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.

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.

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.

Three-dimensional reconstruction of the giant mimivirus particle with an x-ray free-electron laser.

We present a proof-of-concept three-dimensional reconstruction of the giant mimivirus particle from experimentally measured diffraction patterns from an x-ray free-electron laser. Three-dimensional imaging requires the assembly of many two-dimensional patterns into an internally consistent Fourier volume. Since each particle is randomly oriented when exposed to the x-ray pulse, relative orientations have to be retrieved from the diffraction data alone. We achieve this with a modified version of the expand, maximize and compress algorithm and validate our result using new methods.

Nanoparticle dynamics in a nanodroplet.

We describe the dynamics of 3-10 nm gold nanoparticles encapsulated by ∼30 nm liquid nanodroplets on a flat solid substrate and find that the diffusive motion of these nanoparticles is damped due to strong interactions with the substrate. Such damped dynamics enabled us to obtain time-resolved observations of encapsulated nanoparticles coalescing into larger particles. Techniques described here serve as a platform to study chemical and physical dynamics under highly confined conditions.

Bonding pathways of gold nanocrystals in solution.

Nanocrystal bonding is an important phenomenon in crystal growth and nanoscale welding. Here, we show that for gold nanocrystals bonding in solution can follow two distinct pathways: (1) coherent, defect-free bonding occurs when two nanocrystals attach with their lattices aligned to within a critical angle; and (2) beyond this critical angle, defects form at the interfaces where the nanocrystals merge. The critical misalignment angle for ∼10 nm crystals is ∼15° in both in situ experiments and full-atom molecular dynamics simulations. Understanding the origin of this critical angle during bonding may help us predict and manage strain profiles in nanoscale assemblies and inspire techniques toward reproducible and extensible architectures using only basic crystalline blocks.

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.

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.

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.

Sensing the wavefront of x-ray free-electron lasers using aerosol spheres.

Characterizing intense, focused x-ray free electron laser (FEL) pulses is crucial for their use in diffractive imaging. We describe how the distribution of average phase tilts and intensities on hard x-ray pulses with peak intensities of 10(21) W/m(2) can be retrieved from an ensemble of diffraction patterns produced by 70 nm-radius polystyrene spheres, in a manner that mimics wavefront sensors. Besides showing that an adaptive geometric correction may be necessary for diffraction data from randomly injected sample sources, our paper demonstrates the possibility of collecting statistics on structured pulses using only the diffraction patterns they generate and highlights the imperative to study its impact on single-particle diffractive imaging.

Toward unsupervised single-shot diffractive imaging of heterogeneous particles using X-ray free-electron lasers.

Single shot diffraction imaging experiments via X-ray free-electron lasers can generate as many as hundreds of thousands of diffraction patterns of scattering objects. Recovering the real space contrast of a scattering object from these patterns currently requires a reconstruction process with user guidance in a number of steps, introducing severe bottlenecks in data processing. We present a series of measures that replace user guidance with algorithms that reconstruct contrasts in an unsupervised fashion. We demonstrate the feasibility of automating the reconstruction process by generating hundreds of contrasts obtained from soot particle diffraction experiments.

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.

Nanoflow electrospinning serial femtosecond crystallography.

An electrospun liquid microjet has been developed that delivers protein microcrystal suspensions at flow rates of 0.14-3.1 µl min(-1) to perform serial femtosecond crystallography (SFX) studies with X-ray lasers. Thermolysin microcrystals flowed at 0.17 µl min(-1) and diffracted to beyond 4 Å resolution, producing 14,000 indexable diffraction patterns, or four per second, from 140 µg of protein. Nanoflow electrospinning extends SFX to biological samples that necessitate minimal sample consumption.

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.

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.

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.

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.

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).