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Quantification of Dynamic Scattering Effects in Molecular Crystals using Large Angle Rocking Beam Electron Diffraction
Electron crystallography provides a pathway to solve structure of small crystals (< 1um) in size, and thus overcomes difficult synthesis constraints involved in growing large crystals. Generally, electron diffraction data is collected in the form of integrated intensity using continuous rotation or by precession. The measured intensities in 3D are utilized for structure solution. Using this approach, structure solution of difficult crystals, such as small crystals of zeolites, metal-organic frameworks, molecular crystals, and proteins , can be solved by electron diffraction. However, electron structure solutions are regularly reported with higher Rvalues than x-ray or neutron diffraction. While similar structures are found despite the high R-values, the differences in the measure intensity and theory calculated intensity limit information that can be extracted by electron diffraction. Previous work demonstrated that including multiple-scattering effects significantly reduce the R-values . Thus, it is critical to be able to quantify the dynamical diffraction effects in molecular crystals.
Large Angle Rocking Beam Electron Diffraction Utilizing Electron Direct Detector
Electron diffraction of a crystal is fundamentally a function of the potential of that crystal. The intensity of electron diffraction patterns is, as a result, sensitive to the charge density of atoms and bonding inside crystals. Experimentally, the traditional method to probe this information is quantitative Convergent Beam Electron Diffraction (CBED). Quantitative CBED or QCEBD is a method which uses dynamic diffraction theory to quantify CBED intensities and to extract information about crystal structure and bonding. The sensitivity of dynamical scattering is leveraged to measure crystal symmetry and crystal structure factors. At its limit, electron structure factors are measured at high accuracy allowing access to chemical bonding information, which corroborate theoretical calculations through multipole model refinements of the experimental charge density. The primary limit to QCBED is the requirement of a non-overlapping convergent beam. This subsequently limits QCBED to crystals with small unit cells which are stable under the focused probe.
Imaging the Progression of Radiolytic Damage in Molecular Crystals with Scanning Nanobeam Electron Diffraction
Almost every electron microscopy experiment is fundamentally limited by radiation damage. Nevertheless, little is known about the onset and progression of radiolysis in beam-sensitive materials. Here we apply ambient-temperature scanning nanobeam electron diffraction to record simultaneous dual-space movies of organic and organometallic nanocrystals at sequential stages of beam-induced radiolytic decay. We show that the underlying mosaic of coherently diffracting domains undergoes internal rearrangement as a function of accumulating electron fluence, causing the intensities of some associated Bragg reflections to fade nonmonotonically. Furthermore, we demonstrate that repeated irradiation at a single probe position leads to the isotropic propagation of delocalized radiolytic damage well beyond the direct footprint of the incident beam. We refer to these expanding tides of amorphization as “impact craters.”
Large-Angle Rocking Beam Electron Diffraction of Large Unit Cell Crystals Using Direct Electron Detector
We report a large-angle rocking beam electron diffraction (LARBED) technique for electron diffraction analysis. Diffraction patterns are recorded in a scanning transmission electron microscope (STEM) using a direct electron detector with large dynamical range and fast readout. We use a nanobeam for diffraction and perform the beam double rocking by synchronizing the detector with the STEM scan coils for the recording. Using this approach, large-angle convergent beam electron diffraction (LACBED) patterns of different reflections are obtained simultaneously. By using a nanobeam, instead of a focused beam, the LARBED technique can be applied to beam-sensitive crystals as well as crystals with large unit cells. Here, this paper describes the implementation of LARBED and evaluates the performance using silicon and gadolinium gallium garnet crystals as test samples. We demonstrate that our method provides an effective and robust way for recording LARBED patterns and paves the way for quantitative electron diffraction of large unit cell and beam-sensitive crystals.
Random Forest Prediction of Crystal Structure from Electron Diffraction Patterns
Transmission electron microscopy (TEM) diffraction patterns are regularly used to determine the structure of crystalline materials. Electron diffraction is the most common method to solve for unknown or partially known crystal structures, as it provides direct and interpretable feedback on the orientation of crystal grains under the beam [1]. However, it remains a challenge to determine the crystal structure of a new material or even a new phase of an existing material. Analysis of such materials commonly requires manual exploration and comparison with simulated diffraction patterns. This is often a time consuming process with no obvious start point when many similar structures are possible, and this method cannot be used to determine crystal structure or orientation from structures not included in the diffraction libraries. Therefore, we have developed a machine learning model to determine the crystal structure of a material from its electron diffraction pattern.
Unsupervised anomaly detection in MeV ultrafast electron diffraction
MeV ultrafast electron diffraction (MUED) is a pump-probe technique used to study the dynamic structural evolution of materials. An ultrashort laser pulse triggers structural changes, which are then probed by an ultrashort relativistic electron beam. To overcome low signal-to-noise ratios, diffraction patterns are averaged over thousands of shots. However, shot-to-shot instabilities in the electron beam can distort individual patterns, introducing uncertainty. Improving MUED accuracy requires detecting and removing these anomalous patterns from large datasets. In this work, we developed a fully unsupervised methodology for the detection of anomalous diffraction patterns. Using a convolutional autoencoder, we calculate the reconstruction mean squared error of the diffraction patterns. Based on the statistical analysis of this error, we provide the user an estimation of the probability that the pattern is normal, which also allows a posterior visual inspection of the images that are difficult to classify. This method has been trained with only 100 diffraction patterns and tested on 1521 patterns, resulting in a false positive rate between 0.2% and 0.4%, with a training time of 10 s per image and a test time of about 1 s per image. Here, the proposed methodology can also be applied to other diffraction techniques in which large datasets are collected that include faulty images due to instrumental instabilities.
Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction
Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.
Valence Electron Distributions from Sub-Angstrom Convergent Beam Electron Diffraction
Modern aberration-corrected scanning transmission electron microscopes can acquire four-dimensional data sets (“4D STEM”) by recording convergent beam electron diffraction (CBED) patterns, using precisely positioned, sub-angstrom probes. Here, we demonstrate that these patterns can probe the site symmetry, atomic displacements, and valence electron distributions at individual atomic columns. To this end, 4D STEM CBED patterns were acquired from SrTiO 3 single crystals and compared with patterns calculated using scattering potentials derived from density functional theory. Here, we show that an aspherical valence electron charge build-up at the oxygen sites causes intensity asymmetries in the low-angle scattering portion of the patterns. Using strained SrTiO 3 films containing subtle polar displacements within nanometer-sized domains, it is shown that the high-angle scattering portion in each pattern is sensitive to atomic displacements.
Multiple origins of extra electron diffractions in fcc metals
Diffuse intensities in the electron diffraction patterns of concentrated face-centered cubic solid solutions have been widely attributed to chemical short-range order, although this connection has been recently questioned. This article explores the many nonordering origins of commonly reported features using a combination of experimental electron microscopy and multislice diffraction simulations, which suggest that diffuse intensities largely represent thermal and static displacement scattering. A number of observations may reflect additional contributions from planar defects, surface terminations incommensurate with bulk periodicity, or weaker dynamical effects.
Random forest prediction of crystal structure from electron diffraction patterns incorporating multiple scattering
Diffraction is the most common method to solve for unknown or partially known crystal structures. However, it remains a challenge to determine the crystal structure of a new material that may have nanoscale size or heterogeneities. Here, in this study, we train an architecture of hierarchical random forest models capable of predicting the crystal system, space group, and lattice parameters from one or more unknown two-dimensional electron diffraction patterns. Our initial model correctly identifies the crystal system of a simulated electron diffraction pattern from a 20-nm-thick specimen of arbitrary orientation 67% of the time. We achieve a topline accuracy of 79% when aggregating predictions from ten patterns of the same material but different zone axes. The space group and lattice predictions range from 70% to 90% accuracy and median errors of 0.01-0.5Å, respectively, for cubic, hexagonal, trigonal, and tetragonal crystal systems while being less reliable on orthorhombic and monoclinic systems. We apply this architecture to a four-dimensional scanning transmission electron microscopy scan of gold nanoparticles, where it accurately predicts the crystal structure and lattice constants. These random forest models can be used to significantly accelerate the analysis of electron diffraction patterns, particularly in the case of unknown crystal structures. Additionally, due to the speed of inference, these models could be integrated into live transmission electron microscopy experiments, allowing real-Time labeling of a specimen.
Multi-angle Precession Electron Diffraction (MAPED): A Versatile Approach to 4D-STEM Precession
Precession of a converged beam during acquisition of a 4D-STEM dataset improves strain, orientation, and phase mapping accuracy by averaging over continuous angles of illumination. Precession experiments usually rely on integrated systems, where automatic alignments lead to fast, high-quality results. The dependence of these experiments on specific hardware and software is evident even when switching to nonintegrated detectors on a precession tool, as experimental set-up becomes challenging and time-consuming. Here, we introduce multi-angle precession electron diffraction (MAPED): a method to perform electron diffraction by collecting sequential 4D-STEM scans at different incident beam tilts. The multiple diffraction datasets are averaged together postacquisition, resulting in a single dataset that minimizes the impact of the curvature and orientation of the Ewald sphere relative to the crystal under study. Our results demonstrate that even four additional tilts improved measurement of material properties, namely strain and orientation, as compared to single-tilt 4D-STEM experiments. We show the versatility and flexibility of our MAPED approach with data collected on a number of microscopes with different hardware configurations and a variety of detectors.
The UV Photoinduced Ring-Closing Reaction of Cyclopentadiene Probed with Ultrafast Electron Diffraction
Conjugated cyclic organic molecules are common across many fields such as pharmaceuticals, are naturally occurring in biological systems, and are used in synthetic materials. One particular area of interest from a photochemical point of view is the formation of highly strained cyclic organics. We investigate the photoinduced reaction of cyclopentadiene, a five-membered organic ring molecule which can form strained three and four carbon rings after photoexcitation with UV light, with the gas-phase ultrafast electron diffraction instrument at the SLAC MeV-UED facility. Electron diffraction offers a direct probe sensitive to the nuclear geometry during the reaction, allowing for the determination of the distribution of products formed following photoexcitation. We observe the simultaneous formation of the highly strained ring- closed bicyclo[2.1.0]pentene and vibrationally hot cyclopentadiene within the temporal resolution of the experiment, and determine the relative yield of all reaction products. Furthermore, the experimental results are in good agreement with the predictions of trajectory simulations.
Calculation of rf-induced temporal jitter in ultrafast electron diffraction
A significant contribution to the temporal resolution of an ultrafast electron diffraction (UED) instrument is arrival time jitter caused by amplitude and phase variation of radio-frequency (rf) cavities. In this paper, we present a semianalytical approach for calculating rf-induced temporal jitter from klystron and rf cavity parameters. Our approach allows fast estimation of temporal jitter for MeV-UED beamlines and can serve as a virtual timing tool when shot-to-shot measurements of rf amplitude and phase jitters are available. A simulation study for the SLAC MeV-UED instrument is presented, and the temporal resolution of several beamline configurations is compared.
Extreme Longitudinal Compression of Optimized Beams for MEV Ultrafast Electron Diffraction (Final Technical Report)
We worked out the design of a high repetition rate MeV energy ultrafast electron diffraction instrument based on the existing Cornell photoinjector, which can readily be applied to the presented findings. This example is a blueprint of other similarly arranged UED setups. Using particle tracking simulations in conjunction with multiobjective genetic algorithm optimization, we explored the smallest bunch lengths, emittance, and probe spot sizes achievable. As two limits, we defined stroboscopic conditions (with single electrons per pulse) and operation with 10 5 electrons per bunch which may be suitable for single-shot diffraction images. In the stroboscopic case, the flexibility provided by the many cavity bunching and acceleration allows for longitudinal phase space linearization without a higher harmonic field, providing sub-fs bunch lengths at the sample. Given low emittance photoemission conditions, these small bunch lengths can be maintained with probe transverse sizes at the single micron (1 μm) scale and below. In the case of 10 5 electrons per pulse, we simulated state-of-the-art 5D brightness conditions: rms bunch lengths of 10 fs with 3-nm normalized emittances, while permitting repetition rates as high as 1.3 GHz. We showed that in conjunction with collimating apertures, a novel focusing scheme achieves very high-quality emittance compensation for the central core of the beam composing 40% of particles, for a resulting beam size of 5 μm (rms). Finally, to aid in the design of new SRF-based ultrafast electron diffraction machines, we simulated the trade-off between the number of cavities used and achievable bunch length and emittance. In the longitudinal dimension, we made use of the fact that MeV UED requires much lower energy than the 15-MeV maxi mum energy of Cornell’s CBETA injector, and we may therefore use several of the SRF cavities for bunch length compression. In practice, we used a genetic optimization algorithm to choose the phases and amplitudes of the cavities appropriately for optimal bunching. In the zero space charge case, we found that bunching and acceleration are distributed across the six cavities in a way that produces a linearizing effect. And we showed that the ultimate bunch length can be limited by time-of-flight differences arising from transverse size and transverse momentum spread. The space charge code developed and used for this development is now permanent part of the Bmad accelerator simulation code and has already contributed to other developments, e.g., for the EIC electron cooler design.
A large interlaboratory electron diffraction study of monolayer graphene
Standardisation of data collection and analysis is essential to enable commercialisation of 2D materials in a wide range of technologies. Selected area electron diffraction (SAED) in the transmission electron microscope (TEM) is one of the key methods for distinguishing monolayer from bilayer and few-layer graphene by comparing the 1st and 2nd order diffraction spot intensities. Yet there are many factors that can affect the reliability of data collection and interpretation, causing the measurement of monolayer samples to deviate from the literature boundary condition of $I_{\{\bar{2}110\}}$$/$$I_{\{1\bar{1}00\}}$ < 1 for monolayer graphene (1LG). Here we present the results of a large interlaboratory SAED comparison study, where 15 international laboratories measured and analysed nominally identical samples of chemical vapour deposited graphene. Large variations were observed in the measured ratios of diffraction spot intensities, with the largest variance associated with poor quality SAED data resulting from inadequate specimen handling and storage. To inform the reliable determination of monolayer thickness from SAED patterns we provide a description of best practice for specimen handling, TEM operation, data collection and analysis. This work was undertaken within VAMAS Technical Working Area 41: Graphene and related 2D materials—Project 9, the results of which have been directly incorporated into ISO/TS 21356–2 for the characterisation of graphene sheets. We find that when this methodology is followed, 1LG can be distinguished from bilayer or thicker material with high confidence where analysis of a single SAED pattern gives $I_{\{\bar{2}110\}}$$/$$I_{\{1\bar{1}00\}}$ < 1.2, even in the absence of precise specimen tilting.
Imaging the photochemistry of cyclobutanone using ultrafast electron diffraction: Experimental results
We investigated the ultrafast structural dynamics of cyclobutanone following photoexcitation at λ = 200 nm using gas-phase megaelectronvolt ultrafast electron diffraction. Our investigation complements the simulation studies of the same process within this special issue. It provides information about both electronic state population and structural dynamics through well-separable inelastic and elastic electron scattering signatures. We observe the depopulation of the photoexcited S 2 state of cyclobutanone with n3s Rydberg character through its inelastic electron scattering signature with a time constant of (0.29 ± 0.2) ps toward the S 1 state. The S 1 state population undergoes ring-opening via a Norrish Type-I reaction, likely while passing through a conical intersection with S 0 . The corresponding structural changes can be tracked by elastic electron scattering signatures. These changes appear with a delay of (0.14 ± 0.05) ps with respect to the initial photoexcitation, which is less than the S 2 depopulation time constant. This behavior provides evidence for the ballistic nature of the ring-opening once the S 1 state is reached. The resulting biradical species react further within (1.2 ± 0.2) ps via two rival fragmentation channels yielding ketene and ethylene, or propene and carbon monoxide. Furthermore, our study showcases the value of both gas-phase ultrafast diffraction studies as an experimental benchmark for nonadiabatic dynamics simulation methods and the limits in the interpretation of such experimental data without comparison with such simulations.
Capturing Ring Opening in Photoexcited Enolic Acetylacetone upon Hydrogen Bond Dissociation by Ultrafast Electron Diffraction
Photoinduced biological and chemical reactions are often based on key structural transformations of a molecule driven across multiple electronic states. Acetylacetone (AcAc) is a prototypical system for complex chemical pathways involving several conical intersections (CI) and singlet–triplet intersystem crossings (ISC) characterized by distinct geometries. In the gas phase, AcAc is predominantly in a planar ring-like enolic form stabilized by a strong intramolecular O–H···O hydrogen bond. Following excitation into the S 2 (ππ*) state at 266 nm, acetylacetone undergoes rapid internal conversion followed by intersystem crossing. Such relaxation pathways are associated with structural changes including ring opening, deplanarization, and bond elongation. In this work, ultrafast electron diffraction (UED) at the SLAC MeV-UED setup is employed as a direct structural probe with a time resolution of 160 fs. Together with trajectory surface hopping simulations, analysis of the UED data provides a new perspective on the early time nuclear dynamics in acetylacetone. Specifically, AcAc is observed to undergo ring opening, deplanarization, and bond elongation all within the first 700 fs after photoexcitation. The monitored dynamics is associated mainly with the nuclear motion on the S 1 potential energy surface, formed after very rapid transfer from S 2 to S 1 , allowing AcAc to reach the conical intersection to intersystem crossing. Such time scales of nuclear motion are contrasted with the time scales of electronic transitions in AcAc that were previously characterized with spectroscopic methods, specifically internal conversion (<100 fs) and intersystem crossing (∼1.5 ps).