PyNX.Ptycho: a computing library for X-ray coherent diffraction imaging of nanostructures

Anomalous Glide Plane in Platinum Nano- and Microcrystals

At the nanoscale, the properties of materials depend critically on the presence of crystal defects. However, imaging and characterizing the structure of defects in three dimensions inside a crystal remain a challenge. Here, by using Bragg coherent diffraction imaging, we observe an unexpected anomalous {110} glide plane in two Pt submicrometer crystals grown by very different processes and having very different morphologies. The structure of the defects (type, associated glide plane, and lattice displacement) is imaged in these faceted Pt crystals. Using this noninvasive technique, both plasticity and unusual defect behavior can be probed at the nanoscale.

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems.

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.

A modular software framework for the design and implementation of ptychography algorithms

Computational methods are driving high impact microscopy techniques such as ptychography. However, the design and implementation of new algorithms is often a laborious process, as many parts of the code are written in close-to-the-hardware programming constructs to speed up the reconstruction. In this article, we present SciComPty, a new ptychography software framework aiming at simulating ptychography datasets and testing state-of-the-art and new reconstruction algorithms. Despite its simplicity, the software leverages GPU accelerated processing through the PyTorch CUDA interface. This is essential for designing new methods that can readily be employed. As an example, we present an improved position refinement method based on Adam and a new version of the rPIE algorithm, adapted for partial coherence setups. Results are shown on both synthetic and real datasets. The software is released as open-source.

Imaging the facet surface strain state of supported multi-faceted Pt nanoparticles during reaction

Nanostructures with specific crystallographic planes display distinctive physico-chemical properties because of their unique atomic arrangements, resulting in widespread applications in catalysis, energy conversion or sensing. Understanding strain dynamics and their relationship with crystallographic facets have been largely unexplored. Here, we reveal in situ, in three-dimensions and at the nanoscale, the volume, surface and interface strain evolution of single supported platinum nanocrystals during reaction using coherent x-ray diffractive imaging. Interestingly, identical {hkl} facets show equivalent catalytic response during non-stoichiometric cycles. Periodic strain variations are rationalised in terms of O₂ adsorption or desorption during O₂ exposure or CO oxidation under reducing conditions, respectively. During stoichiometric CO oxidation, the strain evolution is, however, no longer facet dependent. Large strain variations are observed in localised areas, in particular in the vicinity of the substrate/particle interface, suggesting a significant influence of the substrate on the reactivity. These findings will improve the understanding of dynamic properties in catalysis and related fields.

Understanding strain dynamics and their relationship with crystallographic facets have been largely unexplored. Here the authors demonstrate how the 3D lattice displacement and strain evolution depend on the crystallographic facets of Pt nanoparticles during CO oxidation reaction, providing new insights in the relationship between facet-related surface strain and chemistry.

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.

Scalable and accurate multi-GPU-based image reconstruction of large-scale ptychography data

While the advances in synchrotron light sources, together with the development of focusing optics and detectors, allow nanoscale ptychographic imaging of materials and biological specimens, the corresponding experiments can yield terabyte-scale volumes of data that can impose a heavy burden on the computing platform. Although graphics processing units (GPUs) provide high performance for such large-scale ptychography datasets, a single GPU is typically insufficient for analysis and reconstruction. Several works have considered leveraging multiple GPUs to accelerate the ptychographic reconstruction. However, most of these works utilize only the Message Passing Interface to handle the communications between GPUs. This approach poses inefficiency for a hardware configuration that has multiple GPUs in a single node, especially while reconstructing a single large projection, since it provides no optimizations to handle the heterogeneous GPU interconnections containing both low-speed (e.g., PCIe) and high-speed links (e.g., NVLink). In this paper, we provide an optimized intranode multi-GPU implementation that can efficiently solve large-scale ptychographic reconstruction problems. We focus on the maximum likelihood reconstruction problem using a conjugate gradient (CG) method for the solution and propose a novel hybrid parallelization model to address the performance bottlenecks in the CG solver. Accordingly, we have developed a tool, called PtyGer (Ptychographic GPU(multiple)-based reconstruction), implementing our hybrid parallelization model design. A comprehensive evaluation verifies that PtyGer can fully preserve the original algorithm's accuracy while achieving outstanding intranode GPU scalability.

A Parameter Refinement Method for Ptychography Based on Deep Learning Concepts

X-ray ptychography is an advanced computational microscopy technique, which is delivering exceptionally detailed quantitative imaging of biological and nanotechnology specimens, which can be used for high-precision X-ray measurements. However, coarse parametrisation in propagation distance, position errors and partial coherence frequently threaten the experimental viability. In this work, we formally introduce these actors, solving the whole reconstruction as an optimisation problem. A modern deep learning framework was used to autonomously correct the setup incoherences, thus improving the quality of a ptychography reconstruction. Automatic procedures are indeed crucial to reduce the time for a reliable analysis, which has a significant impact on all the fields that use this kind of microscopy. We implemented our algorithm in our software framework, SciComPty, releasing it as open-source. We tested our system on both synthetic datasets, as well as on real data acquired at the TwinMic beamline of the Elettra synchrotron facility.

Exploring the 3D structure and defects of a self-assembled gold mesocrystal by coherent X-ray diffraction imaging

Mesocrystals are nanostructured materials consisting of individual nanocrystals having a preferred crystallographic orientation. On mesoscopic length scales, the properties of mesocrystals are strongly affected by structural heterogeneity. Here, we report the detailed structural characterization of a faceted mesocrystal grain self-assembled from 60 nm sized gold nanocubes. Using coherent X-ray diffraction imaging, we determined the structure of the mesocrystal with the resolution sufficient to resolve each gold nanoparticle. The reconstructed electron density of the gold mesocrystal reveals its intrinsic structural heterogeneity, including local deviations of lattice parameters, and the presence of internal defects. The strain distribution shows that the average superlattice obtained by angular X-ray cross-correlation analysis and the real, "multidomain" structure of a mesocrystal are very close to each other, with a deviation less than 10%. These results will provide an important impact to understanding the fundamental principles of structuring and self-assembly including ensuing properties of mesocrystals.

Facet-Dependent Strain Determination in Electrochemically Synthetized Platinum Model Catalytic Nanoparticles

Studying model nanoparticles is one approach to better understand the structural evolution of a catalyst during reactions. These nanoparticles feature well-defined faceting, offering the possibility to extract structural information as a function of facet orientation and compare it to theoretical simulations. Using Bragg Coherent X-ray Diffraction Imaging, the uniformity of electrochemically synthesized model catalysts is studied, here high-index faceted tetrahexahedral (THH) platinum nanoparticles at ambient conditions. 3D images of an individual nanoparticle are obtained, assessing not only its shape but also the specific components of the displacement and strain fields both at the surface of the nanocrystal and inside. The study reveals structural diversity of shapes and defects, and shows that the THH platinum nanoparticles present strain build-up close to facets and edges. A facet recognition algorithm is further applied to the imaged nanoparticles and provides facet-dependent structural information for all measured nanoparticles. In the context of strain engineering for model catalysts, this study provides insight into the shape-controlled synthesis of platinum nanoparticles with high-index facets.

X-ray diffraction reveals the amount of strain and homogeneity of extremely bent single nanowires

Core-shell nanowires (NWs) with asymmetric shells allow for strain engineering of NW properties because of the bending resulting from the lattice mismatch between core and shell material. The bending of NWs can be readily observed by electron microscopy. Using X-ray diffraction analysis with a micro- and nano-focused beam, the bending radii found by the microscopic investigations are confirmed and the strain in the NW core is analyzed. For that purpose, a kinematical diffraction theory for highly bent crystals is developed. The homogeneity of the bending and strain is studied along the growth axis of the NWs, and it is found that the lower parts, i.e. close to the substrate/wire interface, are bent less than the parts further up. Extreme bending radii down to ∼3 µm resulting in strain variation of ∼2.5% in the NW core are found.

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

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.

Mapping Inversion Domain Boundaries along Single GaN Wires with Bragg Coherent X-ray Imaging

Gallium nitride (GaN) is of technological importance for a wide variety of optoelectronic applications. Defects in GaN, like inversion domain boundaries (IDBs), significantly affect the electrical and optical properties of the material. We report, here, on the structural configurations of planar inversion domain boundaries inside n-doped GaN wires measured by Bragg coherent X-ray diffraction imaging. Different complex domain configurations are revealed along the wires with a 9 nm in-plane spatial resolution. We demonstrate that the IDBs change their direction of propagation along the wires, promoting Ga-terminated domains and stabilizing into {11̅00}, that is, m-planes. The atomic phase shift between the Ga- and N-terminated domains was extracted using phase-retrieval algorithms, revealing an evolution of the out-of-plane displacement (∼5 pm, at maximum) between inversion domains along the wires. This work provides an accurate inner view of planar defects inside small crystals.

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.

PtychoShelves, a versatile high-level framework for high-performance analysis of ptychographic data

A new computer program for analysing ptychographic data combines both high-level simplicity and high-performance computing on large-scale computing clusters. It is available with a royalty-free non-exclusive licence for academic and non-commercial purposes.

Over the past decade, ptychography has been proven to be a robust tool for non-destructive high-resolution quantitative electron, X-ray and optical microscopy. It allows for quantitative reconstruction of the specimen’s transmissivity, as well as recovery of the illuminating wavefront. Additionally, various algorithms have been developed to account for systematic errors and improved convergence. With fast ptychographic microscopes and more advanced algorithms, both the complexity of the reconstruction task and the data volume increase significantly. PtychoShelves is a software package which combines high-level modularity for easy and fast changes to the data-processing pipeline, and high-performance computing on CPUs and GPUs.

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.

Towards a quantitative determination of strain in Bragg Coherent X-ray Diffraction Imaging: artefacts and sign convention in reconstructions

Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution. However, BCDI relies on both dataset collection and phase retrieval algorithms that can induce artefacts in the reconstruction. Phase retrieval algorithms are based on the fast Fourier transform (FFT). We demonstrate how to calculate the displacement field inside a nanocrystal from its reconstructed phase depending on the mathematical convention used for the FFT. We use numerical simulations to quantify the influence of experimentally unavoidable detector deficiencies such as blind areas or limited dynamic range as well as post-processing filtering on the reconstruction. We also propose a criterion for the isosurface determination of the object, based on the histogram of the reconstructed modulus. Finally, we study the capability of the phasing algorithm to quantitatively retrieve the surface strain (i.e., the strain of the surface voxels). This work emphasizes many aspects that have been neglected so far in BCDI, which need to be understood for a quantitative analysis of displacement and strain based on this technique. It concludes with the optimization of experimental parameters to improve throughput and to establish BCDI as a reliable 3D nano-imaging technique.

Coherent Bragg imaging of 60 nm Au nanoparticles under electrochemical control at the NanoMAX beamline

Nanoparticles are essential electrocatalysts in chemical production, water treatment and energy conversion, but engineering efficient and specific catalysts requires understanding complex structure-reactivity relations. Recent experiments have shown that Bragg coherent diffraction imaging might be a powerful tool in this regard. The technique provides three-dimensional lattice strain fields from which surface reactivity maps can be inferred. However, all experiments published so far have investigated particles an order of magnitude larger than those used in practical applications. Studying smaller particles quickly becomes demanding as the diffracted intensity falls. Here, in situ nanodiffraction data from 60 nm Au nanoparticles under electrochemical control collected at the hard X-ray nanoprobe beamline of MAX IV, NanoMAX, are presented. Two-dimensional image reconstructions of these particles are produced, and it is estimated that NanoMAX, which is now open for general users, has the requisites for three-dimensional imaging of particles of a size relevant for catalytic applications. This represents the first demonstration of coherent X-ray diffraction experiments performed at a diffraction-limited storage ring, and illustrates the importance of these new sources for experiments where coherence properties become crucial.

The Nanodiffraction beamline ID01/ESRF: a microscope for imaging strain and structure

The ID01 beamline has been built to combine Bragg diffraction with imaging techniques to produce a strain and mosaicity microscope for materials in their native or operando state. A scanning probe with nano-focused beams, objective-lens-based full-field microscopy and coherent diffraction imaging provide a suite of tools which deliver micrometre to few nanometre spatial resolution combined with 10-5 strain and 10-3 tilt sensitivity. A detailed description of the beamline from source to sample is provided and serves as a reference for the user community. The anticipated impact of the impending upgrade to the ESRF - Extremely Brilliant Source is also discussed.

X-ray zoom lens allows for energy scans in X-ray microscopy

We introduce a new design and development of a compound refractive X-ray zoom lens for energy scans in X-ray microscopy. Energy scans are, in principle, equivalent to radial scans in the reciprocal space for X-ray diffraction. Thanks to the absence of sample or detector motions, energy scans are better suited for microscopy, which requires high stability. In addition, close to the absorption edge of an element, energy scans can yield chemical information when coupled with resonant effects in full field diffraction X-ray microscopy (FFDXM) or X-ray absorption near edge structure (XANES) microscopy. Here, we demonstrate the concept by using a customized compound refractive X-ray zoom lens for 11 keV near the Ge K_α-edge. The working distance and magnification were kept constant during the energy scans by adapting the lens composition on switchable zoom lens fingers. This alleviates the need to reposition the lens while changing the energy and makes quantitative analysis more convenient for FFDXM. The fabricated zoom lens was characterized and proven suitable for the proposed measurement.

In situ structural evolution of single particle model catalysts under ambient pressure reaction conditions

The catalytic activity of metal nanoparticles can be altered by applying strain, which changes the crystalline lattice spacing and modifies the electronic properties of the metal. Understanding the role of elastic strain during catalytic reactions is thus crucial for catalyst design. Here, we show how single highly faceted Pt nanoparticles expand or contract upon interaction with different gas atmospheres using in situ nano-focused coherent X-ray diffraction imaging. We also demonstrate inter-particle heterogeneities, as they differ in development of strain under CO oxidation reaction conditions. The reported observations offer new insights into the design of catalysts exploiting strain effects.

Coherent Tabletop EUV Ptychography of Nanopatterns

Coherent diffraction imaging (CDI) or lensless X-ray microscopy has become of great interest for high spatial resolution imaging of, e.g., nanostructures and biological specimens. There is no optics required in between an object and a detector, because the object can be fully recovered from its far-field diffraction pattern with an iterative phase retrieval algorithm. Hence, in principle, a sub-wavelength spatial resolution could be achieved in a high-numerical aperture configuration. With the advances of ultrafast laser technology, high photon flux tabletop Extreme Ultraviolet (EUV) sources based on the high-order harmonic generation (HHG) have become available to small-scale laboratories. In this study, we report on a newly established high photon flux and highly monochromatic 30 nm HHG beamline. Furthermore, we applied ptychography, a scanning CDI version, to probe a nearly periodic nanopattern with the tabletop EUV source. A wide-field view of about 15 × 15 μm was probed with a 2.5 μm−diameter illumination beam at 30 nm. From a set of hundreds of far-field diffraction patterns recorded for different adjacent positions of the object, both the object and the illumination beams were successfully reconstructed with the extended ptychographical iterative engine. By investigating the phase retrieval transfer function, a diffraction-limited resolution of reconstruction of about 32 nm is obtained.