Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles.

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Engineering a Hierarchy of Disorder: A New Route to Synthesize High-Performance 3D Nanoporous All-Carbon Materials*.

A new nanoporous amorphous carbon (NAC) structure that achieves both ultrahigh strength and high electrical conductivity, which are usually incompatible in porous materials is reported. By using modified spark plasma sintering, three amorphous carbon phases with different atomic bonding configurations are created. The composite consisted of an amorphous sp2-carbon matrix mixed with amorphous sp3-carbon and amorphous graphitic motif. NAC structure has an isotropic electrical conductivity of up to 12 000 S m-1, Young's modulus of up to ≈5 GPa, and Vickers hardness of over 900 MPa. These properties are superior to those of existing conductive nanoporous materials. Direct investigation of the multiscale structure of this material through transmission electron microscopy, electron energy loss spectroscopy, and machine learning-based electron tomography revealed that the origin of the remarkable material properties is the well-organized sp2/sp3 amorphous carbon phases with a core-shell-like architecture, where the sp3-rich carbon forms a resilient core surrounded by a conductive sp2-rich layer. This research not only introduces novel materials with exceptional properties but also opens new opportunities for exploring amorphous structures and designing high-performance materials.

Ghostbuster: A phase retrieval diffraction tomography algorithm for cryo-EM.

Ewald sphere curvature correction, which extends beyond the projection approximation, stretches the shallow depth of field in cryo-EM reconstructions of thick particles. Here we show that even for previously assumed thin particles, reconstruction artifacts which we refer to as ghosts can appear. By retrieving the lost phases of the electron exitwaves and accounting for the first Born approximation scattering within the particle, we show that these ghosts can be effectively eliminated. Our simulations demonstrate how such ghostbusting can improve reconstructions as compared to existing state-of-the-art software. Like ptychographic cryo-EM, our Ghostbuster algorithm uses phase retrieval to improve reconstructions, but unlike the former, we do not need to modify the existing data acquisition pipelines.

A multiscale generative model to understand disorder in domain boundaries.

A continuing challenge in atomic resolution microscopy is to identify significant structural motifs and their assembly rules in synthesized materials with limited observations. Here, we propose and validate a simple and effective hybrid generative model capable of predicting unseen domain boundaries in a potassium sodium niobate thin film from only a small number of observations, without expensive first-principles calculations or atomistic simulations of domain growth. Our results demonstrate that complicated domain boundary structures spanning 1 to 100 nanometers can arise from simple interpretable local rules played out probabilistically. We also found previously unobserved, significant, tileable boundary motifs that may affect the piezoelectric response of the material system, and evidence that our system creates domain boundaries with the highest configurational entropy. More broadly, our work shows that simple yet interpretable machine learning models could pave the way to describe and understand the nature and origin of disorder in complex materials, therefore improving functional materials design.

Microstructure and crystal order during freezing of supercooled water drops.

Supercooled water droplets are widely used to study supercooled water1,2, ice nucleation3-5 and droplet freezing6-11. Their freezing in the atmosphere affects the dynamics and climate feedback of clouds12,13 and can accelerate cloud freezing through secondary ice production14-17. Droplet freezing occurs at several timescales and length scales14,18 and is sufficiently stochastic to make it unlikely that two frozen drops are identical. Here we use optical microscopy and X-ray laser diffraction to investigate the freezing of tens of thousands of water microdrops in vacuum after homogeneous ice nucleation around 234-235 K. On the basis of drop images, we developed a seven-stage model of freezing and used it to time the diffraction data. Diffraction from ice crystals showed that long-range crystalline order formed in less than 1 ms after freezing, whereas diffraction from the remaining liquid became similar to that from quasi-liquid layers on premelted ice19,20. The ice had a strained hexagonal crystal structure just after freezing, which is an early metastable state that probably precedes the formation of ice with stacking defects8,9,18. The techniques reported here could help determine the dynamics of freezing in other conditions, such as drop freezing in clouds, or help understand rapid solidification in other materials.

Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging.

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Learning motifs and their hierarchies in atomic resolution microscopy.

Characterizing materials to atomic resolution and first-principles structure-property prediction are two pillars for accelerating functional materials discovery. However, we are still lacking a rapid, noise-robust framework to extract multilevel atomic structural motifs from complex materials to complement, inform, and guide our first-principles models. Here, we present a machine learning framework that rapidly extracts a hierarchy of complex structural motifs from atomically resolved images. We demonstrate how such motif hierarchies can rapidly reconstruct specimens with various defects. Abstracting complex specimens with simplified motifs enabled us to discover a previously unidentified structure in a Mo─V─Te─Nb polyoxometalate (POM) and quantify the relative disorder in a twisted bilayer MoS2. In addition, these motif hierarchies provide statistically grounded clues about the favored and frustrated pathways during self-assembly. The motifs and their hierarchies in our framework coarse-grain disorder in a manner that allows us to understand a much broader range of multiscale samples with functional imperfections and nontrivial topological phases.

Accurate and Robust Calibration of the Uniform Affine Transformation Between Scan-Camera Coordinates for Atom-Resolved In-Focus 4D-STEM Datasets.

Accurate geometrical calibration between the scan coordinates and the camera coordinates is critical in four-dimensional scanning transmission electron microscopy (4D-STEM) for both quantitative imaging and ptychographic reconstructions. For atomic-resolved, in-focus 4D-STEM datasets, we propose a hybrid method incorporating two sub-routines, namely a J-matrix method and a Fourier method, which can calibrate the uniform affine transformation between the scan-camera coordinates using raw data, without a priori knowledge of the crystal structure of the specimen. The hybrid method is found robust against scan distortions and residual probe aberrations. It is also effective even when defects are present in the specimen, or the specimen becomes relatively thick. We will demonstrate that a successful geometrical calibration with the hybrid method will lead to a more reliable recovery of both the specimen and the electron probe in a ptychographic reconstruction. We will also show that, although the elimination of local scan position errors still requires an iterative approach, the rate of convergence can be improved, and the residual errors can be further reduced if the hybrid method can be firstly applied for initial calibration. The code is made available as a simple-to-use tool to correct affine transformations of the scan-camera coordinates in 4D-STEM experiments.

Preventing the Capillary-Induced Collapse of Vertical Nanostructures.

Robust processes to fabricate densely packed high-aspect-ratio (HAR) vertical semiconductor nanostructures are important for applications in microelectronics, energy storage and conversion. One of the main challenges in manufacturing these nanostructures is pattern collapse, which is the damage induced by capillary forces from numerous solution-based processes used during their fabrication. Here, using an array of vertical silicon (Si) nanopillars as test structures, we demonstrate that pattern collapse can be greatly reduced by a solution-phase deposition method to coat the nanopillars with self-assembled monolayers (SAMs). As the main cause for pattern collapse is strong adhesion between the nanopillars, we systematically evaluated SAMs with different surface energy components and identified H-bonding between the surfaces to have the largest contribution to the adhesion. The advantage of the solution-phase deposition method is that it can be implemented before any drying step, which causes patterns to collapse. Moreover, after drying, these SAMs can be easily removed using a gentle air-plasma treatment right before the next fabrication step, leaving a clean nanopillar surface behind. Therefore, our approach provides a facile and effective method to prevent the drying-induced pattern collapse in micro- and nanofabrication processes.

An encryption-decryption framework to validating single-particle imaging.

We propose an encryption-decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes' ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design.

High-Throughput 3D Ensemble Characterization of Individual Core-Shell Nanoparticles with X-ray Free Electron Laser Single-Particle Imaging.

The structures as building blocks for designing functional nanomaterials have fueled the development of versatile nanoprobes to understand local structures of noncrystalline specimens. Progress in analyzing structures of individual specimens with atomic scale accuracy has been notable recently. In most cases, however, only a limited number of specimens are inspected lacking statistics to represent the systems with structural inhomogeneity. Here, by employing single-particle imaging with X-ray free electron lasers and algorithms for multiple-model 3D imaging, we succeeded in investigating several thousand specimens in a couple of hours and identified intrinsic heterogeneities with 3D structures. Quantitative analysis has unveiled 3D morphology, facet indices, and elastic strain. The 3D elastic energy distribution is further corroborated by molecular dynamics simulations to gain mechanical insight at the atomic level. This work establishes a route to high-throughput characterization of individual specimens in large ensembles, hence overcoming statistical deficiency while providing quantitative information at the nanoscale.

A data reduction and compression description for high throughput time-resolved electron microscopy.

Fast, direct electron detectors have significantly improved the spatio-temporal resolution of electron microscopy movies. Preserving both spatial and temporal resolution in extended observations, however, requires storing prohibitively large amounts of data. Here, we describe an efficient and flexible data reduction and compression scheme (ReCoDe) that retains both spatial and temporal resolution by preserving individual electron events. Running ReCoDe on a workstation we demonstrate on-the-fly reduction and compression of raw data streaming off a detector at 3 GB/s, for hours of uninterrupted data collection. The output was 100-fold smaller than the raw data and saved directly onto network-attached storage drives over a 10 GbE connection. We discuss calibration techniques that support electron detection and counting (e.g., estimate electron backscattering rates, false positive rates, and data compressibility), and novel data analysis methods enabled by ReCoDe (e.g., recalibration of data post acquisition, and accurate estimation of coincidence loss).

Pulse-to-pulse wavefront sensing at free-electron lasers using ptychography.

The pressing need for knowledge of the detailed wavefront properties of ultra-bright and ultra-short pulses produced by free-electron lasers has spurred the development of several complementary characterization approaches. Here a method based on ptychography is presented that can retrieve high-resolution complex-valued wavefunctions of individual pulses without strong constraints on the illumination or sample object used. The technique is demonstrated within experimental conditions suited for diffraction experiments and exploiting Kirkpatrick-Baez focusing optics. This lensless technique, applicable to many other short-pulse instruments, can achieve diffraction-limited resolution.

Author Correction: Coherent diffractive imaging of microtubules using an X-ray laser.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Coherent diffractive imaging of microtubules using an X-ray laser.

X-ray free electron lasers (XFELs) create new possibilities for structural studies of biological objects that extend beyond what is possible with synchrotron radiation. Serial femtosecond crystallography has allowed high-resolution structures to be determined from micro-meter sized crystals, whereas single particle coherent X-ray imaging requires development to extend the resolution beyond a few tens of nanometers. Here we describe an intermediate approach: the XFEL imaging of biological assemblies with helical symmetry. We collected X-ray scattering images from samples of microtubules injected across an XFEL beam using a liquid microjet, sorted these images into class averages, merged these data into a diffraction pattern extending to 2 nm resolution, and reconstructed these data into a projection image of the microtubule. Details such as the 4 nm tubulin monomer became visible in this reconstruction. These results illustrate the potential of single-molecule X-ray imaging of biological assembles with helical symmetry at room temperature.

Erratum: Experimental strategies for imaging bioparticles with femtosecond hard X-ray pulses. Corrigendum.

[This corrects the article DOI: 10.1107/S2052252517003591.].

Viscous field-aligned water exhibits cubic-ice-like structural motifs.

Strong electric fields are known to greatly accelerate the freezing of water in molecular dynamics simulations, and have also been shown to affect the thermodynamics of the phase transition. In this work, a mechanistic explanation for field-induced crystallization of water is presented. Due to the coupling between the rotational and the translational degrees of freedom of individual water molecules, an applied field can directly drive the formation of cubic-ice like local motifs in water. Analysis of the angular distributions of water molecules in TIP4P-2005 water at field strengths between 0.0 and 0.32 V Å-1 demonstrates the existence of such motifs in the field-aligned liquid phase that is observed prior to the onset of the freezing transition. The dynamic properties of this field-aligned liquid phase are also studied, and its viscosity is shown to be within a factor of two of that of regular liquid water using the Green-Kubo method as well as mean squared displacements. The choice between the NPT and the NVT ensembles is shown to have a strong impact on the evolution of molecular dynamics trajectories at field strengths close to the threshold for the freezing transition, and the importance of properly accounting for the electric field terms in the pressure virial is emphasized.

Flow-aligned, single-shot fiber diffraction using a femtosecond X-ray free-electron laser.

A major goal for X-ray free-electron laser (XFEL) based science is to elucidate structures of biological molecules without the need for crystals. Filament systems may provide some of the first single macromolecular structures elucidated by XFEL radiation, since they contain one-dimensional translational symmetry and thereby occupy the diffraction intensity region between the extremes of crystals and single molecules. Here, we demonstrate flow alignment of as few as 100 filaments (Escherichia coli pili, F-actin, and amyloid fibrils), which when intersected by femtosecond X-ray pulses result in diffraction patterns similar to those obtained from classical fiber diffraction studies. We also determine that F-actin can be flow-aligned to a disorientation of approximately 5 degrees. Using this XFEL-based technique, we determine that gelsolin amyloids are comprised of stacked ß-strands running perpendicular to the filament axis, and that a range of order from fibrillar to crystalline is discernable for individual α-synuclein amyloids.