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.

Characterization of Pt-coated twin paraboloidal laboratory capillary high energy X-ray optics.

Novel focusing optics composed of twin paraboloidal capillaries coated with Pt, for laboratory X-ray sources are presented and characterized. The optics are designed to focus the X-rays, resulting in an achromatic focused beam with photon energies up to 40 keV. The performance of the optics under different operational conditions is studied by comparing the energy-photon count spectra of the direct and focused beams. Based on these analyses, the optics gain and efficiency as a function of photon energy are determined. A focal spot of 8.5 µm with a divergence angle of 0.59° is observed. The obtained characteristics are discussed and related to theoretical considerations. Moreover, the suitability and advantages of the present optics for X-ray microdiffraction is demonstrated using polycrystalline aluminium. Finally, possibilities for further developments are suggested.

Simultaneous bright- and dark-field X-ray microscopy at X-ray free electron lasers.

The structures, strain fields, and defect distributions in solid materials underlie the mechanical and physical properties across numerous applications. Many modern microstructural microscopy tools characterize crystal grains, domains and defects required to map lattice distortions or deformation, but are limited to studies of the (near) surface. Generally speaking, such tools cannot probe the structural dynamics in a way that is representative of bulk behavior. Synchrotron X-ray diffraction based imaging has long mapped the deeply embedded structural elements, and with enhanced resolution, dark field X-ray microscopy (DFXM) can now map those features with the requisite nm-resolution. However, these techniques still suffer from the required integration times due to limitations from the source and optics. This work extends DFXM to X-ray free electron lasers, showing how the [Formula: see text] photons per pulse available at these sources offer structural characterization down to 100 fs resolution (orders of magnitude faster than current synchrotron images). We introduce the XFEL DFXM setup with simultaneous bright field microscopy to probe density changes within the same volume. This work presents a comprehensive guide to the multi-modal ultrafast high-resolution X-ray microscope that we constructed and tested at two XFELs, and shows initial data demonstrating two timing strategies to study associated reversible or irreversible lattice dynamics.

Real-time imaging of acoustic waves in bulk materials with X-ray microscopy.

The dynamics of lattice vibrations govern many material processes, such as acoustic wave propagation, displacive phase transitions, and ballistic thermal transport. The maximum velocity of these processes and their effects is determined by the speed of sound, which therefore defines the temporal resolution (picoseconds) needed to resolve these phenomena on their characteristic length scales (nanometers). Here, we present an X-ray microscope capable of imaging acoustic waves with subpicosecond resolution within mm-sized crystals. We directly visualize the generation, propagation, branching, and energy dissipation of longitudinal and transverse acoustic waves in diamond, demonstrating how mechanical energy thermalizes from picosecond to microsecond timescales. Bulk characterization techniques capable of resolving this level of structural detail have previously been available on millisecond time scales-orders of magnitude too slow to capture these fundamental phenomena in solid-state physics and geoscience. As such, the reported results provide broad insights into the interaction of acoustic waves with the structure of materials, and the availability of ultrafast time-resolved dark-field X-ray microscopy opens a vista of new opportunities for 3D imaging of materials dynamics on their intrinsic submicrosecond time scales.

Tracing the opposing assimilate and nutrient flows in live conifer needles.

The vasculature along conifer needles is fundamentally different from that in angiosperm leaves as it contains a unique transfusion tissue inside the bundle sheath. In this study, we used specific tracers to identify the pathway of photoassimilates from mesophyll to phloem, and the opposing pathway of nutrients from xylem to mesophyll. For symplasmic transport we applied esculin to the tip of attached pine needles and followed its movement down the phloem. For apoplasmic transport we let detached needles take up a membrane-impermeable contrast agent and used micro-X-ray computed tomography to map critical water exchange interfaces and domain borders. Microscopy and segmentation of the X-ray data enabled us to render and quantify the functional 3D structure of the water-filled apoplasm and the complementary symplasmic domain. The transfusion tracheid system formed a sponge-like apoplasmic domain that was blocked at the bundle sheath. Transfusion parenchyma cell chains bridged this domain as tortuous symplasmic pathways with strong local anisotropy which, as evidenced by the accumulation of esculin, pointed to the phloem flanks as the preferred phloem-loading path. Simple estimates supported a pivotal role of the bundle sheath, showing that a bidirectional movement of nutrient ions and assimilates is feasible and emphasizing the role of the bundle sheath in nutrient and assimilate exchange.

Correlative study of liquid in human bone by 3D neutron microscopy and lab-based X-ray µCT.

Liquid plays an important role in bone that has a complex 3D hierarchical pore structure. However, liquid (water) is difficult to discern from e.g. an organic matrix by X-ray imaging. Therefore, we use a correlative approach using both high resolution X-ray and neutron imaging. Human femoral bone with liquid adsorbed into some of the pores was imaged with both the Neutron Microscope at the ICON beamline, SINQ at PSI, and by lab-based µCT using 2.7 µm voxel size. Segmentation of the two datasets showed that, even though the liquid was clearly distinguishable in the neutron data and not in the X-ray data, it remained challenging to segment it from bone due to overlaps of peaks in the gray level histograms. In consequence, segmentations from X-ray and neutron data varied significantly. To address this issue, the segmented X-ray porosities was overlaid on the neutron data, making it possible to localize the liquid in the vascular porosities of the bone sample and use the neutron attenuation to identify it as H2O. The contrast in the neutron images was lowered slightly between the bone and the liquid compared to the bone and the air. This correlative study shows that the complementary use of X-rays and neutrons is very favorable, since H2O is very distinct in the neutron data, while D2O, H2O, and organic matter can barely be distinguished from air in the X-ray data.

Polychromatic neutron phase-contrast imaging of weakly absorbing samples enabled by phase retrieval.

The use of a phase-retrieval technique for propagation-based phase-contrast neutron imaging with a polychromatic beam is demonstrated. This enables imaging of samples with low absorption contrast and/or improving the signal-to-noise ratio to facilitate e.g. time-resolved measurements. A metal sample, designed to be close to a phase pure object, and a bone sample with canals partially filled with D2O were used for demonstrating the technique. These samples were imaged with a polychromatic neutron beam followed by phase retrieval. For both samples the signal-to-noise ratios were significantly improved and, in the case of the bone sample, the phase retrieval allowed for separation of bone and D2O, which is important for example for in situ flow experiments. The use of deuteration contrast avoids the use of chemical contrast enhancement and makes neutron imaging an interesting complementary method to X-ray imaging of bone.

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].

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°.

Significance of the spectral correction of photon counting detector response in material classification from spectral x-ray CT.

Purpose: Photon counting imaging detectors (PCD) has paved the way for spectral x-ray computed tomography (spectral CT), which simultaneously measures a sample's linear attenuation coefficient (LAC) at multiple energies. However, cadmium telluride (CdTe)-based PCDs working under high flux suffer from detector effects, such as charge sharing and photon pileup. These effects result in the severe spectral distortions of the measured spectra and significant deviation of the extracted LACs from the reference attenuation curve. We analyze the influence of the spectral distortion correction on material classification performance. Approach: We employ a spectral correction algorithm to reduce the primary spectral distortions. We use a method for material classification that measures system-independent material properties, such as electron density, ρ e , and effective atomic number, Z eff . These parameters are extracted from the LACs using attenuation decomposition and are independent of the scanner specification. The classification performance with the raw and corrected data is tested on different numbers of energy bins and projections and different radiation dose levels. We use experimental data with a broad range of materials in the range of 6 ≤ Z eff ≤ 15 , acquired with a custom laboratory instrument for spectral CT. Results: We show that using the spectral correction leads to an accuracy increase of 1.6 and 3.8 times in estimating ρ e and Z eff , respectively, when the image reconstruction is performed from only 12 projections and the 15 energy bins approach is used. Conclusions: The correction algorithm accurately reconstructs the measured attenuation curve and thus gives better classification performance.

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.

Confocal Bragg ptychography for bulk specimens: a numerical demonstration.

We report on a new X-ray imaging method, which generalizes Bragg ptychography to 3D mapping of embedded crystalline volumes within thick specimens. The sample is probed by a pencil X-ray beam. The diffracted beam is magnified by an objective and passes through a slit in the image plane to be monitored by a 2D detector in the far-field of the image plane. The dimensions of the incoming beam and the slit opening define a confocal Bragg volume. Scanning the sample with respect to this probe volume, an iterative oversampling routine is used to reconstruct the shape and projected displacement field of extended internal volumes. This routine takes into account the pupil function and known aberrations of the lens. We demonstrate the method by a numerical study of a 3.5 µm grain comprising a wall of edge dislocations. With a probe volume of ∼0.12 µm3 and a compound refractive lens with a numerical aperture of 0.49×10-3 as the objective, the dislocations are fully resolved with a displacement sensitivity of ∼10 pm. The spatial resolution is 26×27×123 nm3 (rms), with the poor resolution along the optical axis being limited by the probe size. With a four times larger numerical aperture, the resolution becomes 16×8×123 nm3 (rms). The lens aberrations are found to be not critical.

Modelling and Simulation of Compton Scatter Image Formation in Positron Emission Tomography.

We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the Positron Emission Tomography. The formula of the forward model has been obtained using the Single Scatter Simulation approximation under simplified assumptions and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions. Good fits of the formula-based and statistically generated profiles of scatter projections are observed in the presented numerical results.

Fast and quantitative 2D and 3D orientation mapping using Raman microscopy.

Non-destructive orientation mapping is an important characterization tool in materials science and geoscience for understanding and/or improving material properties based on their grain structure. Confocal Raman microscopy is a powerful non-destructive technique for chemical mapping of organic and inorganic materials. Here we demonstrate orientation mapping by means of Polarized Raman Microscopy (PRM). While the concept that PRM is sensitive to orientation changes is known, to our knowledge, an actual quantitative orientation mapping has never been presented before. Using a concept of ambiguity-free orientation determination analysis, we present fast and quantitative single-acquisition Raman-based orientation mapping by simultaneous registration of multiple Raman scattering spectra obtained at different polarizations. We demonstrate applications of this approach for two- and three-dimensional orientation mapping of a multigrain semiconductor, a pharmaceutical tablet formulation and a polycrystalline sapphire sample. This technique can potentially move traditional X-ray and electron diffraction type experiments into conventional optical laboratories.

Multilayer Laue lenses at high X-ray energies: performance and applications.

X-ray microscopy at photon energies above 15 keV is very attractive for the investigation of atomic and nanoscale properties of technologically relevant structural and bio materials. This method is limited by the quality of X-ray optics. Multilayer Laue lenses (MLLs) have the potential to make a major impact in this field because, as compared to other X-ray optics, they become more efficient and effective with increasing photon energy. In this work, MLLs were utilized with hard X-rays at photon energies up to 34.5 keV. The design, fabrication, and performance of these lenses are presented, and their application in several imaging configurations is described. In particular, two "full field" modes of imaging were explored, which provide various contrast modalities that are useful for materials characterisation. These include point projection imaging (or Gabor holography) for phase contrast imaging and direct imaging with both bright-field and dark-field illumination. With high-efficiency MLLs, such modes offer rapid data collection as compared with scanning methods as well as a large field of views.

Nondestructive Mapping of Long-Range Dislocation Strain Fields in an Epitaxial Complex Metal Oxide.

The misfit dislocations formed at heteroepitaxial interfaces create long-ranging strain fields in addition to the epitaxial strain. For systems with strong lattice coupling, such as ferroic oxides, this results in unpredictable and potentially debilitating functionality and device performance. In this work, we use dark-field X-ray microscopy to map the lattice distortions around misfit dislocations in an epitaxial film of bismuth ferrite (BiFeO3), a well-known multiferroic. We demonstrate the ability to precisely quantify weak, long-ranging strain fields and their associated symmetry lowering without modifying the mechanical state of the film. We isolate the screw and edge components of the individual dislocations and show how they result in weak charge heterogeneities via flexoelectric coupling. We show that even systems with small lattice mismatches and additional mechanisms of stress relief (such as mechanical twinning) may still give rise to measurable charge and strain heterogeneities that extend over mesoscopic length scales. This sets more stringent physical limitations on device size, dislocation density, and the achievable degree of lattice mismatch in epitaxial systems.

Numerical study of Bragg CDI on thick polycrystalline specimens.

Bragg coherent diffraction imaging (BCDI) is a powerful X-ray imaging technique for crystalline materials, providing high resolution maps of structure and strain. The technique is typically used to study a small isolated object, and is in general not compatible with a bulk polycrystalline sample, due to overlap of diffraction signals from various crystalline elements. In this paper, we present an imaging method for bulk samples, based on the use of a coherent source. The diffracted X-ray beam from a grain or domain of choice is magnified by an objective before being monitored by a 2D detector in the far field. The reconstruction principle is similar to the case of BCDI, while taking the magnification and pupil function into account. The concept is demonstrated using numerical simulations and reconstructions. We find that by using an object-lens distance shorter than the focal length, the numerical aperture is larger than in a traditional imaging geometry, and at the same time the setup is insensitive to small phase errors by lens imperfections. According to our simulations, we expect to be able to achieve a spatial resolution smaller than 20 nm when using the objective lens in this configuration.

Long-range symmetry breaking in embedded ferroelectrics.

The characteristic functionality of ferroelectric materials is due to the symmetry of their crystalline structure. As such, ferroelectrics lend themselves to design approaches that manipulate this structural symmetry by introducing extrinsic strain. Using in situ dark-field X-ray microscopy to map lattice distortions around deeply embedded domain walls and grain boundaries in BaTiO3, we reveal that symmetry-breaking strain fields extend up to several micrometres from domain walls. As this exceeds the average domain width, no part of the material is elastically relaxed, and symmetry is universally broken. Such extrinsic strains are pivotal in defining the local properties and self-organization of embedded domain walls, and must be accounted for by emerging computational approaches to material design.

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy.

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non-monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.

Simulating and optimizing compound refractive lens-based X-ray microscopes.

A comprehensive optical description of compound refractive lenses (CRLs) in condensing and full-field X-ray microscopy applications is presented. The formalism extends ray-transfer matrix analysis by accounting for X-ray attenuation by the lens material. Closed analytical expressions for critical imaging parameters such as numerical aperture, spatial acceptance (vignetting), chromatic aberration and focal length are provided for both thin- and thick-lens imaging geometries. These expressions show that the numerical aperture will be maximized and chromatic aberration will be minimized at the thick-lens limit. This limit may be satisfied by a range of CRL geometries, suggesting alternative approaches to improving the resolution and efficiency of CRLs and X-ray microscopes.