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We demonstrate the use of physically justified object constraints in x-ray Fresnel coherent diffractive imaging on a sample of nanoporous gold prepared by dealloying. Use of these constraints in the reconstruction algorithm enabled highly reliable imaging of the sample's shape and quantification of the 23- to 52-nm pore structure within it without use of a tight object support constraint.
The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure–function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources – X-ray free-electron lasers (XFELs) – provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal `sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10 −3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.
The proliferation of extremely intense synchrotron sources has enabled ever higher-resolution structures to be obtained using data collected from smaller and often more imperfect biological crystals. Synchrotron beamlines now exist that are capable of measuring data from single crystals that are just a few micrometres in size. This provides renewed motivation to study and understand the radiation damage behaviour of small protein crystals. Reciprocal-space mapping and Bragg coherent diffractive imaging experiments have been performed on cryo-cooled microcrystals of hen egg-white lysozyme as they undergo radiation damage. Several well established metrics, such as intensity-loss and lattice expansion, are applied to the diffraction data and the results are compared with several new metrics that can be extracted from the coherent imaging experiments. Individually some of these metrics are inconclusive. However, combining metrics, the results suggest that radiation damage behaviour in protein micro-crystals differs from that of larger protein crystals and may allow them to continue to diffract for longer. As a result, a possible mechanism to account for these observations is proposed.
Here, we present and demonstrate a formalism by which three-dimensional (3D) Bragg x-ray coherent diffraction imaging (BCDI) can be implemented without moving the sample by scanning the energy of the incident x-ray beam. This capability is made possible by introducing a 3D Fourier transform that accounts for x-ray wavelength variability. We also demonstrate the approach by inverting coherent Bragg diffraction patterns from a gold nanocrystal measured with an x-ray energy scan. Furthermore, variable-wavelength BCDI will expand the breadth of feasible in situ 3D strain imaging experiments towards more diverse materials environments, especially where sample manipulation is difficult.
As upgrades to synchrotrons increase coherent flux, atomic resolution in Bragg Coherent Diffraction Imaging has become a distinct possibility. Here, we present a new method that shows the capability to achieve atomic resolution for small nanoparticles.
The Datasets folder contains 3 datasets, corresponding to the datasets mentioned in the article with 670, 2691 and 586 images. The Runs folder has all the runs used. Besides the images itself it also contains tags for each image under `/entry_1/image_1/detector_and_photon_corrected/tags`. The `headings` attribute gives the name of each tag. The `Jonas Strict` tag corresponds to the 670 images, the `Redflamingo` tag to the 2691 images and the `Redflamingo_Ida_subset` tag to the 586 images. The final dataset with 260 images can be obtained from `Datasets/amoc6914-Redflamingo-manual-586.h5` and use the `/model/diameterNM` group to select the 260 images with size closest to 214 nm.
We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging. We represent the crystals using spherical harmonics (SH) and generate the corresponding synthetic diffraction patterns. We utilize 3D convolutional neural networks (CNNs) to learn a mapping between 3D diffraction volumes and the SH, which describe the boundary of the physical volumes from which they were generated. We use the 3D CNN-predicted SH coefficients as the initial guesses, which are then fine-tuned using adaptive model-independent feedback for improved accuracy. We also adaptively tune the locations, intensities, and decay rates of collections of radial basis functions in order to reproduce the non-uniform internal structure of 3D objects and demonstrate the method for a synthetic volume that has an internal void and a density ramp.
Bimetallic catalysts can undergo segregation or redistribution of the metals driven by oxidizing and reducing environments. Bragg coherent diffraction imaging (BCDI) was used to relate displacement fields to compositional distributions in crystalline Pt-Rh alloy nanoparticles. Three-dimensional images of internal composition showed that the radial distribution of compositions reverses partially between the surface shell and the core when gas flow changes between O 2 and H 2 . Our observation suggests that the elemental segregation of nanoparticle catalysts should be highly active during heterogeneous catalysis and can be a controlling factor in synthesis of electrocatalysts. Additionally, our study exemplifies applications of BCDI for in situ 3D imaging of internal equilibrium compositions in other bimetallic alloy nanoparticles.
A deep neural network model plus automatic differentiation is developed for retrieving phase information from 3D coherent diffraction images. The model is implemented using Tensorflow and the training dataset is generated using physics-based atomistic simulations. Custom codes are written to handle the resampling of diffraction images to oversampling ratios appropriate for the neural network model.
A complex three-dimensional quantitative image of an extended zinc oxide (ZnO) crystal has been obtained using Bragg coherent diffraction imaging integrated with ptychography. By scanning a 2.5 µm-long arm of a ZnO tetrapod across a 1.3 µm X-ray beam with fine step sizes while measuring a three-dimensional diffraction pattern at each scan spot, the three-dimensional electron density and projected displacement field of the entire crystal were recovered. The simultaneously reconstructed complex wavefront of the illumination combined with its coherence properties determined by a partial coherence analysis implemented in the reconstruction process provide a comprehensive characterization of the incident X-ray beam.
Understanding how diffusion takes place within nanocrystals is of great importance for their stability and for controlling their synthesis. In this study, we used the strain sensitivity of Bragg coherent diffraction imaging (BCDI) to study the diffusion of iron into individual gold nanocrystals in situ at elevated temperatures. The BCDI experiments were performed at the I-07 beamline at Diamond Light Source, UK. The diffraction pattern of individual gold nanocrystals was measured around the (11-1) Bragg peak of gold before and after iron deposition as a function of temperature and time. Phase retrieval algorithms were used to obtain real space reconstructions of the nanocrystals from their measured diffraction patterns. Alloying of iron with gold at sample temperatures of 300 °C–500 °C and dealloying of iron from gold at 600 °C were observed. The volume of the alloyed region in the nanocrystals was found to increase with the dose of iron. However, no significant time dependence was observed for the structure following each iron deposition, suggesting that the samples reached equilibrium relatively quickly. The resulting phase distribution within the gold nanocrystals after the iron depositions suggests a contraction due to diffusion of iron. Furthermore, our results show that BCDI is a useful technique for studying diffusion in three dimensions and alloying behaviour in individual crystalline grains.
Dissolution is critical to nanomaterial stability, especially for partially dealloyed nanoparticle catalysts. Unfortunately, highly active catalysts are often not stable in their reactive environments, preventing widespread application. Thus, focusing on the structure–stability relationship at the nanoscale is crucial and will likely play an important role in meeting grand challenges. Recent advances in imaging capability have come from electron, X-ray, and other techniques but tend to be limited to specific sample environments and/or two-dimensional images. Here, we report investigations into the defect-stability relationship of silver nanoparticles to voltage-induced electrochemical dissolution imaged in situ in three dimensional detail by Bragg coherent diffractive imaging. We first determine the average dissolution kinetics by stationary probe rotating disk electrode in combination with inductively coupled plasma mass spectrometry, which allows in situ measurement of Ag+ ion formation. We then observe the dissolution and redeposition processes in single nanocrystals, providing unique insight about the role of surface strain, defects, and their coupling to the dissolution chemistry. Finally, the methods developed and the knowledge gained go well beyond a “simple” silver electrochemistry and are applicable to all electrocatalytic reactions where functional links between activity and stability are controlled by structure and defect dynamics.
The recent commissioning of a movable monochromator at the 34-ID-C endstation of the Advanced Photon Source has vastly simplified the collection of Bragg coherent diffraction imaging (BCDI) data from multiple Bragg peaks of sub-micrometre scale samples. Laue patterns arising from the scattering of a polychromatic beam by arbitrarily oriented nanocrystals permit their crystal orientations to be computed, which are then used for locating and collecting several non-co-linear Bragg reflections. The volumetric six-component strain tensor is then constructed by combining the projected displacement fields that are imaged using each of the measured reflections via iterative phase retrieval algorithms. Complications arise when the sample is heterogeneous in composition and/or when multiple grains of a given lattice structure are simultaneously illuminated by the polychromatic beam. Here, a workflow is established for orienting and mapping nanocrystals on a substrate of a different material using scanning Laue diffraction microscopy. The capabilities of the developed algorithms and procedures with both synthetic and experimental data are demonstrated. The robustness is verified by comparing experimental texture maps obtained with Laue diffraction microscopy at the beamline with maps obtained from electron back-scattering diffraction measurements on the same patch of gold nanocrystals. Such tools provide reliable indexing for both isolated and densely distributed nanocrystals, which are challenging to image in three dimensions with other techniques.
Strain is known to enhance the activity of the oxygen reduction reaction in catalytic platinum alloy nanoparticles, whose inactivity is the primary impediment to efficient fuel cells and metal–air batteries. Here, Bragg coherent diffraction imaging (BCDI) was employed to reveal the strain evolution during the voltammetric cycling in Pt–Ni alloy nanoparticles composed of Pt 2 Ni 3 , Pt 1 Ni 1 , and Pt 3 Ni 2 . Analysis of the 3D strain images using a core–shell model shows that the strain as large as 5% is induced on Pt-rich shells due to Ni dissolution. The composition dependency of the strain on the shells is in excellent agreement with that of the catalytic activity. The present study demonstrates that BCDI enables quantitative determination of the strain on alloy nanoparticles during electrochemical reactions, which provides a means to exploit surface strain to design a wide range of electrocatalysts.
In this study, crystallographic defects such as dislocations can significantly alter material properties and functionality. However, imaging these imperfections during operation remains challenging due to the short length scales involved and the reactive environments of interest. Bragg coherent diffractive imaging (BCDI) has emerged as a powerful tool capable of identifying dislocations, twin domains, and other defects in 3D detail with nanometer spatial resolution within nanocrystals and grains in reactive environments. However, BCDI relies on phase retrieval algorithms that can fail to accurately reconstruct the defect network. Here, we use numerical simulations to explore different guided phase retrieval algorithms for imaging defective crystals using BCDI. We explore different defect types, defect densities, Bragg peaks, and guided algorithm fitness metrics as a function of signal-to-noise ratio. Based on these results, we offer a general prescription for phasing of defective crystals with no a prior knowledge.
InGaAs quantum wells embedded in GaAs nanowires can serve as compact near-infrared emitters for direct integration onto Si complementary metal oxide semiconductor technology. While the core–shell geometry in principle allows for a greater tuning of composition and emission, especially farther into the infrared, the practical limits of elastic strain accommodation in quantum wells on multifaceted nanowires have not been established. One barrier to progress is the difficulty of directly comparing the emission characteristics and the precise microstructure of a single nanowire. Here, in this study, we report an approach to correlating quantum well morphology, strain, defects, and emission to understand the limits of elastic strain accommodation in nanowire quantum wells specific to their geometry. We realize full 3D Bragg coherent diffraction imaging (BCDI) of intact quantum wells on vertically oriented epitaxial nanowires, which enables direct correlation with single-nanowire photoluminescence. By growing In 0.2 Ga 0.8 As quantum wells of distinct thicknesses on different facets of the same nanowire, we identified the critical thickness at which defects are nucleated. A correlation with a traditional transmission electron microscopy analysis confirms that BCDI can image the extended structure of defects. Finite element simulations of electron and hole states explain the emission characteristics arising from strained and partially relaxed regions. This approach, imaging the 3D strain and microstructure of intact nanowire core–shell structures with application-relevant dimensions, can aid the development of predictive models that enable the design of new compact infrared emitters.
Mesoscale thermal transport is of fundamental interest and practical importance in materials such as thermoelectrics. Coherent lattice vibrations (acoustic phonons) govern thermal transport in crystalline solids and are affected by the shape, size, and defect density in nanoscale materials. The advent of hard x-ray free electron lasers (XFELs) capable of producing ultrafast x-ray pulses has significantly impacted the understanding of acoustic phonons by enabling their direct study with x-rays. However, previous studies have reported ensemble-averaged results that cannot distinguish the impact of mesoscale heterogeneity on the phonon dynamics. Here we use Bragg coherent diffractive imaging (BCDI) to resolve the 4D evolution of the acoustic phonons in a single zinc oxide rod with a spatial resolution of 50 nm and a temporal resolution of 25 picoseconds. We observe homogeneous (lattice breathing/rotation) and inhomogeneous (shear) acoustic phonon modes, which are compared to finite element simulations. We investigate the possibility of changing phonon dynamics by altering the crystal through acid etching. Lastly, we find that the acid heterogeneously dissolves the crystal volume, which will significantly impact the phonon dynamics. In general, our results represent the first step towards understanding the effect of structural properties at the individual crystal level on phonon dynamics.
Of current importance for alloy design is controlling chemical ordering through processing routes to optimize an alloy's mechanical properties for a desired application. However, characterization of chemical ordering remains an ongoing challenge, particularly when nondestructive characterization is needed. Here, in this study, Bragg coherent diffraction imaging is used to reconstruct morphology and lattice displacement in model Cu 3 Au nanocrystals that have undergone different heat treatments to produce variation in chemical ordering. The magnitudes and distributions of the scattering amplitudes (proportional to electron density) and lattice strains within these crystals are then analyzed to correlate them to the expected amount of chemical ordering present. Nanocrystals with increased amounts of ordering are found to generally have less extreme strains present and reduced strain distribution widths. In addition, statistical correlations are found between the spatial arrangement of scattering amplitude and lattice strains.