Three-dimensional X-ray Diffraction Research Articles

Controllably Constructing morphology and structure of potassium chloride crystal by green supersaturation modulation

Controllable and green construction of morphology and structure in potassium chloride (KCl) crystals is necessary in the fields of pharmaceuticals, catalysis, minerals, and jewels design. Here, the work presented a lucid way for preparing KCl crystal with various morphology including hopper-, sphere- and hollow cube-like structure through green supersaturation modulation. Parameters including stirring speed, cooling range, cooling rate, and excess inorganic composing ions influenced the growth kinetics of hopper KCl crystal as well as the surficial morphology and structure: (1) Metastable region and stable conditions were beneficial for uniform growth of crystal; (2) Small size of crystal particles were obtained with high shear force; (3) Corner angle of crystal would be abraded in slow cooling rate; (4) Non-uniform crystal appeared in improper cooling range condition; (5) Additional composing ions might introduce deformed structure according to the basic crystal repeating unit with corresponding elements. Based on the above study of growth kinetics, hopper-, sphere- and hollow cube-like crystal were obtained. The morphology and structure properties of various crystal were researched by three-dimensional visualization, X-ray diffraction (XRD), and scanning electron microscope (SEM) for optimized application such as higher exposing surface area of hopper-like crystal than original cubic crystal. The main exposed faces for smooth cubic, hollow cubic, and hopper structure exhibited were (200), (220), and (400) facet, respectively, which could be a consequence of the inner beveling. Surface of spherical structure was a circular arc with relative high roughness, being ascribed to the formation mechanism of spherical structure from cubic structure. Therefore, the work presented a strategy to controllably design KCl crystal with different structure and morphology in a green way.

The development of grain resolved stress fields around notch tips in soft-textured zirconium polycrystals: A three-dimensional synchrotron X-ray diffraction study

Texture, microstructure, and local grain neighbourhood contribute to the development of localized stresses in polycrystals. For hexagonal close-packed materials, crystal's elastic and plastic anisotropy can also be a major contributing factor, yet there is a paucity of experimental studies focusing on the extent of contribution of such parameters on the magnitude of localized stresses at microscales. This study focuses on addressing this knowledge gap by deforming double-edge-notched soft-textured α-zirconium specimens in-situ, while measuring grain scale tensorial stresses using high energy synchrotron X-ray diffraction. The specimens were subjected to cyclic loads to study the evolution of stresses in the vicinity of both shallow and deep notches. The soft-texture of the specimens is such that there are no c-axes of grains aligned along the macroscopic loading direction thereby inhibiting deformation twinning. The “as-measured” microstructures and notch geometries were imported into a crystal plasticity finite element model for further analysis. Results show that despite the absence of c-axes of grains aligned along loading direction, the developed stresses were substantially influenced by crystallographic orientations. Stress drop was observed near the onset of plasticity with further loading and the orientation and position effects were highlighted. A plastic deformation mechanism was revealed where, upon specimen loading, the mechanical constraints enforced during grain-grain interactions led to hardening. Accordingly, a parameter was devised to quantify the grain level hardening arising from this mechanism. It was shown that grain-scale stress concentration factors vary significantly before the onset of plasticity, but they settle in the plastic zone and with the progression of cycles.

In-situ and wavelength-dependent photocatalytic strain evolution of a single Au nanoparticle on a TiO2 film

Photocatalysis is a promising technique due to its capacity to efficiently harvest solar energy and its potential to address the global energy crisis. However, the structure–activity relationships of photocatalyst during wavelength-dependent photocatalytic reactions remains largely unexplored because it is difficult to measure under operating conditions. Here we show the photocatalytic strain evolution of a single Au nanoparticle (AuNP) supported on a TiO2 film by combining three-dimensional (3D) Bragg coherent X-ray diffraction imaging with an external light source. The wavelength-dependent generation of reactive oxygen species (ROS) has significant effects on the structural deformation of the AuNP, leading to its strain evolution. Density functional theory (DFT) calculations are employed to rationalize the induced strain caused by the adsorption of ROS on the AuNP surface. These observations provide insights of how the photocatalytic activity impacts on the structural deformation of AuNP, contributing to the general understanding of the atomic-level catalytic adsorption process.

Revealing per-grain and neighbourhood stress interactions of a deforming ferritic steel via three-dimensional X-ray diffraction

The structural performance of polycrystalline alloys is strongly controlled by the characteristics of individual grains and their interactions, motivating this study to understand the dynamic micromechanical response within the microstructure. Here, a high ductility single-phase ferritic steel during uniaxial deformation is explored using three-dimensional X-ray diffraction. Grains well aligned for dislocation slip are shown to possess a wide intergranular stress range, controlled by per-grain dependent hardening activity. Contrariwise, grains orientated poorly for slip have a narrow stress range. A grain neighbourhood effect is observed of statistical significance: the Schmid factor of serial adjoining grains influences the stress state of a grain of interest, whereas parallel neighbours are less influential. This phenomenon is strongest at low plastic strains, with the effect diminishing as grains rotate during plasticity to eliminate any orientation dependent load shedding. The ability of the ferrite to eliminate such neighbourhood interactions is considered key to the high ductility possessed by these materials.

Grain-level effects on in-situ deformation-induced phase transformations in a complex-phase steel using 3DXRD and EBSD

A novel complex-phase steel alloy is conceived with a deliberately unstable austenite, γ, phase that enables the deformation-induced martensitic transformations (DIMT) to be explored at low levels of plastic strain. The DIMT was thus explored, in-situ and non-destructively, using both far-field Three-Dimensional X-ray Diffraction (3DXRD) and Electron Back-Scatter Diffraction (EBSD). Substantial α′ martensite formation was observed under 10% applied strain with EBSD, and many ɛ grain formation events were captured with 3DXRD, indicative of the indirect transformation of martensite via the reaction γ→ɛ→α′. Using ɛ grain formation as a direct measurement of γ grain stability, the influence of several microstructural properties, such as grain size, orientation and neighbourhood configuration, on γ stability have been identified. Larger γ grains were found to be less stable than smaller grains. Any γ grains oriented with {100} parallel to the loading direction preferentially transformed with lower stresses. Parent ɛ-forming γ grains possessed a neighbourhood with increased ferritic/martensitic volume fraction. This finding shows, unambiguously, that the nearby presence of α and α′ promotes ɛ formation in neighbouring grains. The minimum strain work criterion model for ɛ variant prediction was also evaluated, which worked well for most grains. However, ɛ-forming grains with a lower stress were less well predicted by the model, indicating crystal-level behaviour must be considered for accurate ɛ formation. The findings from this work are considered key for the future design of alloys where the deformation response can be controlled by tailoring microstructure and local or macroscopic crystal orientations.

Electrochemical performance of lithium-ion batteries with two-layer gradient electrode architectures

Thick electrodes whose active materials have high areal density may improve the energy densities of lithium-ion batteries. However, the weakened rate abilities and cycle lifetimes of such electrodes significantly limit their practical applications. In this study, a modified two-dimensional model was built to evaluate the influence of the electrode structure on the lithiation process. Gradient electrodes with different particle sizes along the thickness direction are designed and fabricated via a two-layer coating process. The gradient design in the thickness direction is confirmed by three-dimensional digital microscopy, energy-dispersive spectroscopy, X-ray diffraction, and scanning electron microscopy. Galvanostatic charge/discharge cycling tests and electrochemical impedance spectroscopy are performed to investigate the electrochemical properties of the fabricated gradient electrodes. The simulation results indicate that the gradient electrode structure can enhance the utilization of electrode particles on the current collector side and alleviate the nonuniformity of the solid-phase Li concentration along the thickness direction. High electrochemical performance and long-term cycling stability of the designed gradient electrodes are verified by electrochemical test. The gradient structure fabricated via multi-layer coating processes can be used to improve the electrochemical performance of thick electrodes.

The asymmetric evolution of grain-scale stresses in notched specimens under cyclic loads

Engineering components are often exposed to various cyclic loading conditions. The development of microscale stresses under such conditions depends on the material texture, local microstructure, the degree of crystals elastic and plastic anisotropy, as well as the presence of geometrical irregularities. In this study, the three-dimensional synchrotron X-ray diffraction (3D-XRD) technique is used and coupled with a crystal plasticity finite element (CPFE) model to deconvolute the contribution of such parameters on the magnitude of localized stresses. Special attention is paid to the notch geometry, where two double-edge-notched α-zirconium specimens with different geometries but the same texture were deformed in-situ while grain-scale stresses were measured both in the vicinity of the notches and in the far-field zones. Deep and shallow notches were cut to the dimensions comparable with the specimens’ average grain sizes. For each specimen, the center of mass, orientation, elastic strain, stress, and relative volume of more than 6,000 grains were measured and studied. Post-deformation analysis with Electron Backscatter Diffraction (EBSD) was conducted to further validate the observed trends. It is shown that the distribution of grain-scale stresses is asymmetric within each specimen. This asymmetry develops from the early stages of the applied cyclic load and remains intact with further loading. A new method is introduced for quantifying the effects of grain neighbourhood on load sharing, where it is shown that such effects relax the stresses acting on “hard” grains, altering grain-scale stress concentration factors.

The emergence of super-resolution beyond the probe size in scanning 3DXRD microscopy.

The spatial resolution in scanning-based two-dimensional microscopy is normally limited by the size of the probe, thereby a smaller probe is a prerequisite for enhancing the spatial resolution. For three-dimensional microscopy that combines translation and rotation motions of a specimen, however, complex trajectories of the probe highly overlap in the specimen, which could change the postulate above. Here, the spatial resolution achieved in scanning three-dimensional X-ray diffraction (s3DXRD) microscopy is investigated. In this method, the most appropriate orientation of the pixel in the specimen coordinate is selected by comparing the completeness of diffraction peaks with theory. Therefore, the superposed area of the beam trajectory has a strong effect on the spatial resolution, in terms of the completeness of diffraction peaks. It was found that the highly superposed area by the incident X-rays, which has the highest completeness factor in the pixel of the specimen, is much smaller than the X-ray probe size, and that sub-pixel analysis by dividing a pixel into small pieces leads to drastic improvement of the spatial resolution ins3DXRD.

A three-dimensional X-ray diffraction study of intergranular stress relationships in a body-centred cubic ferritic steel

A three-dimensional X-ray diffraction study of intergranular stress relationships in a body-centred cubic ferritic steel

Scanning Three-Dimensional X-ray Diffraction Microscopy for Carbon Steels

Plastically deformed low-carbon steel has been analyzed by nondestructive three-dimensional orientation and strain mapping using scanning three-dimensional X-ray diffraction microscopy (S3DXRD). However, the application of S3DXRD is limited to single-phase alloys. In this study, we propose a modified S3DXRD analysis for dual-phase alloys, such as ferrite–pearlite carbon steel, which is composed of grains detectable as diffraction spots and a phase undetectable as diffraction spots. We performed validation experiments for ferrite–pearlite carbon steel with different pearlite fractions, in which the ferrite grains and the pearlite corresponded to the detectable grains and an undetectable phase, respectively. The regions of pearlite appeared more remarkably in orientation maps of the ferrite grains obtained from the carbon steel samples than that of the single-phase low-carbon steel and increased with the increase in the carbon concentration. The fractions of the detectable grains and the undetectable phase were determined with an uncertainty of 15%–20%. These results indicate that the proposed modified analysis is qualitatively valid for dual-phase alloys comprising detectable grains and an undetectable phase.

Scanning Three-Dimensional X-ray Diffraction Microscopy with a Spiral Slit

Recently, nondestructive evaluation of the stresses localized in grains was achieved for plastically deformed low-carbon steel using scanning three-dimensional X-ray diffraction (S3DXRD) microscopy with a conical slit. However, applicable metals and alloys were restricted to a single phase and evaluated stress was underestimated due to the fixed Bragg angles of the conical slit optimized to αFe. We herein propose S3DXRD with a rotating spiral slit adaptable to various metals and alloys and accurate stress evaluation with sweeping Bragg angles. Validation experiments with a 50-keV X-ray microbeam were conducted for low-carbon steel as a body-centered cubic (BCC) phase and pure Cu as a face-centered cubic (FCC) phase. As a result of orientation mapping, polygonal grain shapes and clear grain boundaries were observed for both BCC and FCC metals. Thus, it was demonstrated that S3DXRD with a rotating spiral slit will be applicable to various metals and alloys, multiphase alloys, and accurate stress evaluation using a X-ray microbeam with a higher photon energy within an energy range determined by X-ray focusing optics. In principle, this implies that S3DXRD becomes applicable to larger and thicker metal and alloy samples instead of current miniature test or wire-shaped samples if a higher-energy X-ray microbeam is available.

Analysis of the crystal phase and orientation of nanocrystals and nanorods of MoOx thin films

Nanoscale materials, which are also known as nanomaterials, have attracted considerable attention owing to their unique physical properties and discrete band structures. Recently, studies have focused on the enhanced chemical reactions of nanomaterials with large specific surface areas for several applications, such as gas sensing. In this study, we investigated the orientation of MoOx nanorods and plate-like crystals constituting molybdenum oxide nanostructured thin films by transmission electron microscopy and three-dimensional X-ray diffraction. The nanorods are composed of Mo8O23 (non-stoichiometric composition) and are elongated along the b-axis, although they are developed in random directions with respect to the substrate. The plate-like crystals comprise α-MoO3 and they are strongly oriented along the 0k0 plane horizontally to the substrate surface. Thus, the crystal structure and orientation of individual components of MoOx nanostructured thin films are clarified via transmission electron microscopy and three-dimensional X-ray diffraction studies.

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.

Observation of grain motion during semisolid deformation by using 4D-CT and 3DXRD

A technique combining time-resolved computed tomography (4D-CT) and three-dimensional X-ray diffraction (3DXRD) was employed to investigate semisolid deformation in an Al-10mass%Cu alloy with the equiaxed grain structure. The diffraction patterns and reconstructed 3D images were used to quantitatively analyse the translational and rotational motions of solid grains in the semisolid alloy. Finally, the motion of solid grains and the expansion of porosity during the compression tests are discussed on the basis of in situ observations.

High-resolution 3D X-ray diffraction microscopy: 3D mapping of deformed metal microstructures.

Three-dimensional X-ray diffraction microscopy, 3DXRD, has become an established tool for orientation and strain mapping of bulk polycrystals. However, it is limited to a finite spatial resolution of ∼1.5-3 µm. Presented here is a high-resolution modality of the technique, HR-3DXRD, for 3D mapping of submicrometre-sized crystallites or subgrains with high spatial and angular resolution. Specifically, the method is targeted to visualization of metal microstructures at industrially relevant degrees of plastic deformation. Exploiting intrinsic crystallographic properties of such microstructures, the high resolution is obtained by placing a high-resolution imaging detector in between the near-field and far-field regimes. This configuration enables 3D mapping of deformation microstructure by determining the centre of mass and volume of the subgrains and generating maps by tessellation. The setup is presented, together with a data analysis approach. Full-scale simulations are used to determine limitations and to demonstrate HR-3DXRD on realistic phantoms. Misalignments in the setup are shown to cause negligible shifts in the position and orientation of the subgrains. Decreasing the signal-to-noise ratio is observed to lead primarily to a loss in the number of determined diffraction spots. Simulations of an α-Fe sample deformed to a strain of ε vM = 0.3 and comprising 828 subgrains show that, despite the high degree of local texture, 772 of the subgrains are retrieved with a spatial accuracy of 0.1 µm and an orientation accuracy of 0.0005°.

Implementing and evaluating far-field 3D X-ray diffraction at the I12 JEEP beamline, Diamond Light Source.

Three-dimensional X-ray diffraction (3DXRD) is shown to be feasible at the I12 Joint Engineering, Environmental and Processing (JEEP) beamline of Diamond Light Source. As a demonstration, a microstructually simple low-carbon ferritic steel was studied in a highly textured and annealed state. A processing pipeline suited to this beamline was created, using software already established in the 3DXRD user community, enabling grain centre-of-mass positions, orientations and strain tensor elements to be determined. Orientations, with texture measurements independently validated from electron backscatter diffraction (EBSD) data, possessed a ∼0.1° uncertainty, comparable with other 3DXRD instruments. The spatial resolution was limited by the far-field detector pixel size; the average of the grain centre of mass position errors was determined as ±∼80 µm. An average per-grain error of ∼1 × 10-3 for the elastic strains was also measured; this could be reduced in future experiments by improving sample preparation, geometry calibration, data collection and analysis techniques. Application of 3DXRD onto I12 shows great potential, where its implementation is highly desirable due to the flexible, open architecture of the beamline. User-owned or designed sample environments can be used, thus 3DXRD could be applied to previously unexplored scientific areas.

B4/32Ga28/32Sb10/32As22/32 three-dimensional semiconductor superlattice

Self-assembly of BD-rich AxB1−xCyD1−y was studied for a lot of semiconductor alloys. An occurrence of identical clusters should be due to a decrease of the bond energy, internal strain energy or both of them. An arrangement of clusters is disordered since the contents of minority atoms are in the dilute or ultra dilute limits in the considered alloys. B4/32Ga28/32Sb10/32As22/32 semiconductor alloy with the three-dimensional superlattice is presented. Such superlattice should be stable against disordering due to its minimal free energy. The superlattice is formed by the identical cubic units consisting of 64 atoms and is the three-dimensional semiconductor soft X-ray diffraction grating.

Efficient Fitting of 3D Tessellations to Curved Polycrystalline Grain Boundaries

The curvature of grain boundaries in polycrystalline materials is an important characteristic, since it plays a key role in phenomena like grain growth. However, most traditional tessellation models that are used for modeling the microstructure morphology of these materials, e.g., Voronoi or Laguerre tessellations, have flat faces and thus fail to incorporate the curvature of the latter. For this reason, we consider generalizations of Laguerre tessellations—variations of so-called generalized balanced power diagrams (GBPDs)—that exhibit non-convex cells. With as many as ten parameters for each cell, it is computationally demanding to fit GBPDs to three-dimensional image data containing hundreds of grains. We therefore propose a modification of the traditional definition of GBDPs that allows gradient-based optimization methods to be employed. The resulting reduction in runtime makes it feasible to find approximations to real experimental datasets. We demonstrate this on a three-dimensional x-ray diffraction (3DXRD) mapping of an AlCu alloy, but we also evaluate the modeling errors for simulated data. Furthermore, we investigate the effect of noisy image data and whether the smoothing of image data prior to the fitting step is advantageous.

Three-dimensional coherent X-ray diffraction imaging via deep convolutional neural networks

As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.

Non-destructive determination of phase, size, and strain of individual grains in polycrystalline photovoltaic materials

The non-destructive structural characterization of individual grains in thin-films photovoltaics based on polycrystalline materials is a powerful tool for revealing important details of the microstructure of solar cell absorbers. Here, we use three-dimensional X-ray diffraction (3DXRD) to obtain statistics on the phase, size, orientation and strain tensors of the grains, as well as their twin relations in Cu2ZnSnS4 (CZTS) absorbers. Moreover, this powerful approach allows the non-ambiguous determination of phases with distinct optical and electrical properties but similar lattice parameters, such as CZTS and ZnS. Our analysis over cumulative statistics of nearly 600 grains in polycrystalline CZTS reveals that a fraction of 2.5% corresponds to the ZnS secondary phase. Statistics of the strain distribution in the polycrystalline CZTS layer indicate an average tensile stress in the plane of the film of ~70 MPa and a compressive stress along the normal to the film of ~145 MPa. We found that 41% of the total number of grains in CZTS absorbers are Σ3 twins. We calculate the frequency of the six types of Σ3 boundaries, revealing that the 180° rotation along the axis<221>is the most frequent. Accessing the microstructure opens the possibility to study its influence on the properties of the film, such as bandgap variations due to strain or the role of twin boundaries in the charge transport mechanisms.