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Thermal neutron scattering cross sections for amorphous carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm{sup 3}. From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical optical peak at 0.25 eV for the ideal graphite disappears for amorphous carbon, in good agreement with the expected structure. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Thermal Neutron Scattering Cross Sections for Graphitic Amorphous Carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm 3 . From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical features and the optical graphitic peak at 0.25 eV for the ideal graphite DOS disappear for graphite-like amorphous carbon, which shows good agreement with the expected structure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Deciphering the Scattering of Mechanically Driven Polymers Using Deep Learning

Here, we present a deep learning approach for analyzing two-dimensional scattering data of semiflexible polymers under external forces. In our framework, scattering functions are compressed into a three-dimensional latent space using a Variational Autoencoder (VAE), and two converter networks establish a bidirectional mapping between the polymer parameters (bending modulus, stretching force, and steady shear) and the scattering functions. The training data are generated using off-lattice Monte Carlo simulations to avoid the orientational bias inherent in lattice models, ensuring robust sampling of polymer conformations. The feasibility of this bidirectional mapping is demonstrated by the organized distribution of polymer parameters in the latent space. By integrating the converter networks with the VAE, we obtain a generator that produces scattering functions from given polymer parameters and an inferrer that directly extracts polymer parameters from scattering data. While the generator can be utilized in a traditional least-squares fitting procedure, the inferrer produces comparable results in a single pass and operates 3 orders of magnitude faster. This approach offers a scalable automated tool for polymer scattering analysis and provides a promising foundation for extending the method to other scattering models, experimental validation, and the study of time-dependent scattering data.

Ding, Lijie [Oak Ridge National Laboratory (ORNL),↗

Machine learning-assisted profiling of a kinked ladder polymer structure using scattering

Ladder polymers consisting of fused rings in the backbone have very limited conformational freedom, which results in very different properties from traditional linear polymers. However, accurately determining their size and chain conformations from solution scattering remains a challenge. Their chain conformations of kinked ladder polymers are largely governed by the structures and relative orientations or configurations of the repeat units, unlike conventional polymer chains whose bending angles between repeat units follow a unimodal Gaussian distribution. Meanwhile, traditional scattering models for polymer chains do not account for these unique structural features. This work introduces a novel approach that integrates machine learning with Monte Carlo simulations to construct a model that can describe the geometry of a type of kinked CANAL ladder polymers. We first develop a Monte Carlo simulation model for sampling the configuration space of CANAL ladder polymers, where each repeat unit is modeled as a biaxial segment. Then, we establish a machine learning-assisted scattering analysis framework based on Gaussian Process Regression. Finally, we conduct small-angle neutron scattering experiments on a CANAL ladder polymer solution to apply our approach. Our method uncovers structural features of such ladder polymers that conventional methods fail to capture.

Ding, Lijie [Oak Ridge National Laboratory (ORNL),↗

The role of annealing and grain boundary controls on the mechanical properties of limestones and marbles

Chemical and mechanical processes are coupled in many geological and geochemical environments. Reactive processes anneal defects and restructure grain boundaries, modifying their elastic properties, levels of internal friction, wave propagation rates and fracture behaviors. The nature of these changes is, however, contingent on the initial state of the rock. Here, in this study, impulse excitation was used to measure changes in mechanical properties as a function of dry and steam heating time at 300 °C for three carbonate rocks: Carrara marble, Carthage marble (Burlington Limestone), and Texas Cream limestone (Edwards limestone), with initial porosities of about 1 %, 3 %, and 27 %, respectively. Frequency-dependent phenomena along with mineral recrystallization were observed. This was coupled with small-angle X-ray and neutron scattering analysis to determine the relationship between changes in bulk mechanical and microstructural properties. An observed decrease in both the Young's and shear moduli in the experimental limestones as a function of heating time reflects and quantifies a reduction in the stiffness of the rock due to annealing. The internal friction of the samples first increases then decreases with reaction time, reflecting defect annealing, but this was balanced against grain boundary dissolution apparently driven by condensation of steam in the confined grain-boundary environment. This suggests an increase in the boiling point under confinement leading to dissolution, increased porosity and widening of the grain boundaries. In addition, comparison of small-angle X-ray and neutron scattering results suggests that it is inappropriate to assume that pores are empty for quantitative analysis of typical small-angle scattering samples.

58 GEOSCIENCES↗

Probing three-dimensional mesoscopic interfacial structures in a single view using multibeam X-ray coherent surface scattering and holography imaging

Abstract Visualizing surface-supported and buried planar mesoscale structures, such as nanoelectronics, ultrathin-film quantum dots, photovoltaics, and heterogeneous catalysts, often requires high-resolution X-ray imaging and scattering. Here, we discovered that multibeam scattering in grazing-incident reflection geometry is sensitive to three-dimensional (3D) structures in a single view, which is difficult in conventional scattering or imaging approaches. We developed a 3D finite-element-based multibeam-scattering analysis to decode the heterogeneous electric-field distribution and to faithfully reproduce the complex scattering and surface features. This approach further leads to the demonstration of hard-X-ray Lloyd’s mirror interference of scattering waves, resembling dark-field, high-contrast surface holography under the grazing-angle scattering conditions. A first-principles calculation of the single-view holographic images resolves the surface patterns’ 3D morphology with nanometer resolutions, which is critical for ultrafine nanocircuit metrology. The holographic method and simulations pave the way for single-shot structural characterization for visualizing irreversible and morphology-transforming physical and chemical processes in situ or operando .

47 OTHER INSTRUMENTATION↗

Progress on Light-Element Standard Cross Sections at Los Alamos [Slides]

Presenters identified the following statuses of the light-element standards: Extension of N-N scattering analysis to 200 MeV will likely come in time for ENDF/B VIII.1 and new data are to be added even in the energy range up to 100 MeV; for n- 3 He, a more recent 4 He R-matrix analysis from which updated n+ 3 He cross sections could be obtained for ENDF/B VIII.1; for n- 6 Li, more work is required to get a reasonable fit to all data up to E n = 8 MeV. Of particular concern are the t+ 4 He scattering data at E t > 14 MeV. For n- 10 B, new work on the 11 B system has not yet been started and there is much new data to add for n+ 10 B reactions, and maybe also for &#945 + 7 Li reactions. The proliferation of excited-state channels will limit the upper neutron energy of the analysis to a few MeV. For n- 12 C, new elastic and inelastic scattering data from Vanhoy support the results of the present analysis. More work is needed to extend the fit successfully above 6.5 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Unbiased particle conformation extraction from scattering spectra using orthonormal basis expansions

A strategy is outlined for quantitatively evaluating the particle density profiles from small-angle scattering spectra of dilute solutions. The approach employs an orthonormal basis function expansion method, enabling the determination of characteristic mass distributions in self-assembled structures without the need for a specific structural model. Through computational benchmarking, the efficacy of this approach is validated by effectively reconstructing the density profile of soft-ball systems with varying fuzziness from their scattering signatures. Further, the feasibility of the method is demonstrated by fitting small-angle neutron scattering data obtained from Pluronic L64 micelles at different temperatures. This proposed approach is both simple and analytical, eliminating the requirement for a presumptive structural model in scattering analysis. The new method could therefore facilitate quantitative descriptions of complex nanoscopic structures inherent to numerous soft-matter systems using small-angle scattering techniques.

36 MATERIALS SCIENCE↗

Correlation between ferroelectricity and ferroelectric orthorhombic phase of Hf x Zr 1-x O 2 thin films using synchrotron x-ray analysis

The change in the interplanar spacing ( d -spacing) including the ferroelectric orthorhombic (O) phase in the low-temperature fabricated Hf x Zr 1-x O 2 (HZO) films was studied using synchrotron grazing-incidence wide-angle x-ray scattering analysis. The 10-nm-thick HZO films were fabricated by thermal and plasma-enhanced atomic layer deposition (TH- and PE-ALD) methods using H 2 O gas and O 2 plasma as oxidants, respectively, and a post-metallization annealing (PMA) was performed at 300–400 °C. The d -spacing of the mixture of (111)-, (101)-, and (111)-planes of O, tetragonal (T), and cubic (C) phases, respectively, for the TH- and PE-ALD HZO films increased up to 2.99 Å with an increase in PMA temperature, while the d -spacing estimated by conventional x-ray diffraction was 2.92 Å regardless of the PMA temperature. The remanent polarization (2 P r = P r + - P r - ) of the HZO films increased as the PMA temperature increased. It is clear that the 2 P r value satisfied a linear relationship as a function of the d -spacing of O(111)/T(101)/C(111) phases. Furthermore, the wake-up effect was found to depend on the ferroelectric O phase formation. The wake-up effect was significantly reduced in both the TH- and PE-ALD HZO films after the PMA at 400 °C due to the increase in the ferroelectric O phase formation. The leakage current density ( J )–electric field properties of the PE-ALD HZO film with the lowest d -spacing were divided into three steps, such as low, middle, and large J values, in the wake-up (10 3 cycles), pristine (10 0 cycle), and fatigue (10 7 cycles) states, respectively. Therefore, an analysis of the ferroelectric O phase is very important for understanding the ferroelectricity including endurance.

36 MATERIALS SCIENCE↗

Atomic Level Interactions and Suprastructural Configuration of Plant Cell Wall Polymers in Dialkylimidazolium Ionic Liquids

Ionic liquids (ILs) have been widely investigated for the pretreatment and deconstruction of lignocellulosic feedstocks. However, the modes of interaction between IL-anions and cations, and plant cell wall polymers, namely, cellulose, hemicellulose, and lignin, as well as the resulting ultrastructural changes are still unclear. In this study, we investigated the atomic level and suprastructural interactions of microcrystalline cellulose, birch wood xylan, and organosolv lignin with 1,3-dialkylimidazolium ILs having varying sizes of carboxylate anions. Analysis by 13 C NMR spectroscopy indicated that cellulose and lignin exhibited stronger hydrogen bonding with acetate ions than with formate ions, as evidenced by greater chemical shift changes. Small-angle X-ray scattering analysis showed that while both cellulose and xylan adopted a single-stranded conformation in acetate-ILs, twice as many acetate ions were bound to one anhydroglucose unit than to an anhydroxylose unit. Further, we also determined that a minimum of seven representative carbohydrate units must interact with an anion for that IL to effectively dissolve cellulose or xylan. Lignin is associated as groups of four polymer molecules in formate-ILs and dispersed as single molecules in acetate-ILs, which indicates that it is highly soluble in the latter. In summary, our study demonstrated that 1,3-dialkylimidazolium acetates displayed stronger binding interactions with cellulose and lignin, as compared to formates, and thus have superior potential to fractionate these polymers from lignocellulosic feedstocks.

13C NMR↗

Background optimization of powder electron diffraction for implementation of the e-PDF technique and study of the local structure of iron oxide nanocrystals

The local structural characterization of iron oxide nanoparticles is explored using a total scattering analysis method known as pair distribution function (PDF) (also known as reduced density function) analysis. The PDF profiles are derived from background-corrected powder electron diffraction patterns (the e-PDF technique). Due to the strong Coulombic interaction between the electron beam and the sample, electron diffraction generally leads to multiple scattering, causing redistribution of intensities towards higher scattering angles and an increased background in the diffraction profile. In addition to this, the electron–specimen interaction gives rise to an undesirable inelastic scattering signal that contributes primarily to the background. The present work demonstrates the efficacy of a pre-treatment of the underlying complex background function, which is a combination of both incoherent multiple and inelastic scatterings that cannot be identical for different electron beam energies. Therefore, two different background subtraction approaches are proposed for the electron diffraction patterns acquired at 80 kV and 300 kV beam energies. From the least-square refinement (small-box modelling), both approaches are found to be very promising, leading to a successful implementation of the e-PDF technique to study the local structure of the considered nanomaterial.

36 MATERIALS SCIENCE↗

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas , vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci. , vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Physics↗

Interaction of radio frequency waves with cylindrical density filaments -- scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal

Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Advancing Molecular Weight Determination of Lignin by Multi-Angle Light Scattering

Due to the complexity and recalcitrance of lignin, its chemical characterization is a key factor preventing the valorization of this abundant material. Multi-angle light scattering (MALS) is becoming a sought-after technique for absolute molecular weight (MW) determination of polymers and proteins. Lignin is a suitable candidate for MW determination via MALS, yet further investigation is required to confirm its absolute MW values and molecular size. Studies aiming to break down lignin into a variety of renewable products will benefit greatly from a simple and reliable determination method like MALS. Recent pioneering studies, discussed in this review, addressed several key challenges in lignin’s MW characterization. Nevertheless, some lignin-specific issues still need to be considered for in-depth characterization. This study explores how MALS instrumentation manages the complexities of determining lignin’s MW, e.g., with simultaneous fractionation and fluorescence interference mitigation. Additionally, we rationalize the importance of a more detailed light scattering analysis for lignin characterization, including aspects like the second virial coefficient and radius of gyration.

differential refractive index increment↗

Illustrated formalisms for total scattering data: a guide for new practitioners

The total scattering method is the simultaneous study of both the real- and reciprocal-space representations of diffraction data. While conventional Bragg-scattering analysis (employing methods such as Rietveld refinement) provides insight into the average structure of the material, pair distribution function (PDF) analysis allows for a more focused study of the local atomic arrangement of a material. Generically speaking, a PDF is generated by Fourier transforming the total measured reciprocal-space diffraction data (Bragg and diffuse) into a real-space representation. However, the details of the transformation employed and, by consequence, the resultant appearance and weighting of the real-space representation of the system can vary between different research communities. As the worldwide total scattering community continues to grow, these subtle differences in nomenclature and data representation have led to conflicting and confusing descriptions of how the PDF is defined and calculated. This paper provides a consistent derivation of many of these different forms of the PDF and the transformations required to bridge between them. Some general considerations and advice for total scattering practitioners in selecting and defining the appropriate choice of PDF in their own research are presented. This contribution aims to benefit people starting in the field or trying to compare their results with those of other researchers.

36 MATERIALS SCIENCE↗

Thermal scattering law for structure-dependent-Doppler broadening in FLASSH

Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗