Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale features. We demonstrate that dynamical scattering effects can be accurately predicted using an optical model combined with the Darwin theory of dynamical x-ray diffraction. The model includes the highly divergent coherent x-ray nanobeams produced by Fresnel zone plate focusing optics and accounts for primary extinction, multiple scattering, and absorption. The simulation accurately reproduces the dynamical scattering features of experimental diffraction patterns acquired from a GaAs/AlGaAs epitaxial heterostructure on a GaAs (001) substrate.
Hierarchical Unsupervised Clustering of Nanobeam Electron Diffraction Data Using Sparse Bragg-Vector Representations
University of Glasgow（格拉斯哥大学）；Optimum Instrument Ltd（Optimum Instrument有限公司）；Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿罗森多夫研究中心）；University of Oxford（牛津大学）；University of Sydney（悉尼大学）
Strain engineering enables the direct modification of the atomic bonding and is currently an active area of research aimed at improving the electrocatalytic activity. However, directly measuring the lattice strain of individual catalyst nanoparticles is challenging, especially at the scale of a single unit cell. Here, we quantitatively map the strain present in rhodium@platinum (core@shell) nanocube electrocatalysts using conventional aberration-corrected scanning transmission electron microscopy (STEM) and the recently developed technique of 4D-STEM nanobeam electron diffraction. We demonstra…
Advancements in fast electron detectors have enabled the statistically significant sampling of crystal structures on the nanometre scale by means of Scanning Electron Nanobeam Diffraction (SEND). Characterisation of structural similarity across this length scale is key to bridging the gap between local atomic structure (using atomic resolution techniques such as High Resolution Scanning Transmission Electron Microscopy (HR-STEM)) and the macro-scale (using bulk techniques such as powder X-ray and neutron diffraction). The use of SEND technique allows for structural investigation of a broad ran…
Investigating the Electromechanical Behavior of Unconventionally Ferroelectric $Hf_{0.5}Zr_{0.5}O_{2}$-based Capacitors Through Operando Nanobeam X-ray Diffraction
We construct an electron optical system to investigate Bragg diffraction (the crystal lattice plane, $10^{-2}$-$10^{-3}$ rad) with the objective lens turned off by adjusting the current in the intermediate lenses. A crossover was located on the selected-area aperture plane. Thus, the dark-field imaging can be performed by using a selected-area aperture to select Bragg diffraction spots. The camera length can be controlled in the range of 0.8 to 4 m without exciting the objective lens. Furthermore, we can observe the magnetic-field dependence of electron diffraction using the objective lens und…
Scanning nanobeam electron diffraction (NBED) with fast pixelated detectors is a valuable technique for rapid, spatially resolved mapping of lattice structure over a wide range of length scales. However, intensity variations caused by dynamical diffraction and sample mistilts can hinder the measurement of diffracted disk centers as necessary for quantification. Robust data processing techniques are needed to provide accurate and precise measurements for complex samples and non-ideal conditions. Here we present an approach to address these challenges using a transform, called the exit wave powe…
Mapping Order in Semicrystalline Polymers using Machine Learning of Nanobeam Electron Diffraction
Department of Materials Science and Engineering, Stanford University（材料科学与工程系，斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory（电子显微镜国家中心、分子发现所、伯克利国家实验室）
Coherent diffraction imaging (CDI) on Bragg reflections is a promising technique for the study of three-dimensional (3D) composition and strain fields in nanostructures, which can be recovered directly from the coherent diffraction data recorded on single objects. In this article we report results obtained for single homogeneous and heterogeneous nanowires with a diameter smaller than 100 nm, for which we used CDI to retrieve information about deformation and faults existing in these wires. The article also discusses the influence of stacking faults, which can create artefacts during the recon…
A new chiral phase of ferric ions in bismuth ferrite, the only material known to support multiferroic behaviour at room temperature, is inferred from extensive sets of data gathered by resonant x-ray Bragg diffraction. Values of all ferric multipoles participating in a minimal model of Fe electronic structure are deduced from azimuthal-angle scans. Extensive sets of azimuthal-angle data, gathered by resonant x-ray Bragg diffraction, yield values of all ferric multipoles participating in a minimal model of Fe electronic structure. Paramagnetic (700 K) and magnetically ordered (300 K) phases of …
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 mea…
The use of highly efficient and solarblind GaN photocathodes as part of multichannel plate UV detectors for applications in astronomy would strongly benefit from the direct growth of GaN on typical window materials with high transmission down to the deep UV range. GaN growth on MgF$_2$ substrates by plasma-assisted molecular beam epitaxy has recently been demonstrated. Here, we report an extensive scanning transmission electron microscopy study of the thin film microstructure for growth at 525 $^{\circ}$C and 650 $^{\circ}$C on (100) MgF$_2$. These results are systematically supported by X-ray…
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 …
Chiral properties of the two phases - collinear motif (below Morin transition temperature, TM=250 K) and canted motif (above TM) - of magnetically ordered hematite (α-Fe2O3) have been identified in single crystal resonant x-ray Bragg diffraction, using circular polarized incident x-rays tuned near the iron K-edge. Magneto-electric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time-odd. Orbital angular momentum accompanies the collinear motif, while …
In correlated oxides the coupling of quasiparticles to other degrees of freedom such as spin and lattice plays critical roles in the emergence of symmetry-breaking quantum ordered states such as high temperature superconductivity. We report a strong lattice coupling of photon induced Hubbard excitonic quasiparticles in spin-orbital coupling Mott insulator Sr2IrO4. Combining time-resolved optical spectroscopy techniques, we further reconstructed spatiotemporal map of the diffusion of quasiparticles via time-dependent coherence analysis of the x-ray Bragg diffraction peak. Due to the unique elec…
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 condi…
We present simulations of Bragg Coherent X-ray Diffractive Imaging (CXDI) data from finite crystals in the frame of the dynamical theory of x-ray diffraction. The developed approach is based on numerical solution of modified Takagi-Taupin equations and can be applied for modeling of a broad range of x-ray diffraction experiments with finite three-dimensional crystals of arbitrary shape also in the presence of strain. We performed simulations for nanocrystals of a cubic and hemispherical shape of different sizes and provided a detailed analysis of artifacts in the Bragg CXDI reconstructions int…
We report on ultrafast electron diffraction on high quality single crystal silicon. The ultrafast dynamics of the Bragg peaks exhibits a giant photo-induced response which can only be explained in the framework of dynamical diffraction theory, taking into account multiple scattering of the probing electrons in the sample. In particular, we show that lattice heating following photo-excitation can cause an unexpected increase of the Bragg peak intensities, in contradiction with the well-known Debye-Waller effect. We anticipate that multiple scattering should be systematically considered in ultra…
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 ge…
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 com…
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,…
Bragg coherent X-ray diffraction imaging (BCDI) is a non-destructive, lensless method for 3D-resolved, nanoscale strain imaging in micro-crystals. A challenge, particularly for new users of the technique, is accurate mapping of experimental data, collected in the detector reciprocal space coordinate frame, to more convenient orthogonal coordinates, e.g. attached to the sample. This is particularly the case since different coordinate conventions are used at every BCDI beamline. The reconstruction algorithms and mapping scripts composed for individual beamlines are not readily interchangeable. T…
We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor $ω/Δω$ ($ω$: frequency of an x ray, $Δω$: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction …
We report on a polarized-neutron Laue diffraction experiment on a single crystal of neodynium doped lanthanum magnesium nitrate hydrate containing polarized proton spins. By using dynamic nuclear polarization to polarize the proton spins, we demonstrate that the intensities of the Bragg peaks can be enhanced or diminished significantly, whilst the incoherent background, due to proton spin disorder, is reduced. It follows that the method offers unique possibilities to tune continuously the contrast of the Bragg reflections and thereby represents a new tool for increasing substantially the signa…
Bragg scattering of polaritons by a coherent acoustic wave is mediated and strongly enhanced by the relevant exciton states resonant with the acoustic and optic fields simultaneously. In this case, in sharp contrast with conventional acousto-optics, the resonantly enhanced Bragg spectra reveal the multiple orders of diffracted light, i.e., a Brillouin band structure of parametrically driven polaritons can be directly visualized. We analyze the above scheme for polaritons in (GaAs) semiconductor microcavities driven by a surface acoustic wave (SAW) and show that for realistic values of the SAW,…
Coherent diffraction imaging enables the imaging of individual defects, such as dislocations or stacking faults, in materials.These defects and their surrounding elastic strain fields have a critical influence on the macroscopic properties and functionality of materials. However, their identification in Bragg coherent diffraction imaging remains a challenge and requires significant data mining. The ability to identify defects from the diffraction pattern alone would be a significant advantage when targeting specific defect types and accelerates experiment design and execution. Here, we exploit…
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 me…
A common way of speeding up powder diffraction measurements is the use of one or two dimensional detectors. This usually goes along with worse resolution and asymmetric peak profiles. In this work the influence of a straight linear detector on the resolution function in the Bragg-Brentano focusing geometry is discussed. Due to the straight nature of most modern detectors geometrical defocusing occurs which heavily influences the line shape of diffraction lines at low angles. An easy approach to limit the resolution degrading effects is presented. The presented algorithm selects an adaptive ran…
We demonstrate that the highly sensitive phase-contrast properties of Bragg coherent diffraction measurements combined with the translational diversity of ptychography can provide a Bragg "dark field" imaging method capable of revealing the finger print of domain structure in metallic thin films. Experimental diffraction data was taken from a epitaxially grown niobium metallic thin film on sapphire; and analysed with the help of a careful combination of implemented refinement mechanisms.
Morphological evolution of an Au crystalline domain in a nano-particle investigated by Bragg coherent diffraction imaging
Gwangju Institute of Science and Technology（光州科学技术院）；Advanced Photon Source, Argonne National Laboratory（阿贡国家实验室先进光子源）；Chosun University（朝鲜大学）；European XFEL（欧洲自由电子激光设施）
Nanoscale heterogeneity (including size, shape, strain, and defects) significantly impacts material properties and how they function. Bragg coherent x-ray imaging methods have emerged as a powerful tool to investigate, in three-dimensional detail, the local material response to external stimuli in reactive environments, thereby enabling explorations of the structure-defect-function relationship at the nanoscale. Although progress has been made in understanding this relationship, coherent imaging of extended samples is relatively slow (typically requiring many minutes) due to the experimental c…
We report a benchmark experiment that demonstrates shortening of hard x-ray pulses in a synchrotron-based optical pump - x-ray probe experiment. The pulse shortening device, a picosecond Bragg switch, reduces the temporal resolution of an incident x-ray pulse to 7.5 ps. We employ the Bragg switch to monitor propagating sound waves in nanometer-thin epitaxial films. With the experimental data we infer pulse duration, diffraction efficiency and switching contrast of the device. A detailed efficiency analysis shows, that the switch can deliver up to 1010 photons/sec in high-repetition rate synchr…
We present a general analytic approach to spatially resolve the nano-scale lattice distortion field of strained and defected compact crystals with Bragg coherent x-ray diffraction imaging (BCDI). Our approach relies on fitting a differentiable forward model simultaneously to multiple BCDI datasets corresponding to independent Bragg reflections from the same single crystal. It is designed to be faithful to heterogeneities that potentially manifest as phase discontinuities in the coherently diffracted wave, such as lattice dislocations in an imperfect crystal. We retain fidelity to such small fe…
Bragg Coherent Diffraction Imaging (BCDI) is a powerful strain imaging tool, often limited by beam-induced sample instability for small particles and high power densities. Here, we devise and validate an adapted diffraction volume assembly algorithm, capable of recovering three-dimensional datasets from particles undergoing uncontrolled and unknown rotations. We apply the method to gold nanoparticles which rotate under the influence of a focused coherent X-ray beam, retrieving their three-dimensional shapes and strain fields. The results show that the sample instability problem can be overcome…
We report the first high-field x-ray diffraction experiment using synchrotron x-rays and pulsed magnetic fields exceeding 30 T. Lattice deformation due to a magnetic-field-induced valence transition in YbInCu4 is studied. It has been found that the Bragg reflection profile at 32 K changes significantly at around 27 T due to the structural transition. In the vicinity of the transition field the low-field and the high-field phases are observed simultaneously as the two distinct Bragg reflection peaks: This is a direct evidence of the fact that the field-induced valence state transition is the fi…
Aluminum single crystals are tested using X-Ray Bragg diffraction, which may have applications in microscopy and electronics fabrication industry. Yet, their efficiency for x- ray beam diffraction depends on the accurate crystal orientation, the microstructure and imperfections. Moreover, the final sample that is formed from the as-grown crystal by cutting, grinding, polishing and chemical etching, introduces various surface defects that penetrate deep into the crystal affecting its natural structure. Defect penetration is attributed to the fact that ultra-pure aluminum single crystals are sof…
The problem of phase retrieval, or the algorithmic recovery of lost phase information from measured intensity alone, underlies various imaging methods from astronomy to nanoscale imaging. Traditional methods of phase retrieval are iterative in nature, and are therefore computationally expensive and time consuming. More recently, deep learning (DL) models have been developed to either provide learned priors to iterative phase retrieval or in some cases completely replace phase retrieval with networks that learn to recover the lost phase information from measured intensity alone. However, such m…
Louis deBroglie's connection between momentum and spatial-frequency vectors is perhaps most viscerally-experienced via the real-time access that electron-diffraction provides to transverse slices of a nano-crystal's reciprocal-lattice. The classic introductory (and/or advanced) physics lab-experiment on microwave Bragg-scattering can with a bit of re-arrangement also give students access to "zone-axis-pattern" slices through the 3D spatial-frequency (i.e. reciprocal) lattice of a ball-bearing crystal, which may likewise contain only a few unit-cells. In this paper we show how data from the sta…
AI-Driven Structure Refinement of X-ray Diffraction
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Shanghai University（上海大学）；University of Science and Technology of China（中国科学技术大学）
