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*

We report a new nanoporous amorphous carbon (NAC) structure that achieves both ultrahigh strength and high electrical conductivity, which are usually incompatible in porous materials. By using modified spark plasma sintering, we create three amorphous carbon phases with different atomic bonding configurations. The composite consists of an amorphous sp2-carbon matrix mixed with amorphous sp3-carbon and amorphous graphitic motif. NAC structure has isotropic electrical conductivity of up to 12,000 S/m, a 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 (TEM), electron energy loss spectroscopy (EELS), 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. Our research not only introduces novel material with exceptional properties, but also opens new opportunities for exploring amorphous structures and designing high-performance materials. This article is protected by copyright. All rights reserved.

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.

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.

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.

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.

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.

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.

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.

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.

How Cubic Can Ice Be?

Using an X-ray laser, we investigated the crystal structure of ice formed by homogeneous ice nucleation in deeply supercooled water nanodrops (r ≈ 10 nm) at ∼225 K. The nanodrops were formed by condensation of vapor in a supersonic nozzle, and the ice was probed within 100 μs of freezing using femtosecond wide-angle X-ray scattering at the Linac Coherent Light Source free-electron X-ray laser. The X-ray diffraction spectra indicate that this ice has a metastable, predominantly cubic structure; the shape of the first ice diffraction peak suggests stacking-disordered ice with a cubicity value, χ, in the range of 0.78 ± 0.05. The cubicity value determined here is higher than those determined in experiments with micron-sized drops but comparable to those found in molecular dynamics simulations. The high cubicity is most likely caused by the extremely low freezing temperatures and by the rapid freezing, which occurs on a ∼1 μs time scale in single nanodroplets.

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 β-strands running perpendicular to the filament axis, and that a range of order from fibrillar to crystalline is discernable for individual α-synuclein amyloids.

Experimental strategies for imaging bioparticles with femtosecond hard X-ray pulses

This study explores the capabilities of the Coherent X-ray Imaging Instrument at the Linac Coherent Light Source to image small biological samples. The weak signal from small samples puts a significant demand on the experiment. Aerosolized Omono River virus particles of ∼40 nm in diameter were injected into the submicrometre X-ray focus at a reduced pressure. Diffraction patterns were recorded on two area detectors. The statistical nature of the measurements from many individual particles provided information about the intensity profile of the X-ray beam, phase variations in the wavefront and the size distribution of the injected particles. The results point to a wider than expected size distribution (from ∼35 to ∼300 nm in diameter). This is likely to be owing to nonvolatile contaminants from larger droplets during aerosolization and droplet evaporation. The results suggest that the concentration of nonvolatile contaminants and the ratio between the volumes of the initial droplet and the sample particles is critical in such studies. The maximum beam intensity in the focus was found to be 1.9 × 10¹² photons per µm² per pulse. The full-width of the focus at half-maximum was estimated to be 500 nm (assuming 20% beamline transmission), and this width is larger than expected. Under these conditions, the diffraction signal from a sample-sized particle remained above the average background to a resolution of 4.25 nm. The results suggest that reducing the size of the initial droplets during aerosolization is necessary to bring small particles into the scope of detailed structural studies with X-ray lasers.

Open data set of live cyanobacterial cells imaged using an X-ray laser

Structural studies on living cells by conventional methods are limited to low resolution because radiation damage kills cells long before the necessary dose for high resolution can be delivered. X-ray free-electron lasers circumvent this problem by outrunning key damage processes with an ultra-short and extremely bright coherent X-ray pulse. Diffraction-before-destruction experiments provide high-resolution data from cells that are alive when the femtosecond X-ray pulse traverses the sample. This paper presents two data sets from micron-sized cyanobacteria obtained at the Linac Coherent Light Source, containing a total of 199,000 diffraction patterns. Utilizing this type of diffraction data will require the development of new analysis methods and algorithms for studying structure and structural variability in large populations of cells and to create abstract models. Such studies will allow us to understand living cells and populations of cells in new ways. New X-ray lasers, like the European XFEL, will produce billions of pulses per day, and could open new areas in structural sciences.

CCP-FEL: a collection of computer programs for free-electron laser research

The latest virtual special issue ofJournal of Applied Crystallography(http://journals.iucr.org/special_issues/2016/ccpfel) collects software for free-electron laser research and presents tools for a range of topics such as simulation of experiments, online monitoring of data collection, selection of hits, diagnostics of data quality, data management, data analysis and structure determination for both nanocrystallography and single-particle diffractive imaging. This article provides an introduction to the special issue.

Coherent diffraction of single Rice Dwarf virus particles using hard X-rays at the Linac Coherent Light Source

Single particle diffractive imaging data from Rice Dwarf Virus (RDV) were recorded using the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). RDV was chosen as it is a well-characterized model system, useful for proof-of-principle experiments, system optimization and algorithm development. RDV, an icosahedral virus of about 70 nm in diameter, was aerosolized and injected into the approximately 0.1 μm diameter focused hard X-ray beam at the CXI instrument of LCLS. Diffraction patterns from RDV with signal to 5.9 Ångström were recorded. The diffraction data are available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development, the contents of which are described here.

Dragonfly: an implementation of the expand-maximize-compress algorithm for single-particle imaging

A description is given of a single-particle X-ray imaging reconstruction and simulation package using the expand–maximize–compress algorithm, named Dragonfly.

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a three-dimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand–maximize–compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.

A comprehensive simulation framework for imaging single particles and biomolecules at the European X-ray Free-Electron Laser

The advent of newer, brighter, and more coherent X-ray sources, such as X-ray Free-Electron Lasers (XFELs), represents a tremendous growth in the potential to apply coherent X-rays to determine the structure of materials from the micron-scale down to the Angstrom-scale. There is a significant need for a multi-physics simulation framework to perform source-to-detector simulations for a single particle imaging experiment, including (i) the multidimensional simulation of the X-ray source; (ii) simulation of the wave-optics propagation of the coherent XFEL beams; (iii) atomistic modelling of photon-material interactions; (iv) simulation of the time-dependent diffraction process, including incoherent scattering; (v) assembling noisy and incomplete diffraction intensities into a three-dimensional data set using the Expansion-Maximisation-Compression (EMC) algorithm and (vi) phase retrieval to obtain structural information. We demonstrate the framework by simulating a single-particle experiment for a nitrogenase iron protein using parameters of the SPB/SFX instrument of the European XFEL. This exercise demonstrably yields interpretable consequences for structure determination that are crucial yet currently unavailable for experiment design.

Anomalous Behavior of the Homogeneous Ice Nucleation Rate in "No-Man's Land"

We present an analysis of ice nucleation kinetics from near-ambient pressure water as temperature decreases below the homogeneous limit T_H by cooling micrometer-sized droplets (microdroplets) evaporatively at 10³-10⁴ K/s and probing the structure ultrafast using femtosecond pulses from the Linac Coherent Light Source (LCLS) free-electron X-ray laser. Below 232 K, we observed a slower nucleation rate increase with decreasing temperature than anticipated from previous measurements, which we suggest is due to the rapid decrease in water's diffusivity. This is consistent with earlier findings that microdroplets do not crystallize at <227 K, but vitrify at cooling rates of 10⁶-10⁷ K/s. We also hypothesize that the slower increase in the nucleation rate is connected with the proposed "fragile-to-strong" transition anomaly in water.

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.

A minimal view of single-particle imaging with X-ray lasers

The ability to serially interrogate single biomolecules with femtosecond X-ray pulses from free-electron lasers has ushered in the possibility of determining the three-dimensional structure of biomolecules without crystallization. However, the complexity of imaging a sample's structure from very many of its noisy and incomplete diffraction data can be daunting. In this review, we introduce a simple analogue of this imaging workflow, use it to describe a structure reconstruction algorithm based on the expectation maximization principle, and consider the effects of extraneous noise. Such a minimal model can aid experiment and algorithm design in future studies.

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.

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.

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.

The extraction of single-particle diffraction patterns from a multiple-particle diffraction pattern

The structures of biological molecules may soon be determined with X-ray free-electron lasers without crystallization by recording the coherent diffraction patterns of many identical copies of a molecule. Most analysis methods require a measurement of each molecule individually. However, current injection methods deliver particles to the X-ray beam stochastically and the maximum yield of single particle measurements is 37% at optimal concentration. The remaining 63% of pulses intercept no particles or multiple particles. We demonstrate that in the latter case single particle diffraction patterns can be extracted provided the particles are sufficiently separated. The technique has the potential to greatly increase the amount of data available for three-dimensional imaging of identical particles with X-ray lasers.

Single-particle structure determination by correlations of snapshot X-ray diffraction patterns

Diffractive imaging with free-electron lasers allows structure determination from ensembles of weakly scattering identical nanoparticles. The ultra-short, ultra-bright X-ray pulses provide snapshots of the randomly oriented particles frozen in time, and terminate before the onset of structural damage. As signal strength diminishes for small particles, the synthesis of a three-dimensional diffraction volume requires simultaneous involvement of all data. Here we report the first application of a three-dimensional spatial frequency correlation analysis to carry out this synthesis from noisy single-particle femtosecond X-ray diffraction patterns of nearly identical samples in random and unknown orientations, collected at the Linac Coherent Light Source. Our demonstration uses unsupported test particles created via aerosol self-assembly, and composed of two polystyrene spheres of equal diameter. The correlation analysis avoids the need for orientation determination entirely. This method may be applied to the structural determination of biological macromolecules in solution.

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.

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.

Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight

The morphology of micrometre-size particulate matter is of critical importance in fields ranging from toxicology to climate science, yet these properties are surprisingly difficult to measure in the particles' native environment. Electron microscopy requires collection of particles on a substrate; visible light scattering provides insufficient resolution; and X-ray synchrotron studies have been limited to ensembles of particles. Here we demonstrate an in situ method for imaging individual sub-micrometre particles to nanometre resolution in their native environment, using intense, coherent X-ray pulses from the Linac Coherent Light Source free-electron laser. We introduced individual aerosol particles into the pulsed X-ray beam, which is sufficiently intense that diffraction from individual particles can be measured for morphological analysis. At the same time, ion fragments ejected from the beam were analysed using mass spectrometry, to determine the composition of single aerosol particles. Our results show the extent of internal dilation symmetry of individual soot particles subject to non-equilibrium aggregation, and the surprisingly large variability in their fractal dimensions. More broadly, our methods can be extended to resolve both static and dynamic morphology of general ensembles of disordered particles. Such general morphology has implications in topics such as solvent accessibilities in proteins, vibrational energy transfer by the hydrodynamic interaction of amino acids, and large-scale production of nanoscale structures by flame synthesis.

Femtosecond dark-field imaging with an X-ray free electron laser

The emergence of femtosecond diffractive imaging with X-ray lasers has enabled pioneering structural studies of isolated particles, such as viruses, at nanometer length scales. However, the issue of missing low frequency data significantly limits the potential of X-ray lasers to reveal sub-nanometer details of micrometer-sized samples. We have developed a new technique of dark-field coherent diffractive imaging to simultaneously overcome the missing data issue and enable us to harness the unique contrast mechanisms available in dark-field microscopy. Images of airborne particulate matter (soot) up to two microns in length were obtained using single-shot diffraction patterns obtained at the Linac Coherent Light Source, four times the size of objects previously imaged in similar experiments. This technique opens the door to femtosecond diffractive imaging of a wide range of micrometer-sized materials that exhibit irreproducible complexity down to the nanoscale, including airborne particulate matter, small cells, bacteria and gold-labeled biological samples.

Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns

We reconstructed the 3D Fourier intensity distribution of monodisperse prolate nanoparticles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast x-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the expansion-maximization-compression framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.