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At least 469 records · Page 26

Insights into the Nanostructure, Solvation, and Dynamics of Liquid Electrolytes through Small-Angle X-Ray Scattering

The fundamental understanding of nanostructures of liquid electrolytes is expected to enable transformative gains in electrochemical energy storage capacities. However, the solvation structures and molecular dynamics in electrolytes are hard to probe, which limits further performance improvements in macroscopic properties such as ionic conductivity, viscosity, and stability. Small-angle X-ray scattering (SAXS), a non-destructive method for nanostructures characterization in liquids, offers a unique perspective on molecular clusters, anion-cation pairs, solvation sheath, percolating network, aggregates, and domain sizes of electrolytes. Notably, the SAXS method has excellent time-resolution, enabling the study of molecular dynamics by operando characterization. This review focuses on the microscopic understanding of liquid electrolytes by SAXS and operando SAXS. The unique capabilities of X-ray scattering for intra- and inter-molecular relationship and nanostructure characterization of electrolytes are highlighted.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Observation of Ion Electrosorption in Metal–Organic Framework Micropores with In Operando Small-Angle Neutron Scattering

A molecular-level understanding of transport and adsorption mechanisms of electrolyte ions in nanoporous electrodes under applied potentials is essential to control the performance of double-layer capacitors. In this paper, in operando small-angle neutron scattering (SANS) is used to directly detect ion movements into the nanopores of a conductive metal–organic framework (MOF) electrode under operating conditions. Neutron-scattering data reveals that most of the void space within the MOF is accessible to the solvent. Upon the addition of the electrolyte sodium triflate (NaOTf), the ions are adsorbed on the outer surface of the protrusions to form a 30 Å layer instead of entering the ionophobic pores in the absence of an applied charging potential. The changes in scattering intensity when potentials are applied suggests the ion rearrangement in the micropores following different mechanisms depending on the electrode polarization. These observations shed insights on ion electrosorption in electrode materials.

36 MATERIALS SCIENCE↗

Structural Changes during the Growth of Atomically Precise Metal Oxido Nanoclusters from Combined Pair Distribution Function and Small-Angle X-ray Scattering Analysis

The combination of in situ pair distribution function (PDF) analysis and small-angle X-ray scattering (SAXS) enables analysis of the formation mechanism of metal oxido nanoclusters and cluster–solvent interactions as they take place. Herein, we demonstrate the method for the formation of clusters with a [Bi 38 O 45 ] core. Upon dissolution of crystalline [Bi 6 O 5 (OH) 3 (NO 3 ) 5 ]∙3 H 2 O in DMSO, an intermediate rapidly forms, which slowly grows to stable [Bi 38 O 45 ] clusters. To identify the intermediate, we developed an automated modeling method, where smaller [Bi x O y ] structures based on the [Bi 38 O 45 ] framework are tested against the data. [Bi 22 O 26 ] was identified as the main intermediate species, illustrating how combined PDF and SAXS analysis is a powerful tool to gain insight into nucleation on an atomic scale. PDF also provides information on the interaction between nanoclusters and solvent, which is shown to depend on the nature of the ligands on the cluster surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Small Molecule Activation with Intramolecular “Inverse” Frustrated Lewis Pairs

The intramolecular “inverse” frustrated Lewis pairs (FLPs) of general formula 1-BR 2 -2-[(Me 2 N) 2 C=N]-C 6 H 4 (3-6) [BR 2 = BMes 2 (3), BC 12 H 8 , (4), BBN (5), BBNO (6)] were synthesized and structurally characterized by multinuclear NMR spectroscopy and X-ray analysis. Furthermore, these novel types of pre-organized FLPs, featuring strongly basic guanidino units rigidly linked to weakly Lewis acidic boryl moieties via an ortho-phenylene linker, are capable of activating H-H, C-H, N-H, O-H, Si-H, B-H and C=O bonds. 4 and 5 deprotonated terminal alkynes to form the zwitterionic borates 1-(RC≡C-BR 2 )-2-[(Me 2 N) 2 C=NH]-C 6 H 4 (R = Ph, H) and reacted with ammonia, BnNH 2 and pyrrolidine, to generate the adducts 1-(R 2 HN→BR 2 )-2-[(Me 2 N) 2 C=NH]-C 6 H 4 , where the N-H functionality is activated by intramolecular H-bond interactions. In addition, 5 was found to rapidly add across the double bond of H 2 CO, PhCHO and PhNCO to form cyclic zwitterionic guanidinium borates in excellent yields. Likewise, 5 is capable of cleaving H 2 , HBPin and PhSiH 3 to form various amino boranes. Collectively, the results demonstrate that these new types of intramolecular FLPs featuring weakly Lewis acidic boryl and strongly basic guanidino moieties are as potent as conventional intramolecular FLPs with strongly Lewis acidic units in activating small molecules.

08 HYDROGEN↗

Probing the Behavior of Composition‐Tunable Ultrathin PtNi Nanowires for CO Oxidation and Small‐Molecule Electrocatalytic Reactions

We have successfully synthesized ultrathin nanowires of pure Pt, Pt 99 Ni 1 , Pt 9 Ni 1 , and Pt 7 Ni 3 using a modified room-temperature soft-template method. Analysis of both methanol oxidation reaction (MOR) and ethanol oxidation reaction (EOR) results found that the Pt 7 Ni 3 samples yielded the best performance with specific activities of 0.36 and 0.34 mA/cm 2 respectively. Additionally, formic acid oxidation reaction (FAOR) tests noted that both Pt and PtNi nanowires oxidize small organic molecules (SOMs) via an indirect pathway. CO oxidation data suggests little measurable performance without any pre-reduction treatment; however, after annealing in H 2 , we detected significantly improved CO 2 formation for both Pt 9 Ni 1 and Pt 7 Ni 3 motifs. These observations highlight the importance of pre-treating these nanowires under a reducing atmosphere to enhance their performance for CO oxidation. To explain these findings, we collected extended x-ray adsorption fine structure (EXAFS) spectroscopy data, consistent with the presence of partial alloying with a tendency for Pt and Ni to segregate, thereby implying the formation of a Pt-rich shell coupled with a Ni-rich core. Here, we also observed that the degree of alloying within the nanowires increased after annealing in a reducing atmosphere, a finding deduced through analysis of the coordination numbers and calculations of Cowley's short range order parameters.

36 MATERIALS SCIENCE↗

Examining polymer‐protein biophysical interactions with small‐angle x‐ray scattering and quartz crystal microbalance with dissipation

Abstract Polymer‐protein hybrids can be deployed to improve protein solubility and stability in denaturing environments. While previous work used robotics and active machine learning to inform new designs, further biophysical information is required to ascertain structure–function behavior. Here, we show the value of tandem small‐angle x‐ray scattering (SAXS) and quartz crystal microbalance with dissipation (QCMD) experiments to reveal detailed polymer‐protein interactions with horseradish peroxidase (HRP) as a test case. Of particular interest was the process of polymer‐protein complex formation under thermal stress whereby SAXS monitors formation in solution while QCMD follows these dynamics at an interface. The radius of gyration ( R g ) of the protein as measured by SAXS does not change significantly in the presence of polymer under denaturing conditions, but thickness and dissipation changes were observed in QCMD data. SAXS data with and without thermal stress were utilized to create bead models of the potential complexes and denatured enzyme, and each model fit provided insight into the degree of interactions. Additionally, QCMD data demonstrated that HRP deforms by spreading upon surface adsorption at low concentration as shown by longer adsorption times and smaller frequency shifts. In contrast, thermally stressed and highly inactive HRP had faster adsorption kinetics. The combination of SAXS and QCMD serves as a framework for biophysical characterization of interactions between proteins and polymers which could be useful in designing polymer‐protein hybrids.

60 APPLIED LIFE SCIENCES↗

Intact archeological human bones and age at death studied with transmission x–ray diffraction and small angle x–ray scattering

In this work, high-energy, wide-angle x-ray scattering (WAXS, x-ray diffraction) and small-angle x-ray scattering (SAXS) were used to study intact human second metacarpal bones (mc2) from two UK archeological sites. A novel method correcting for irregular mass distribution was applied in these transmission geometry experiments done at beamline 1-ID of the Advanced Photon Source. The authors asked whether there were age-at-death-related changes in carbonated apatite (cAp) lattice parameters and whether SAXS could detect collagen D-period peaks in the archeological mc2. For each of the two sites, Ancaster and Wharram Percy in England, six female mc2s were studied; for each site, two were from each of three age-at-death cohorts (young, 18-29 years; middle, 30-49 years; old >= 50 years) along with a modern control mc2. The Rietveld method was applied to the WAXS patterns to provide precise lattice parameter values. The cAp lattice parameters did not correlate with age-at-death estimated from dental wear. From WAXS and the 00.2 diffraction peak widths, four archeological mc2s possessed coherently scattering domain lengths (crystallite c-axis sizes) that matched that of the modern mc2; SAXS revealed the same four archeological mc2 had D-period peak intensities equivalent to that of the modern mc2. The other eight archeological mc2s had significantly larger crystallite sizes (than the modern mc2) and weak or absent D-period peaks, differences attributed to diagenetic changes. Based on these data, the authors suggest that WAXS 00.2 peak width and SAXS D-period peak intensity can be used with intact bones to select those likely to retain largely unaltered tissue nanostructure, which might be required for other analyses. Taken as a whole, the results suggest detecting age-related deterioration in nanostructural features may be difficult in bone showing significant bioerosion.

59 BASIC BIOLOGICAL SCIENCES↗

Small Signaling Peptides in Sorghum bicolor : Integrating Phylogeny and Gene Expression to Characterize Roles in Stem Development

Small signaling peptides (SSPs) are important regulators of plant growth, development, and responses to biotic and abiotic stress, yet their role in the C4 grass Sorghum bicolor is largely uncharacterized. To help fill this knowledge gap, 219 sorghum genes that encode SSPs were identified based on SSP sequences previously identified in Arabidopsis thaliana, Zea mays, Oryza sativa, Triticum aestivum , and Brachypodium distachyon . The 219 sorghum SSP-encoding genes were assigned to 19 gene families, analyzed for the presence of motifs, and aligned with genes that encode SSPs in other plants using phylogenetic analysis. Sorghum genes in 12 of the 19 SSP gene families had not been previously characterized. Expression of the 219 SSP-encoding genes in sorghum organs, during stem development, and in stem tissues and cell types revealed distinct spatial, temporal, and developmental patterns of expression. Genes associated with the SbCEP and SbRGF families were preferentially expressed in roots, whereas SbEPF genes were expressed in stem epidermal and pith parenchyma cells and panicles. The expression of genes during bioenergy sorghum stem growth and development was investigated because stems account for ~80% of harvested biomass and serve as conduits for water and nutrient transport between leaves and roots. During stem development, 28 SSP genes in several families ( CLE, EPF, CEP, GASS, PSY, ES, PSK, CAPE, POE ) were expressed at higher levels in zones of cell proliferation. For example, the TDIF homologs SbCLE41 and SbCLE42 were expressed at high levels in nascent stem nodes where they may regulate vascular bundle cambial activity and cell differentiation. A different set of 15 genes in the CIF, POE, CAPE, PSY, CEP, RALF , and CLE families were expressed at higher levels in zones of stem tissue differentiation highlighted by elevated expression of five SbRALFR s in the stem nodal plexus. Cell type–specific expression of many sorghum genes that encode SSPs was observed in fully elongated internodes indicating gene expression is regulated with high spatial resolution. Overall, the results provide a foundation of information for analysis of SSP function in sorghum that can be integrated with knowledge of sorghum gene regulatory networks to modulate traits important for production of sorghum crops.

bioenergy sorghum↗

Inline small-angle X-ray scattering-coupled chromatography under extreme hydrostatic pressure

As continuing discoveries highlight the surprising abundance and resilience of deep ocean and subsurface microbial life, the effects of extreme hydrostatic pressure on biological structure and function have attracted renewed interest. Biological small-angle X-ray scattering (BioSAXS) is a widely used method of obtaining structural information from biomolecules in solution under a wide range of solution conditions. Due to its ability to reduce radiation damage, remove aggregates, and separate monodisperse components from complex mixtures, size-exclusion chromatography-coupled SAXS (SEC-SAXS) is now the dominant form of BioSAXS at many synchrotron beamlines. While BioSAXS can currently be performed with some difficulty under pressure with non-flowing samples, it has not been clear how, or even if, continuously flowing SEC-SAXS, with its fragile media-packed columns, might work in an extreme high-pressure environment. Here we show, for the first time, that reproducible chromatographic separations coupled directly to high-pressure BioSAXS can be achieved at pressures up to at least 100 MPa and that pressure-induced changes in folding and oligomeric state and other properties can be observed. Further, the apparatus described here functions at a range of temperatures (0°C–50°C), expanding opportunities for understanding biomolecular rules of life in deep ocean and subsurface environments.

59 BASIC BIOLOGICAL SCIENCES↗

Identification and expression of small multidrug resistance transporters in early‐branching anaerobic fungi

Abstract Membrane‐embedded transporters impart essential functions to cells as they mediate sensing and the uptake and extrusion of nutrients, waste products, and effector molecules. Promiscuous multidrug exporters are implicated in resistance to drugs and antibiotics and are highly relevant for microbial engineers who seek to enhance the tolerance of cell factory strains to hydrophobic bioproducts. Here, we report on the identification of small multidrug resistance (SMR) transporters in early‐branching anaerobic fungi (Neocallimastigomycetes). The SMR class of transporters is commonly found in bacteria but has not previously been reported in eukaryotes. In this study, we show that SMR transporters from anaerobic fungi can be produced heterologously in the model yeast Saccharomyces cerevisiae , demonstrating the potential of these proteins as targets for further characterization. The discovery of these novel anaerobic fungal SMR transporters offers a promising path forward to enhance bioproduction from engineered microbial strains.

59 BASIC BIOLOGICAL SCIENCES↗

Structural characterization of an intrinsically disordered protein complex using integrated small-angle neutron scattering and computing

Characterizing structural ensembles of intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) of proteins is essential for studying structure–function relationships. Due to the different neutron scattering lengths of hydrogen and deuterium, selective labeling and contrast matching in small-angle neutron scattering (SANS) becomes an effective tool to study dynamic structures of disordered systems. However, experimental timescales typically capture measurements averaged over multiple conformations, leaving complex SANS data for disentanglement. We hereby demonstrate an integrated method to elucidate the structural ensemble of a complex formed by two IDRs. We use data from both full contrast and contrast matching with residue-specific deuterium labeling SANS experiments, microsecond all-atom molecular dynamics (MD) simulations with four molecular mechanics force fields, and an autoencoder-based deep learning (DL) algorithm. From our combined approach, we show that selective deuteration provides additional information that helps characterize structural ensembles. We find that among the four force fields, a99SB-disp and CHARMM36m show the strongest agreement with SANS and NMR experiments. In addition, our DL algorithm not only complements conventional structural analysis methods but also successfully differentiates NMR and MD structures which are indistinguishable on the free energy surface. Finally, we present an ensemble that describes experimental SANS and NMR data better than MD ensembles generated by one single force field and reveal three clusters of distinct conformations. Our results demonstrate a new integrated approach for characterizing structural ensembles of IDPs.

59 BASIC BIOLOGICAL SCIENCES↗

Gluon splitting at small x: a unified derivation for the JIMWLK, DGLAP and CSS equations

We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small x. We focus on the back-to-back configuration where the relative transverse momentum P ⊥ of the measured jets is much larger than both their momentum imbalance K ⊥ and the target saturation momentum Q s (x, A). In this regime, we present for the first time a complete calculation of the real NLO corrections, associated with gluon emissions outside the jet cones, at leading power in 1/P ⊥ . Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for K ⊥ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both K ⊥ and the transverse momentum transferred by the target are large compared to Q s , all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO

In [1], we performed the first complete computation of the back-to-back inclusive dijet cross-section in Deeply Inelastic Scattering (DIS) at small x Bj to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for dijets with relative transverse momentum P ⊥ and transverse momentum imbalance q ⊥ , to leading power in q ⊥ /P ⊥ , the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the non-perturbative Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in P ⊥ /q ⊥ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in Q s /q ⊥ for q ⊥ , Q s << P ⊥ , where Q s is the semi-hard saturation scale that grows with rapidity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Association of small vessel disease with tau pathology

Emerging evidence suggests that small vessel disease (SVD) is a risk factor for clinical dementia and may contribute to AD neuropathological changes. Watershed brain regions are located at the most distal areas between arterial territories, making them vulnerable to SVD-related changes. We examined the association of pathologic markers of SVD, specifically arteriolosclerosis in watershed brain regions, with AD pathologic changes. Participants (N= 982; mean age-at-death = 90; 69% women) were enrolled as part of one of two cohort studies of aging and dementia. At autopsy, neuropathological evaluation included semi-quantitative grading of arteriolosclerosis pathology from 2 cortical watershed regions: the anterior watershed (AWS) and posterior watershed (PWS), densities for cortical β-amyloid and tau-tangle pathology, and other common age-related pathologies. Linear regression models examined the association of watershed arteriolosclerosis pathology with β-amyloid and tau-tangle burden. In follow-up analyses, available ex-vivo MRI and proteomics data in a subset of decedents were leveraged to examine the association of whole brain measure of WMH, as a presumed MRI marker of SVD, with β-amyloid and tau-tangle burden, as well as to examine the association of watershed arteriolosclerosis with proteomic tau. Watershed arteriolosclerosis was common, with 45% of older persons having moderate-to-severe arteriolosclerosis pathology in the AWS region, and 35% in the PWS. In fully adjusted models that controlled for demographics and common age-related pathologies, an increase in severity of PWS arteriolosclerosis was associated with a higher burden of tau-tangle burden, specifically neocortical tau burden, but not with β-amyloid. AWS arteriolosclerosis was not associated with β-amyloid or tau pathology. Ex-vivo WMH was associated with greater tau-tangle pathology burden but not β-amyloid. Furthermore, PWS arteriolosclerosis was associated with higher abundance of tau phosphopeptides, that promote formation of tau aggregates. These data provide compelling evidence that SVD, specifically posterior watershed arteriolosclerosis pathology, is linked with tau pathological changes in the aging brain.

60 APPLIED LIFE SCIENCES↗

Stimulating β -Series Precipitation in Mg–Nd Alloys Via Microalloying: A Comparison of Electron Microscopy and Small-Angle Scattering Techniques

The Mg–Nd alloy system is of particular interest in the development of high-strength, lightweight structural alloys due to the formation of strengthening metastable Mg–Nd β-series precipitates during heat treatment. The strengthening is primarily provided by a combination of the β''' and β 1 precipitation. It is therefore important to understand how the precipitation behavior can be enhanced by other common alloying elements. In this work, the effects of 0.2 wt pct Zn and Ca on β-series precipitation were studied. Small-angle/ultra-small-angle X-ray scattering (SAXS/USAXS) techniques in combination with scanning transmission electron microscopy (STEM) were used to study the evolution of precipitation microstructure. Here, it is found that the Zn additions refine the precipitates, leading to an increase in hardness with aging at 200 °C. On the other hand, the Ca additions result in an acceleration in the formation of larger β 1 precipitates and chains which provides less strengthening. The β 1 chains are surrounded by precipitate-free zones (PFZs) that further contribute to the decreases in hardness observed in the over-aged condition. This paper demonstrated that SAXS/USAXS provides a powerful tool for an in situ study of the early stages of precipitation in the Mg–Nd-based alloys.

36 MATERIALS SCIENCE↗

Small Scale Creep Testing of 14YWT via In-situ Transmission Electron Microscopy Irradiation and Nanoindentation

The next generation of nuclear materials must withstand harsh operating conditions such as high temperatures and irradiation doses. Nanostructured ferritic alloys like oxide dispersion strengthened steels, especially 14YWT, have shown promise as a structural material to withstand these harsh operating conditions. For application, understanding the irradiation enhanced creep of the structural components is fundamental to evaluating the service life in a reactor. Challenges with evaluating irradiation enhanced creep are related to the limited space in nuclear reactors and the expense of conducting post irradiation experiments on irradiated cladding. Ion irradiations are considered to expedite irradiation testing, but such experiments have restricted depth of penetration into the material, limiting the ability to characterize changes to material properties after irradiation. Small scale mechanical testing can be used with ion beam irradiations as a potential avenue to evaluate the irradiation enhanced creep of materials. In this study, in-situ transmission electron microscopy nanopillar creep studies on 14YWT were performed and simultaneously ion beam irradiated with 2.8 MeV Au4+ ions. It was observed that the ion beam irradiation did increase the measured strain rate of the materials. In addition, ex-situ nanoindentation creep studies were performed over a range of temperatures on control 14YWT, and it was observed that there was a change in the deformation mechanism between 873 K and 1073 K that agrees well with macro-scale mechanical testing. Furthermore, these results show promise for applying these techniques to nuclear materials in the future.

14 YWT↗

Imaging crossing fibers in mouse, pig, monkey, and human brain using small-angle X-ray scattering

Myelinated axons (nerve fibers) efficiently transmit signals throughout the brain via action potentials. Multiple methods that are sensitive to axon orientations, from microscopy to magnetic resonance imaging, aim to reconstruct the brain's structural connectome. As billions of nerve fibers traverse the brain with various possible geometries at each point, resolving fiber crossings is necessary to generate accurate structural connectivity maps. However, doing so with specificity is a challenging task because signals originating from oriented fibers can be influenced by brain (micro)structures unrelated to myelinated axons. X-ray scattering can specifically probe myelinated axons due to the periodicity of the myelin sheath, which yields distinct peaks in the scattering pattern. Here, in this work, we show that small-angle X-ray scattering (SAXS) can be used to detect myelinated, axon-specific fiber crossings. We first demonstrate the capability using strips of human corpus callosum to create artificial double- and triple-crossing fiber geometries, and we then apply the method in mouse, pig, vervet monkey, and human brains. We compare results to polarized light imaging (3D-PLI), tracer experiments, and to outputs from diffusion MRI that sometimes fails to detect crossings. Given its specificity, capability of 3-dimensional sampling and high resolution, SAXS could serve as a ground truth for validating fiber orientations derived using diffusion MRI as well as microscopy-based methods.

59 BASIC BIOLOGICAL SCIENCES↗

High bias machine learning for antineutrino-based safeguards for small reactors

The statistical methods used for antineutrino detection will need to be improved to effectively monitor the inventory of next-generation nuclear reactors. In this sensitivity study, we evaluate machine learning models compared to previously used statistical approaches to identify diversion scenarios in a simulated Advanced Fast Reactor (AFR)-100. A chi-square goodness-of-fit technique, which individually compares the simulated antineutrino yields to the expected antineutrino yield, resulted in precise but low diversion detection probability. Various support vector machine (SVM) models were applied with diverse training datasets to evaluate the robustness of the method towards unexpected or “unseen” diversion scenarios. Furthermore, our results indicate that while the SVM models significantly improved the detection probability of near-field antineutrino-based safeguards, up to a probability of ~0.04, for the simulated small reactor, the detection system still needs improvements to reach the 0.2 detection limit established by the International Atomic Energy Agency.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗