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DOE OSTI2023

Effect of the Nature of Both Cation and Anion Substitution on the Structural Symmetry of Li‐Rich 3 d ‐Metal Chalcogenide Electrodes

Abstract Li‐rich layered chalcogenides have recently led to better understanding of the anionic redox process and its associated high capacity while providing ways to overcome its practical limitations of voltage fade and irreversibility. This study reports on the feasibility of triggering anionic activity in Li 2 TiS 3 , through anionic substitution (Se for S) or cationic substitution (Fe for Ti). Herein, the chalcogenide chemical space is further explored to prepare mono‐substituted Li 1.7 Ti 0.85 Mn 0.45 Ch 3 (Ch = S/Se) and doubly substituted cationic and anionic phases (Li 1.7 Ti 0.85 Fe 0.45 S 3‐z Se z ) which crystallize either in the O3‐ or O1‐type structures depending upon substituents. All series show a bell‐shape capacity variation as function of the transition metal (TM) substitution degree with values up to 240 mAh g −1 . For specific compositions, a structural O3 to O1 phase transition is observed upon Li removal, which is not reversible upon Li re‐insertion due to kinetic limitations and negatively affects long‐term cycling performance. Density functional theory (DFT) calculations confirm the O3/O1 relative stability along the different series and point subtle electronic differences in the TM‐doping, rationalizing the structural and electrochemical behaviors of these phases upon cycling. These findings provide further insights into the link between structural and electronic stability, which is of key importance for designing chalcogenide‐based anionic redox compounds.

Chemistry↗
DOE OSTI2024

Trace benzene capture by decoration of structural defects in metal–organic framework materials

Abstract Capture of trace benzene is an important and challenging task. Metal–organic framework materials are promising sorbents for a variety of gases, but their limited capacity towards benzene at low concentration remains unresolved. Here we report the adsorption of trace benzene by decorating a structural defect in MIL-125-defect with single-atom metal centres to afford MIL-125-X (X = Mn, Fe, Co, Ni, Cu, Zn; MIL-125, Ti 8 O 8 (OH) 4 (BDC) 6 where H 2 BDC is 1,4-benzenedicarboxylic acid). At 298 K, MIL-125-Zn exhibits a benzene uptake of 7.63 mmol g −1 at 1.2 mbar and 5.33 mmol g −1 at 0.12 mbar, and breakthrough experiments confirm the removal of trace benzene (from 5 to <0.5 ppm) from air (up to 111,000 min g −1 of metal–organic framework), even after exposure to moisture. The binding of benzene to the defect and open Zn(II) sites at low pressure has been visualized by diffraction, scattering and spectroscopy. This work highlights the importance of fine-tuning pore chemistry for designing adsorbents for the removal of air pollutants.

Chemistry↗
DOE OSTI2025

Dissipative Phase Transition in the Two-Photon Dicke Model

We explore the dissipative phase transition of the two-photon Dicke model, a topic that has garnered significant attention recently. Our analysis reveals that while single-photon loss does not stabilize the intrinsic instability in the model, the inclusion of two-photon loss restores stability, leading to the emergence of superradiant states, which coexist with the normal vacuum states. Using a second-order cumulant expansion for the photons, we derive an analytical description of the system in the thermodynamic limit, which agrees well with the exact calculation results. Additionally, we present the Wigner function for the system, shedding light on the breaking of the 𝑍4 symmetry inherent in the model. These findings offer valuable insights into stabilization mechanisms in open quantum systems and pave the way for exploring complex nonlinear dynamics in two-photon Dicke models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Entanglement Structure of Non-Gaussian States and How to Measure It

Rapidly growing capabilities of quantum simulators to probe quantum many-body phenomena require new methods to characterize increasingly complex states. Here, we present a protocol that constrains quantum states using experimentally measured correlation functions. This method enables measurement of a quantum state’s entanglement structure, opening a new route to study entanglement-related phenomena. Our approach extends Gaussian state parameterizations by systematically incorporating higher-order correlations. We show the protocol’s usefulness in conjunction with current and forthcoming experimental capabilities, focusing on weakly interacting fermions as a proof of concept. Here, the lowest nontrivial expansion quantitatively predicts early time thermalization dynamics, including signaling the onset of quantum chaos indicated by the entanglement Hamiltonian.

Fermi gases↗
DOE OSTI1975

Nuclear Safety [Vol. 16, No. 2, March-April 1975]

Nuclear Safety covers significant developments in the field of nuclear safety. The scope is limited to topics relevant to the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, safety considerations in regard to the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 127 Quality Assurance in the Construction of Nuclear Power Plants by Sidney A. Bernsen, 141 1974 ANS Topical Meeting on Fast Reactor Safety by M. H. Fontana; CONTROL AND INSTRUMENTATION: 150 GBR-4 Protection Systems: Failures and Their Consequences by Peter Burgsmüller, J. J. Dekais, Albert Krähe, Raffaello Pignatelli, and Gottfried Vieider, 162 Standby Emergency Power Systems. Part 2—The Later Plants by E. W. Hagen; PLANT SAFETY FEATURES: 180 Radiotoxic Hazard Measure for Buried Solid Radioactive Waste by J. Hamstra, 190 The Thirteenth AEC Air-Cleaning Conference by D. W. Moeller, D. W. Underhill, and M. W. First, 203 Book Review: Nuclear Criticality Safety; CONSEQUENCES OF EFFLUENT RELEASE: 204 Environmental Radiation Effects of Nuclear Facilities in New York State by M. S. Terpilak and B. L. Jorgensen, 222 Book Review: Thermal Ecology; OPERATING EXPERIENCES: 223 Set-Point Drift in Nuclear Power-Plant Safety-Related Instrumentation Adapted by the Nuclear Safety Staff, 224 Diesel-Generator Operating Experience at Nuclear Power Plants, 227 Summary of Operating U. S. Power Reactors as of Jan. 1, 1975, 232 Selected Safety-Related Occurrences Reported in November and December 1974 Compiled by William R. Casto, 235 Recent Occurrences at Nuclear Reactors and Their Causes Compiled by William R. Casto; CURRENT EVENTS: 243 General Administrative Activities Compiled by Wm. B. Cottrell, 251 Action on Power-Reactor Projects Undergoing Regulatory Review or Consideration Compiled by Wm. B. Cottrell, 266 Action on Nonreactor Projects Undergoing Regulatory Review or Consideration Compiled by Wm. B Cottrell, 268 Proposed Rule Changes as of Jan. 1, 1975; MISCELLANY: 149 Course in Italy on High-Energy Radiation Dosimetry and Protection (Announcement), 250 Course at Northwestern on Safety of Light-Water-Cooled Nuclear Power Plants (Announcement), 266 Symposium of the Combined Effects on the Environment of Radioactive, Chemical, and Thermal Releases from the Nuclear Industry (Announcement), 271 Short Course on Engineering for Extreme Winds and Tornadoes (Announcement), 272 Three 1-Week Courses at MIT on Nuclear Power-Reactor Safety (Announcement), 272 Harvard University Short Courses (Announcement).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Why Perovskite Thermal Stress is Unaffected by Thin Contact Layers

Metal halide perovskite photovoltaics have emerged as a high efficiency, low-cost alternative that can potentially rival or enhance conventional silicon technology. Despite exceptional initial power conversion efficiencies, achieving compliance with international standards and widespread adoption requires further enhancements to their operational stability. Notably, addressing mechanical strain and stress in brittle perovskites has emerged as a pivotal approach to mitigate chemical degradation and improve reliability during thermal cycling. Here, in this study, a popularized strain engineering strategy is investigated in which a high coefficient of thermal expansion (CTE) hole transport layer (i.e., PDCBT) is cast onto inorganic perovskite (CsPbI 2 Br) at 100 °C. Contrary to previously published results, the X-ray diffraction (XRD):Sin 2 ψ and substrate curvature measurement techniques show that the hole transport layer has no discernible impact on perovskite strain. The accuracy of the XRD:Sin 2 ψ method for measuring strain is highlighted in contrast to an analysis based on shifts of single XRD peaks which can be influenced by multiple artifacts. The findings in this study are in accordance with mechanics theory: thin layers are unable to induce significant strain changes in perovskite thin films as the force they apply is negligible compared to that applied by a thick and stiff substrate.

14 SOLAR ENERGY↗
DOE OSTI2026

Uncovering the linear boron environment in Na 3 BP 2 through solid-state 11 B NMR spectroscopy

Boron-based compounds exhibit a wide range of structural diversity, with potential applications spanning organic and inorganic chemistry. Herein, we focus on the characterization of the linear boron-phosphorus unit P═B═P in Na 3 BP 2 using solid-state nuclear magnetic resonance (ssNMR) spectroscopy and density functional theory (DFT) calculations. High-resolution 11 B ssNMR spectra were recorded at two fields, and key parameters such as chemical shift anisotropy (CSA), quadrupolar coupling constants (C Q ), and electric field gradient (EFG) tensors were extracted. The 11 B NMR results revealed a distinct chemical environment for the two-coordinate boron atom, with a CSA span (Ω) of 280 ppm and a C Q of 3.0 MHz. These values were further validated through periodic plane-wave DFT calculations, which showed good agreement with experimental results. The obtained spectral parameters are compared to other linear boron units, such as the BO 2 motif, providing a broader context for understanding boron coordination in inorganic compounds. This work expands the body of NMR knowledge on boron-containing materials, particularly for linear boron motifs. The findings contribute to the growing field of boron chemistry and its potential applications in advanced materials.

Porter, Andrew P. [Ames Laboratory (AMES), Ames, I↗
DOE OSTI2025

Robust Biaxial Anisotropy and Switchable Néel Vectors in LaFeO 3 Epitaxial Films

Antiferromagnets with highly stable but switchable Néel vectors are desired for antiferromagnetic spintronics with ultrafast speed and terahertz frequencies. Electrical switching of antiferromagnetic insulators has been demonstrated using binary antiferromagnets, while large families of complex antiferromagnets such as perovskites are largely unexplored. Here, we show that epitaxial LaFeO 3 thin films on SrTiO 3 (001) exhibit clear, robust biaxial anisotropy with a spin-flop field of a few tesla. Angular-dependent spin-Hall magnetoresistance (SMR) characterizations of Pt/LaFeO 3 bilayers with the current channel along SrTiO 3 [100] and [110] reveal distinct, intriguing shapes and field dependence. Simulations using a macrospin model accurately describe the main behavior and fine features of the SMR data from which key antiferromagnetic parameters are extracted. Furthermore, remanent SMR measurement confirms the high fidelity of the Néel vector along either easy axis of the biaxial anisotropy, indicating that epitaxial films of LaFeO 3 and potentially other perovskite antiferromagnets offer an attractive platform for antiferromagnetic spintronics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena↗
DOE OSTI2026

Diffraction-quality, ultraflexible protein single crystals engineered with DNA

DNA-functionalized colloidal nanoparticles assemble through flexible, nanoscale DNA hybridization interactions that limit atomic-level structural order. Here, we report a valence-centric strategy that enables DNA-bonded, protein single crystals with unconventional mechanical properties. An octameric enzyme, glutarate L-2-hydroxylase, was site- and number-selectively conjugated with eight self-complementary single-stranded DNA, yielding octavalent molecular bonds. The resulting conjugate assembled into the designed body-centered tetragonal crystals that diffracted to 1.42- to 2.61-angstrom resolution, with contacts mediated by B-form DNA helices spanning 17 to 25 angstroms. Increasing oligonucleotide length induces anisotropic lattice expansion while preserving atomic periodicity, even with partial DNA occupancy. Mechanistic studies suggest that the dynamic motion of unhybridized DNA facilitates crystallization, analogous to fluctuating electron clouds in atomic bonding. Compared with native protein crystals, DNA-hybridized crystals are 23-fold softer. These results challenge the assumption that flexibility is incompatible with structural order and establish a programmable framework for biomolecular crystallization and nanomaterials engineering with atomic precision.

Han, Zhenyu [Department of Chemistry, Northwestern↗
DOE OSTI2026

Reconstruction and Dissolution of Copper Catalysts during Electrocatalytic Nitrate Reduction

Copper-based electrocatalysts are widely explored for electrochemical nitrate remediation, yet their stability under operating conditions remains poorly understood. While nanoscale and subnanoscale Cu motifs are known to restructure during the nitrate reduction reaction (NO 3 RR), how these transformations translate into irreversible material loss remains unclear. Here, we quantify Cu dissolution during NO 3 RR as a function of catalyst architecture and electrolyte chemistry using two model systems: single-atom Cu (Cu 1 ) and Cu nanoparticles (Cu NP ). Time-resolved leaching measurements, integrated with in situ X-ray absorption spectroscopy (XAS), reveal measurable Cu loss for both catalysts during NO 3 RR. Dissolution is concentrated at the initiation of electrolysis, coinciding with rapid restructuring, and depends strongly on morphology, with Cu NP consistently exhibiting greater Cu loss than Cu 1 . In situ XAS reveals that Cu 1 forms transient metallic clusters under reduction that largely redisperse upon returning to open-circuit voltage, whereas Cu NP undergoes reduction of an oxidized surface layer accompanied by sustained Cu loss during electrolysis. Notably, the presence of nitrate significantly intensifies restructuring and Cu loss, highlighting the critical role of electrolyte composition. Furthermore, these findings establish a direct link between electrochemical restructuring and Cu dissolution, unveiling electrolyte-dependent interactions as key determinants of catalyst durability in electrochemical nitrate conversion.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Interfacial Adhesion Mechanism of Anionic Polyelectrolyte Brushes Induced by Oppositely Charged Macromolecular Counterions

Abstract Polyelectrolyte brushes are widely used as model systems for investigating electrostatic interactions at soft interfaces and to achieve exceptional lubrication properties. Previous studies have primarily focused on their behavior in the presence of multivalent counterions, which induce brush collapse, ionic crosslinking, and pronounced changes in interfacial structures. However, interactions between polyelectrolyte brushes and oppositely charged macromolecular counterions, such as polycations, remain poorly understood. Here, we prepare well-defined polystyrene sulfonate (PSS) brushes fabricated via surface-initiated grafting and employ surface forces apparatus measurements to investigate their interactions with oppositely charged polycations. In contrast to multivalent ions, polycations do not induce noticeable brush collapse, but instead generate significant adhesion between symmetric PSS brush layers. This adhesion increases with both contact time and applied load, eventually reaching a steady plateau, indicating that the interaction is governed not simply by electrostatic screening but by the gradual formation of polycation-mediated bridging under confinement. Furthermore, the introduction of monovalent Na+ ions disrupts the adhesive interaction even at very low concentrations, suggesting that the bridging function of the adsorbed polycation is highly sensitive to competitive ionic screening. In comparison, measurements with trivalent counterions reveal the expected brush collapse behavior but minimal dependence of adhesion on contact time, highlighting a clear mechanistic distinction from the polymeric counterion case. Collectively, these results demonstrate that molecular size, configurational restriction, and confinement-induced rearrangement, rather than charge valency alone, govern the interaction behavior of macromolecular counterions at brush interfaces. This work provides new insight into the molecular origins of adhesion and the regulation of interfacial interactions in charged polymer brush systems.

Park, Jinwoo [Argonne National Laboratory , , , ,;↗
DOE OSTI2025

Machine Learning for Predicting Multipactor Susceptibility in Planar RF Structures

Multipactor discharge is a persistent challenge in high-power microwave (HPM) and accelerator systems, where secondary electron avalanches can cause heating, vacuum degradation, and failure. This work presents the first supervised machine learning (ML) framework for multipactor prediction, trained on high-fidelity 3D Particle-in-Cell (PIC) simulation data in planar geometries. The model maps operational, geometric, and material-dependent secondary electron yield (SEY) parameters to the time-averaged electron growth rate, enabling rapid reconstruction of susceptibility charts. Among the models evaluated, tree-based ensemble methods such as Random Forest and Extra Trees demonstrate superior generalization to unseen materials compared to neural networks such as multilayer perceptron (MLP). Performance metrics, including Intersection over Union (IoU), Structural Similarity Index Measure (SSIM), and Pearson correlation, show close agreement with simulation benchmarks. Principal Component Analysis attributes generalization limits to material feature-space disjointedness.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

AUTOIGNITION DELAY TIMES FOR REFORMATE GAS MIXTURES FROM METHANE GAS ENGINES

Methane slip is a prominent issue in natural gas reciprocating engines that are used in transportation and marine applications. The incomplete combustion that results in methane slip can be resolved with the introduction of hydrogen within the combustion mixture to improve methane oxidation and further enable combustion within the engine crevices where methane has previously remained unreacted. Steam methane reforming (SMR) is a common method used to produce hydrogen and can be used to design an onboard device to reduce methane slip from reciprocating engines. The development of this reformer device requires the validation of high-fidelity chemical kinetic models at the low temperatures of the crevice volumes of these engines. In this work, auto-ignition data is obtained using a shock tube at lean (φ—0.714 or λ—1.4) and stoichiometric (φ, λ = 1) equivalence ratios spanning a temperature range of 1042–1234 K at the 80-bar operating pressure of the test engine. Blends of methane, hydrogen, and reformate products from the SMR reaction are shock-heated in synthetic air, with the ignition delay time measured using an OH* chemiluminescence detector at 310 nm and a CH* detector at 430 nm. The experimental results are compared to several state-of-the-art chemical kinetic mechanisms from the literature. In general, most of the mechanisms show very good agreement with experiments at higher temperatures, with simulation results showing little deviation from experiments at lower temperatures. A sensitivity analysis was conducted, and the results reveal that the reaction H2 + CH3O2 = H + CH3O2H has a very significant role in determining low-temperature ignition delay times (IDTs) of SMR mixtures. These findings provide valuable insights into the chemical kinetics governing methane reformate combustion and contribute to the optimization of onboard reformer designs aimed at mitigating methane slip in natural gas-fueled engines.

Fraze, Matthew↗
DOE OSTI2025

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Abstract Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon–photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh–Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.

Optics↗
DOE OSTI2025

Nuclear quantum effects in molecular liquids across chemical space

Abstract Nuclear quantum effects (NQEs) influence many physical and chemical phenomena, particularly those involving light atoms or occurring at low temperatures. However, their impact has been carefully quantified in few systems-like water-and is rarely considered more broadly. Here we use path-integral molecular dynamics to systematically investigate NQEs on thermophysical properties of 92 organic liquids at ambient conditions. Depending on chemical constitution, we find substantial impact across thermal expansivity, compressibility, dielectric constant, enthalpy of vaporization, and notably molar volume, which shows consistent, positive quantum-classical differences up to 5%; similar, less pronounced trends manifest as isotope effects from deuteration. Using data-driven analysis, we identify three features-molar mass, classical hydrogen density, and classical thermal expansivity-that accurately predict NQEs and facilitate understanding of how characteristics like branching and heteroatom content influence behavior. This work highlights the broad relevance of NQEs in molecular liquids, while also providing a conceptual and practical framework to anticipate their impact.

Science & Technology - Other Topics↗
DOE OSTI2024

Accessing bands with extended quantum metric in kagome Cs 2 Ni 3 S 4 through soft chemical processing

Flat bands that do not merely arise from weak interactions can produce exotic physical properties, such as superconductivity or correlated many-body effects. The quantum metric can differentiate whether flat bands will result in correlated physics or are merely dangling bonds. A potential avenue for achieving correlated flat bands involves leveraging geometrical constraints within specific lattice structures, such as the kagome lattice; however, materials are often more complex. In these cases, quantum geometry becomes a powerful indicator of the nature of bands with small dispersions. We present a simple, soft-chemical processing route to access a flat band with an extended quantum metric below the Fermi level. By oxidizing Ni-kagome material Cs 2 Ni 3 S 4 to CsNi 3 S 4 , we see a two orders of magnitude drop in the room temperature resistance. However, CsNi 3 S 4 is still insulating, with no evidence of a phase transition. Using experimental data, density functional theory calculations, and symmetry analysis, our results suggest the emergence of a correlated insulating state of unknown origin.

Science & Technology - Other Topics↗
DOE OSTI2023

Fabrication of Large-Area Metal-on-Carbon Catalytic Condensers for Programmable Catalysis

Catalytic condensers stabilize charge on either side of a high-k dielectric film to modulate the electronic states of a catalytic layer for the electronic control of surface reactions. Here, carbon sputtering provided for fast, large-scale fabrication of metal–carbon catalytic condensers required for industrial application. Carbon films were sputtered on HfO 2 dielectric/p-type Si with different thicknesses (1, 3, 6, and 10 nm), and the enhancement of conductance and capacitance of carbon films was observed upon increasing the carbon thickness following thermal treatment at 400 °C. After Pt deposition on the carbon films, the Pt catalytic condenser exhibited a high capacitance of ∼210 nF/cm 2 that was maintained at a frequency ∼1000 Hz, satisfying the requirement for a dynamic catalyst to implement catalytic resonance. Temperature-programmed desorption of carbon monoxide yielded CO desorption peaks that shifted in temperature with the varying potential applied to the condenser (−6 or +6 V), indicating a shift in the binding energy of carbon monoxide on the Pt condenser surface. A substantial increase in capacitance (∼2000 nF/cm 2 ) of the Pt-on-carbon devices was observed at elevated temperatures of 400 °C that can modulate ∼10% of charge per metal atom when 10 V potential was applied. A large catalytic condenser of 42 cm 2 area Pt/C/HfO 2 /Si exhibited a high capacitance of 9393 nF with a low leakage current/capacitive current ratio (<0.1), demonstrating the practicality and versatility of the facile, large-scale fabrication method for metal–carbon catalytic condensers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗