Bragg Coherent X-ray Diffraction Imaging Research Articles

Imaging and ferroelectric orientation mapping of photostriction in a single Bismuth Ferrite nanocrystal

The exploration of multiferroic materials and their interaction with light at the nanoscale presents a captivating frontier in materials science. Bismuth Ferrite (BiFeO3, BFO), a standout among these materials, exhibits room-temperature ferroelectric and antiferromagnetic behaviour and magnetoelectric coupling. Of particular interest is the phenomenon of photostriction, the light-induced deformation of crystal structures, which enhances the prospect for device functionality based on these materials. Understanding and harnessing multiferroic phenomena holds significant promise in various technological applications, from optoelectronics to energy storage. The orientation of the ferroelectric axis is an important design parameter for devices formed from multiferroic materials. Determining its orientation in the laboratory frame of reference usually requires knowing multiple wavevector transfer (Q-Vector) directions, which can be challenging to establish due to the need for extensive reciprocal-space searches. Our study demonstrates a method to identify the ferroelectric axis orientation using Bragg Coherent X-ray Diffraction Imaging (BCDI) measurements at a single Q-vector direction. This method involves applying photostriction-inducing laser illumination across various laser polarisations. Our findings reveal that photostriction primarily occurs as a surface phenomenon at the nanoscale. Moreover, a photo-induced crystal length change ranging from 30 to 60 nm was observed, consistent with earlier findings on bulk material.

Three-dimensional domain identification in a single hexagonal manganite nanocrystal

The three-dimensional domain structure of ferroelectric materials significantly influences their properties. The ferroelectric domain structure of improper multiferroics, such as YMnO3, is driven by a non-ferroelectric order parameter, leading to unique hexagonal vortex patterns and topologically protected domain walls. Characterizing the three-dimensional structure of these domains and domain walls has been elusive, however, due to a lack of suitable imaging techniques. Here, we present a multi-peak Bragg coherent x-ray diffraction imaging determination of the domain structure in single YMnO3 nanocrystals. We resolve two ferroelectric domains separated by a domain wall and confirm that the primary atomic displacements occur along the crystallographic c-axis. Correlation with atomistic simulations confirms the Mexican hat symmetry model of domain formation, identifying two domains with opposite ferroelectric polarization and adjacent trimerization, manifesting in a clockwise arrangement around the hat’s brim.

Lattice strain visualization inside a 400 nm single grain of BaTiO3 in polycrystalline ceramics by Bragg coherent X-ray diffraction imaging

The degree of anisotropy and the domain arrangement of crystal structures in ferroelectrics are affected by the grain boundaries and by the shape and size of the grains. To understand the grain boundary effects that occur in ferroelectric ceramics, we introduce a technique for nondestructively observing the internal lattice strain distribution of a submicrometer-sized ferroelectric grain in polycrystalline materials. The ferroelectric phase transition of a single grain in the polycrystalline materials was evaluated by tracking the changes in the Bragg coherent X-ray diffraction (CXD) patterns. The internal lattice strain distribution of the grains in the paraelectric phase was visualized via Bragg CXD imaging. A pair of 90° domains in the ferroelectric phase were also imaged in three dimensions, and showed a domain boundary correlated with the internal lattice strain caused by the stresses from the adjacent grains.

Strain and crystallographic identification of the helically concaved gap surfaces of chiral nanoparticles

Identifying the three-dimensional (3D) crystal plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. However, it remains a challenge to image concave surfaces of nanoparticles. Here, we develop a methodology for visualizing the 3D information of chiral gold nanoparticles ≈ 200 nm in size with concave gap structures by Bragg coherent X-ray diffraction imaging. The distribution of the high-Miller-index planes constituting the concave chiral gap is precisely determined. The highly strained region adjacent to the chiral gaps is resolved, which was correlated to the 432-symmetric morphology of the nanoparticles and its corresponding plasmonic properties are numerically predicted from the atomically defined structures. This approach can serve as a comprehensive characterization platform for visualizing the 3D crystallographic and strain distributions of nanoparticles with a few hundred nanometers, especially for applications where structural complexity and local heterogeneity are major determinants, as exemplified in plasmonics.

Concurrent multi-peak Bragg coherent x-ray diffraction imaging of 3D nanocrystal lattice displacement via global optimization

In this paper we demonstrated a method to reconstruct vector-valued lattice distortion fields within nanoscale crystals by optimization of a forward model of multi-reflection Bragg coherent diffraction imaging (MR-BCDI) data. The method flexibly accounts for geometric factors that arise when making BCDI measurements, is amenable to efficient inversion with modern optimization toolkits, and allows for globally constraining a single image reconstruction to multiple Bragg peak measurements. This is enabled by a forward model that emulates the multiple Bragg peaks of a MR-BCDI experiment from a single estimate of the 3D crystal sample. We present this forward model, we implement it within the stochastic gradient descent optimization framework, and we demonstrate it with simulated and experimental data of nanocrystals with inhomogeneous internal lattice displacement. We find that utilizing a global optimization approach to MR-BCDI affords a reliable path to convergence of data which is otherwise challenging to reconstruct.

Polar–Nonpolar Transition-Type Negative Thermal Expansion with 11.1% Volume Shrinkage by Design

Chemical substitution for the tuning of the working temperature of phase-transition-type negative thermal expansion (NTE) materials generally reduces the volume shrinkage during the transition. We have investigated the effects of electron doping and reduction of 6s2 lone-pair activity in PbVO3 with a large polar distortion (c/a = 1.23) and found that the combination of Bi and Sr substitutions for Pb enables a temperature-induced polar to non-polar transition with 11% volume shrinkage, even larger than the pressure-induced volume collapse of PbVO3 (∼10.6%), and is the largest value among the NTE materials reported so far. The domain structure of the coexisting cubic and tetragonal phases with such a huge volume difference was successfully observed by high-angle annular dark-field scanning transmission electron microscopy and the spatial distribution of domains by Bragg coherent X-ray diffraction imaging. The temperature hysteresis is reduced by repeated heating/cooling cycles, suggesting that the changes in the domain structure dominate the NTE properties.

In-Situ/Operando Bragg Coherent X-Ray Diffraction Imaging for Nanoscale Imaging of Strain and Defect

In the last two decades, Bragg Coherent X-ray Diffraction Imaging (BCDI) has become a powerful nanoscale characterization technique [1]. Its extreme sensitivity to lattice displacements enables to image three-dimensional morphology as well as internal deformation field distribution of nano- or micro-scaled various materials. In-situ and operando capabilities have been combined to BCDI to address scientific questions on materials under realistic conditions. Nowadays, in-situ/operando BCDI on electrochemistry successfully shows strain evolution and dislocation dynamics inside materials.In this talk, I will introduce current state-of-the-art of BCDI and the 34-ID-C beamline in the Advanced Photon Source which is dedicated to BCDI. This talk will also cover recent experimental results on in-situ/operando BCDI, for example, electrochemical dissolution/deposition [2] and battery materials during charging/discharging cycles [3,4].[1] M. A. Pfeifer, et al., Nature 442, 63 (2006).[2] Y. Liu, et al., Nano Lett. 17, 1595 (2017).[3] A. Ulvestad, et al., Science 348, 1344 (2015).[4] A. Singer, et al., Nat. Energy 3, 641 (2018).

Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation.

Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe-Ni and Co-Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe-Ni microcrystal via multi-reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.

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.

Strain Evolution in Pt-Ni Alloy Nanoparticles during Electrochemical Ni Leaching Revealed By Bragg Coherent Diffraction Imaging

Alloy catalysts such as Pt-M (M: other metal elements) have been extensively developed to improve the sluggish oxygen reduction reaction (ORR) that limits the efficiencies of fuel cells and metal-air batteries. Their catalytic activity is potentially enhanced by strain induced in a nearly pure Pt "shell" formed by dissolving the alloyed metal (M) from the surface. It is, therefore, of great importance to reveal the strain distribution on the Pt shell in situ so that we can exploit this mechanism to design new alloy catalysts. Yet, it has been challenging to analyze the strain on the shell because it inevitably requires a technique that can image the strain field of the nanoparticles with high spatial resolution.In this study,1 we successfully revealed the strain of the exemplary Pt-Ni alloy nanoparticles in detail from the 3D images obtained by using a novel synchrotron technique, “Bragg Coherent X-ray Diffraction Imaging” (BCDI), which can directly image minute atomic displacement field owing to the X-ray coherence. Pt-Ni nanoparticles with compositions of Pt2Ni3 (Ni rich), Pt1Ni1 (moderate Ni), and Pt3Ni2 (Ni poor) were observed by BCDI during cyclic voltammetry cycles, in which the less noble metal Ni electrochemically leached from the alloy. This cycling induced tensile strain inside particles in all the compositions, implying that the formation of a Pt shell on the surface strained the core of the particle because of the lattice mismatch between the Pt-Ni alloys and Pt. The strain in the shell was evaluated from a core-shell elastic model using the parameters obtained in the 3D images.A compressive circumferential strain in the shell was observed in all the compositions, and the Pt1Ni1 particle showed the largest compressive circumferential strain of 5%. Since the compressive strain is reported to facilitate the enhanced ORR,2 the compositional dependence of the strain magnitude observed in this study was in excellent agreement with the previous study performed with nm-size particles where Pt1Ni1 exhibits the highest activity among a wide range of compositions.3 A similar strain-activity relation was also inferred in a powder X-ray diffraction studies of core-shell Pt x Co1-x alloys,4 suggesting it is a widely applicable phenomenon. The present study demonstrated that the strain on alloy nanoparticles can be quantitatively determined by BCDI during electrochemical reactions, which enables us to exploit surface strain in designing a wide range of electrocatalysts. T. Kawaguchi et al., Nano Letters, 21, 5945–5951 (2021).H. Wang et al., Science, 354, 1031–1036 (2016).C. Wang et al., Advanced Functional Materials, 21, 147–152 (2011).D. Wang et al., Nature Materials, 12, 81–87 (2013).

Three-dimensional coherent X-ray diffraction imaging via deep convolutional neural networks

As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.

Strain Development of Selective Adsorption of Hydrocarbons in a Cu-ZSM-5 Crystal.

Zeolites are 3D aluminosilicate materials having subnanometer pore channels. The Lewis basic pores have charge-balancing cations, easily tuned to metallic ions as more chemically active sites. Among the ion-exchanged zeolites, Cu2+ ion-exchanged ZSM-5 (Cu-ZSM-5) is one of the most active zeolites with chemical interactions of Lewis basic compounds. Even though the chemical interactions of hydrocarbons with Cu2+ sites in Cu-ZSM-5 have been tremendously studied in the category of zeolite catalysts, it is not yet thoroughly investigated how such interactions affect the structural lattice of the zeolite. Hydrocarbons with different chemical properties and their relative size can induce lattice strain by different chemical adsorption effects on the Cu2+ sites. In this work, we investigate the internal deformation of the Cu-ZSM-5 crystal using Bragg coherent X-ray diffraction imaging during the adsorption of four hydrocarbons depending on the alkyl chain length, the existence of a double bond in the molecule, linear structure versus benzene ring structure, and so forth. In the three-carbon system (propane and propene), relatively weak chemical adsorption occurred at room temperature and 100 °C, whereas strong adsorption was observed over 150 °C. For the six-carbon system (n-hexane and benzene), strong strains evolved in the crystal by active chemical adsorption from 150 °C. The observations suggest that propene and propane adsorb at the Cu2+ sites from the outer shell to the center with increasing temperature. In comparison, n-hexane and benzene adsorb at both parts at the same temperature. The results provide the internal structural information for the lattice with the chemical interactions of hydrocarbons in the Cu-ZSM-5 zeolite and help to understand zeolite-based chemisorption or catalysis research.

Bragg coherent diffraction imaging allowing simultaneous retrieval of three-dimensional shape and strain distribution for 40–500 nm particles

We report the improvement of an apparatus for Bragg coherent X-ray diffraction imaging (Bragg-CDI) at BL22XU in SPring-8 to expand the applicable particle size and the application of the Bragg-CDI technique for Pd and ferroelectric barium titanate (BaTiO3) fine crystals with particle sizes of 40–500 nm. Preparing a vacuum environment around the sample enabled us to obtain the high-contrast diffraction pattern of a 40 nm particle. The reconstructed three-dimensional image showed the outer shape, size, and internal phase (strain) for a single particle. A single 500 nm BaTiO3 particle showed a straight and sharp antiphase-boundary shape, whereas smaller BaTiO3 particles showed different phase boundary shapes. The present Bragg-CDI apparatus, thus, allows the observation of the outer shape, size, and inner phase distribution for a single particle with a size of 40–500 nm.

The influence of strain on image reconstruction in Bragg coherent X-ray diffraction imaging and ptychography.

A quantitative analysis of the effect of strain on phase retrieval in Bragg coherent X-ray diffraction imaging is reported. It is shown in reconstruction simulations that the phase maps of objects with strong step-like phase changes are more precisely retrieved than the corresponding modulus values. The simulations suggest that the reconstruction precision for both phase and modulus can be improved by employing a modulus homogenization (MH) constraint. This approach was tested on experimental data from a highly strained Fe-Al crystal which also features antiphase domain boundaries yielding characteristic π phase shifts of the (001) superlattice reflection. The impact of MH is significant and this study outlines a successful method towards imaging of strong phase objects using the next generation of coherent X-ray sources, including X-ray free-electron lasers.

Three-dimensional coherent x-ray diffraction imaging of ferroelastic domains in single CsPbBr3 perovskite nanoparticles

Metal halide perovskites attract significant interest due to their remarkable performance in optoelectronic devices. However, the gap in understanding the relationship between their nanoscale structure and properties limits their application towards novel devices. In this work, twinned ferroelastic domains in single 500 nm CsPbBr3 particles are studied with 3D Bragg coherent x-ray diffraction imaging. A preferential double-domain structure is revealed in four identical particles, with one domain oriented along the [110] and the other along the [002] direction. The particles exhibit similar scattering volume ratios of 0.12 ± 0.026 between twin phases, suggesting the possibility of a deterministic formation process. The domains exhibit a difference in lattice tilt of 0.59 degrees, in excellent agreement with calculations of the lattice mismatch at the (112) twin boundary. These results provide important insights both for the fundamental understanding of ferroelastic nanoscale materials and for the performance improvement of perovskite-based devices. Moreover, this work paves the way towards real-time imaging of the domain dynamics in ferroic systems.

Operando 3D imaging of defects dynamics of twinned-nanocrystal during catalysis

Using operando Bragg coherent x-ray diffraction imaging, we visualised three-dimensionally a single twinned-gold nanocrystal during the CO oxidation reaction. We describe the defect dynamics process occurring under operating conditions and indicate the correlation between the nucleation of highly strained regions at the surface of the nanocrystal and its catalytic activity. Understanding the twinning deformation mechanism sheds light on the creation of active sites, and could well contribute to the understanding of the catalytic behaviour of other catalysts. With the start-up of 4th generation synchrotron sources, we anticipate that coherent hard x-ray diffraction imaging techniques will play a major role in imaging in situ chemical processes.

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.

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 usedtocalculate 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 onwhich reflection is being considered. These observations highlight the importance of measuring multiple reflections to unambiguously interpret material behaviour.

(Invited) 4D Nanoscale Imaging of Corrosion through Coherent x-Ray Diffraction Imaging

Bragg coherent X-ray diffraction imaging (BCDI) is a powerful means of operando materials characterization at the nanoscale. With the ability to measure 3D structure and strain in materials at few nm resolution and under real-world conditions, BCDI has provided unique insight into a variety of materials processes. We apply BCDI to directly image the 3D structural and strain field evolution in copper nanoparticles corroding in saline solution. We observe a defect driven, anisotropic corrosion process that is accompanied by nanoscale pit formation and lattice strain variation. To understand the origin of these phenomena, we build experimentally informed atomistic models of the corrosion process. Figure 1

Evolution of ferroelastic domain walls during phase transitions in barium titanate nanoparticles

In this work, ferroelastic domain walls inside ${\mathrm{BaTiO}}_{3}$ (BTO) tetragonal nanocrystals are distinguished by Bragg peak position and studied with Bragg coherent x-ray diffraction imaging (BCDI). Convergence-related features of the BCDI method for strongly phased objects are reported. A ferroelastic domain wall inside a BTO crystal has been tracked and imaged across the tetragonal-cubic phase transition and proves to be reversible. The linear relationship of relative displacement between two twin domains with temperature is measured and shows a different slope for heating and cooling, while the tetragonality reproduces well over temperature changes in both directions. An edge dislocation is also observed and found to annihilate when heating the crystal close to the phase transition temperature.