT, and confocal XRF) represents the state-of-the-art of currently available laboratory techniques. The integration of these techniques enables linking the (quantitative) spatial distribution of chemical elements within the investigated materials to their three-dimensional (3D) internal morphology/structure down to 1-10 μm resolution level, which has not been achieved so-far using laboratory X-ray techniques. The concept of Herakles relies strongly on its high precision (around 100 nm) air-bearing motor system that connects the different end-stations, allowing combined measurements based on the above X-ray techniques while retaining the coordinate system. In-house developed control and analysis software further ensures a smooth integration of the techniques. Case studies on a Cu test pattern, a Daphnia magna model organism and a perlite biocatalyst support material demonstrate the attainable resolution, elemental sensitivity of the instrument, and the strength of combining these three complementary methodologies.

Microstructural evolution during sintering of copper particles studied by laboratory diffraction contrast tomography (LabDCT)

Pressureless sintering of loose or compacted granular bodies at elevated temperature occurs by a combination of particle rearrangement, rotation, local deformation and diffusion, and grain growth. Understanding of how each of these processes contributes to the densification of a powder body is still immature. Here we report a fundamental study coupling the crystallographic imaging capability of laboratory diffraction contrast tomography (LabDCT) with conventional computed tomography (CT) in a time-lapse study. We are able to follow and differentiate these processes non-destructively and in three-dimensions during the sintering of a simple copper powder sample at 1050 °C. LabDCT quantifies particle rotation (to <0.05° accuracy) and grain growth while absorption CT simultaneously records the diffusion and deformation-related morphological changes of the sintering particles. We find that the rate of particle rotation is lowest for the more highly coordinated particles and decreases during sintering. Consequently, rotations are greater for surface breaking particles than for more highly coordinated interior ones. Both rolling (cooperative) and sliding particle rotations are observed. By tracking individual grains the grain growth/shrinkage kinetics during sintering are quantified grain by grain for the first time. Rapid, abnormal grain growth is observed for one grain while others either grow or are consumed more gradually.

Nanox: a miniature mechanical stress rig designed for near-field X-ray diffraction imaging techniques

Multi-modal characterization of polycrystalline materials by combined use of three-dimensional (3D) X-ray diffraction and imaging techniques may be considered as the 3D equivalent of surface studies in the electron microscope combining diffraction and other imaging modalities. Since acquisition times at synchrotron sources are nowadays compatible with four-dimensional (time lapse) studies, suitable mechanical testing devices are needed which enable switching between these different imaging modalities over the course of a mechanical test. Here a specifically designed tensile device, fulfilling severe space constraints and permitting to switch between X-ray (holo)tomography, diffraction contrast tomography and topotomography, is presented. As a proof of concept the 3D characterization of an Al-Li alloy multicrystal by means of diffraction contrast tomography is presented, followed by repeated topotomography characterization of one selected grain at increasing levels of deformation. Signatures of slip bands and sudden lattice rotations inside the grain have been shown by means of in situ topography carried out during the load ramps, and diffraction spot peak broadening has been monitored throughout the experiment.

Tomography and imaging at the PSICHE beam line of the SOLEIL synchrotron

PSICHE (Pressure, Structure and Imaging by Contrast at High Energy) is the high-energy beam line of the SOLEIL synchrotron. The beam line is designed to study samples at extreme pressures, using diffraction, and to perform imaging and tomography for materials science and other diverse applications. This paper presents the tomograph and the use of the beam line for imaging, with emphasis on developments made with respect to existing instruments. Of particular note are the high load capacity rotation stage with free central aperture for installing large or complex samples and sample environments, x-ray mirror and filter optics for pink beam imaging, and multiple options for combining imaging and diffraction measurement. We describe how x-ray imaging techniques have been integrated into high-pressure experiments. The design and the specifications of the beam line are described, and several case studies drawn from the first user experiments are presented.

Multigrain indexing of unknown multiphase materials

A multigrain indexing algorithm for use with samples comprising an arbitrary number of known or unknown phases is presented. No a priori crystallographic knowledge is required. The algorithm applies to data acquired with a monochromatic beam and a conventional two-dimensional detector for diffraction. Initially, candidate grains are found by searching for crystallographic planes, using a Dirac comb convoluted with a box function as a filter. Next, candidate grains are validated and the unit cell is optimized. The algorithm is validated by simulations. Simulations of 500 cementite grains and ∼100 reflections per grain resulted in 99.2% of all grains being indexed correctly and 99.5% of the reflections becoming associated with the right grain. Simulations with 200 grains associated with four mineral phases and 50-700 reflections per grain resulted in 99.9% of all grains being indexed correctly and 99.9% of the reflections becoming associated with the right grain. The main limitation is in terms of overlap of diffraction spots and computing time. Potential areas of use include three-dimensional grain mapping, structural solution and refinement studies of complex samples, and studies of dilute phases.

A feasibility study of full-field X-ray orientation microscopy at the onset of deformation twinning

Three-dimensional X-ray orientation microscopy based on X-ray full-field imaging techniques such as diffraction contrast tomography is a challenging task when it comes to materials displaying non-negligible intragranular orientation spread and/or intricate grain microstructures as a result of plastic deformation and deformation twinning. As shown in this article, the optimization of the experimental conditions and a number of modifications of the data analysis routines enable detection and three-dimensional reconstruction of twin lamellae down to micrometre thickness, as well as more accurate three-dimensional reconstruction of grains displaying intragranular orientation spreads of up to a few degrees. The reconstruction of spatially resolved orientation maps becomes possible through the use of a recently introduced six-dimensional reconstruction framework, which has been further extended in order to enable simultaneous reconstruction of parent and twin orientations and to account for the finite impulse response of the X-ray imaging detector. The simultaneous reconstruction of disjoint orientation domains requires appropriate scaling of the scattering intensities based on structure and Lorentz factors and yields three-dimensional reconstructions with comparable density values for all the grains. This in turn enables the use of a global intensity-guided assembly procedure and avoids problems related to the single-grain thresholding procedure used previously. Last but not least, carrying out a systematic search over the list of known twin variants (forward modelling) for each of the indexed parent grains, it is possible to identify additional twins which have been left undetected at the previous stage of grain indexing based on diffraction spot peak positions. The enhanced procedure has been tested on a 1% deformed specimen made from a Ti–4% Al alloy and the result has been cross-validated against a two-dimensional electron backscatter diffraction orientation map acquired on one of the lateral sample surfaces.

Probing surface recombination velocities in semiconductors using two-photon microscopy

The determination of minority-carrier lifetimes and surface recombination velocities is essential for the development of semiconductor technologies such as solar cells. The recent development of two-photon time-resolved microscopy allows for better measurements of bulk and subsurface interfaces properties. Here we analyze the diffusion problem related to this optical technique. Our three-dimensional treatment enables us to separate lifetime (recombination) from transport effects (diffusion) in the photoluminescence intensity. It also allows us to consider surface recombination occurring at a variety of geometries: a single plane (representing an isolated exposed or buried interface), two parallel planes (representing two inequivalent interfaces), and a spherical surface (representing the enclosing surface of a grain boundary). We provide fully analytical results and scalings directly amenable to data fitting, and apply those to experimental data collected on heteroepitaxial CdTe/ZnTe/Si.

Three-dimensional full-field X-ray orientation microscopy

A previously introduced mathematical framework for full-field X-ray orientation microscopy is for the first time applied to experimental near-field diffraction data acquired from a polycrystalline sample. Grain by grain tomographic reconstructions using convex optimization and prior knowledge are carried out in a six-dimensional representation of position-orientation space, used for modelling the inverse problem of X-ray orientation imaging. From the 6D reconstruction output we derive 3D orientation maps, which are then assembled into a common sample volume. The obtained 3D orientation map is compared to an EBSD surface map and local misorientations, as well as remaining discrepancies in grain boundary positions are quantified. The new approach replaces the single orientation reconstruction scheme behind X-ray diffraction contrast tomography and extends the applicability of this diffraction imaging technique to material micro-structures exhibiting sub-grains and/or intra-granular orientation spreads of up to a few degrees. As demonstrated on textured sub-regions of the sample, the new framework can be extended to operate on experimental raw data, thereby bypassing the concept of orientation indexation based on diffraction spot peak positions. This new method enables fast, three-dimensional characterization with isotropic spatial resolution, suitable for time-lapse observations of grain microstructures evolving as a function of applied strain or temperature.

Comparison between diffraction contrast tomography and high-energy diffraction microscopy on a slightly deformed aluminium alloy

The grain structure of an Al-0.3 wt%Mn alloy deformed to 1% strain was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). 14 equally spaced HEDM layers were acquired and their exact location within the DCT volume was determined using a generic algorithm minimizing a function of the local disorientations between the two data sets. The microstructures were then compared in terms of the mean crystal orientations and shapes of the grains. The comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other. The results are important for studies targeting the determination of grain volume. For the case of a polycrystal with an average grain size of about 100 µm, a relative deviation of about ≤10% was found between the two techniques.

Diffraction scattering computed tomography: a window into the structures of complex nanomaterials

Modern functional nanomaterials and devices are increasingly composed of multiple phases arranged in three dimensions over several length scales. Therefore there is a pressing demand for improved methods for structural characterization of such complex materials. An excellent emerging technique that addresses this problem is diffraction/scattering computed tomography (DSCT). DSCT combines the merits of diffraction and/or small angle scattering with computed tomography to allow imaging the interior of materials based on the diffraction or small angle scattering signals. This allows, e.g., one to distinguish the distributions of polymorphs in complex mixtures. Here we review this technique and give examples of how it can shed light on modern nanoscale materials.

Non-destructive mapping of grain orientations in 3D by laboratory X-ray microscopy

The ability to characterise crystallographic microstructure, non-destructively and in three-dimensions, is a powerful tool for understanding many aspects related to damage and deformation mechanisms in polycrystalline materials. To this end, the technique of X-ray diffraction contrast tomography (DCT) using monochromatic synchrotron and polychromatic laboratory X-ray sources has been shown to be capable of mapping crystal grains and their orientations non-destructively in 3D. Here we describe a novel laboratory-based X-ray DCT modality (LabDCT), enabling the wider accessibility of the DCT technique for routine use and in-depth studies of, for example, temporal changes in crystallographic grain structure non-destructively over time through ‘4D’ in situ time-lapse studies. The capability of the technique is demonstrated by studying a titanium alloy (Ti-β21S) sample. In the current implementation the smallest grains that can be reliably detected are around 40 μm. The individual grain locations and orientations are reconstructed using the LabDCT method and the results are validated against independent measurements from phase contrast tomography and electron backscatter diffraction respectively. Application of the technique promises to provide important insights related to the roles of recrystallization and grain growth on materials properties as well as supporting 3D polycrystalline modelling of materials performance.

Polycrystal orientation mapping using scanning three-dimensional X-ray diffraction microscopy

A modified three-dimensional X-ray diffraction (3DXRD) technique is proposed as a solution to the main problem with 3DXRD-type experiments, namely, polycrystalline diffraction spot overlap. The modified method, termed scanning 3DXRD, enables three-dimensional crystallographic orientation mapping in polycrystals using a narrow incident X-ray beam with a beam size sufficiently smaller than the average grain size. This method can potentially allow one to apply a 3DXRD-type technique to specimens with a larger number of grains. Moreover, because of the use of a far-field area detector, scanning 3DXRD provides spacious specimen surroundings for equipment such as stress rigs, which are not feasible in 3DXRD methods using a near-field detector. As a first demonstration, a three-dimensional orientation map was obtained by an experiment using a 20 × 20 µm beam and a well annealed iron specimen with an average grain size of 60 µm. Scanning 3DXRD compared reasonably well with orientation image microscopy by electron backscatter diffraction (EBSD), considering the influence of the beam size in the case of scanning 3DXRD. The spatial resolution was estimated to be about twice the incident beam size from a scanning 3DXRD reconstruction simulation using an orientation map modeled on the EBSD orientation image of the specimen.

Characteristics of Friedel pairs and diffraction contrast tomography with non-perpendicular rotation axis

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.

Quantitative voxel-to-voxel comparison of TriBeam and DCT strontium titanate three-dimensional data sets

Recently, techniques for the acquisition of three-dimensional tomographic and four-dimensional time-resolved data sets have emerged, allowing for the analysis of mm3volumes of material with nm-scale resolution. The ability to merge multi-modal data sets acquiredviamultiple techniques for the quantitative analysis of structure, chemistry and phase information is still a significant challenge. Large three-dimensional data sets have been acquired by time-resolved diffraction contrast tomography (DCT) and a new TriBeam tomography technique with high spatial resolution to address grain growth in strontium titanate. A methodology for combining three-dimensional tomographic data has been developed. Algorithms for the alignment of orientation reference frames, unification of sampling grids and automated grain matching have been integrated, and the resulting merged data set permits the simultaneous analysis of all tomographic data on a voxel-by-voxel and grain-by-grain basis. Quantitative analysis of merged data sets collected using DCT and TriBeam tomography shows that the spatial resolution of the DCT technique is limited near grain boundaries and the sample edge, resolving grains down to 10 µm diameter for the reconstruction method used. While the TriBeam technique allows for higher-resolution analysis of boundary plane location, it is a destructive tomography approach and can only be employed at the conclusion of a four-dimensional experiment.

Dark-field X-ray microscopy for multiscale structural characterization

Many physical and mechanical properties of crystalline materials depend strongly on their internal structure, which is typically organized into grains and domains on several length scales. Here we present 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. The technique, which allows 'zooming' in and out in both direct and angular space, is demonstrated by an annealing study of plastically deformed aluminium. Facilitating the direct study of the interactions between crystalline elements is a key step towards the formulation and validation of multiscale models that account for the entire heterogeneity of a material. Furthermore, dark-field X-ray microscopy is well suited to applied topics, where the structural evolution of internal nanoscale elements (for example, positioned at interfaces) is crucial to the performance and lifetime of macro-scale devices and components thereof.

Cold neutron diffraction contrast tomography of polycrystalline material

Traditional neutron imaging is based on the attenuation of a neutron beam through scattering and absorption upon traversing a sample of interest. It offers insight into the sample's material distribution at high spatial resolution in a non-destructive way. In this work, it is expanded to include the diffracted neutrons that were ignored so far and obtain a crystallographic distribution (grain mapping). Samples are rotated in a cold neutron beam of limited wavelength band. Projections of the crystallites formed by the neutrons they diffract are captured on a two dimensional imaging detector. Their positions on the detector reveal their orientation whereas the projections themselves are used to reconstruct the shape of the grains. Indebted to established synchrotron diffraction contrast tomography, this 'cold neutron diffraction contrast tomography' is performed on recrystallized aluminium for experimental comparison between both. Differences between set-up and method are discussed, followed by the application range in terms of sample properties (crystallite size and number, mosaicity and typical materials). Neutron diffraction contrast tomography allows to study large grains in bulky metallic structures.

Reconstruction of local orientation in grains using a discrete representation of 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.

Comparison between a near-field and a far-field indexing approach for characterization of a polycrystalline sample volume containing more than 1500 grains

A comparison of the performance of X-ray diffraction tomography, a near-field diffraction technique, and a far-field diffraction technique for indexing X-ray diffraction data of polycrystalline materials has been carried out by acquiring two sets of diffraction data from the same polycrystalline sample volume. Both approaches used in this study are variants of the three-dimensional X-ray diffraction (3DXRD) methodology, but they rely on different data-collection and analysis strategies. Previous attempts to assess the quality of 3DXRD indexing results from polycrystalline materials have been restricted to comparisons with two-dimensional electron backscatter diffraction cross sections containing a limited number of grains. In the current work, the relative performance of two frequently used polycrystalline-material indexing algorithms is assessed, comparing the indexing results obtained from a three-dimensional sample volume containing more than 1500 grains. The currently achievable accuracy of three-dimensional grain maps produced with these algorithms has been assessed using a statistical analysis of the measurement of the size, position and orientation of the grains in the sample. The material used for this comparison was a polycrystalline commercially pure titanium grade 2 sample, which has a hexagonal close-packed crystal structure. The comparison of the two techniques shows good agreement for the measurements of the grain position, size and orientation. Cross-validation between the indexing results shows that about 99% of the sample volume has been indexed correctly by either of these indexing approaches. The remaining discrepancies have been analysed and the strengths and limitations of both approaches are discussed.

Connecting heterogeneous single slip to diffraction peak evolution in high-energy monochromatic X-ray experiments

A forward modeling diffraction framework is introduced and employed to identify slip system activity in high-energy diffraction microscopy (HEDM) experiments. In the framework, diffraction simulations are conducted on virtual mosaic crystals with orientation gradients consistent with Nye's model of heterogeneous single slip. Simulated diffraction peaks are then compared against experimental measurements to identify slip system activity. Simulation results compared against diffraction data measured in situ from a silicon single-crystal specimen plastically deformed under single-slip conditions indicate that slip system activity can be identified during HEDM experiments.

First laboratory X-ray diffraction contrast tomography for grain mapping of polycrystals

The first results of three-dimensional grain mapping using a laboratory tomograph equipped with a microfocus W target X-ray tube source, operated at 90 kV and 350 µA, are presented. Adapted algorithms exploit the polychromatic radiation spectrum and the projection magnification arising from the cone-beam geometry. The first map of grain shapes and crystallographic orientations from a titanium sample containing 42 grains is presented and its validity confirmed by a phase contrast reconstruction of the grain boundaries. Perspectives are given for the further development of the technique to accommodate samples with more grains or with greater intragranular orientation spread.

Validation of three-dimensional diffraction contrast tomography reconstructions by means of electron backscatter diffraction characterization

Microstructure reconstructions resulting from diffraction contrast tomography data of polycrystalline bulk strontium titanate were reinvestigated by means of electron backscatter diffraction (EBSD) characterization. Corresponding two-dimensional grain maps from the two characterization methods were aligned and compared, focusing on the spatial resolution at the internal interfaces. The compared grain boundary networks show a remarkably good agreement both morphologically and in crystallographic orientation. Deviations are critically assessed and discussed in the context of diffraction data reconstruction and EBSD data collection techniques.

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

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 < 2θ < 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.

A method for intragranular orientation and lattice strain distribution determination

A novel approach to quantifying intragranular distributions is developed and applied to the α → ∊ phase transition in iron. The approach captures both the distribution of lattice orientation within a grain and the orientation dependence of the lattice strain. Use of a finite element discretization over a ball in Rodrigues space allows for the efficient use of degrees of freedom in the numerical approach and provides a convenient framework for gradient-based regularization of the inverse problem. Application to the α → ∊ phase transition in iron demonstrates the utility of the method in that intragranular orientation and lattice strain distributions in the α phase are related to the observed ∊ orientations. Measurement of the lattice strain distribution enables quantitative analysis of the driving forces for ∊ variant selection. The measurement and analysis together indicate quantitatively that the Burgers mechanism is operative under the experimental conditions examined here.

Three-dimensional plastic response in polycrystalline coppervianear-field high-energy X-ray diffraction microscopy

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.

An introduction to three-dimensional X-ray 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.

High-energy transmission Laue micro-beam X-ray diffraction: a probe for intra-granular lattice orientation and elastic strain in thicker samples

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern-matching approach. The results highlight the inability of a simple Schmid-factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.