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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Birefringent Glass‐Engraved Tilted Pillar Metasurfaces for High Power Laser Applications

Abstract Birefringent materials—which are highly needed in high power laser systems—may be limited in usage due to the laser‐induced damage threshold of traditional birefringent materials. This work reports here on all‐glass metasurfaces, fabricated by angled etching through sacrificial metal nanoparticle (NP) etching masks, for generation of effective birefringence in the formed layer. As a result, a fused silica metasurface, monolithic to the underlying substrate, is demonstrated to exhibit a birefringence of 6.57° under 375 nm illumination. Full‐wave analysis shows a good agreement with the measurement and presents potential paths forward to increasing the effective metasurface birefringence. This is the first demonstration, to the best of knowledge, of an etching technique to obtain the resulting tilted pillar‐like nanofeatures. The anisotropy of the metasurface nanoelements along the two window in‐plane major axes presents different effective paths for the two polarizations and thus generates birefringence in a nonbirefringent material. Additionally, the imparted anisotropy lends itself to manipulation of physical properties of the surface as well, with metasurface feature orientation suppressing water flow along one principal axis and giving rise to water flow steering capabilities.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Sensitivity study of hydrogen Soret transport in yttrium Hydride-Based nuclear fuel

Yttrium hydride is an excellent solid neutron moderator material for high temperature nuclear reactor applications due to its high hydrogen density and exceptional hydride stability at high temperatures. Despite these attractive characteristics, the details of how hydrogen behaves within yttrium hydride while temperature gradients exist are still not well understood. The evolution of the hydrogen composition profile resulting from a temperature gradient requires knowledge of hydrogen’s heat of transport, a critical parameter that has not yet been measured for this material. In this work, we perform hydride redistribution, hydrogen dissociation, and hydrogen leakage calculations while varying the Soret heat of transport of hydrogen in yttrium hydride to elucidate the sensitivity of hydride stability under temperature gradients to this parameter. This study analyzes hydride stability of a hypothetical uranium-yttrium hydride nuclear fuel design during operation of a high temperature liquid metal-cooled nuclear reactor. Assuming U-YH x could be fabricated in a physically stabilized manner, this fuel system can likely maintain hydride stability while operating at very high power densities and temperatures. We find that even though the hydrogen dissociation pressure in the gas gap does vary by several percent as the heat of transport temperature parameter is varied, the hydrogen content in the U-YH x fuel meat is relatively insensitive to this parameter over the course of a high burnup fuel cycle; this is due to yttrium hydride’s excellent hydrogen retention under the high temperature conditions considered here. Here, this suggests that hydride stability analyses are insensitive to the value of the Soret heat of transport in U-YH x under steady state liquid metal-cooled reactor conditions. However, the susceptibility to internal gas overpressurization-induced stress-rupture of the cladding during a high temperature transient is more sensitive to this parameter due to the non-linear dependence of hydrogen gas dissociation pressure vs. composition and temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Unveiling Structural Heterogeneity and Imbalance of Gold Decahedral Nanoparticles using Four-dimensional Scanning Transmission Electron Microscopy

Multi-twinned structures have been observed in technologically important crystal systems, for example diamond cubic and face-centered cubic (FCC) lattices, that include materials such as diamond, silicon, a wide range of noble metals, and their nanoscale counterparts. Beyond atomic building blocks, the special arrangements also occur in the self-assembly of nanoparticles (NP) and μm-sized colloidal particles and occupy parts of their phase diagrams. Spanning a wide range of length scales, the universality of the structures arises when the systems attempt to achieve multitwinned structures by overcoming geometric misfits during minimizing surface energies with entirely {111} or close-packing facets. While it is fundamental to understand how strain is sustained upon twinned structures and symmetry breaking, the knowledge will be paramount in practical aspects such as guiding and controlling the thin film growth, anisotropic NP growth, and self-assembly of NPs. Au decahedral (Dh) NP, as the most prevalent multi-twinned model system, fits five tetrahedral motifs into a circle by sharing an axis resulting in a geometric misfit angle of 7.35°, or a disclination with power of -7.35°. Postulating how Au FCC lattice adopts the misfit, theoretical models have been developed to address the underlying lattice symmetry and inhomogeneous strain distribution separately. Yet, experimental reports regarding the former have been limited due to the relatively large X-ray beam sizes that do not fit the sizes of NPs. On the other hand, though the latter has been widely adapted in the thermodynamics of small (<10 nm) multi-twinned nanoparticles, previous literature has shown that, at edge length of 17 nm, the theory’s is invalidated by shear strain that is observed in a defect-free Au Dh NP by high-resolution transmission electron microscopy (HR-TEM) imaging. Though the advancement of aberrationcorrected scanning transmission electron microscopy (AC-STEM) imaging and ab initio calculation techniques brings new opportunities, along with challenges in complicated image analysis and limitation in particle size (usually below 10 nm), the gap between nanoscale and mesoscale has never been extended to gain insight from atomic system with straightforward interaction potentials.

4D-STEM↗
DOE OSTI2025

Ice sculpting: An artificial spin ice Tutorial on controlling microstate and geometry for magnonics and neuromorphic computing

Artificial spin ice, arrays of strongly interacting nanomagnets, are complex magnetic systems with many emergent properties, rich microstate spaces, intrinsic physical memory, high-frequency dynamics in the GHz range, and compatibility with a broad range of measurement approaches. This Tutorial article aims to provide the foundational knowledge needed to understand, design, develop, and improve the dynamic properties of artificial spin ice. Special emphasis is placed on introducing the theory of micromagnetics, which describes the complex dynamics within these systems, along with their design, fabrication methods, and standard measurement and control techniques. The article begins with a review of the historical background, introducing the underlying physical phenomena and interactions that govern artificial spin ice. We then explore the standard experimental techniques used to prepare the microstate space of the nanomagnetic array and to characterize magnetization dynamics, both in artificial spin ice and more broadly in ferromagnetic materials. Finally, we introduce the basics of neuromorphic computing applied to the case of artificial spin ice systems with a goal to help researchers new to the field grasp these exciting new developments.

Sultana, Rawnak [Univ. of Delaware, Newark, DE (Un↗
DOE OSTI2025

Generation and Study of Am(IV) by Temperature-Controlled Electron Pulse Radiolysis

Used nuclear fuel (UNF) separation techniques that strive to separate radiotoxic americium (Am) from trivalent lanthanide fission products through oxidation state control have increased research efforts surrounding Am(V) and Am(VI). However, equivalent knowledge of the tetravalent state, Am(IV), has remained elusive, particularly in conditions more representative of UNF reprocessing, i.e., in concentrated nitric acid (HNO3). With this in mind, we have used electron pulse radiolysis to study the radiation-induced redox reaction of Am(III) with the oxidizing nitrate radical (NO3?) in 6 M HNO3: Am(III) + NO3? ? Am(IV) + NO3? . These experiments enabled us to observe the growth and decay of Am(IV) in a concentrated acidic solution for the first time. The transient Am(IV) species was found to have a lifetime of ~16 µs?sufficiently long-lived to play a critical mechanistic role in UNF reprocessing systems. Additionally, we performed the first-ever temperature-dependent kinetics study of an actinide element, elucidating unprecedented Arrhenius and Eyring activation parameters for the reaction of Am(III) with NO3?. This new knowledge provides much-needed molecular-level insights into the radiation-induced behavior of Am.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

Crystal structure and magnetism of actinide oxides: a review

In actinide systems, the 5f electrons experience a uniquely delicate balance of effects and interactions having similar energy scales, which are often difficult to properly disentangle. This interplay of factors such as the dual nature of 5f-states, strong electronic correlations, and strong spin–orbit coupling results in electronically unusual and intriguing behavior such as multi-k antiferromagnetic ordering, multipolar ordering, Mott-physics, mixed valence configurations, and more. Despite the inherent allure of their exotic properties, the exploratory science of even the more basic, binary systems like the actinide oxides has been limited due to their toxicity, radioactivity, and reactivity. In this article, we provide an overview of the available synthesis techniques for selected binary actinide oxides, including the actinide dioxides, sesquioxides, and a selection of higher oxides. For these oxides, here we also review and evaluate the current state of knowledge of their crystal structures and magnetic properties. In many aspects, substantial knowledge gaps exist in the current body of research on actinide oxides related to understanding their electronic ground states. Bridging these gaps is vital for improving not only a fundamental understanding of these systems but also of future nuclear technologies. To this end, we note the experimental techniques and necessary future investigations which may aid in better elucidating the nature of these fascinating systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Energy Storage in Local Zoning Ordinances

Increasing policy support and declining prices for battery energy storage systems (BESS) are driving rapid growth in the installation of these systems in the United States and around the world. Because a BESS is modular in nature and has limited infrastructure requirements, it can be built in close proximity to existing uses, which creates the potential for conflict. As the use of BESS grows, local planning and zoning staff are increasingly being asked to determine where the systems can be built and how their impacts on surrounding uses can be mitigated. While a large-scale BESS offers significant electric grid and societal benefits, it can also pose safety, visual, auditory, and environmental impacts on the community in which it is located. While these are material impacts, current safety codes for energy storage systems and land use frameworks provide planners with the necessary tools and processes to mitigate those impacts and ensure that their communities safely receive the benefits of energy storage systems. This report provides an overview of BESS from a land use perspective and describes their implications for zoning and project permitting. It concludes with an analysis of current energy storage zoning standards adopted by local jurisdictions in the U.S. Its intent is to objectively inform land use decisions for energy storage projects by equipping planning officials with relevant information about these technologies and knowledge of what questions to ask during review processes, so that energy storage projects can move forward in ways that will benefit electric systems while not unduly affecting host communities.

25 ENERGY STORAGE↗
DOE OSTI2022

Subcomponent Validation of Composite Joints for Marine Energy Structures

The Marine Energy Advanced Materials project addresses the barriers and uncertainties facing marine renewable energy developers in using composite materials for load-bearing structures. Sponsored by the U.S. Department of Energy's Water Power Technologies Office, the multiyear project comprises of collaborators from the National Renewable Energy Laboratory (NREL), Sandia National Laboratories, Pacific Northwest National Laboratory (PNNL), Montana State University (MSU), Florida Atlantic University (FAU), and industry stakeholders. As part of the Marine Energy Advanced Materials project, marine renewable energy industry surveys and assessments were conducted to identify key materials and knowledge gaps that hinder the adoption of composite materials in marine renewable energy structures. Specific knowledge gaps highlighted for composite materials were environmental effects, fatigue strengths, and bonded and bolted interconnects (composite/composite and composite/metal). It was concluded that many of these gaps could be addressed through subcomponent validation; consequently, a program was developed at NREL with the goals of developing subcomponent validation methods for appropriate marine energy materials, which would improve the understanding of design allowables for full-scale structural components and joints. Ultimately, the aim is to reduce timelines and costs associated with full-scale structural validation efforts while also providing near-net-scale static and fatigue data of composite/metal subcomponents for marine renewable energy systems. To approach these goals, a testing program was developed at NREL to investigate a variety of materials and structural design details at the subcomponent scale to understand (a) the effects of harsh and corrosive marine energy environments and (b) the static and fatigue strengths of the complex geometries. The recent study from this testing program is perhaps the largest that has ever been conducted with respect to specimen scale and geographic diversity of underwater environmental conditions that the specimens were subjected to. A variety of specimen geometries were designed by NREL to highlight key features of multimaterial (composite/composite or metal/composite) interconnects that may be used in marine renewable energy structural designs. The designs used several different composite matrices, adhesives, and marine-grade steels, which were highlighted in the surveys as being the most appropriate for harsh marine environments. Composite panels were then manufactured at MSU, and were subsequently manufactured into test specimens by NREL. The specimens were shipped to FAU and PNNL for conditioning in ocean water tanks at various temperatures for an extended period. The specimens were then returned to NREL for structural validation. This presentation will provide an overview of recent advances within the testing program in terms of specimen design and test methods, and will discuss results and key findings of the subcomponent testing program to date at NREL.

adhesives↗
DOE OSTI2025

Evaluation of Cease Fire CFP 640 for Use in Gloveboxes (Final Report)

A Los Alamos National Laboratory (LANL) task group was established to discuss and evaluate a candidate fire suppression system (FSS) for gloveboxes (GB) and dropboxes (DB, for brevity, this report will simply refer to gloveboxes). Suitability criteria include compliance, compatibility, and capability. LANL contracted with New Mexico Tech (NMT) to quantitatively evaluate the perfor mance of one of those systems including its ability to extinguish GB fires, limit over-pressurization of the GB, etc. Additionally, the results of these experiments provide data points that could be used when fire hazard evaluations (FHEs) are conducted for determining when to require a fire suppres sion system installation within a GB (as required by NFPA 801, Standard for Facilities Handling Radioactive Materials, DOE Standard 1066-2012 Fire Protection, and AGS-G010-2011 Standard of Practice for Glovebox Fire Protection).

42 ENGINEERING↗
DOE OSTI2023

Loss of Coolant High Burnup (LOC-HBu) Program

LOC-HBu is a joint experimental program (JEEP) operating within the Nuclear Energy Agency’s (NEA’s) framework for irradiation experiments II (FIDES-II). LOC-HBu is dedicated to the understanding of light water reactor (LWR) fuel performance at high burnup under loss of coolant accident (LOCA) conditions. LOC-HBu aims to support burnup extension needs by addressing identified R&D priorities to achieve an improved understanding of fuel fragmentation, relocation, and dispersal (FFRD) of HBu fuel during LOCA events. The need for such experiments was identified in the United States by the Fuel Performance Testing Technical Expert Group (FPTTEG) under the Electric Power Research Institute (EPRI)’s Collaborative Research on Advanced Fuel Technologies (CRAFT) framework. A combined in-pile and furnace testing program plan was developed by researchers at Idaho National Laboratory (INL) and Oak Ridge National Laboratory (ORNL) which was reviewed and approved by the FPTTEG Combined TREAT-LOC and SATS LOCA Experiment Plan. The first 4 tests identified in this plan are being put forward by the U.S. Department of Energy (U.S. DOE) and INL for inclusion in the FIDES-II second triannual work period. The data produced under this plan will be used to further validate and confirm existing models and inform future R&D and model development. The experimental program was specifically developed to address data gaps and opportunities identified via detailed review of the existing public knowledge base on LOCA FFRD, as well as reviewing specific experimental development activities regarding prototypic LOCA conditions for light-water reactor (LWR) systems. The program will systematically investigate the impacts of prototypic HBu fuel/cladding thermomechanical behaviors under postulated LWR LOCA conditions not yet fully investigated. These conditions correspond with prototypic decay-energy heatup (DEH) and stored-energy heatup (SEH) conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Deep-freeze graph training for latent learning

Scientific and engineering advances are primarily driven by multi-tier conceptual constructs and conditional theoretical frameworks. The theories allow predictions of hypothetical system responses, given a set of approximate conditions (ranges of applicability) imposed on latent parameters that cannot be measured directly. Learning to estimate the latent variables (Latent Learning) helps to pinpoint the anticipated range-edge anomalies and improves the confidence in interpretation, interpolation and extrapolation of limited experimental data. Due to high dimensionality and extreme non-linearity of the materials science problems, very large datasets are typically required for conventional data-driven model development. The vital experimental data collection, particularly on microstructural phases, is very challenging, which makes it difficult to compile a high-quality database. Incorporation of the domain knowledge into the computational graph structure, initialization and optimization processes presents a viable mechanism for developing accurate models, with limited datasets. Furthermore, this study successfully utilized the approach to build the Deep Freeze Graph (DeepFreG) by mapping known causality relationships and by digitizing empirical domain knowledge for Latent Learning (LL), with specific applications in materials science.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Sources of error and methods to improve accuracy in interface state density analysis using quasi-static capacitance–voltage measurements in wide bandgap semiconductors

Characterizing interface trap states in commercial wide bandgap devices using frequency-based measurements requires unconventionally high probing frequencies to account for both fast and slow traps associated with wide bandgap materials. The C - ψs technique has been suggested as a viable quasi-static method for determining the interface trap state densities in wide bandgap systems, but the results are shown to be susceptible to errors in the analysis procedure. Here this work explores the primary sources of errors present in the C - ψs technique using an analytical model that describes the apparent response for wide bandgap MOS capacitor devices. Measurement noise is shown to greatly impact the linear fitting routine of the 1/C$^{*2}_s$ vs Ψ s plot to calibrate the additive constant in the surface potential/gate voltage relationship, and an inexact knowledge of the oxide capacitance is also shown to impede interface trap state analysis near the band edge. In addition, a slight nonlinearity that is typically present throughout the 1/C$^{*2}_s$ vs Ψ s plot hinders the accurate estimation of interface trap densities, which is demonstrated for a fabricated n-SiC MOS capacitor device. Methods are suggested to improve quasi-static analysis, including a novel method to determine an approximate integration constant without relying on a linear fitting routine.

42 ENGINEERING↗
DOE OSTI2020

Self-Assembly of Virus Particle Based Materials for Hydrogen Catalysis

Viruses are sophisticated protein-based containers and their self-assembly from a small number of subunits into symmetrical, monodisperse architectures has inspired the work performed under this award. We have taken advantage of the robust self-assembly of the bacteriophage P22 for the encapsulation of enzymatic cargo materials and studied their activity in energy harvesting systems. The large internal cavity of the P22 is ideal for high-capacity loading of enzymes resulting in very high local catalyst concentrations. We have exploited the self-assembly properties of the bacteriophage P22 system for the packaging of a number of different enzymes, including a [NiFe] hydrogenase as well as enzymes capable of butanol biosynthesis, to create active and stable individual “nano-reactors”. Individual viral capsid-based nanoreactors are also ideal building blocks for the construction of higher order assemblies. We have demonstrated the construction of ordered 3-D arrays from active nanoparticle building blocks to form materials with collective behavior and properties beyond those of the individual particles and capable of catalyzing multi-step reactions. The successful implementation of the work performed under this DOE grant provides us with a great deal of knowledge about directed self-assembly at multiple lengthscales for the development of bioinspired catalytic materials for energy harvesting.

08 HYDROGEN↗
DOE OSTI2020

Design strategies for nonaqueous multivalent-ion and monovalent-ion battery anodes

The inability of current battery technologies to keep up with the performance requirements of industry is pushing forward developments in electrochemistry. Specifically, the battery's negative electrode, the anode, presents many unique chemical, physical and engineering challenges. Lithium-based battery technologies have dominated the past decade, but concerns about the limited supply of lithium in the Earth's crust have led researchers to look towards alternative metal-ion technologies. Furthermore, various alkali metals (such as sodium and potassium) and alkali earth metals (such as magnesium and calcium) have attracted significant research interest. In this Review, we analyse these technologies in a coherent manner, addressing the problems of each type of anode, rather than those of specific types of metal-ion batteries. Covering direct metal plating and stripping, intercalation-based, alloy-based and conversion-reaction-based anode technologies, this analysis will offer the reader a comprehensive understanding of the behaviour of different metal-ion anodes and of what can be learned by transferring knowledge between these different systems. Increasing demand for energy-storage systems will inevitably stress the Earth's lithium supply; thus, the research focus is shifting towards other alkali and alkali earth metals. In summary, this Review compares and connects strategies to enable different multivalent and monovalent metal-ion battery anodes, including metal anodes and intercalation-based, alloy-based and conversion-reaction-based anodes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Multipartite entanglement in the one-dimensional spin- 1 2 Heisenberg antiferromagnet

Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as T→0. This implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale of the system. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. Furthermore, the 1D spin- 1 2 antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges nontrivially as ~ln(1/T) 3/2 . We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally, we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF 3 , a material well described by the Heisenberg chain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Scalable Electrolytic Systems for Renewable Hydrogen Production (Cooperative Research and Development Final Report, CRADA Number CRD-18-747)

The project focuses on offshore wind energy which is an emergent renewable energy source in the United States. Onsite hydrogen production for this sector is not available. The overall goal of GTA's work is development of scalable multi-megawatt water electrolysis systems that exclude platinum group metals, are constructed from readily available commodity materials and are mass produced using advanced manufacturing and robotics. They fabricated and successfully tested a scalable TRL 4 laboratory prototype that demonstrated promising results for achieving the goal. They further performed calculations and prepared scale drawings for an envisioned onsite TRL 8 electrolytic hydrogen production system at an offshore 8 MW wind turbine. The work plan of the CRADA proposal between NREL and GTA focuses on validation of the current TRL 4 prototype with potential development and refinement for advancement to a TRL 5 system. GTA, Inc. proposes joining the H2@Scale consortium to leverage DOE funds, benefit from and contribute to the common knowledge-base and work with NREL as a CRADA partner.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

2020 Multiscale Microbial Dynamics Modeling Course

The 2020 Multiscale Microbial Dynamics course is adapted from the virtual 2020 Mutliscale Microbial Dynamics Summer School that was hosted by Environmental Molecular Sciences Laboratory (EMSL), a U.S. Department of Energy (DOE) science user facility located on the Pacific Northwest National Laboratory (PNNL) campus, in collaboration with the Joint Genome Institute (JGI) and the DOE Systems Biology Knowledgebase (KBase). The course course covers how to incorporate microbial metagenomic and environmental metabolite data from watershed ecosystems into metabolic and community modeling using computational frameworks, such as KBase and PFLOTRAN. The curriculum includes lectures and software and data analysis tutorials. All materials are freely accessible to the community as part of the 2020 Microbial Dynamics Summer School Organization in KBase.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Rapid Adaptation of Chemical Named Entity Recognition Using Few-Shot Learning and LLM Distillation

Named entity recognition (NER) has been widely used in chemical text mining for the automatic identification and extraction of chemical entities. However, existing chemical NER systems primarily focus on scenarios with abundant training data, requiring significant human effort on annotations. This poses challenges for applications in the chemical field, such as catalysis, where many advancements have traditionally relied on trial-and-error investigations and incremental adjustment of variables. This hinders catalysis science and technology progress in addressing emerging energy and environmental crises. In this work, we propose a few-shot NER model that can quickly adapt to extract new types of chemical entities by using only a limited number of annotated examples. Our model employs a metric-learning approach to transfer entity similarity knowledge from high-resource chemical domains (with abundant annotations) to enable effective entity recognition in low-resource specialized domains (limited annotation). We validate the effectiveness of our model on a few-shot chemical NER benchmark built based on six existing chemical NER data sets. Experiments show that the proposed few-shot NER model can achieve reasonable performance with only 5 examples per entity type and shows consistent improvement as the number of examples increases. Furthermore, we demonstrate how the proposed model can be trained with large language model (LLM) annotated data, opening a new pathway for rapid adaptation of NER systems. Furthermore, our approach leverages the knowledge broadness of large language models for chemistry while distilling this knowledge into a lightweight model suitable for efficient and in-house use.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗