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The dynamic control of novel states of matter beyond thermodynamic equilibrium is a fundamental pursuit in condensed matter physics. Intense terahertz fields have enabled metal-insulator transitions, superconductivity, quantum paraelectric ferroelectricity, and room-temperature magnetization via circularly polarized terahertz electric fields. These effects hinge on the excitation of infrared-active soft phonon modes by terahertz fields. Expanding this concept, recent theory suggests that ferroelectric polarization may be manipulated through terahertz twisted light, transferring orbital angular momentum to create ferroelectric skyrmions. Our study experimentally demonstrates that such control is possible in quasi-2D ferroelectric CsBiNb2O7 using twisted UV light with orbital angular momentum (OAM). By resonantly exciting both the ferroelectric mode and the octahedral tilting mode, twisted UV light dynamically modulates the ferroelectric polarization. We employ in-situ X-ray Bragg coherent diffractive imaging, twisted optical Raman spectroscopy, and density functional theory to three-dimensionally resolve ionic displacement fields and polarization texture changes. Our observations reveal deterministic, reversible twisted light-induced strain and ionic displacements within the unit cell, causing substantial microscopic polarization changes. This interaction between twisted photons, phonon modes, and induced ionic displacements breaks symmetry and stabilizes a non-equilibrium ferroelectric phase with topological solitons. These findings offer a new path to control ferroelectricity and magnetism, opening avenues for novel optoelectronic devices such as ultrafast non-volatile memory switches by using light to coherently control ferroic states., Comment: 14 pages, 5 figures

The temperature-dependent behavior of magnetic domains plays an essential role in the magnetic properties of materials, leading to widespread applications. However, experimental methods to access the three-dimensional (3D) magnetic domain structures are very limited, especially for antiferromagnets. Over the past decades, the spin-orbit Mott insulator iridate $Sr_2IrO_4$ has attracted particular attention because of its interesting magnetic structure and analogy to superconducting cuprates. Here, we apply resonant x-ray magnetic Bragg coherent diffraction imaging to track the real-space 3D evolution of antiferromagnetic ordering inside a $Sr_2IrO_4$ single crystal as a function of temperature, finding that the antiferromagnetic domain shows anisotropic changes. The anisotropy of the domain shape reveals the underlying anisotropy of the antiferromagnetic coupling strength within $Sr_2IrO_4$. These results demonstrate the high potential significance of 3D domain imaging in magnetism research.

The piezoelectric response is a measure of the sensitivity of a material's polarization to stress or its strain to an applied field. Using in-operando x-ray Bragg coherent diffraction imaging, we observe that topological vortices are the source of a five-fold enhancement of the piezoelectric response near the vortex core. The vortices form where several low symmetry ferroelectric phases and phase boundaries coalesce. Unlike bulk ferroelectric solid solutions in which a large piezoelectric response is associated with coexisting phases in the proximity of the triple point, the largest responses for pure BaTiO3 at the nanoscale are in spatial regions of extremely small spontaneous polarization at vortex cores. The response decays inversely with polarization away from the vortex, analogous to the behavior in bulk ceramics as the cation compositions are varied away from the triple point. We use first-principles-based molecular dynamics to augment our observations, and our results suggest that nanoscale piezoelectric materials with large piezoelectric response can be designed within a parameter space governed by vortex cores. Our findings have implications for the development of next-generation nanoscale piezoelectric materials., Comment: 13 pages, 5 figures

Identifying the three-dimensional (3D) crystal-plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. Here, we developed a methodology for visualizing the 3D information of chiral gold nanoparticles with concave gap structures by Bragg coherent X-ray diffraction imaging. The distribution of the high-Miller-index planes constituting the concave chiral gap was precisely determined. The highly strained region adjacent to the chiral gaps was resolved, which was correlated to the 432-symmetric morphology of the nanoparticles and its corresponding plasmonic properties were numerically predicted from the atomically defined structures. This approach can serve as a general characterization platform for visualizing the 3D crystallographic and strain distributions of nanoparticles, especially for applications where structural complexity and local heterogeneity are major determinants, as exemplified in plasmonics., Comment: Sungwook Choi and Sang Won Im contributed equally to this work. Corresponding author. Email: nkitae@snu.ac.kr, hkim@sogang.ac.kr

Bragg coherent X-ray diffraction imaging (BCDI) allows the three-dimensional (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 micro-beam Laue diffraction measurements. Here, we present an alternative method to determine the crystal orientation for BCDI measurements, by 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 to the orientation determined using micro-beam Laue diffraction. The average angular mismatch between the orientation matrices is less than ~6 degrees, which is reasonable for the search for Bragg reflections. We demonstrate the use of an orientation matrix derived from EBSD to align and measure five reflections for a single Fe-Ni microcrystal using multi-reflection BCDI. Using this dataset, 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. Our results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the lattice strain tensor with greater accuracy., Comment: 39 pages, 12 figures

Corrosion is a major concern for many industries, as corrosive environments can induce structural and morphological changes that lead to material dissolution and accelerate material failure. The progression of corrosion depends on nanoscale morphology, stress, and defects present. Experimentally monitoring this complex interplay is challenging. Here we implement in situ Bragg coherent X-ray diffraction imaging (BCDI) to probe the dissolution of a Co-Fe alloy microcrystal exposed to hydrochloric acid (HCl). By measuring five Bragg reflections from a single isolated microcrystal at ambient conditions, we compare the full three-dimensional (3D) strain state before corrosion and the strain along the [111] direction throughout the corrosion process. We find that the strained surface layer of the crystal dissolves to leave a progressively less strained surface. Interestingly, the average strain closer to the centre of the crystal increases during the corrosion process. We determine the localised corrosion rate from BCDI data, revealing the preferential dissolution of facets more exposed to the acid stream, highlighting an experimental geometry effect. These results bring new perspectives to understanding the interplay between crystal strain, morphology, and corrosion; a prerequisite for the design of more corrosion-resistant materials., Comment: 10 pages, 11 figures

Structural and ion-ordering phase transitions limit the viability of sodium-ion intercalation materials in grid scale battery storage by reducing their lifetime. However, the combination of phenomena in nanoparticulate electrodes creates complex behavior that is difficult to investigate, especially on the single nanoparticle scale under operating conditions. In this work, operando single-particle x-ray diffraction (oSP-XRD) is used to observe single-particle rotation, interlayer spacing, and layer misorientation in a functional sodium-ion battery. oSP-XRD is applied to Na$_{2/3}$[Ni$_{1/3}$Mn$_{2/3}$]O$_{2}$, an archetypal P2-type sodium-ion positive electrode material with the notorious P2-O2 phase transition induced by sodium (de)intercalation. It is found that during sodium extraction, the misorientation of crystalline layers inside individual particles increases before the layers suddenly align just prior to the P2-O2 transition. The increase in the long-range order coincides with an additional voltage plateau signifying a phase transition prior to the P2-O2 transition. To explain the layer alignment, a model for the phase evolution is proposed that includes a transition from localized to correlated Jahn-Teller distortions. The model is anticipated to guide further characterization and engineering of sodium-ion intercalation materials with P2-O2 type transitions. oSP-XRD therefore opens a powerful avenue for revealing complex phase behavior in heterogeneous nanoparticulate systems., Comment: 23 pages, 4 main figures, 9 supplemental figures

Nanostructured proton-conducting ceramics (PCCs) have attracted considerable interest as moderate-temperature proton conductors. Structure dynamics during proton conduction, particularly at grain boundaries, are crucial for stability and proton transport in nanostructured PCCs. A common assumption is that PCCs are structurally stable at low operating temperatures; however, material polycrystallinity, absorption, and reactive operating conditions have so far prevented verifying this assumption by nano resolved in-situ structure measurements. Here, in an archetypal PCC BaZr0.8Y0.2O3-d the premise of structural stability is demonstrated to be inaccurate at temperatures as low as 200 {\deg}C. Coherent X-ray diffraction on a nanostructured BaZr0.8Y0.2O3-d sintered pellet is adapted to image in-situ three-dimensional structural processes inside the constituent submicron grains in a humid nitrogen atmosphere at 200 {\deg}C. Direct observation reveals non-equilibrium defect generation and subsequent grain cracking on a timescale of hours, forming new, otherwise energetically unfavorable facets in BaZr0.8Y0.2O3-d. Furthermore, the structural rearrangements correlate with dynamic inhomogeneities of the lattice constant within the grains, showing potential heterogeneous H+ transport. Our results elucidate the mechanisms behind PCCs structural degradation, overturn existing assumptions about the structure dynamics in PCCs, and fill a method gap for further in-depth in-situ studies of the PCC nanostructure.

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.

All-solid-state lithium batteries promise significant improvements in energy density and safety over traditional liquid electrolyte batteries. The Al-doped AlxLi7-3xLa3Zr2O12 (LLZO) solid-state electrolyte shows excellent potential given its high ionic conductivity and good thermal, chemical, and electrochemical stability. Nevertheless, further improvements on LLZOs electrochemical and mechanical properties call for an incisive understanding of its local microstructure. Here, we employ Bragg Coherent Diffractive Imaging to investigate the atomic displacements inside single grains of LLZO with various Al-doping concentrations, resulting in cubic, tetragonal, and cubic-tetragonal mixed structures. We observe coexisting domains of different crystallographic orientations in the tetragonal structure. We further show that Al doping leads to crystal defects such as dislocations and phase boundary in the mixed- and cubic-phase grain. This study addresses the effect of Al-doping on the nanoscale structure within individual grains of LLZO, which is informative for the future development of solid-state batteries.

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 we use non-destructive Bragg coherent X-ray diffraction imaging to study the in situ annealing of FIB-milled gold microcrystals. We simultaneously measure two non-collinear reflections 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 to thermocouple readings, which are shown to be substantially affected by thermal resistance. To evaluate the annealing process, we analyse each reflection by considering facet area evolution, cross-correlation maps of displacement field and binarised 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{\deg}C and the self-diffusion of gold above ~280{\deg}C. The majority of FIB-induced strains are removed by 380-410\degree C, depending on which reflection is being considered. Our observations highlight the importance of measuring multiple reflections to unambiguously interpret material behaviour., Comment: 51 pages, 16 figures

Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding signal from a single nanoscale crystal object, which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus, localizing in reciprocal space other Bragg reflections becomes in reality impossible or requires good knowledge of the orientation of the crystal. We report the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C end station of the Advanced Photon Source, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables this through rapid switching from monochromatic to broadband (pink) beam permitting the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. We discuss the design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal.

In this two-part article series we provide a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent to the resulting three-dimensional (3D) image from current phase retrieval methods and strategies to mitigate this distortion. In this Part I, we derive in general terms the real-space coordinate transformation to correct this shear, which originates in the more fundamental relationship between the representations of mutually conjugate 3D spaces. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an un-distorted and physically meaningful image of the 3D scatterer. As the relevance of BCDI grows in the field of materials characterization, we take this opportunity to generalize the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods. This aspect, specific to coherent Bragg diffraction and absent in two-dimensional transmission CDI experiments, gains particular importance concerning spatially-resolved characterization of 3D crystalline materials in a realiable, non-destructive manner. These articles describe this theory, from the diffraction in Bragg geometry, to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I provides the experimental BCDI communitcy with the theoretical underpinnings of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase retrieval algorithm itself, allowing more physically realistic constraints to be applied., Comment: Double-spaced, 31 pages, 4 figures, 1 table, under review

Bragg coherent diffraction imaging (BCDI), the well-established technique for imaging internal strain of nanoparticles, was used to image the internal compositional distribution of binary alloys in thermal equilibrium. The images experimentally obtained for Pd-Rh alloy nanoparticles are presented and discussed. The direct correspondence between the lattice strain and the compositional deviation is discussed in the derivation of the BCDI displacement field aided by illustrations.

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. 3D 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 O2 and H2. 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. In addition, our study exemplifies applications of BCDI for in situ 3D imaging of internal equilibrium compositions in other bimetallic alloy nanoparticles.

Lattice defects play a key role in determining the properties of crystalline materials. Probing the 3D lattice strains that govern their interactions remains a challenge. Bragg Coherent Diffraction Imaging (BCDI) allows strain to be measured with nano-scale 3D resolution. However, it is currently limited to materials that form micro-crystals. Here we introduce a new technique that allows the manufacture of BCDI samples from bulk materials. Using tungsten as an example, we show that focussed ion beam (FIB) machining can be used to extract, from macroscopic crystals, micron-sized BCDI samples containing specific pre-selected defects. To interpret the experimental data, we develop a new displacement-gradient-based analysis for multi-reflection BCDI. This allows accurate recovery of the full lattice strain tensor from samples containing multiple dislocations. These new capabilities open the door to BCDI as a microscopy tool for studying complex real-world materials., Comment: 26 pages, 6 figures

Coherent X-ray beams with energies $\geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier space compression at high X-ray energies renders conventional phase retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem we utilize a phase retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable., Comment: 10 pages, 8 figures

We demonstrate that the resolution of three-dimensional (3D) real-space images obtained from Bragg x-ray coherent diffraction measurements is direction dependent. We propose and demonstrate the effectiveness of a metric to determine the spatial resolution of images that accounts for the direc- tional dependence. The measured direction dependent resolution of ~ 4-9nm is about 2 times higher than the best previously obtained 3D measurements. Finally, we quantify the relationship between the resolution of recovered real-space images and dosage, and discuss its implications in the light of next generation synchrotrons.