3D Imaging of a Dislocation Loop at the Onset of Plasticity in an Indented Nanocrystal

In Situ Nano-Indentation of a Gold Sub-Micrometric Particle Imaged by Multi-Wavelength Bragg Coherent X-ray Diffraction

The microstructure of a sub-micrometric gold crystal during nanoindentation is visualized by in situ multi-wavelength Bragg coherent X-ray diffraction imaging. The gold crystal is indented using a custom-built atomic force microscope. A band of deformation attributed to a shear band oriented along the (221) lattice plane is nucleated at the lower left corner of the crystal and propagates towards the crystal center with increasing applied mechanical load. After complete unloading, an almost strain-free and defect-free crystal is left behind, demonstrating a pseudo-elastic behavior that can only be studied by in situ imaging while it is invisible to ex situ examinations. The recovery is probably associated with reversible dislocations nucleation/annihilation at the side surface of the particle and at the particle-substrate interface, a behavior that has been predicted by atomistic simulations. The full recovery of the particle upon unloading sheds new light on extraordinary mechanical properties of metal nanoparticles obtained by solid-state dewetting.

Shear displacement gradient in X-ray Bragg coherent diffractive imaging

Bragg coherent X-ray diffractive imaging is a cutting-edge method for recovering three-dimensional crystal structure with nanoscale resolution. Phase retrieval provides an atomic displacement parallel to the Bragg peak reciprocal lattice vector. The derivative of the displacement along the same vector provides the normal strain field, which typically serves as a proxy for any structural changes. In this communication it is found that the other component of the displacement gradient, perpendicular to the reciprocal lattice vector, provides additional information from the experimental data collected from nanocrystals with mobile dislocations. Demonstration on published experimental data show how the perpendicular component of the displacement gradient adds to existing analysis, enabling an estimate for the external stresses, pinpointing the location of surface dislocations, and predicting the dislocation motion in in situ experiments.

X-ray Diffraction Imaging of Deformations in Thin Films and Nano-Objects

The quantification and localization of elastic strains and defects in crystals are necessary to control and predict the functioning of materials. The X-ray imaging of strains has made very impressive progress in recent years. On the one hand, progress in optical elements for focusing X-rays now makes it possible to carry out X-ray diffraction mapping with a resolution in the 50–100 nm range, while lensless imaging techniques reach a typical resolution of 5–10 nm. This continuous evolution is also a consequence of the development of new two-dimensional detectors with hybrid pixels whose dynamics, reading speed and low noise level have revolutionized measurement strategies. In addition, a new accelerator ring concept (HMBA network: hybrid multi-bend achromat lattice) is allowing a very significant increase (a factor of 100) in the brilliance and coherent flux of synchrotron radiation facilities, thanks to the reduction in the horizontal size of the source. This review is intended as a progress report in a rapidly evolving field. The next ten years should allow the emergence of three-dimensional imaging methods of strains that are fast enough to follow, in situ, the evolution of a material under stress or during a transition. Handling massive amounts of data will not be the least of the challenges.

4th generation synchrotron source boosts crystalline imaging at the nanoscale

New 4^th-generation synchrotron sources, with their increased brilliance, promise to greatly improve the performances of coherent X-ray microscopy. This perspective is of major interest for crystal microscopy, which aims at revealing the 3D crystalline structure of matter at the nanoscale, an approach strongly limited by the available coherent flux. Our results, based on Bragg ptychography experiments performed at the first 4^th-generation synchrotron source, demonstrate the possibility of retrieving a high-quality image of the crystalline sample, with unprecedented quality. Importantly, the larger available coherent flux produces datasets with enough information to overcome experimental limitations, such as strongly deteriorated scanning conditions. We show this achievement would not be possible with 3^rd-generation sources, a limit that has inhibited the development of this otherwise powerful microscopy method, so far. Hence, the advent of next-generation synchrotron sources not only makes Bragg ptychography suitable for high throughput studies but also strongly relaxes the associated experimental constraints, making it compatible with a wider range of experimental set-ups at the new synchrotrons.

Lattice Strain and Defects Analysis in Nanostructured Semiconductor Materials and Devices by High-Resolution X-Ray Diffraction: Theoretical and Practical Aspects

The reliability of semiconductor materials with electrical and optical properties are connected to their structures. The elastic strain field and tilt analysis of the crystal lattice, detectable by the variation in position and shape of the diffraction peaks, is used to quantify defects and investigate their mobility. The exploitation of high-resolution X-ray diffraction-based methods for the evaluation of structural defects in semiconductor materials and devices is reviewed. An efficient and non-destructive characterization is possible for structural parameters such as, lattice strain and tilt, layer composition and thickness, lattice mismatch, and dislocation density. The description of specific experimental diffraction geometries and scanning methods is provided. Today's X-ray diffraction based methods are evaluated and compared, also with respect to their applicability limits. The goal is to understand the close relationship between lattice strain and structural defects. For different material systems, the appropriate analytical methods are highlighted.

Sub-pixel high-resolution imaging of high-energy x-rays inspired by sub-wavelength optical imaging

We have developed and demonstrated an image super-resolution method-XR-UNLOC: X-Ray UNsupervised particle LOCalization-for hard x-rays measured with fast-frame-rate detectors that is an adaptation of the principle of photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), which enabled biological fluorescence imaging at sub-optical-wavelength scales. We demonstrate the approach on experimental coherent Bragg diffraction data measured with 52 keV x-rays from a nanocrystalline sample. From this sample, we resolve the fine fringe detail of a high-energy x-ray Bragg coherent diffraction pattern to an upsampling factor of 16 of the native pixel pitch of 30 μm of a charge-integrating fastCCD detector. This was accomplished by analysis of individual photon locations in a series of "nearly-dark" instances of the diffraction pattern that each contain only a handful of photons. Central to our approach was the adaptation of the UNLOC photon fitting routine for PALM/STORM to the hard x-ray regime to handle much smaller point spread functions, which required a different statistical test for photon detection and for sub-pixel localization. A comparison to a photon-localization strategy used in the x-ray community ("droplet analysis") showed that XR-UNLOC provides significant improvement in super-resolution. We also developed a metric by which to estimate the limit of reliable upsampling with XR-UNLOC under a given set of experimental conditions in terms of the signal-to-noise ratio of a photon detection event and the size of the point spread function for guiding future x-ray experiments in many disciplines where detector pixelation limits must be overcome.

On the use of the scattering amplitude in coherent X-ray Bragg diffraction imaging

Lens-less imaging of crystals with coherent X-ray diffraction offers some unique possibilities for strain-field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X-rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X-ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future.

Bragg Coherent Diffraction Imaging for In Situ Studies in Electrocatalysis

Electrocatalysis is at the heart of a broad range of physicochemical applications that play an important role in the present and future of a sustainable economy. Among the myriad of different electrocatalysts used in this field, nanomaterials are of ubiquitous importance. An increased surface area/volume ratio compared to bulk makes nanoscale catalysts the preferred choice to perform electrocatalytic reactions. Bragg coherent diffraction imaging (BCDI) was introduced in 2006 and since has been applied to obtain 3D images of crystalline nanomaterials. BCDI provides information about the displacement field, which is directly related to strain. Lattice strain in the catalysts impacts their electronic configuration and, consequently, their binding energy with reaction intermediates. Even though there have been significant improvements since its birth, the fact that the experiments can only be performed at synchrotron facilities and its relatively low resolution to date (∼10 nm spatial resolution) have prevented the popularization of this technique. Herein, we will briefly describe the fundamentals of the technique, including the electrocatalysis relevant information that we can extract from it. Subsequently, we review some of the computational experiments that complement the BCDI data for enhanced information extraction and improved understanding of the underlying nanoscale electrocatalytic processes. We next highlight success stories of BCDI applied to different electrochemical systems and in heterogeneous catalysis to show how the technique can contribute to future studies in electrocatalysis. Finally, we outline current challenges in spatiotemporal resolution limits of BCDI and provide our perspectives on recent developments in synchrotron facilities as well as the role of machine learning and artificial intelligence in addressing them.

Annealing of focused ion beam damage in gold microcrystals: an in situ Bragg coherent X-ray diffraction imaging study

Focused ion beam (FIB) techniques are commonly used to machine, analyse and image materials at the micro- and nanoscale. However, FIB modifies the integrity of the sample by creating defects that cause lattice distortions. Methods have been developed to reduce FIB-induced strain; however, these protocols need to be evaluated for their effectiveness. Here, non-destructive Bragg coherent X-ray diffraction imaging is used to study the in situ annealing of FIB-milled gold microcrystals. Two non-collinear reflections are simultaneously measured for two different crystals during a single annealing cycle, demonstrating the ability to reliably track the location of multiple Bragg peaks during thermal annealing. The thermal lattice expansion of each crystal is used to calculate the local temperature. This is compared with thermocouple readings, which are shown to be substantially affected by thermal resistance. To evaluate the annealing process, each reflection is analysed by considering facet area evolution, cross-correlation maps of the displacement field and binarized morphology, and average strain plots. The crystal's strain and morphology evolve with increasing temperature, which is likely to be caused by the diffusion of gallium in gold below ∼280°C and the self-diffusion of gold above ∼280°C. The majority of FIB-induced strains are removed by 380-410°C, depending on which reflection is being considered. These observations highlight the importance of measuring multiple reflections to unambiguously interpret material behaviour.

Imaging defects in vanadium(iii) oxide nanocrystals using Bragg coherent diffractive imaging

Here, Fohtung and colleagues capture nanoscale three-dimensional defects in vanadium(iii) oxide nanocrystals using X-ray Bragg coherent diffractive imaging.

Bragg coherent imaging of nanoprecipitates: role of superstructure reflections

Coherent precipitation of ordered phases is responsible for providing exceptional high-temperature mechanical properties in a wide range of compositionally complex alloys. Ordered phases are also essential to enhance the magnetic or catalytic properties of alloyed nanoparticles. The present work aims to demonstrate the relevance of Bragg coherent diffraction imaging (BCDI) for studying bulk and thin-film samples or isolated nanoparticles containing coherent nanoprecipitates/ordered phases. The structures of crystals of a few tens of nanometres in size are modelled with realistic interatomic potentials and are relaxed after introduction of coherent ordered nanoprecipitates. Diffraction patterns from fundamental and superstructure reflections are calculated in the kinematic approximation and used as input to retrieve the strain fields using algorithmic inversion. First, the case of single nanoprecipitates is tackled and it is shown that the strain field distribution from the ordered phase is retrieved very accurately. Then, the influence of the order parameter S on the strain field retrieved from the superstructure reflections is investigated. A very accurate strain distribution can be retrieved for partially ordered phases with large and inhomogeneous strains. Subsequently, the relevance of BCDI is evaluated for the study of systems containing many precipitates, and it is demonstrated that the technique is relevant for such systems. Finally, the experimental feasibility of using BCDI to image ordered phases is discussed in the light of the new possibilities offered by fourth-generation synchrotron sources.

Continuous scanning for Bragg coherent X-ray imaging

We explore the use of continuous scanning during data acquisition for Bragg coherent diffraction imaging, i.e., where the sample is in continuous motion. The fidelity of continuous scanning Bragg coherent diffraction imaging is demonstrated on a single Pt nanoparticle in a flow reactor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$400\,^\circ \hbox {C}$$\end{document}400∘C in an Ar-based gas flowed at 50 ml/min. We show a reduction of 30% in total scan time compared to conventional step-by-step scanning. The reconstructed Bragg electron density, phase, displacement and strain fields are in excellent agreement with the results obtained from conventional step-by-step scanning. Continuous scanning will allow to minimise sample instability under the beam and will become increasingly important at diffraction-limited storage ring light sources.

In-situ observation of the initiation of plasticity by nucleation of prismatic dislocation loops

The elastic-to-plastic transition during the deformation of a dislocation-free nanoscale volume is accompanied by displacement bursts associated with dislocation nucleation. The dislocations that nucleate during the so-called “pop-in” burst take the form of prismatic dislocation loops (PDLs) and exhibit characteristic burst-like emission and plastic recovery. Here, we report the in-situ transmission electron microscopy (TEM) observation of the initial plasticity ensued by burst-like emission of PDLs on nanoindentation of dislocation-free Au nanowires. The in-situ TEM nanoindentation showed that the nucleation and subsequent cross slip of shear loop(s) are the rate-limiting steps. As the indentation size increases, the cross slip of shear loop becomes favored, resulting in a transition from PDLs to open half-loops to helical dislocations. In the present case of nanoindentation of dislocation-free volumes, the PDLs glide out of the indentation stress field while spreading the plastic zone, as opposed to the underlying assumption of the Nix-Gao model.

Prismatic dislocation loops (PDLs) form during the elastic-to-plastic transition of a dislocation-free volume under nanoindentation. Here the authors observe the initial plasticity and burst-like emission of PDLs in Au nanowires by in-situ transmission electron microscopy, elucidating fundamental aspects of the formation process.

Variable-Wavelength Quick Scanning Nanofocused X-Ray Microscopy for In Situ Strain and Tilt Mapping

Compression of micropillars is followed in situ by a quick nanofocused X-ray scanning microscopy technique combined with 3D reciprocal space mapping. Compared to other attempts using X-ray nanobeams, it avoids any motion or vibration that would lead to a destruction of the sample. The technique consists of scanning both the energy of the incident nanofocused X-ray beam and the in-plane translations of the focusing optics along the X-ray beam. Here, the approach by imaging the strain and lattice orientation of Si micropillars and their pedestals during in situ compression is demonstrated. Varying the energy of the incident beam instead of rocking the sample and mapping the focusing optics instead of moving the sample supplies a vibration-free measurement of the reciprocal space maps without removal of the mechanical load. The maps of strain and lattice orientation are in good agreement with the ones recorded by ordinary rocking-curve scans. Variable-wavelength quick scanning X-ray microscopy opens the route for in situ strain and tilt mapping toward more diverse and complex materials environments, especially where sample manipulation is difficult.

Multi-wavelength Bragg coherent X-ray diffraction imaging of Au particles

Multi-wavelength (mw) Bragg coherent X-ray diffraction imaging (BCDI) is demonstrated on a single Au particle. The multi-wavelength Bragg diffraction patterns are inverted using conventional phase-retrieval algorithms where the dilation of the effective pixel size of a pixelated 2D detector caused by the variation of the X-ray beam energy is mitigated by interpolating the raw data. The reconstructed Bragg electron density and phase field are in excellent agreement with the results obtained from conventional rocking scans of the same particle. Voxel sizes of about 63 nm3 are obtained for reconstructions from both approaches. Phase shifts as small as 0.41 rad, which correspond to displacements of 14 pm and translate into strain resolution better than 10−4 in the Au particle, are resolved. The displacement field changes shape during the experiment, which is well reproduced by finite element method simulations considering an inhomogeneous strained carbon layer deposited on the Au particle over the course of the measurements. These experiments thus demonstrate the very high sensitivity of BCDI and mw-BCDI to strain induced by contaminations. Furthermore, mw-BCDI offers new opportunities for in situ and operando 3D strain imaging in complex sample environments.

Simultaneous scanning near-field optical and X-ray diffraction microscopy for correlative nanoscale structure-property characterization

A multimodal imaging instrument has been developed that integrates scanning near-field optical microscopy with nanofocused synchrotron X-ray diffraction imaging. The instrument allows for the simultaneous nanoscale characterization of electronic/near-field optical properties of materials together with their crystallographic structure, facilitating the investigation of local structure-property relationships. The design, implementation and operating procedures of this instrument are reported. The scientific capabilities are demonstrated in a proof-of-principle study of the insulator-metal phase transition in samarium sulfide (SmS) single crystals induced by applying mechanical pressure via a scanning tip. The multimodal imaging of an in situ tip-written region shows that the near-field optical reflectivity can be correlated with the heterogeneously transformed structure of the near-surface region of the crystal.

Oxidation induced strain and defects in magnetite crystals

Oxidation of magnetite (Fe₃O₄) has broad implications in geochemistry, environmental science and materials science. Spatially resolving strain fields and defect evolution during oxidation of magnetite provides further insight into its reaction mechanisms. Here we show that the morphology and internal strain distributions within individual nano-sized (~400 nm) magnetite crystals can be visualized using Bragg coherent diffractive imaging (BCDI). Oxidative dissolution in acidic solutions leads to increases in the magnitude and heterogeneity of internal strains. This heterogeneous strain likely results from lattice distortion caused by Fe(II) diffusion that leads to the observed domains of increasing compressive and tensile strains. In contrast, strain evolution is less pronounced during magnetite oxidation at elevated temperature in air. These results demonstrate that oxidative dissolution of magnetite can induce a rich array of strain and defect structures, which could be an important factor that contributes to the high reactivity observed on magnetite particles in aqueous environment.

In Situ Coherent X-ray Diffraction during Three-Point Bending of a Au Nanowire: Visualization and Quantification

The three-point bending behavior of a single Au nanowire deformed by an atomic force microscope was monitored by coherent X-ray diffraction using a sub-micrometer sized hard X-ray beam. Three-dimensional reciprocal-space maps were recorded before and after deformation by standard rocking curves and were measured by scanning the energy of the incident X-ray beam during deformation at different loading stages. The mechanical behavior of the nanowire was visualized in reciprocal space and a complex deformation mechanism is described. In addition to the expected bending of the nanowire, torsion was detected. Bending and torsion angles were quantified from the high-resolution diffraction data.

Nucleation-Controlled Plasticity of Metallic Nanowires and Nanoparticles

Nanowires and nanoparticles are envisioned as important elements of future technology and devices, owing to their unique mechanical properties. Metallic nanowires and nanoparticles demonstrate outstanding size-dependent strength since their deformation is dislocation nucleation-controlled. In this context, the recent experimental and computational studies of nucleation-controlled plasticity are reviewed. The underlying microstructural mechanisms that govern the strength of nanowires and the origin of their stochastic nature are also discussed. Nanoparticles, in which the stress state under compression is nonuniform, exhibit a shape-dependent strength. Perspectives on improved methods to study nucleation-controlled plasticity are discussed, as well the insights gained for microstructural-based design of mechanical properties at the nanoscale.

In situ Bragg coherent X-ray diffraction during tensile testing of an individual Au nanowire

Systematic tensile tests were performed on single defect-free 〈110〉 Au nanowires grown by physical vapor deposition while simultaneously recording three-dimensional Bragg peaks using coherent X-rays. The trajectory of three-dimensional Bragg peaks in reciprocal space during tensile testing allowed for measurements of the evolution of strains and rotations of the nanowire, thus sensitively uncovering the full deformation geometry of the nanowire. The transition from elastic to plastic deformation is accompanied by rotations of the nanowire as quantified by analysis of the motion of Bragg peaks, showing the importance of boundary conditions in interpreting nanoscale mechanical deformations.