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

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.

Unveiling Core-Shell Structure Formation in a Ni3Fe Nanoparticle with In Situ Multi-Bragg Coherent Diffraction Imaging

Solid-state reactions play a key role in materials science. The evolution of the structure of a single 350 nm Ni3Fe nanoparticle, i.e., its morphology (facets) as well as its deformation field, has been followed by applying multireflection Bragg coherent diffraction imaging. Through this approach, we unveiled a demixing process that occurs at high temperatures (600 °C) under an Ar atmosphere. This process leads to the gradual emergence of a highly strained core-shell structure, distinguished by two distinct lattice parameters with a difference of 0.4%. Concurrently, this transformation causes the facets to vanish, ultimately yielding a rounded core-shell nanoparticle. This final structure comprises a Ni3Fe core surrounded by a 40 nm Ni-rich outer shell due to preferential iron oxidation. Providing in situ 3D imaging of the lattice parameters at the nanometer scale while varying the temperature, this study─with the support of atomistic simulations─not only showcases the power of in situ multireflection BCDI but also provides valuable insights into the mechanisms at work during a solid-state reaction characterized by a core-shell transition.

Development of the multiplex imaging chamber at PAL-XFEL

Various X-ray techniques are employed to investigate specimens in diverse fields. Generally, scattering and absorption/emission processes occur due to the interaction of X-rays with matter. The output signals from these processes contain structural information and the electronic structure of specimens, respectively. The combination of complementary X-ray techniques improves the understanding of complex systems holistically. In this context, we introduce a multiplex imaging instrument that can collect small-/wide-angle X-ray diffraction and X-ray emission spectra simultaneously to investigate morphological information with nanoscale resolution, crystal arrangement at the atomic scale and the electronic structure of specimens.

Enhanced EMC-Advantages of partially known orientations in x-ray single particle imaging

Single particle imaging of proteins in the gas phase with x-ray free-electron lasers holds great potential to study fast protein dynamics, but is currently limited by weak and noisy data. A further challenge is to discover the proteins' orientation as each protein is randomly oriented when exposed to x-rays. Algorithms such as the expand, maximize, and compress (EMC) exist that can solve the orientation problem and reconstruct the three-dimensional diffraction intensity space, given sufficient measurements. If information about orientation were known, for example, by using an electric field to orient the particles, the reconstruction would benefit and potentially reach better results. We used simulated diffraction experiments to test how the reconstructions from EMC improve with particles' orientation to a preferred axis. Our reconstructions converged to correct maps of the three-dimensional diffraction space with fewer measurements if biased orientation information was considered. Even for a moderate bias, there was still significant improvement. Biased orientations also substantially improved the results in the case of missing central information, in particular in the case of small datasets. The effects were even more significant when adding a background with 50% the strength of the averaged diffraction signal photons to the diffraction patterns, sometimes reducing the data requirement for convergence by a factor of 10. This demonstrates the usefulness of having biased orientation information in single particle imaging experiments, even for a weaker bias than what was previously known. This could be a key component in overcoming the problems with background noise that currently plague these experiments.

Chaotic dynamics in X-ray free-electron lasers with an optical undulator

In this work, the chaotic motions of relativistic electrons in X-ray free-electron lasers are investigated using an optical undulator in the presence of a magnetized ion-channel background. To miniaturize X-ray light sources, the optical undulator is a promising concept. The optical undulator provides higher optical gain than conventional magnetostatic undulators due to its micrometer wavelength. In addition, it reduces the required electron beam energy from several GeV to the multi-MeV range to produce X-ray pulses. The interaction of an optical undulator with an intense relativistic electron beam is a highly non-linear phenomenon that can lead to chaotic dynamics. At synchrotron radiation sources, the possibility of chaos control for X-ray FELs can be critical for certain classes of experimental studies. The equations of motion for a relativistic electron propagating through the optical undulator in the presence of a magnetized ion-channel can be derived from the Hamiltonian of the interaction region. Simulation results revealed that the intensity of the perturbation route from orderly behavior to chaos depends on the beam density, axial magnetic field strength, ion-channel density parameter, and pump laser undulator. Specific values of parameters were obtained for the transition from regular to chaotic paths. Bifurcation diagrams of the system were plotted to demonstrate the origin of chaos at a critical point, and Poincaré maps were created to distinguish between chaotic and orderly motions of electrons. The proposed new scheme can help to improve X-ray FELs, which have potential usages in basic sciences, medicine, and industry.

Similarity score for screening phase-retrieved maps in X-ray diffraction imaging - characterization in reciprocal space

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

Protocol using similarity score and improved shrink-wrap algorithm for better convergence of phase-retrieval calculation in X-ray diffraction imaging

In X-ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase-retrieval (PR) algorithms. However, the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero-scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study [Sekiguchi et al. (2017), J. Synchrotron Rad. 24, 1024-1038]. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron-density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non-crystalline particles using synchrotron X-rays and X-ray free-electron laser pulses.

Nanoscale Three-Dimensional Network Structure of a Mesoporous Particle Unveiled via Adaptive Multidistance Coherent X-ray Tomography

Mesoporous nanoparticles provide rich platforms to devise functional materials by customizing the three-dimensional (3D) structures of nanopores. With the pore network as a key tuning parameter, the noninvasive and quantitative characterization of these 3D structures is crucial for the rational design of functional materials. This has prompted researchers to develop versatile nanoprobes with a high penetration power to inspect various specimens sized a few micrometers at nanoscale 3D resolutions. Here, with adaptive phase retrievals on independent data sets with different sampling frequencies, we introduce multidistance coherent X-ray tomography as a noninvasive and quantitative nanoprobe to realize high-resolution 3D imaging of micrometer-sized specimens. The 3D density distribution of an entire mesoporous silica nanoparticle was obtained at 13 nm 3D resolution for quantitative physical and morphological analyses of its 3D pore structure. The morphological features of the whole 3D pore network and pore connectivity were examined to gain insight into the potential functions of the particles. The proposed multidistance tomographic imaging scheme with quantitative structural analyses is expected to advance studies of functional materials by facilitating their structure-based rational design.

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at  https://zenodo.org/record/7273314 .

Three-dimensional femtosecond snapshots of isolated faceted nanostructures

The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of x-ray free-electron lasers. Wide-angle scattering images encode three-dimensional (3D) morphological information of the samples, but its retrieval remains a challenge. Up to now, effective 3D morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometries. Here, we present a much more generic imaging approach. Relying on a model that allows for any sample morphology described by a convex polyhedron, we reconstruct wide-angle diffraction patterns from individual silver nanoparticles. In addition to known structural motives with high symmetries, we retrieve imperfect shapes and agglomerates that were not previously accessible. Our results open unexplored routes toward true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.

Artificial intelligence to bring nanomedicine to life

The technology of drug delivery systems (DDSs) has demonstrated an outstanding performance and effectiveness in production of pharmaceuticals, as it is proved by many FDA-approved nanomedicines that have an enhanced selectivity, manageable drug release kinetics and synergistic therapeutic actions. Nonetheless, to date, the rational design and high-throughput development of nanomaterial-based DDSs for specific purposes is far from a routine practice and is still in its infancy, mainly due to the limitations in scientists' capabilities to effectively acquire, analyze, manage, and comprehend complex and ever-growing sets of experimental data, which is vital to develop DDSs with a set of desired functionalities. At the same time, this task is feasible for the data-driven approaches, high throughput experimentation techniques, process automatization, artificial intelligence (AI) technology, and machine learning (ML) approaches, which is referred to as The Fourth Paradigm of scientific research. Therefore, an integration of these approaches with nanomedicine and nanotechnology can potentially accelerate the rational design and high-throughput development of highly efficient nanoformulated drugs and smart materials with pre-defined functionalities. In this Review, we survey the important results and milestones achieved to date in the application of data science, high throughput, as well as automatization approaches, combined with AI and ML to design and optimize DDSs and related nanomaterials. This manuscript mission is not only to reflect the state-of-art in data-driven nanomedicine, but also show how recent findings in the related fields can transform the nanomedicine's image. We discuss how all these results can be used to boost nanomedicine translation to the clinic, as well as highlight the future directions for the development, data-driven, high throughput experimentation-, and AI-assisted design, as well as the production of nanoformulated drugs and smart materials with pre-defined properties and behavior. This Review will be of high interest to the chemists involved in materials science, nanotechnology, and DDSs development for biomedical applications, although the general nature of the presented approaches enables knowledge translation to many other fields of science.

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.

Recent Progress of the PAL-XFEL

The X-ray free-electron laser of the Pohang Accelerator Laboratory (PAL-XFEL) was opened to users in 2017. Since then, significant progress has been made in PAL-XFEL operation and beamline experiments. This includes increasing the FEL pulse energy, increasing the FEL photon energy, generating self-seeding FEL, and trials of two-color operation. In the beamline, new instruments or endstations have been added or are being prepared. Overall, beamline operation has been stabilized since its initiation, which has enabled excellent scientific results through efficient user experiments. In this paper, we describe details of the recent progress of the PAL-XFEL.

Exploring the 3D structure and defects of a self-assembled gold mesocrystal by coherent X-ray diffraction imaging

Mesocrystals are nanostructured materials consisting of individual nanocrystals having a preferred crystallographic orientation. On mesoscopic length scales, the properties of mesocrystals are strongly affected by structural heterogeneity. Here, we report the detailed structural characterization of a faceted mesocrystal grain self-assembled from 60 nm sized gold nanocubes. Using coherent X-ray diffraction imaging, we determined the structure of the mesocrystal with the resolution sufficient to resolve each gold nanoparticle. The reconstructed electron density of the gold mesocrystal reveals its intrinsic structural heterogeneity, including local deviations of lattice parameters, and the presence of internal defects. The strain distribution shows that the average superlattice obtained by angular X-ray cross-correlation analysis and the real, "multidomain" structure of a mesocrystal are very close to each other, with a deviation less than 10%. These results will provide an important impact to understanding the fundamental principles of structuring and self-assembly including ensuing properties of mesocrystals.

Single-Shot Coherent X-ray Imaging Instrument at PAL-XFEL

We developed a single-shot coherent X-ray imaging instrument at the hard X-ray beamline of the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL). This experimental platform was established to conduct a variety of XFEL experiments, including coherent diffraction imaging (CDI), X-ray photon correlation spectroscopy (XPCS), and coherent X-ray scattering (CXS). Based on the forward-scattering geometry, this instrument utilizes a fixed-target method for sample delivery. It is well optimized for single-shot-based experiments in which one expects to observe the ultrafast phenomena of nanoparticles at picosecond temporal and nanometer spatial resolutions. In this paper, we introduce a single-shot coherent X-ray imaging instrument and report pump–probe coherent diffraction imaging (PPCDI) of Ag nanoparticles as an example of its applications.