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.

Electric-field-induced non-ergodic relaxor to ferroelectric transition in BiFeO3-xSrTiO3 ceramics.

While BiFeO3-based solid solutions show great promise for applications in energy conversion and storage, realizing this promise necessitates understanding the structure-property relationship in particular pertaining to the relaxor-like characteristics often exhibited by solid solutions with polar-to-non-polar morphotropic phase boundaries. To this end, we investigated the role of the compositionally-driven relaxor state in (100 - x)BiFeO3-xSrTiO3 [BFO-xSTO], via in situ synchrotron X-ray diffraction under bipolar electric-field cycling. The electric-field induced changes to the crystal structure, phase fraction and domain textures were monitored via the {111}pc, {200}pc, and 1/2{311}pc Bragg peaks. The dynamics of the intensities and positions of the (111) and (111̄) reflections reveal an initial non-ergodic regime followed by long-range ferroelectric ordering after extended poling cycles. The increased degree of random multi-site occupation in BFO-42STO compared to BFO-35STO is correlated with an increase of the critical electric field needed to induce the non-ergodic-to-ferroelectric transition, and a decrease in the degree of domain reorientation. Although both compositions show an irreversible transition to a long-range ferroelectric state, our results suggest that the weaker ferroelectric response in BFO-42STO is related to an increase in ergodicity. This, in turn, serves to guide the development of BFO-based systems into promising platform for further property engineering towards specific capacitor applications.

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.

A finite difference scheme for integrating the Takagi-Taupin equations on an arbitrary orthogonal grid.

Calculating dynamical diffraction patterns for X-ray diffraction imaging techniques requires numerical integration of the Takagi-Taupin equations. This is usually performed with a simple, second-order finite difference scheme on a sheared computational grid in which two of the axes are aligned with the wavevectors of the incident and scattered beams. This dictates, especially at low scattering angles, an oblique grid of uneven step sizes. Here a finite difference scheme is presented that carries out this integration in slab-shaped samples on an arbitrary orthogonal grid by implicitly utilizing Fourier interpolation. The scheme achieves the expected second-order convergence and a similar error to the traditional approach for similarly dense grids.

An automated approach to the alignment of compound refractive lenses.

Compound refractive lenses (CRLs) are established X-ray focusing optics, and are used to focus the beam or image the sample in many beamlines at X-ray facilities. While CRLs are quite established, the stack of single lens elements affords a very small numerical aperture because of the thick lens profile, making them far more difficult to align than classical optical lenses that obey the thin-lens approximation. This means that the alignment must be very precise and is highly sensitive to changes to the incident beam, often requiring regular readjustments. Some groups circumvent the full realignment procedure by using engineering controls (e.g. mounting optics) that sacrifice some of the beam's focusing precision, i.e. spot size, or resolution. While these choices minimize setup time, there are clear disadvantages. This work presents a new automated approach to align CRLs using a simple alignment apparatus that is easy to adapt and install at different types of X-ray experiments or facilities. This approach builds on recent CRL modeling efforts, using an approach based on the Stochastic Nelder-Mead (SNM) simplex method. This method is outlined and its efficacy is demonstrated with numerical simulation that is tested in real experiments conducted at the Advanced Photon Source to confirm its performance with a synchrotron beam. This work provides an opportunity to automate key instrumentation at X-ray facilities.

Unveiling the Interaction Mechanisms of Electron and X-ray Radiation with Halide Perovskite Semiconductors using Scanning Nanoprobe Diffraction.

The interaction of high-energy electrons and X-ray photons with beam-sensitive semiconductors such as halide perovskites is essential for the characterization and understanding of these optoelectronic materials. Using nanoprobe diffraction techniques, which can investigate physical properties on the nanoscale, studies of the interaction of electron and X-ray radiation with state-of-the-art (FA0.79 MA0.16 Cs0.05 )Pb(I0.83 Br0.17 )3 hybrid halide perovskite films (FA, formamidinium; MA, methylammonium) are performed, tracking the changes in the local crystal structure as a function of fluence using scanning electron diffraction and synchrotron nano X-ray diffraction techniques. Perovskite grains are identified, from which additional reflections, corresponding to PbBr2 , appear as a crystalline degradation phase after fluences of 200 e- Å- 2 . These changes are concomitant with the formation of small PbI2 crystallites at the adjacent high-angle grain boundaries, with the formation of pinholes, and with a phase transition from tetragonal to cubic. A similar degradation pathway is caused by photon irradiation in nano-X-ray diffraction, suggesting common underlying mechanisms. This approach explores the radiation limits of these materials and provides a description of the degradation pathways on the nanoscale. Addressing high-angle grain boundaries will be critical for the further improvement of halide polycrystalline film stability, especially for applications vulnerable to high-energy radiation such as space photovoltaics.

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.

Oxygen Vacancies Nucleate Charged Domain Walls in Ferroelectrics.

We study the influence of oxygen vacancies on the formation of charged 180° domain walls in ferroelectric BaTiO_{3} using first principles calculations. We show that it is favorable for vacancies to assemble in crystallographic planes, and that such clustering is accompanied by the formation of a charged domain wall. The domain wall has negative bound charge, which compensates the nominal positive charge of the vacancies and leads to a vanishing density of free charge at the wall. This is in contrast to the positively charged domain walls, which are nearly completely compensated by free charge from the bulk. The results thus explain the experimentally observed difference in electronic conductivity of the two types of domain walls, as well as the generic prevalence of charged domain walls in ferroelectrics. Moreover, the explicit demonstration of vacancy driven domain wall formation implies that specific charged domain wall configurations may be realized by bottom-up design for use in domain wall based information processing.

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.

Conceptual Framework for Dislocation-Modified Conductivity in Oxide Ceramics Deconvoluting Mesoscopic Structure, Core, and Space Charge Exemplified for SrTiO3.

The introduction of dislocations is a recently proposed strategy to tailor the functional and especially the electrical properties of ceramics. While several works confirm a clear impact of dislocations on electrical conductivity, some studies raise concern in particular when expanding to dislocation arrangements beyond a geometrically tractable bicrystal interface. Moreover, the lack of a complete classification on pertinent dislocation characteristics complicates a systematic discussion and hampers the design of dislocation-modified electrical conductivity. We proceed by mechanically introducing dislocations with three different mesoscopic structures into the model material single-crystal SrTiO3 and extensively characterizing them from both a mechanical as well as an electrical perspective. As a final result, a deconvolution of mesoscopic structure, core structure, and space charge enables us to obtain the complete picture of the effect of dislocations on functional properties, focusing here on electric properties.

Impact of dual-layer solid-electrolyte interphase inhomogeneities on early-stage defect formation in Si electrodes.

While intensive efforts have been devoted to studying the nature of the solid-electrolyte interphase (SEI), little attention has been paid to understanding its role in the mechanical failures of electrodes. Here we unveil the impact of SEI inhomogeneities on early-stage defect formation in Si electrodes. Buried under the SEI, these early-stage defects are inaccessible by most surface-probing techniques. With operando full field diffraction X-ray microscopy, we observe the formation of these defects in real time and connect their origin to a heterogeneous degree of lithiation. This heterogeneous lithiation is further correlated to inhomogeneities in topography and lithium-ion mobility in both the inner- and outer-SEI, thanks to a combination of operando atomic force microscopy, electrochemical strain microscopy and sputter-etched X-ray photoelectron spectroscopy. Our multi-modal study bridges observations across the multi-level interfaces (Si/LixSi/inner-SEI/outer-SEI), thus offering novel insights into the impact of SEI homogeneities on the structural stability of Si-based lithium-ion batteries.

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.

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.

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.

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.