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Bragg coherent X‐ray diffraction imaging (BCDI) has emerged as a powerful technique for strain imaging and morphology reconstruction of nanometre‐scale crystals. However, BCDI often suffers from angular distortions that appear during data acquisition, caused by radiation pressure, heating or imperfect scanning stages. This limits the applicability of BCDI, in particular for small crystals and high‐flux X‐ray beams. Here, we present a pre‐processing algorithm that recovers the 3D datasets from the BCDI dataset measured under the impact of large angular distortions. We systematically investigate the performance of this method for different levels of distortion and find that the algorithm recovers the correct angles for distortions up to 16.4× (1640%) the angular step size dθ = 0.004°. We also show that the angles in a continuous scan can be recovered with high accuracy. As expected, the correction provides marked improvements in the subsequent phase retrieval. An algorithm has been developed that effectively corrects and tracks angular distortions, enabling BCDI to work much more robustly and accurately in a wider range of challenging experimental scenarios.

Bragg coherent diffraction imaging (BCDI) is a lens-less technique capable of imaging the strain in a particle in the size range from 20 nm up to several micrometres. This indirect measurement technique, used in X-ray synchrotrons or free-electron lasers all over the world, requires an inversion step using iterative algorithms in order to recover the real-space complex object encoding the particle shape and deformation field. However, artefacts such as scattering peaks called `aliens' from nearby particles can affect the accuracy of the final reconstruction and require meticulous and time-consuming manual masking of the raw data. This becomes problematic for BCDI reconstructions during an experiment and/or for large volumes of data. Here, we explore the potential of machine learning, and specifically clustering techniques, to speed up this procedure while keeping the maximum spatial resolution of the object reconstruction. We also provide a user-friendly Python Jupyter notebook program available on Github.

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. Our results show that BCDI is a useful technique for studying diffusion in three dimensions and alloying behaviour in individual crystalline grains.

Multiferroic materials that exhibit interacting and coexisting properties, like ferroelectricity and ferromagnetism, possess significant potential in the development of novel technologies that can be controlled through the application of external fields. They also exhibit varying regions of polarity, known as domains, with the interfaces that separate the domains referred to as domain walls. In this study, using three-dimensional (3D) bragg coherent diffractive imaging (BCDI), we investigate the dynamics of multiferroic domain walls in a single hexagonal dysprosium manganite (h-DyMnO 3 ) nanocrystal under varying applied electric field. Our analysis reveals that domain wall motion is influenced by the pinning effects, and a threshold voltage of +3 V is required to overcome them. Using circular mean analysis and phase gradient mapping, we identified localised phase realignment and high-gradient regions corresponding to domain walls, providing insights into the behaviour of multiferroic systems under external stimuli.

We used a soft X-ray free-electron laser and the Bragg coherent diffraction imaging method to characterize the defect structure of colloidal crystals. The single-shot X-ray pulse allowed us to reach four powder rings and measured all six reflections of the hexagonal lattice. We reproduced the static shape of the 2D crystal and mapped out the 2D strain tensors inside the crystal. The observed defect structures agreed with electron microscope images of similar colloidal samples.

Understanding atomic-level imperfections is crucial in various technological applications. Bragg coherent X-ray diffraction imaging (BCDI) enables non-destructive, three-dimensional imaging of those materials under in situ and operando conditions but has limited spatial resolution. This limitation hinders accurate calculations of physical quantities, e.g. strain field energy and strain correlation lengths. In this study, we introduce the extended image restoration (ExImRes) method, which infers enhanced resolution images based primarily on the process of averaging and combining multiple datasets obtained by restricting the original measured datasets through binning or cropping. We apply ExImRes to two nanocrystal examples—a chiral gold nanoparticle and a platinum nanoparticle—with an improved spatial resolution that allowed us to obtain precise calculation results of strain field energy and the correlation lengths of atomic deformations. The enhanced images reveal detailed lattice-scale information previously inaccessible through traditional BCDI methods. Our findings advance ExImRes to obtain high-resolution analysis in imaging techniques that involve reciprocal to real space transformations and understand underlying phenomena in materials science.

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.

The simultaneous measurement of two Bragg reflections by Bragg coherent X-ray diffraction is demonstrated on a twinned Au crystal, which was prepared by the solid-state dewetting of a 30 nm thin gold film on a sapphire substrate. The crystal was oriented on a goniometer so that two lattice planes fulfill the Bragg condition at the same time. The Au 111 and Au 200 Bragg peaks were measured simultaneously by scanning the energy of the incident X-ray beam and recording the diffraction patterns with two two-dimensional detectors. While the former Bragg reflection is not sensitive to the twin boundary, which is oriented parallel to the crystal–substrate interface, the latter reflection is only sensitive to one part of the crystal. The volume ratio between the two parts of the twinned crystal is about 1:9, which is also confirmed by Laue microdiffraction of the same crystal. The parallel measurement of multiple Bragg reflections is essential for future in situ and operando studies, which are so far limited to either a single Bragg reflection or several in series, to facilitate the precise monitoring of both the strain field and defects during the application of external stimuli.

In Bragg coherent diffractive imaging, the precise location of the measured crystals in the interior of the sample is usually missing. Obtaining this information would help the study of the spatially dependent behavior of particles in the bulk of inhomogeneous samples, such as extra‐thick battery cathodes. This work presents an approach to determine the 3D position of particles by precisely aligning them at the instrument axis of rotation. In the test experiment reported here, with a 60 µm‐thick LiNi0.5Mn1.5O4 battery cathode, the particles were located with a precision of 20 µm in the out‐of‐plane direction, and the in‐plane coordinates were determined with a precision of 1 µm. A method to determine the 3D position of particles in Bragg coherent diffractive imaging experiments is proposed. Test measurements demonstrate depth‐resolution with a precision of 20 µm along the beam.

The reconstruction of a single-particle image from the modulus of its Fourier transform, by phase-retrieval methods, has been extensively applied in X-ray structural science. Particularly for strong-phase objects, such as the phase domains found inside crystals by Bragg coherent diffraction imaging (BCDI), conventional iteration methods are time consuming and sensitive to their initial guess because of their iterative nature. Here, a deep-neural-network model is presented which gives a fast and accurate estimate of the complex single-particle image in the form of a universal approximator learned from synthetic data. A way to combine the deep-neural-network model with conventional iterative methods is then presented to refine the accuracy of the reconstructed results from the proposed deep-neural-network model. Improved convergence is also demonstrated with experimental BCDI data.