Unraveling the Correlation between the Interface Structures and Tunable Magnetic Properties of La1-xSrxCoO3-δ/La1-xSrxMnO3-δ Bilayers Using Deep Learning Models.

Perovskite oxides are gaining significant attention for use in next-generation magnetic and ferroelectric devices due to their exceptional charge transport properties and the opportunity to tune the charge, spin, lattice, and orbital degrees of freedom. Interfaces between perovskite oxides, exemplified by La1-xSrxCoO3-δ/La1-xSrxMnO3-δ (LSCO/LSMO) bilayers, exhibit unconventional magnetic exchange switching behavior, offering a pathway for innovative designs in perovskite oxide-based devices. However, the precise atomic-level stoichiometric compositions and chemophysical properties of these interfaces remain elusive, hindering the establishment of surrogate design principles. We leverage first-principles simulations, evolutionary algorithms, and neural network searches with on-the-fly uncertainty quantification to design deep learning model ensembles to investigate over 50,000 LSCO/LSMO bilayer structures as a function of oxygen deficiency (δ) and strontium concentration (x). Structural analysis of the low-energy interface structures reveals that preferential segregation of oxygen vacancies toward the interfacial La0.7Sr0.3CoO3-δ layers causes distortion of the CoOx polyhedra and the emergence of magnetically active Co2+ ions. At the same time, an increase in the Sr concentration and a decrease in oxygen vacancies in the La0.7Sr0.3MnO3-δ layers tend to retain MnO6 octahedra and promote the formation of Mn4+ ions. Electronic structure analysis reveals that the nonuniform distributions of Sr ions and oxygen vacancies on both sides of the interface can alter the local magnetization at the interface, showing a transition from ferromagnetic (FM) to local antiferromagnetic (AFM) or ferrimagnetic regions. Therefore, the exotic properties of La1-xSrxCoO3-δ/La1-xSrxMnO3-δ are strongly coupled to the presence of hard/soft magnetic layers, as well as the FM to AFM transition at the interface, and can be tuned by changing the Sr concentration and oxygen partial pressure during growth. These insights provide valuable guidance for the precise design of perovskite oxide multilayers, enabling tailoring of their functional properties to meet specific requirements for various device applications.

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.

Observation of a single protein by ultrafast X-ray diffraction.

The idea of using ultrashort X-ray pulses to obtain images of single proteins frozen in time has fascinated and inspired many. It was one of the arguments for building X-ray free-electron lasers. According to theory, the extremely intense pulses provide sufficient signal to dispense with using crystals as an amplifier, and the ultrashort pulse duration permits capturing the diffraction data before the sample inevitably explodes. This was first demonstrated on biological samples a decade ago on the giant mimivirus. Since then, a large collaboration has been pushing the limit of the smallest sample that can be imaged. The ability to capture snapshots on the timescale of atomic vibrations, while keeping the sample at room temperature, may allow probing the entire conformational phase space of macromolecules. Here we show the first observation of an X-ray diffraction pattern from a single protein, that of Escherichia coli GroEL which at 14 nm in diameter is the smallest biological sample ever imaged by X-rays, and demonstrate that the concept of diffraction before destruction extends to single proteins. From the pattern, it is possible to determine the approximate orientation of the protein. Our experiment demonstrates the feasibility of ultrafast imaging of single proteins, opening the way to single-molecule time-resolved studies on the femtosecond timescale.

Graph-EAM: An Interpretable and Efficient Graph Neural Network Potential Framework.

The development of deep learning interatomic potentials has enabled efficient and accurate computations in quantum chemistry and materials science, circumventing computationally expensive ab initio calculations. However, the huge number of learnable parameters in deep learning models and their complex architectures hinder physical interpretability and affect the robustness of the derived potential. In this work, we propose graph-EAM, a lightweight graph neural network (GNN) inspired by the empirical embedded atom method to model the interatomic potential of single-element structures. Four material systems: platinum, niobium, silicon, and amorphous-carbon, for which quantum simulation data sets are publicly available, are examined to demonstrate that graph-EAM can achieve high energy and force prediction accuracy─comparable or better than existing state-of-the-art machine learning models─with much fewer parameters. It is also shown that the explicit inclusion of the angular information via three-body atomic density increases the prediction accuracy. The accuracy and efficiency of potentials obtained from graph-EAM can help accelerate the molecular dynamics simulation.

Time-Resolved Single-Particle X-ray Scattering Reveals Electron-Density Gradients As Coherent Plasmonic-Nanoparticle-Oscillation Source.

Dynamics of optically excited plasmonic nanoparticles are presently understood as a series of scattering events involving the initiation of nanoparticle breathing oscillations. According to established models, these are caused by statistical heat transfer from thermalized electrons to the lattice. An additional contribution by hot-electron pressure accounts for phase mismatches between theory and experimental observations. However, direct experimental studies resolving the breathing-oscillation excitation are still missing. We used optical transient-absorption spectroscopy and time-resolved single-particle X-ray diffractive imaging to access the electron system and lattice. The time-resolved single-particle imaging data provided structural information directly on the onset of the breathing oscillation and confirmed the need for an additional excitation mechanism for thermal expansion. We developed a new model that reproduces all of our experimental observations. We identified optically induced electron density gradients as the initial driving source.

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.

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange.

Electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact-exchange or hybrid functionals are associated with a large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Although orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with a significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use a gradient expansion of the kinetic energy nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional (1D) systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C4H2, C4N2, and C3O2. We show that by using the data from model 1D KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems and electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it is possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

Accurate parameterization of the kinetic energy functional.

The absence of a reliable formulation of the kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions, which have been proposed in the literature, and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals-a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H2, LiH, LiF, and a one-dimensional chain of eight hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures.

Optimizing the geometry of aerodynamic lens injectors for single-particle coherent diffractive imaging of gold nanoparticles.

Single-particle X-ray diffractive imaging (SPI) of small (bio-)nanoparticles (NPs) requires optimized injectors to collect sufficient diffraction patterns to allow for the reconstruction of the NP structure with high resolution. Typically, aerodynamic lens-stack injectors are used for NP injection. However, current injectors were developed for larger NPs (>100 nm), and their ability to generate high-density NP beams suffers with decreasing NP size. Here, an aerodynamic lens-stack injector with variable geometry and a geometry-optimization procedure are presented. The optimization for 50 nm gold-NP (AuNP) injection using a numerical-simulation infrastructure capable of calculating the carrier-gas flow and the particle trajectories through the injector is also introduced. The simulations were experimentally validated using spherical AuNPs and sucrose NPs. In addition, the optimized injector was compared with the standard-installation 'Uppsala injector' for AuNPs. Results for these heavy particles showed a shift in the particle-beam focus position rather than a change in beam size, which results in a lower gas background for the optimized injector. Optimized aerodynamic lens-stack injectors will allow one to increase NP beam density, reduce the gas background, discover the limits of current injectors and contribute to structure determination of small NPs using SPI.

Quantized Grain Boundary States Promote Nanoparticle Alignment During Imperfect Oriented Attachment.

Oriented attachment (OA) has become a well-recognized mechanism for the growth of metal, ceramic, and biomineral crystals. While many computational and experimental studies of OA have shown that particles can attach with some misorientation then rotate to remove adjoining grain boundaries, the underlying atomistic pathways for this "imperfect OA" process remain the subject of debate. In this study, molecular dynamics and in situ transmission electron microscopy (TEM) are used to probe the crystallographic evolution of up to 30 gold nanoparticles during aggregation. It is found that Imperfect OA occurs because 1) grain boundaries become quantized when their size is comparable to the separation between constituent dislocations and 2) kinetic barriers associated with the glide of grain boundary dislocations are small. In support of these findings, TEM experiments show the formation of a single crystal aggregate after annealing nine initially misoriented, agglomerated particles with evidence of dislocation activity and twin formation during particle/grain alignment. These observations motivate future work on assembled nanocrystals with tailored defects and call for a revision of Read-Shockley models for grain boundary energies in nanocrystalline materials.

Controlled beams of shock-frozen, isolated, biological and artificial nanoparticles.

X-ray free-electron lasers promise diffractive imaging of single molecules and nanoparticles with atomic spatial resolution. This relies on the averaging of millions of diffraction patterns of identical particles, which should ideally be isolated in the gas phase and preserved in their native structure. Here, we demonstrated that polystyrene nanospheres and Cydia pomonella granulovirus can be transferred into the gas phase, isolated, and very quickly shock-frozen, i.e., cooled to 4 K within microseconds in a helium-buffer-gas cell, much faster than state-of-the-art approaches. Nanoparticle beams emerging from the cell were characterized using particle-localization microscopy with light-sheet illumination, which allowed for the full reconstruction of the particle beams, focused to < 100 µ m , as well as for the determination of particle flux and number density. The experimental results were quantitatively reproduced and rationalized through particle-trajectory simulations. We propose an optimized setup with cooling rates for particles of few-nanometers on nanosecond timescales. The produced beams of shock-frozen isolated nanoparticles provide a breakthrough in sample delivery, e.g., for diffractive imaging and microscopy or low-temperature nanoscience.

Light-sheet imaging for the recording of transverse absolute density distributions of gas-phase particle-beams from nanoparticle injectors.

Imaging biological molecules in the gas-phase requires novel sample delivery methods, which generally have to be characterized and optimized to produce high-density particle beams. A non-destructive characterization method of the transverse particle beam profile is presented. It enables the characterization of the particle beam in parallel to the collection of, for instance, x-ray-diffraction patterns. As a rather simple experimental method, it requires the generation of a small laser-light sheet using a cylindrical telescope and a microscope. The working principle of this technique was demonstrated for the characterization of the fluid-dynamic-focusing behavior of 220 nm polystyrene beads as prototypical nanoparticles. The particle flux was determined and the velocity distribution was calibrated using Mie-scattering calculations.

The thermodynamics of a liquid-solid interface at extreme conditions: A model close-packed system up to 100 GPa.

The first experimental insight into the nature of the liquid-solid interface occurred with the pioneering experiments of Turnbull, which simultaneously demonstrated both that metals could be deeply undercooled (and therefore had relatively large barriers to nucleation) and that the inferred interfacial free energy γ was linearly proportional to the enthalpy of fusion [D. Turnbull, J. Appl. Phys. 21, 1022 (1950)]. By an atomistic simulation of a model face-centered cubic system via adiabatic free energy dynamics, we extend Turnbull's result to the realm of high pressure and demonstrate that the interfacial free energy, evaluated along the melting curve, remains linear with the bulk enthalpy of fusion, even up to 100 GPa. This linear dependence of γ on pressure is shown to be a consequence of the entropy dominating the free energy of the interface in conjunction with the fact that the entropy of fusion does not vary greatly along the melting curve for simple monoatomic metals. Based on this observation, it appears that large undercoolings in liquid metals can be achieved even at very high pressure. Therefore, nucleation rates at high pressure are expected to be non-negligible, resulting in observable solidification kinetics.

Rapid sample delivery for megahertz serial crystallography at X-ray FELs.

Liquid microjets are a common means of delivering protein crystals to the focus of X-ray free-electron lasers (FELs) for serial femtosecond crystallography measurements. The high X-ray intensity in the focus initiates an explosion of the microjet and sample. With the advent of X-ray FELs with megahertz rates, the typical velocities of these jets must be increased significantly in order to replenish the damaged material in time for the subsequent measurement with the next X-ray pulse. This work reports the results of a megahertz serial diffraction experiment at the FLASH FEL facility using 4.3 nm radiation. The operation of gas-dynamic nozzles that produce liquid microjets with velocities greater than 80 m s-1 was demonstrated. Furthermore, this article provides optical images of X-ray-induced explosions together with Bragg diffraction from protein microcrystals exposed to trains of X-ray pulses repeating at rates of up to 4.5 MHz. The results indicate the feasibility for megahertz serial crystallography measurements with hard X-rays and give guidance for the design of such experiments.

Predicting phase behavior of grain boundaries with evolutionary search and machine learning.

The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in the exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that can predict interface structure. Here we develop a computational tool based on evolutionary algorithms that performs efficient grand-canonical grain boundary structure search and we design a clustering analysis that automatically identifies different grain boundary phases. Its application to a model system of symmetric tilt boundaries in Cu uncovers an unexpected rich polymorphism in the grain boundary structures. We find new ground and metastable states by exploring structures with different atomic densities. Our results demonstrate that the grain boundaries within the entire misorientation range have multiple phases and exhibit structural transitions, suggesting that phase behavior of interfaces is likely a general phenomenon.

Representing local atomic environment using descriptors based on local correlations.

Statistical learning of material properties is an emerging topic of research and has been tremendously successful in areas such as representing complex energy landscapes as well as in technologically relevant areas, like identification of better catalysts and electronic materials. However, analysis of large data sets to efficiently learn characteristic features of a complex energy landscape, for example, depends on the ability of descriptors to effectively screen different local atomic environments. Thus, discovering appropriate descriptors of bulk or defect properties and the functional dependence of such properties on these descriptors remains a difficult and tedious process. To this end, we develop a framework to generate descriptors based on many-body correlations that can effectively capture intrinsic geometric features of the local environment of an atom. These descriptors are based on the spectrum of two-body, three-body, four-body, and higher order correlations between an atom and its neighbors and are evaluated by calculating the corresponding two-body, three-body, and four-body overlap integrals. They are invariant to global translation, global rotation, reflection, and permutations of atomic indices. By systematically testing the ability to capture the local atomic environment, it is shown that the local correlation descriptors are able to successfully reconstruct structures containing 10-25 atoms which was previously not possible.

Descriptor-Based Approach for the Prediction of Cation Vacancy Formation Energies and Transition Levels.

Point defects largely determine the observed optical and electrical properties of a given material, yet the characterization and identification of defects has remained a slow and tedious process, both experimentally and theoretically. We demonstrate a computationally-cheap model that can reliably predict the formation energies of cation vacancies as well as the location of their electronic states in a large set of II-VI and III-V materials using only parameters obtained from the bulk primitive unit cell (2-4 atoms). We apply our model to ordered alloys within the CdZnSeTe, CdZnS, and ZnMgO systems and predict the positions of cation vacancy charge-state transition levels with a mean absolute error of < 0.2 eV compared to the explicitly calculated values, showing useful accuracy without the need for the expensive and large-scale calculations typically required. This suggests the properties of other point defects may also be predicted with useful accuracy from only bulk-derived properties.

Antagonistic Interplay Between an Intermolecular CH···O and an Intramolecular OH···O Hydrogen Bond in a 1:1 Complex Between 1,2-Cyclohexanedione and Chloroform: A Combined Matrix Isolation Infrared and Quantum Chemistry Study.

Matrix isolation infrared spectra of a weak C-H···O hydrogen-bonded complex between the keto-enol form of 1,2-cyclohexanedione (HCHD) and chloroform have been measured. The spectra reveal that the intramolecular O-H···O H-bond of HCHD is weakened as a result of complex formation, manifesting in prominent blue shift (∼23 cm-1) of the νO-H band and red shifts (∼7 cm-1) of νC═O bands of the acceptor (HCHD). The νC-H band of donor CHCl3 undergoes a large red shift of ∼33 cm-1. Very similar spectral effects are also observed for formation of the complex in CCl4 solution at room temperature. Our analysis reveals that out of several possible iso-energetic conformational forms of the complex, the one involving antagonistic interplay between the two hydrogen bonds (intermolecular C-H···O and intramolecular O-H···O) is preferred. The combined experimental and calculated data presented here suggest that in condensed media, conformational preferences are guided by directional hyperconjugative charge transfer interactions at the C-H···O hydrogen bonding site of the complex.

Vibrational Predissociation of the HCl-(H2O)3 Tetramer.

The vibrational predissociation of the HCl-(H2O)3 tetramer, the largest HCl-(H2O)n cluster for which HCl is not predicted to be ionized, is reported. This work focuses on the predissociation pathway giving rise to H2O + HCl-(H2O)2 following IR laser excitation of the H-bonded OH stretch fundamental. H2O fragments are monitored state selectively by 2 + 1 resonance-enhanced multiphoton ionization (REMPI) combined with time-of-flight mass spectrometry (TOF-MS). Velocity map images of H2O in selected rotational levels are used to determine translational energy distributions from which the internal energy distributions in the pair-correlated cofragments are derived. From the maximum translational energy release, the bond dissociation energy, D0 = 2400 ± 100 cm-1, is determined for the investigated channel. The energy distributions in the fragments are broad, encompassing the entire range of allowed states. The importance of cooperative (nonpairwise) interactions is discussed.

Exploring the free energy surface using ab initio molecular dynamics.

Efficient exploration of configuration space and identification of metastable structures in condensed phase systems are challenging from both computational and algorithmic perspectives. In this regard, schemes that utilize a set of pre-defined order parameters to sample the relevant parts of the configuration space [L. Maragliano and E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006); J. B. Abrams and M. E. Tuckerman, J. Phys. Chem. B 112, 15742 (2008)] have proved useful. Here, we demonstrate how these order-parameter aided temperature accelerated sampling schemes can be used within the Born-Oppenheimer and the Car-Parrinello frameworks of ab initio molecular dynamics to efficiently and systematically explore free energy surfaces, and search for metastable states and reaction pathways. We have used these methods to identify the metastable structures and reaction pathways in SiO2 and Ti. In addition, we have used the string method [W. E, W. Ren, and E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002); L. Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] within the density functional theory to study the melting pathways in the high pressure cotunnite phase of SiO2 and the hexagonal closed packed to face centered cubic phase transition in Ti.