Simulations of dislocation contrast in dark-field X-ray microscopy.

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10-2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources.

Multiscale in-situ characterization of static recrystallization using dark-field X-ray microscopy and high-resolution X-ray diffraction.

Dark-field X-ray microscopy (DFXM) is a high-resolution, X-ray-based diffraction microstructure imaging technique that uses an objective lens aligned with the diffracted beam to magnify a single Bragg reflection. DFXM can be used to spatially resolve local variations in elastic strain and orientation inside embedded crystals with high spatial (~ 60 nm) and angular (~ 0.001°) resolution. However, as with many high-resolution imaging techniques, there is a trade-off between resolution and field of view, and it is often desirable to enrich DFXM observations by combining it with a larger field-of-view technique. Here, we combine DFXM with high-resolution X-ray diffraction (HR-XRD) applied to an in-situ investigation of static recrystallization in an 80% hot-compressed Mg-3.2Zn-0.1Ca wt.% (ZX30) alloy. Using HR-XRD, we track the relative grain volume of > 8000 sub-surface grains during annealing in situ. Then, at several points during the annealing process, we "zoom in" to individual grains using DFXM. This combination of HR-XRD and DFXM enables multiscale characterization, used here to study why particular grains grow to consume a large volume fraction of the annealed microstructure. This technique pairing is particularly useful for small and/or highly deformed grains that are often difficult to resolve using more standard diffraction microstructure imaging techniques.

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.

Tilting refractive x-ray lenses for fine-tuning of their focal length.

In this work, we measure and model tilted x-ray refractive lenses to investigate their effects on an x-ray beam. The modelling is benchmarked against at-wavelength metrology obtained with x-ray speckle vector tracking experiments (XSVT) at the BM05 beamline at the ESRF-EBS light source, showing very good agreement. This validation permits us to explore possible applications of tilted x-ray lenses in optical design. We conclude that while tilting 2D lenses does not seem interesting from the point of view of aberration-free focusing, tilting 1D lenses around their focusing direction can be used for smoothly fine-tuning their focal length. We demonstrate experimentally this continuous change in the apparent lens radius of curvature R: a reduction up to a factor of two and beyond is achieved and possible applications in beamline optical design are proposed.

Extensive 3D mapping of dislocation structures in bulk aluminum.

Thermomechanical processing such as annealing is one of the main methods to tailor the mechanical properties of materials, however, much is unknown about the reorganization of dislocation structures deep inside macroscopic crystals that give rise to those changes. Here, we demonstrate the self-organization of dislocation structures upon high-temperature annealing in a mm-sized single crystal of aluminum. We map a large embedded 3D volume ([Formula: see text] [Formula: see text]m[Formula: see text]) of dislocation structures using dark field X-ray microscopy (DFXM), a diffraction-based imaging technique. Over the wide field of view, DFXM's high angular resolution allows us to identify subgrains, separated by dislocation boundaries, which we identify and characterize down to the single-dislocation level using computer-vision methods. We demonstrate how even after long annealing times at high temperatures, the remaining low density of dislocations still pack into well-defined, straight dislocation boundaries (DBs) that lie on specific crystallographic planes. In contrast to conventional grain growth models, our results show that the dihedral angles at the triple junctions are not the predicted 120[Formula: see text], suggesting additional complexities in the boundary stabilization mechanisms. Mapping the local misorientation and lattice strain around these boundaries shows that the observed strain is shear, imparting an average misorientation around the DB of [Formula: see text] 0.003 to 0.006[Formula: see text].

darfix - data analysis for dark-field X-ray microscopy.

A Python package for the analysis of dark-field X-ray microscopy (DFXM) and rocking curve imaging (RCI) data is presented. DFXM is a non-destructive diffraction imaging technique that provides three-dimensional maps of lattice strain and orientation. The darfix package enables fast processing and visualization of these data, providing the user with the essential tools to extract information from the acquired images in a fast and intuitive manner. These data processing and visualization tools can be either imported as library components or accessed through a graphical user interface as an Orange add-on. In the latter case, the different analysis modules can be easily chained to define computational workflows. Operations on larger-than-memory image sets are supported through the implementation of online versions of the data processing algorithms, effectively trading performance for feasibility when the computing resources are limited. The software can automatically extract the relevant instrument angle settings from the input files' metadata. The currently available input file format is EDF and in future releases HDF5 will be incorporated.

Simulating dark-field X-ray microscopy images with wavefront propagation techniques.

Dark-field X-ray microscopy is a diffraction-based synchrotron imaging technique capable of imaging defects in the bulk of extended crystalline samples. Numerical simulations are presented of image formation in such a microscope using numerical integration of the dynamical Takagi-Taupin equations and wavefront propagation. The approach is validated by comparing simulated images with experimental data from a near-perfect single crystal of diamond containing a single stacking-fault defect in the illuminated volume.

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°.

Large-Scale Defect Clusters with Hexagonal Honeycomb-like Arrangement in Ammonothermal GaN Crystals.

In this paper, we investigate, using X-ray Bragg diffraction imaging and defect selective etching, a new type of extended defect that occurs in ammonothermally grown gallium nitride (GaN) single crystals. This hexagonal "honeycomb" shaped defect is composed of bundles of parallel threading edge dislocations located in the corners of the hexagon. The observed size of the honeycomb ranges from 0.05 mm to 2 mm and is clearly correlated with the number of dislocations located in each of the hexagon's corners: typically ~5 to 200, respectively. These dislocations are either grouped in areas that exhibit "diameters" of 100-250 µm, or they show up as straight long chain alignments of the same size that behave like limited subgrain boundaries. The lattice distortions associated with these hexagonally arranged dislocation bundles are extensively measured on one of these honeycombs using rocking curve imaging, and the ensemble of the results is discussed with the aim of providing clues about the origin of these "honeycombs".

Identification of a coherent twin relationship from high-resolution reciprocal-space maps.

Twinning is a common crystallographic phenomenon which is related to the formation and coexistence of several orientation variants of the same crystal structure. It may occur during symmetry-lowering phase transitions or during the crystal growth itself. Once formed, twin domains play an important role in defining physical properties: for example, they underpin the giant piezoelectric effect in ferroelectrics, superelasticity in ferroelastics and the shape-memory effect in martensitic alloys. Regrettably, there is still a lack of experimental methods for the characterization of twin domain patterns. Here, a theoretical framework and algorithm are presented for the recognition of ferroelastic domains, as well as the identification of the coherent twin relationship using high-resolution reciprocal-space mapping of X-ray diffraction intensity around split Bragg peaks. Specifically, the geometrical theory of twinned ferroelastic crystals [Fousek & Janovec (1969). J. Appl. Phys. 40, 135-142] is adapted for the analysis of the X-ray diffraction patterns. The necessary equations are derived and an algorithm is outlined for the calculation of the separation between the Bragg peaks, diffracted from possible coherent twin domains, connected to one another via a mismatch-free interface. It is demonstrated that such separation is always perpendicular to the planar interface between mechanically matched domains. For illustration purposes, the analysis is presented of the separation between the peaks diffracted from tetragonal and rhombohedral domains in the high-resolution reciprocal-space maps of BaTiO3 and PbZr1-xTixO3 crystals. The demonstrated method can be used to analyse the response of multi-domain patterns to external perturbations such as electric field, change of temperature or pressure.

Untangling the Mechanisms of Lattice Distortions in Biogenic Crystals across Scales.

Biomineralized structures are complex functional hierarchical assemblies composed of biomineral building blocks joined together by an organic phase. The formation of individual mineral units is governed by the cellular tissue component that orchestrates the process of biomineral nucleation, growth, and morphogenesis. These processes are imprinted in the structural, compositional, and crystallographic properties of the emerging biominerals on all scales. Measurement of these properties can provide crucial information on the mechanisms that are employed by the organism to form these complex 3D architectures and to unravel principles of their functionality. Nevertheless, so far, this has only been possible at the macroscopic scale, by averaging the properties of the entire composite assembly, or at the mesoscale, by looking at extremely small parts of the entire picture. In this study, the newly developed synchrotron-based dark-field X-ray microscopy method is employed to study the link between 3D crystallographic properties of relatively large calcitic prisms in the shell of the mollusc Pinna nobilis and their local lattice properties with extremely high angular resolution down to 0.001°. Mechanistic links between variations in local lattice parameters and spacing, crystal orientation, chemical composition, and the deposition process of the entire mineral unit are unraveled.

Fourier ptychographic dark field x-ray microscopy.

Dark-field x-ray microscopy (DFXM) is an x-ray imaging technique for mapping three-dimensional (3D) lattice strain and rotation in bulk crystalline materials. At present, these maps of local structural distortions are derived from the raw intensity images using an incoherent analysis framework. In this work, we describe a coherent, Fourier ptychographic approach that requires little change in terms of instrumentation and acquisition strategy, and may be implemented on existing DFXM instruments. We demonstrate the method experimentally and are able to achieve quantitative phase reconstructions of thin film samples and maps of the aberrations in the objective lens. The method holds particular promise for the characterization of crystalline materials containing weak structural contrast.

Dislocation-toughened ceramics.

Functional and structural ceramics have become irreplaceable in countless high-tech applications. However, their inherent brittleness tremendously limits the application range and, despite extensive research efforts, particularly short cracks are hard to combat. While local plasticity carried by mobile dislocations allows desirable toughness in metals, high bond strength is widely believed to hinder dislocation-based toughening of ceramics. Here, we demonstrate the possibility to induce and engineer a dislocation microstructure in ceramics that improves the crack tip toughness even though such toughening does not occur naturally after conventional processing. With modern microscopy and simulation techniques, we reveal key ingredients for successful engineering of dislocation-based toughness at ambient temperature. For many ceramics a dislocation-based plastic zone is not impossible due to some intrinsic property (e.g. bond strength) but limited by an engineerable quantity, i.e. the dislocation density. The impact of dislocation density is demonstrated in a surface near region and suggested to be transferrable to bulk ceramics. Unexpected potential in improving mechanical performance of ceramics could be realized with novel synthesis strategies.

Thermal optimization of a high-heat-load double-multilayer monochromator.

Finite-element analysis is used to study the thermal deformation of a multilayer mirror due to the heat load from the undulator beam at a low-emittance synchrotron source, specifically the ESRF-EBS upgrade beamline EBSL-2. The energy bandwidth of the double-multilayer monochromator is larger than that of the relevant undulator harmonic, such that a considerable portion of the heat load is reflected. Consequently, the absorbed power is non-uniformly distributed on the surface. The geometry of the multilayer substrate is optimized to minimize thermally induced slope errors. We distinguish between thermal bending with constant curvature that leads to astigmatic focusing or defocusing and residual slope errors. For the EBSL-2 system with grazing angles θ between 0.2 and 0.4°, meridional and sagittal focal lengths down to 100 m and 2000 m, respectively, are found. Whereas the thermal bending can be tuned by varying the depth of the `smart cut', it is found that the geometry has little effect on the residual slope errors. In both planes they are 0.1-0.25 µrad. In the sagittal direction, however, the effect on the beam is drastically reduced by the `foregiveness factor', sin(θ). Optimization without considering the reflected heat load yields an incorrect depth of the `smart cut'. The resulting meridional curvature in turn leads to parasitic focal lengths of the order of 100 m.

In situ visualization of long-range defect interactions at the edge of melting.

Connecting a bulk material's microscopic defects to its macroscopic properties is an age-old problem in materials science. Long-range interactions between dislocations (line defects) are known to play a key role in how materials deform or melt, but we lack the tools to connect these dynamics to the macroscopic properties. We introduce time-resolved dark-field x-ray microscopy to directly visualize how dislocations move and interact over hundreds of micrometers deep inside bulk aluminum. With real-time movies, we reveal the thermally activated motion and interactions of dislocations that comprise a boundary and show how weakened binding forces destabilize the structure at 99% of the melting temperature. Connecting dynamics of the microstructure to its stability, we provide important opportunities to guide and validate multiscale models that are yet untested.

Design simulations of a horizontally deflecting high-heat-load monochromator.

The performance of a liquid-nitrogen-cooled high-heat-load monochromator with a horizontal scattering plane has been analysed, aiming to preserve the high quality of the X-ray beam in the vertical plane for downstream optics. Using finite-element analysis, height profiles of the crystal surface for various heat loads and the corresponding slope errors in the meridional and sagittal planes were calculated. Then the angular distortions of the reflected beam in both meridional and sagittal planes were calculated analytically and also modelled by ray tracing, revealing a good agreement of the two approaches. The results show that with increasing heat load in the crystal the slope errors of the crystal surface reach their smallest values first in the sagittal and then in the meridional plane. For the considered case of interest at a photon energy of 14.412 keV and the Si(111) reflection with a Bragg angle of 7.88°, the angular distortions of the reflected beam in the sagittal plane are an order of magnitude smaller than in the meridional one. Furthermore, they are smaller than the typical angular size of the beam source at the monochromator position. For a high-heat-load monochromator operating in the horizontal scattering plane, the sagittal angular distortions of the reflected beam appear in the vertical plane. Thus, such an instrument perfectly preserves the high quality of the X-ray beam in the vertical plane for downstream optics. Compared with vertical scattering, the throughput of the monochromatic beam with the horizontal scattering plane is reduced by only 3.3% for the new EBS source, instead of 34.3% for the old ESRF-1 machine. This identifies the horizontal-scattering high-heat-load monochromator as a device essentially free of the heat-load effects in the vertical plane and without significant loss in terms of throughput.

Imaging microstructural dynamics and strain fields in electro-active materials in situ with dark field x-ray microscopy.

The electric-field-induced and temperature induced dynamics of domains, defects, and phases play an important role in determining the macroscopic functional response of ferroelectric and piezoelectric materials. However, distinguishing and quantifying these phenomena remains a persistent challenge that inhibits our understanding of the fundamental structure-property relationships. In situ dark field x-ray microscopy is a new experimental technique for the real space mapping of lattice strain and orientation in bulk materials. In this paper, we describe an apparatus and methodology for conducting in situ studies of thermally and electrically induced structural dynamics and demonstrate their use on ferroelectric BaTiO3 single crystals. The stable temperature and electric field apparatus enables simultaneous control of electric fields up to ≈2 kV/mm at temperatures up to 200 °C with a stability of ΔT = ±0.01 K and a ramp rate of up to 0.5 K/min. This capability facilitates studies of critical phenomena, such as phase transitions, which we observe via the microstructural change occurring during the electric-field-induced cubic to tetragonal phase transition in BaTiO3 at its Curie temperature. With such systematic control, we show how the growth of the polar phase front and its associated ferroelastic domains fall along unexpected directions and, after several cycles of electric field application, result in a non-reversible lattice strain at the electrode-crystal interface. These capabilities pave the way for new insights into the temperature and electric field dependent electromechanical transitions and the critical influence of subtle defects and interfaces.

Quantifying microscale drivers for fatigue failure via coupled synchrotron X-ray characterization and simulations.

During cyclic loading, localization of intragranular deformation due to crystallographic slip acts as a precursor for crack initiation, often at coherent twin boundaries. A suite of high-resolution synchrotron X-ray characterizations, coupled with a crystal plasticity simulation, was conducted on a polycrystalline nickel-based superalloy microstructure near a parent-twin boundary in order to understand the deformation localization behavior of this critical, 3D microstructural configuration. Dark-field X-ray microscopy was spatially linked to high energy X-ray diffraction microscopy and X-ray diffraction contrast tomography in order to quantify, with cutting-edge resolution, an intragranular misorientation and high elastic strain gradients near a twin boundary. These observations quantify the extreme sub-grain scale stress gradients present in polycrystalline microstructures, which often lead to fatigue failure.

Translative lens-based full-field coherent X-ray imaging.

A full-field coherent imaging approach suitable for hard X-rays based on a classical (i.e. Galilean) X-ray microscope is described. The method combines a series of low-resolution images acquired at different transverse lens positions into a single high-resolution image, overcoming the spatial resolution limit set by the numerical aperture of the objective lens. The optical principles of the approach are described, the successful reconstruction of simulated phantom data is demonstrated, and aspects of the reconstruction are discussed. The authors believe that this approach offers some potential benefits over conventional scanning X-ray ptychography in terms of spatial bandwidth and radiation dose rate.

Experimental investigation of Gaussian random phase screen model for x-ray diffusers.

The beam diffusing properties of stacked layers of diffuser material were evaluated experimentally and compared to a Gaussian random phase screen model. The model was found to give promising accuracy in combination with a Lorentzian auto-correlation model. The tail behaviour of the angular scattering distribution as a function of number of diffusing layers was particularly well described by the model, and in the case of an amorphous carbon diffuser, the model could describe the whole of the scattering distribution convincingly.