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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Seeing structural evolution of organic molecular nano-crystallites using 4D scanning confocal electron diffraction (4D-SCED)

Abstract Direct observation of organic molecular nanocrystals and their evolution using electron microscopy is extremely challenging, due to their radiation sensitivity and complex structure. Here, we introduce 4D-scanning confocal electron diffraction (4D-SCED), which enables direct in situ observation of bulk heterojunction (BHJ) thin films. 4D-SCED combines confocal electron optic setup with a pixelated detector to record focused spot-like diffraction patterns with high angular resolution, using an order of magnitude lower dose than previous methods. We apply it to study an active layer in organic solar cells, namely DRCN5T:PC 71 BM BHJ thin films. Structural details of DRCN5T nano-crystallites oriented both in- and out-of-plane are imaged at ~5 nm resolution and dose budget of ~5 e − /Å 2 . We use in situ annealing to observe the growth of the donor crystals, evolution of the crystal orientation, and progressive enrichment of PC 71 BM at interfaces. This highly dose-efficient method opens more possibilities for studying beam sensitive soft materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Scanning electrochemical probe microscopy investigation of two-dimensional materials

Research interests in two-dimensional (2D) materials have seen exponential growth owing to their unique and fascinating properties. The highly exposed lattice planes coupled with tunable electronic states of 2D materials have created manifold opportunities in the design of new platforms for energy conversion and sensing applications. Still, challenges in understanding the electrochemical (EC) characteristics of these materials arise from the complexity of both intrinsic and extrinsic heterogeneities that can obscure structure–activity correlations. Scanning EC probe microscopic investigations offer unique benefits in disclosing local EC reactivities at the nanoscale level that are otherwise inaccessible with macroscale methods. This review summarizes recent progress in applying techniques of scanning EC microscopy (SECM) and scanning EC cell microscopy (SECCM) to obtain distinctive insights into the fundamentals of 2D electrodes. We showcase the capabilities of EC microscopies in addressing the roles of defects, thickness, environments, strain, phase, stacking, and many other aspects in the heterogeneous electron transfer, ion transport, electrocatalysis, and photoelectrochemistry of representative 2D materials and their derivatives. Perspectives for the advantages, challenges, and future opportunities of scanning EC probe microscopy investigation of 2D structures are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Synthesis, crystal and electronic structure of the Zintl phase Ba 16 Sb 11 . A case study uncovering greater structural complexity via monoclinic distortion of the tetragonal Ca 16 Sb 11 structure type

The binary Zintl phase Ba 16 Sb 11 has been synthesized and structurally characterized. Detailed studies via single-crystal X-ray diffraction methods indicate that although Ba 16 Sb 11 appears to crystallize in the tetragonal Ca 16 Sb 11 structure type (space group $P\bar{4}2_1$m with a=13.5647(9) Å, c=12.4124(12)Å, Z=2, R 1 = 3.14%; wR 2 = 4.77%), there exists an extensive structural disorder. Some Ba 16 Sb 11 crystals were found to be monoclinic and the structure was solved and refined in space group P2 1 (a=18.3929(12) Å, b=13.5233(8) Å, c=18.3978(12) Å, β=94.6600(10)°; Z=4, R 1 =5.84 %; wR 2 =9.58 %). The latter corresponds to a 2-fold superstructure of the tetragonal one, which provides a disorder-free structural model. In both descriptions, the disordered tetragonal and the ordered monoclinic superstructure, the basic building units that make up the structure of this Ba-rich compound are pairs of face-shared square antiprisms of Ba atoms, which are centered by Sb atoms. The dimerized antiprisms are linked into parallel chains via square prisms of Ba atoms, which are also centered by Sb atoms. The Zintl concept can be applied in a straightforward manner and as result, the structure of Ba 32 Sb 22 (=2×Ba 16 Sb 11 ) can be rationalized as (Ba 2+ ) 32 (Sb 3– ) 20 [Sb 2 ] 4– . Notably, the partitioning of the valence electrons is done taking into an account the homoatomic Sb–Sb contacts (d=3.01 Å), which can be clearly distinguished in the lower symmetry space group. Electronic structure calculations of Ba 16 Sb 11 are in good accordance with the Zintl rationalization and predict a semiconductor with a band gap of 0.77 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum computation of silicon electronic band structure

Development of quantum architectures during the last decade has inspired hybrid classical–quantum algorithms in physics and quantum chemistry that promise simulations of fermionic systems beyond the capability of modern classical computers, even before the era of quantum computing fully arrives. Strong research efforts have been recently made to obtain minimal depth quantum circuits which could accurately represent chemical systems. Here, we show that unprecedented methods used in quantum chemistry, designed to simulate molecules on quantum processors, can be extended to calculate properties of periodic solids. In particular, we present minimal depth circuits implementing the variational quantum eigensolver algorithm and successfully use it to compute the band structure of silicon on a quantum machine for the first time. We are convinced that the presented quantum experiments performed on cloud-based platforms will stimulate more intense studies towards scalable electronic structure computation of advanced quantum materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Validation of the single-event method for low-energy electron transport via stopping power calculations with $\mathrm{MCNP}$

Monte Carlo simulations of low-energy ( <50 keV) electron transport in matter are essential for a broad range of application fields. Several Monte Carlo codes have developed specialized treatments for this case, but a comprehensive validation of low-energy electron transport for general-purpose simulations remains lacking in the literature. One approach to accomplish this validation is calculation of stopping power using low-energy electron transport physics, as stopping power is a fundamental radiation transport quantity which must be simulated accurately for nearly any application. Here in this work, we use the Monte Carlo N-Particle (MCNP) radiation transport code with the single-event method for electron transport to calculate stopping powers of low-energy electrons (50 eV to 30 keV) in 41 elemental solids, 14 compound solids, and five rare gas solids, comparing simulation results to published semi-empirical stopping power calculations from optical measurements. In general, the simulations give good agreement (typically within ±10%) with semi-empirical stopping power values at higher energies: 300 eV and above for most elemental solids, 1 keV and above for compound solids, and 400 eV and above for rare gas solids. Agreement between MCNP and semi-empirical values is worse below these energies. The most significant source of error is the EPRDATA14 cross section data, which does not account for changes in electronic structure due to solid-state bonding, particularly in compound materials. The simplistic model of atomic excitation used to generate the EPRDATA14 cross sections is another key source of error. Additionally, the breakdown of the continuous slowing-down approximation introduces significant uncertainty at low energies, although this is a limitation of the calculation method and not of the simulation procedure. Accounting for these and other uncertainty sources, the single event method in MCNP is robust and able to give good accuracy for a variety of low-energy electron transport problems through diverse kinds of materials.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

Cryogenic Correlative Single‐Particle Photoluminescence Spectroscopy and Electron Tomography for Investigation of Nanomaterials

Abstract Cryogenic single‐particle photoluminescence (PL) spectroscopy has been used with great success to directly observe the heterogeneous photophysical states present in a population of luminescent particles. Cryogenic electron tomography provides complementary nanometer scale structural information to PL spectroscopy, but the two techniques have not been correlated due to technical challenges. Here, we present a method for correlating single‐particle information from these two powerful microscopy modalities. We simultaneously observe PL brightness, emission spectrum, and in‐plane excitation dipole orientation of CdSSe/ZnS quantum dots suspended in vitreous ice. Stable and fluctuating emitters were observed, as well as a surprising splitting of the PL spectrum into two bands with an average energy separation of 80 meV. In some cases, the onset of the splitting corresponded to changes in the in‐plane excitation dipole orientation. These dynamics were assigned to structures of individual quantum dots and the excitation dipoles were visualized in the context of structural features.

Dahlberg, Peter D.↗
DOE OSTI2022

Expanding the Scope of Pnictogen‐Assisted Cyclophane Self‐Assembly

Cyclophanes are a fundamentally interesting class of compounds that host a wide range of unique and emergent properties. Furthermore, synthesis of complex and/or functionalized cyclophanes can often suffer from harsh reaction conditions, long reaction times, and sometimes low yields using stepwise methods. We have previously reported an efficient, high-yielding, metalloid-directed self-assembly method to prepare disulfide, thioether, and hydrocarbon cyclophanes and cages that feature mercaptomethyl-arenes as starting materials. Herein, we report the synthesis of 21 new disulfide and thioether assemblies that expand this high yielding self-assembly method to a wide breadth of macrocycles and cages with diverse structures. Remarkably, the high-yielding, efficient syntheses still proceed under dynamic covalent control using electron-deficient, heteroaryl, cycloalkyl, spiro, and even short alkenyl/alkynyl substrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Emerging Electrochemical Techniques for Probing Site Behavior in Single-Atom Electrocatalysts

Single-atom catalysts (SACs) have aroused tremendous interest over the past decade, particularly in the community of energy and environment-related electrocatalysis. A rapidly growing number of recent publications have recognized it as a promising candidate with maximum atomic utilization, distinct activity, and selectivity in comparison to bulk catalysts and nanocatalysts. However, the complexity of localized coordination environments and the dispersion of isolated sites lead to significant difficulties when it comes to gaining insight into the intrinsic behavior of electrocatalytic reactions. Furthermore, the low metal loadings of most SACs make conventional ensemble measurements less likely to be accurate on the subnanoscale. Thus, it remains challenging to probe the activity and properties of individual atomic sites by available commercial instruments and analytical methods. In spite of this, continuing efforts have lately focused on the development of advanced measurement methodologies, which are very useful to the fundamental understanding of SACs. There have recently been a number of in situ/operando techniques applied to SACs, such as electron microscopy, spectroscopy, and other analysis methods, which support relevant functions to identify the active sites and reaction intermediates and to investigate the dynamic behavior of localized structures of the catalytic sites. This Account aims to present recent electrochemical probing techniques which can be used to identify single-atomic catalytic sites within solid supports. First, we describe the basic principles of molecular probe methods for the study and analysis of electrocatalytic site behavior. In particular, the in situ probing technique enabled by surface interrogation scanning electrochemical microscopy (SISECM) can measure the active site density and kinetic rate with high resolution. An alternative electrochemical probing technique is further demonstrated on the basis of single-entity electrochemistry, which allows the unique electrochemical imaging of the size and catalytic rate of single atoms, molecules, and clusters. Next, the merits and limitations of different electrochemical techniques are then discussed, along with perspectives for future prospects. Apart from this, we further showcase the powerful capability of emerging electrochemical probing techniques for determining significant effects and properties of SACs for various electrocatalytic reactions, including oxygen reduction and evolution, hydrogen evolution, and nitrate reduction. Overall, electrochemical techniques with atomic resolution have greatly increased opportunities for observing, measuring, and understanding the surface and interface chemistry during energy conversion. In the future, it is anticipated that the development of electrochemical probing techniques will be advanced with innovative perspectives on the behavior and features of SACs. We hope that this Account can contribute in several ways to promoting the fundamental knowledge and technical progress of emerging electrochemical measurements for studying SACs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

High-Resolution Comonomer Sequencing of Blocky Brominated Syndiotactic Polystyrene Copolymers Using 13C NMR Spectroscopy and Computer Simulations

This work demonstrates the first high-resolution comonomer sequencing of Blocky brominated syndiotactic polystyrene (sPS-co-sPS-Br) copolymers based on pentad assign- ments of the quaternary carbon region of the nuclear magnetic resonance spectrum. Copolymers containing p-bromostyrene (Br-Sty) units were prepared in matched sets using postpolymerization bromination methods carried out in the heterogeneous gel state (Blocky) and homogeneous solution state (Random). Quantitative information from the quaternary carbon spectra, heteronuclear multiple bond correlation spectroscopy, electronic structure calculations, and simulated statistically random copolymers was correlated to confirm the carbon resonance assignments for all 20 possible pentad comonomer sequences. Using the experimental pentad sequence prevalences, a computer code was developed to simulate chains with microstructures typical of each sample as a means to visually represent the copolymer blockiness with quantitative precision. Based on the microstructure and distribution of run lengths in these chains, the simulations revealed that the Blocky copolymers contain a high degree of blockiness. By comparing the run lengths in the simulated chains to the average number of styrene units in a crystalline segment of sPS (found by small-angle X-ray scattering), copolymer crystallizability was predicted. For the simulated Blocky B-21% (21 mol % Br-Sty) chain, the probability of randomly selecting a styrene unit in a crystallizable block was 25.8%, while that in the simulated Random R-18% was zero, in excellent agreement with the experimental crystallization behavior measured by differential scanning calorimetry. Additionally, these predictions confirmed that the simulated chains accurately represent the ensemble of chains in their respective copolymer samples. Furthermore, each simulated Blocky chain contained one or more long sPS blocks that paralleled the measured 38-40 styrene units spanning a crystalline segment within the sPS/CCl4 gel. This finding affirmed that the long sPS segments originated from the precise lamellar structure within the heterogeneous gel morphology (i.e., block length is correlated with lamellar thickness). Overall, the ability to tailor the copolymer microstructure through control of the semicrystalline gel morphology opens the door to synthesizing ordered copolymers by postpolymerization functionalization processes with unprecedented levels of compositional control.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Tailoring MoS 2 for Small-Molecule Electroreduction: The Role of Metal Doping and Heterostructures

The electrification of chemical transformations central to sustainable fuel production and waste valorization, such as overall water splitting (OWS), hydrogen evolution reaction (HER), and electrochemical reduction of CO 2 (CO 2 R), presents a powerful opportunity to advance carbon-neutral energy technologies. Transition metal dichalcogenides (TMDs), particularly MoS 2 , have emerged as promising electrocatalyst candidates, owing to their abundance, tunable active sites, and defect-rich structures. This review highlights recent progress in leveraging metal doping and heterostructure engineering of MoS 2 to enhance the electrocatalytic activity and selectivity. By compiling insights from experimental studies and density functional theory (DFT) predictions, we examine how defect creation, electronic structure modification, and interface design contribute to improved charge transport and catalytic efficiency. Particular emphasis is placed on rational design principles, synthetic strategies, and operando characterization methods that provide a pathway to understanding and optimizing MoS 2 -based materials. We also discuss the challenges of stability, mechanistic ambiguity, and scaling while outlining opportunities to bridge theory and experiment. Collectively, this review underscores how defect and heterostructure engineering of MoS 2 can accelerate the development of efficient, sustainable electrocatalysts for both fuel generation and waste-to-value generation.

CO2 reduction↗
DOE OSTI2025

Controlled Synthesis of SnO 2 Nanocrystals with Tunable Band Gaps

Tin(IV) oxide nanocrystals (SnO 2 NCs) have significant potential in various applications, with their performance closely related to their band gap. The band gap is influenced by the size and shape of the NCs, which can be precisely controlled by adjusting reaction conditions. In this study, we present deliberately designed synthesis protocols to produce high-quality SnO 2 NCs with tunable band gaps using different methods. Key factors affecting the synthesis include control of the oxidizing agent, reaction temperature, solvent selection, and reaction time optimization. The resulting NCs were characterized by using TEM, XRD, XPS, and optical spectroscopy. Notably, SnO 2 NCs synthesized by controlling the oxidizing agent (air injection) in a hot organic solution were smaller in size and exhibited abundant oxygen vacancies. In contrast, extending the reaction time or using ethanol as a solvent in hydrothermal systems facilitated larger spherical or rod-like SnO 2 NCs with fewer oxygen vacancies. Further analysis of the band gap and valence band maximum energy revealed that the abundant vacancies in SnO 2 NCs synthesized with the air-controlled hot organic solution method resulted in a narrower band gap and an upshifted valence band. These synthetic strategies illustrate the potential for deliberately designing SnO 2 NCs with optimized electronic structures for various applications.

band gap↗
DOE OSTI2022

Machine learning molecular dynamics simulations toward exploration of high-temperature properties of nuclear fuel materials: case study of thorium dioxide

Predicting materials properties of nuclear fuel compounds is a challenging task in materials science. Their thermodynamical behaviors around and above the operational temperature are essential for the design of nuclear reactors. However, they are not easy to measure, because the target temperature range is too high to perform various standard experiments safely and accurately. Moreover, theoretical methods such as first-principles calculations also suffer from the computational limitations in calculating thermodynamical properties due to their high calculation-costs and complicated electronic structures stemming from f-orbital occupations of valence electrons in actinide elements. Here, we demonstrate, for the first time, machine-learning molecular-dynamics to theoretically explore high-temperature thermodynamical properties of a nuclear fuel material, thorium dioxide. The target compound satisfies first-principles calculation accuracy because f-electron occupation coincidentally diminishes and the scheme meets sampling sufficiency because it works at the computational cost of classical molecular-dynamics levels. We prepare a set of training data using first-principles molecular dynamics with small number of atoms, which cannot directly evaluate thermodynamical properties but captures essential atomistic dynamics at the high temperature range. Then, we construct a machine-learning molecular-dynamics potential and carry out large-scale molecular-dynamics calculations. Consequently, we successfully access two kinds of thermodynamic phase transitions, namely the melting and the anomalous λ transition induced by large diffusions of oxygen atoms. Furthermore, we quantitatively reproduce various experimental data in the best agreement manner by selecting a density functional scheme known as SCAN. Our results suggest that the present scale-up simulation-scheme using machine-learning techniques opens up a new pathway on theoretical studies of not only nuclear fuel compounds, but also a variety of similar materials that contain both heavy and light elements, like thorium dioxide.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Electrode-molecule energy level offsets in a gold-benzene diamine-gold single molecule tunnel junction

One means for describing electron transport across single molecule tunnel junctions (MTJs) is to use density functional theory (DFT) in conjunction with a nonequilibrium Green’s function formalism. This description relies on interpreting solutions to the Kohn–Sham (KS) equations used to solve the DFT problem as quasiparticle (QP) states. Many practical DFT implementations suffer from electron self-interaction errors and an inability to treat charge image potentials for molecules near metal surfaces. For MTJs, the overall effect of these errors is typically manifested as an overestimation of electronic currents. Correcting KS energies for self-interaction and image potential errors results in MTJ current–voltage characteristics in close agreement with measured currents. An alternative transport approach foregoes a QP picture and solves for a many-electron wavefunction on the MTJ subject to open system boundary conditions. It is demonstrated that this many-electron method provides similar results to the corrected QP picture for electronic current. The analysis of these two distinct approaches is related through corrections to a junction’s electronic structure beyond the KS energies for the case of a benzene diamine molecule bonded between two gold electrodes.

Szepieniec, Mark S.↗
DOE OSTI2021

Monte Carlo transport analysis to assess intensity dependent response of a carbon-doped GaN photoconductor

In this report evaluation of the photoresponse in wurtzite GaN photoconductive switches is presented based on kinetic Monte Carlo simulations. The focus is on electron transport physics and assessment of high frequency operation. The roles of GaN band structure, Pauli exclusion, and treatment of internal fields based on the fast multipole method are all comprehensively included. The implementation was validated through comparisons of velocity-field characteristics for GaN with computational results in the literature. Photocurrent widths of less than ~7 ps for the 1 μm device can be expected, which translates into a 100 GHz upper bound. Photocurrent pulse compression below the laser full width at half maxima at high applied fields are predicted based on the interplay of space-charge effects and the negative differential velocity characteristics of GaN.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Characterizing coherences in chemical dynamics with attosecond time-resolved x-ray absorption spectroscopy

Coherence can drive wave-like motion of electrons and nuclei in photoexcited systems, which can yield fast and efficient ways to exert materials’ functionalities beyond the thermodynamic limit. The search for coherent phenomena has been a central topic in chemical physics although their direct characterization is often elusive. Here, we highlight recent advances in time-resolved x-ray absorption spectroscopy (tr-XAS) to investigate coherent phenomena, especially those that utilize the eminent light source of isolated attosecond pulses. The unparalleled time and state sensitivities of tr-XAS in tandem with the unique element specificity render the method suitable to study valence electronic dynamics in a wide variety of materials. The latest studies have demonstrated the capabilities of tr-XAS to characterize coupled electronic–structural coherence in small molecules and coherent light–matter interactions of core-excited excitons in solids. Furthermore, we address current opportunities and challenges in the exploration of coherent phenomena, with potential applications for energy- and bio-related systems, potential crossings, strongly driven solids, and quantum materials, and so with the ongoing developments in both theory and light sources, tr-XAS holds great promise for revealing the role of coherences in chemical dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Toward direct spatial and intensity characterization of ultra-high-intensity laser pulses using ponderomotive scattering of free electrons

Spatial distributions of electrons ionized and scattered from ultra-low-pressure gases are proposed and experimentally demonstrated as a method to directly measure the intensity of an ultra-high-intensity laser pulse. Analytic models relating the peak scattered electron energy to the peak laser intensity are derived and compared to paraxial Runge–Kutta simulations highlighting two models suitable for describing electrons scattered from weakly paraxial beams (f#>5) for intensities in the range of 1018−1021 W cm−2. Scattering energies are shown to be dependent on gas species, emphasizing the need for specific gases for given intensity ranges. Direct measurements of the laser intensity at full power of two laser systems are demonstrated, both showing a good agreement between indirect methods of intensity measurement and the proposed method. One experiment exhibited the role of spatial aberrations in the scattered electron distribution, motivating a qualitative study on the effect. We propose the use of convolutional neural networks as a method for extracting quantitative information on the spatial structure of the laser at full power. We believe the presented technique to be a powerful tool that can be immediately implemented in many high-power laser facilities worldwide.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Importance of van der Waals interactions for ab initio studies of topological insulators

We investigate the lattice and electronic structures of the bulk and surface of the prototypical layered topological insulators Bi 2 Se 3 and Bi 2 Te 3 using ab initio density functional methods, and systematically compare the results of different methods of including van der Waals (vdW) interactions. We show that the methods utilizing semi-empirical energy corrections yield accurate descriptions of these materials, with the most precise results obtained by properly accounting for the long-range tail of the vdW interactions. The bulk lattice constants, distances between quintuple layers and the Dirac velocity of the topological surface states (TSS) are all in excellent agreement with experiment. In Bi 2 Te 3 , hexagonal warping of the energy dispersion leads to complex spin textures of the TSS at moderate energies, while in Bi 2 Se 3 these states remain almost perfectly helical away from the Dirac point, showing appreciable signs of hexagonal warping at much higher energies, above the minimum of the bulk conduction band. Furthermore, our results establish a framework for unified and systematic self-consistent first principles calculations of topological insulators in bulk, slab and interface geometries, and provides the necessary first step toward ab initio modeling of topological heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

SINGLE: Atomic-resolution structure identification of nanocrystals by graphene liquid cell EM

Analysis of the three-dimensional (3D) structures of nanocrystals with solution-phase transmission electron microscopy is beginning to reveal their unique physiochemical properties. We developed a “one-particle Brownian 3D reconstruction method” based on imaging of ensembles of colloidal nanocrystals using graphene liquid cell electron microscopy. Projection images of differently rotated nanocrystals are acquired using a direct electron detector with high temporal (<2.5 ms) resolution and analyzed to obtain an ensemble of 3D reconstructions. Here, we introduce computational methods required for successful atomic-resolution 3D reconstruction: (i) tracking of the individual particles throughout the time series, (ii) subtraction of the interfering background of the graphene liquid cell, (iii) identification and rejection of low-quality images, and (iv) tailored strategies for 2D/3D alignment and averaging that differ from those used in biological cryo–electron microscopy. Our developments are made available through the open-source software package SINGLE.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗