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At least 325 records · Page 18

Validation of Artemis I Aerothermal Design Models Using Developmental Flight Instrumentation

The inaugural flight of the Space Launch System (SLS) Block 1 launch vehicle, Artemis I, occurred on November 16, 2022, and featured a full suite of Developmental Flight Instrumentation (DFI) that provided aerothermodynamic measurements to assess thermal design and substantiate aerothermodynamic models. The Block 1 launch vehicle aerothermal instrumentation consisted of approximately 277 aerothermal gauges mounted throughout the Orion Multi-Purpose Crew Vehicle (MPCV), Integrated Spacecraft and Payload Element (ISPE), Core Stage (CS) and Solid Rocket Boosters (SRB) and an additional 179 thermal gauges on the Orion Crew Module (CM). Instrumentation included calorimeters, radiometers, pressure transducers, gas temperature probes, and thermocouples. Data was collected from lift-off through CS Main Engine Cut-Off (MECO). The flight data was invaluable for determining aerothermal model performance and developing flight-derived aerothermal environments for flight reconstruction thermal analysis and future SLS aerothermal models. The data offered critical insights into the aerothermodynamic conditions experienced during the launch and ascent of the SLS vehicle. This study compares the flight derived environments to pre-existing design models. The aerothermal models were constructed using MINIVER, the aerothermal engineering code which predicts aerodynamic heating and acts as an integration tool for incorporating databases from computational fluid dynamics (CFD) simulations and wind tunnel test data. The comparisons reveal the fidelity of the design models, highlighting areas where the design models accurately predicted flight conditions and instances where deviations were observed. Preliminary results suggest that while the design models largely aligned with the observed flight data, there were unique observations that reflected needed areas of model refinement. Aerothermal flight data from Artemis I for the SLS Block 1 vehicle will be further utilized to enhance the accuracy of Block 1B and Block 2 aerothermal models, ensuring improved safety and performance for subsequent Artemis missions.

aerothermodynamics↗

Validation of Artemis I Aerothermal Design Models Using Developmental Flight Instrumentation

The inaugural flight of the Space Launch System (SLS) Block 1 launch vehicle, Artemis I, occurred on November 16, 2022, and featured a full suite of Developmental Flight Instrumentation (DFI) that provided aerothermodynamic measurements to assess thermal design and substantiate aerothermodynamic models. The Block 1 launch vehicle aerothermal instrumentation consisted of approximately 277 aerothermal gauges mounted throughout the Orion Multi-Purpose Crew Vehicle (MPCV), Integrated Spacecraft and Payload Element (ISPE), Core Stage (CS) and Solid Rocket Boosters (SRB) and an additional 179 thermal gauges on the Orion Crew Module (CM). Instrumentation included calorimeters, radiometers, pressure transducers, gas temperature probes, and thermocouples. Data was collected from lift-off through CS Main Engine Cut-Off (MECO). The flight data was invaluable for determining aerothermal model performance and developing flight-derived aerothermal environments for flight reconstruction thermal analysis and future SLS aerothermal models. The data offered critical insights into the aerothermodynamic conditions experienced during the launch and ascent of the SLS vehicle. This study compares the flight derived environments to pre-existing design models. The aerothermal models were constructed using MINIVER, the aerothermal engineering code which predicts aerodynamic heating and acts as an integration tool for incorporating databases from computational fluid dynamics (CFD) simulations and wind tunnel test data. The comparisons reveal the fidelity of the design models, highlighting areas where the design models accurately predicted flight conditions and instances where deviations were observed. Preliminary results suggest that while the design models largely aligned with the observed flight data, there were unique observations that reflected needed areas of model refinement. Aerothermal flight data from Artemis I for the SLS Block 1 vehicle will be further utilized to enhance the accuracy of Block 1B and Block 2 aerothermal models, ensuring improved safety and performance for subsequent Artemis missions.

aerothermodynamics↗

Quench process modeling & simulation in the heat-treatment of critical aerospace components

To manufacture light-weight, advanced metal alloy components for gas turbine engines, quench heat-treatment processes are typically used. By quenching the component from elevated temperatures, the alloy sometimes undergoes a solid-state phase transformation which produces special microstructures with the required, enhanced mechanical properties. However, the quenching can also lead to cracks forming in the component. Addressing the quench cracking problems adds a significant burden to the cost, schedule, and energy demand of manufacture. Currently, optimizing the quench process to mitigate or avoid the cracking is performed largely by trial-and-error, relying heavily on costly experimental (thermocouple)trials to understand the local thermal gradients which cause the cracks to form. In this first part (Phase 1) of the work, high-performance computing is employed to establish the ability of modern CFD (computational fluid dynamics) to alleviate or wholly replace the experimental quenching trials by virtual testing. A Baseline CFD model is defined and its accuracy established to be comparable to(and which usually exceeds) the accuracy of existing HTC (heat-transfer coefficient) based simulation methods of quenching. As a first-principles based approach, “calibration” of the Baseline CFD model is independent of the quench process itself, but instead relies on the accuracy of the underlying (modeled),generic two-phase fluid processes which cannot be currently resolved by CFD for large, industrial-scale cases. A novel, high-fidelity DNS capability has been developed and verified to examine and further improve upon the mean-field closure submodels on which the Baseline CFD approach is based.1

99 GENERAL AND MISCELLANEOUS↗

Space station molecular sieve development

An essential function of a space environmental control system is the removal of carbon dioxide (CO2) from the atmosphere to control the partial pressure of this gas at levels lower than 3 mm Hg. The use of regenerable solid adsorbents for this purpose was demonstrated effectively during the Skylab mission. Earlier sorbent systems used zeolite molecular sieves. The carbon molecular sieve is a hydrophobic adsorbent with excellent potential for space station application. Although carbon molecular sieves were synthesized and investigated, these sieves were designed to simulate the sieving properties of 5A zeolite and for O2/N2 separation. This program was designed to develop hydrophobic carbon molecular sieves for CO2 removal from a space station crew environment. It is a first phase effort involved in sorbent material development and in demonstrating the utility of such a material for CO2 removal on space stations. The sieve must incorporate the following requirements: it must be hydrophobic; it must have high dynamic capacity for carbon dioxide at the low partial pressure of the space station atmosphere; and it must be chemiclly stable and will not generate contaminants.

Chang, C.↗

Quantitative Species Measurements in Microgravity Combustion Flames using Near-Infrared Diode Lasers

Understanding the physical phenomena controlling the ignition and spread of flames in microgravity has importance for space safety as well as for characterizing dynamical and chemical combustion processes which are normally masked by buoyancy and other gravity-related effects. Unfortunately, combustion is highly complicated by fluid mechanical and chemical kinetic processes, requiring the use of numerical modeling to compare with carefully designed experiments. More sophisticated diagnostic methods are needed to provide the kind of quantitative data necessary to characterize the properties of microgravity combustion as well as provide accurate feedback to improve the predictive capabilities of the models. Diode lasers are a natural choice for use under the severe conditions of low gravity experiments. Reliable, simple solid state operation at low power satisfies the operational restrictions imposed by drop towers, aircraft and space-based studies. Modulation wavelength absorption spectroscopy (WMS) provides a means to make highly sensitive and quantitative measurements of local gas concentration and, in certain cases, temperature. With near-infrared diode lasers, detection of virtually all major combustion species with extremely rapid response time is possible in an inexpensive package. Advancements in near-infrared diode laser fabrication technology and concurrent development of optical fibers for these lasers led to their use in drop towers. Since near-infrared absorption line strengths for overtone and combination vibrational transitions are weaker than the mid-infrared fundamental bands, WMS techniques are applied to increase detection sensitivity and allow measurement of the major combustion gases. In the first microgravity species measurement, Silver et al. mounted a fiber-coupled laser at the top of the NASA 2.2-sec drop tower and piped the light through a single-mode fiber to the drop rig. A fiber splitter divided the light into eight channels that directed the laser beam across a methane or propane diffusion jet flame. The light beams were recaptured by a set of gradient index lenses, coupled back into separate fiber optic lines, and transmitted back to detectors and electronics in the instrument package. In these experiments a 6-mm od fiber cable (containing the nine optical fibers) fell with the drop rig. Using separate detection and demodulation channels, spatial and temporal (up to 20 Hz) maps of water vapor and methane concentrations were obtained at differing heights in the flames. While this apparatus was useful from a demonstration standpoint, several drawbacks needed attention before useful scientific measurements could be obtained. First, eight lines of sight are somewhat insufficient for detailing the spatial profiles of the gas. Second, multiple detection channels operating in parallel are both expensive and present a challenge for accurate calibration. As a result, a newer scanning system was developed in our first contract under this program. The primary characteristic of this system is that it contains a single detection channel and achieves "continuous" spatial resolution by scanning the laser beam across the flame region, then directing this beam onto a single detector. Thus spatial measurements are converted to a temporal series of data. The true spatial resolution is limited only by the beam diameter and width of the sweep. In these experiments the beam is focused to about 1-mm diameter and scans across a region up to 4-cm wide.

Silver, Joel A.↗

Quench process modeling & simulation in the heat-treatment of critical aerospace components

To manufacture light-weight, advanced metal alloy components for gas turbine engines, quench heat-treatment processes are typically used. By quenching the component from elevated tempera-tures, the alloy sometimes undergoes a solid-state phase transformation which produces special microstructures with the required, enhanced mechanical properties. However, the quenching can also lead to cracks forming in the component. Addressing the quench cracking problems adds a significant burden to the cost, schedule, and energy demand of manufacture. Currently, optimizing the quench process to mitigate or avoid the cracking is performed largely by trial-and-error, relying heavily on costly experimental (thermocouple) trials to understand the local thermal gradients which cause the cracks to form. In this first part (Phase 1) of the work, high-performance computing is employed to establish the ability of modern CFD (computational fluid dynamics) to alleviate or wholly replace the experimental quenching trials by virtual testing. A baseline CFD model is defined and its accuracy established to be comparable to (and which usually exceeds) the accuracy of existing HTC (heat-transfer correlation) based simulation methods of quenching. As a first-principles based approach, “calibration” of the Baseline CFD model is independent of the quench process itself, but instead relies on the accuracy of the underlying (modeled), generic two-phase fluid processes which cannot be currently resolved by CFD for large, industrial-scale cases. A novel, high-fidelity DNS capability has been developed and verified to examine and further improve upon the mean-field closure submodels on which the Baseline CFD approach is based.

36 MATERIALS SCIENCE↗

Dynamical defects in a two-dimensional Wigner crystal: Self-doping and kinetic magnetism

We study the quantum dynamics of interstitials and vacancies in a two-dimensional Wigner crystal (WC) using a semi-classical instanton method that is asymptotically exact at low density, i.e., in the r s → ∞ limit. Here, the dynamics of these point defects mediates magnetism with much higher energy scales than the exchange energies of the pure WC. Via exact diagonalization of the derived effective Hamiltonians in the single-defect sectors, we find the dynamical corrections to the defect energies. The resulting expression for the interstitial (vacancy) energy extrapolates to 0 at r s = r mit ≈ 70 (r s ≈ 30), suggestive of a self-doping instability to a partially melted WC for some range of r s below r mit . We thus propose a “metallic electron crystal” phase of the two-dimensional electron gas at intermediate densities between a low density insulating WC and a high density Fermi fluid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Lunar surface dynamics: Some general conclusions and new results from Apollo 16 and 17

Exposure ages of Apollo 17 rocks as measured by tracks and the Kr-Kr rare gas method are reported. Concordant ages of 22 - or + 1 million year (my) are obtained for the station 6 boulder sample 76315. This value is interpreted as the time when the station 6 boulder was emplaced in its present position. Reasonable agreement is also obtained by the two methods for another station 6 boulder, sample 76015. Discordant ages (respectively 5 and 28 my by the track and rare gas methods) are obtained for the station 7 boulder sample, 77135, indicating that the boulder was emplaced at least 5 my ago. The 72 my exposure age of 75035, in general agreement with previous measurements of approximately 85 my for another Camelot boulder, may well date the formation of Camelot. Rock 76015 was split and one surface exposed to the sky through a very small solid angle.

Crozaz, G.↗

Sub‐5 Ångstrom Porosity Tuning in Calixarene‐Derived Porous Liquids via Supramolecular Complexation Construction

Abstract Sub‐Ångstrom‐level porosity engineering, which is appealing in gas separations, has been demonstrated in solid carbon, polymer, and framework materials but rarely achieved in the liquid phase. In this work, a gas molecular sieving effect in the liquid phase at sub‐5 Ångstrom scale is created via sophisticated porosity tuning in calixarene‐derived porous liquids (PLs). Type II PLs are constructed via supramolecular complexation between the sodium salts of calixarene derivatives and crown ether solvents. The chemical structure variation and assembly behavior of the porous host upon PL construction are monitored by spectroscopy‐, X‐ray‐, and neutron‐scattering techniques. The presence of permanent porosity in calixarene‐derived PLs is verified by pressure swing gas uptake, altered CO 2 physisorption behavior, and molecular simulations. Sub‐5 Ångstrom porosity tuning within the PL phase is achieved by introducing bulky substituted groups on the benzene ring of the calixarene host, which then greatly affects the dynamic motion and transport behavior of CO 2 molecules and the Xe uptake performance. The approach being demonstrated in this work represents a promising pathway to tune and leverage the porosity effect for enhanced gas uptake capacity and selectivity in liquid sorbents.

Li, Errui [Department of Chemistry University of T↗

Computational model development and validation of fuel dispersal phenomena

As the US nuclear industry is renewing efforts to extend the rod average burnup limits in existing pressurized water reactors, it becomes imperative to investigate the safety implications associated with high burnup fuel fragmentation and the potential dispersal of fragmented fuel into the reactor coolant system. Additionally, as there is a growing interest in transitioning to new nuclear fuel designs to accommodate higher fuel burnup levels, it becomes essential to conduct studies on fuel behavior during design basis accident scenarios, particularly during a postulated loss-of-coolant accident, in order to ensure the safe operation of light-water reactors. The present study develops a computational model to simulate the complex three-phase flow of the fuel dispersal phenomena that occur following a breach in the cladding, when the stream of solid fuel particles and carrier fission gas stream may interact with the surrounding liquid medium. Furthermore, the proposed framework considers the solid phase as discrete Lagrangian particles while the interpenetrating gas–liquid continuum is modeled using a Eulerian framework. The developed simulation framework is validated with experimental results performed in a separate-effect test facility by comparing predicted particle settlement locations with the experimental observations reported in the literature. Key highlights of this study include the interpretation of the high-pressure boundary conditions and the three-phase flow coupling strategy. Also discussed are the gas–liquid hydrodynamics and the behavior of particles as they are transported through the gas and liquid phases.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Theory of Pulsating Flow in Conical Nozzles

A knowledge of the dynamic characteristics of nozzles and orifices is important in many control and stability analyses of engineering devices. It is usual to assume that the instantaneous flow-rate, for a given set of inlet conditions and outlet pressure, is the same as the nontransient value for the same operating conditions. Recently, in connection with the stability analysis of an externally pressurized thrust bearing, the validity of this assumption was questioned. The analysis presented in this paper was undertaken to provide an answer. The present analysis applies to any fluid, liquid, or gas flowing into a simple conical nozzle. The amplitude and phase of the mass-flux response to a sinusoidally time-varying pressure fluctuation at the nozzle exit are determined. An approximate formula is given for these quantities in terms of the nozzle throat area, the solid angle subtended by the cone, the velocity of the fluid at the nozzle throat, the acoustic velocity at the throat, and the frequency of the pressure fluctuation.

Elrod, H. G., Jr.↗

A machine learning-based interaction force model for non-spherical and irregular particles in low Reynolds number incompressible flows

In this study, interaction force of non-spherical particles in low Reynolds number gas-solid flow is investigated by neural network approaches. An artificial neural network (ANN) model is developed to correlate the non-spherical particle shape and the flow conditions with the interaction force. To define the particle shape, spherical harmonic expansion is applied. Furthermore, variational autoencoder model is then used to extract latent geometric features. The latent vector is utilized as an input with the Reynolds number for the ANN. The interaction force data, which is used as output data of the ANN, is obtained by particle resolved direct numerical simulation for 5200 non-spherical particles. The proposed model enables unsupervised extraction for non-spherical particle shapes and accurate predictions on the interaction force without heavy computation. This study provides the model that can explain complicated shapes of particles and be applied to a large scale, computational fluid dynamics simulation.

01 COAL, LIGNITE, AND PEAT↗

Cold Flow Determination of the Internal Flow Environment Around the Submerged TVC Nozzle for the Space Shuttle SRM

A series of subscale cold flow tests was performed to quantify the gas flow characteristics at the aft end of the Space Shuttle Solid Rocket Motor. This information was used to support the analyses of the redesigned nozzle/case joint. A portion of the thermal loads at the joint are due to the circumferential velocities and pressure gradients caused primarily by the gimbaling of the submerged nose TVC nozzle. When the nozzle centerline is vectored with respect to the motor centerline, asymmetries are set up in the flow field under the submerged nozzle and immediately adjacent to the nozzle/case joint. Specific program objectives included: determination of the effects of nozzle gimbal angle and propellant geometry on the circumferential flow field; measurement of the static pressure and gas velocities in the vicinity of the nozzle/case joint; use of scaling laws to apply the subscale cold flow data to the full scale SRM; and generation of data for use in validation of 3-D computational fluid dynamic, CFD, models of the SRM flow field. These tests were conducted in the NASA Marshall Space Flight Center Airflow Facility with a 7.5 percent scale model of the aft segment of the SRM. Static and dynamic pressures were measured in the model to quantify the flow field. Oil flow data was also acquired to obtain qualitative visual descriptions of the flow field. Nozzle gimbal angles of 0, 3.5, and 7 deg were used with propellant grain configurations corresponding to motor burn times of 0, 9, 19, and 114 seconds. This experimental program was successful in generating velocity and pressure gradient data for the flow field around the submerged nose nozzle of the Space Shuttle SRM at various burn times and gimbal angles. The nature of the flow field adjacent to the nozzle/case joint was determined with oil droplet streaks, and the velocity and pressure gradients were quantified with pitot probes and wall static pressure measurements. The data was applied to the full scale SRM thru a scaling analysis and the results compared well with the 3-D computational fluid dynamics computer model.

Whitesides, R. H.↗

Sub-5 Ångstrom Porosity Tuning in Calixarene-Derived Porous Liquids via Supramolecular Complexation Construction

Sub-Ångstrom-level porosity engineering, which is appealing in gas separations, has been demonstrated in solid carbon, polymer, and framework materials but rarely achieved in the liquid phase. In this work, a gas molecular sieving effect in the liquid phase at sub-5 Ångstrom scale is created via sophisticated porosity tuning in calixarene-derived porous liquids (PLs). Type II PLs are constructed via supramolecular complexation between the sodium salts of calixarene derivatives and crown ether solvents. The chemical structure variation and assembly behavior of the porous host upon PL construction are monitored by spectroscopy-, X-ray-, and neutron-scattering techniques. The presence of permanent porosity in calixarene-derived PLs is verified by pressure swing gas uptake, altered CO 2 physisorption behavior, and molecular simulations. Sub-5 Ångstrom porosity tuning within the PL phase is achieved by introducing bulky substituted groups on the benzene ring of the calixarene host, which then greatly affects the dynamic motion and transport behavior of CO 2 molecules and the Xe uptake performance. Further, the approach being demonstrated in this work represents a promising pathway to tune and leverage the porosity effect for enhanced gas uptake capacity and selectivity in liquid sorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Late-stage planetesimals: How big?

Numerical simulation of the early stages of planet growth show that a few bodies nearly 1000 km in diameter may have formed within approx. 100,000 yr after solid material grew into km scale planetesimals by gravitational instability. Even after such large bodies formed, the bulk of the mass of the future terrestrial planet zone resided in small bodies. Subsequent evolution is difficult to model because it requires simultaneous consideration of continuum (multitudinous small bodies) and discrete (a few large bodies) evolution. Some relevant issues include definition of accretional feeding zones, evaluation of the range of gravitational influence, viscous transport and diffusion, orbital commensurabilities, role of gas, etc. The first large bodies may have been (1) the embryos of the final planets, which grew by accreting tiny planetesimals, or (2) merely the first of many 1000+ km bodies, which grew independently and later collided to form the planets. Models of late stage accretion that assume all bodies to be initially nearly Moon sized provide insight into relevant collisional and dynamical processes. The chief point in this research is that the correct size distribution during the later stages of planet growth remains unknown.

Greenberg, R.↗

Computational Fluid Dynamics Analysis of a 12 MW Circulating Fluidized Bed Rise

A three-dimensional (3D) two fluid model (TFM) model of the 12 MW circulating fluidized bed (CFB) riser at Chalmers University was developed using the open-source Multiphase Flow with Interphase eXchanges (MFiX) Software Suite. The hydrodynamic behavior of the riser was validated by comparing axial pressure profiles from experimental measurements with the results from the simulations. Under some of the operating conditions where there was no external circulation of solids, the pressure profiles from the simulation matched well with the experimental measurements. For the cases where there was external circulation of solids, the pressure profiles with the monodisperse solid phase modeling underpredicted the solids concentration in the freeboard region. With the inclusion of polydispersity in the model, the predicted pressure profiles agreed well with the experimental measurements. A two-dimensional (2D) model of the riser was used to perform simulations of coal combustion. The predicted flue gas outlet compositions of oxygen and carbon dioxide compared reasonably to experiments. The experiments also reported some concentration of carbon monoxide which was overpredicted in the simulations. Additional experimental data such as axial oxygen concentration profile and pressure profiles were also compared with the experiment. It was observed that the oxygen concentration in the bottom bed from the simulations was higher than in the experiments, which suggested that most of the oxidation reactions occurred in the bottom bed. The concentration of volatiles and char in the simulations was lower in the bottom bed than in the experiments, which suggest that there is not sufficient penetration of the solid phase species into the bed.

20 FOSSIL-FUELED POWER PLANTS↗

Operando XPS for Plasma Process Monitoring: A Case Study on the Hydrogenation of Copper Oxide Confined under h-BN

Here, we demonstrate that ambient pressure x-ray photoelectron spectroscopy (APXPS) can be used for in situ studies of dynamic changes in surface chemistry in a plasma environment. This opens a new and vast application space for XPS and greatly complements modern spectroscopy techniques to probe plasma-solid/liquid interactions relevant to process monitoring in the semiconductor industry, bio-medical plasma applications and plasma remediation technologies. Hexagonal boron nitride (h-BN) grown on Cu was used in this study as a well-defined model system for plasma process monitoring and because of its unique chemical, optical and electrical properties that make it a prospective material for advanced electronics. To better understand the stability and surface chemistry of h-BN during plasma assisted processing, we track in real time the plasma-induced chemical state changes of B, N and the underlying Cu substrate using APXPS equipped with an AC discharge plasma source operating at 13 Pa. Residual gas analysis (RGA) mass-spectra were concurrently collected during plasma-XPS to track reaction products formed during plasma exposure. A clear reduction of Cu x O is seen, while an h-BN layer remains intact, suggesting hydrogen radical (H • ) species can attack the exposed and h-BN covered Cu oxide patches and partially reduce the underlying substrate without significantly damaging the overlaying h-BN, which is of practical importance for development of h-BN encapsulated devices and interfaces. In addition to demonstration of plasma-XPS capabilities we discuss the observed challenges (e.g., parasitic plasma-chamber walls reactions and charging effects) and propose potential solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Critical role of solvent-modulated hydrogen-binding strength in the catalytic hydrogenation of benzaldehyde on palladium

Protic and non-protic solvents influence the rate of benzaldehyde hydrogenation on Pd by one order of magnitude in the following sequence of increasing reactivity, dioxane < tetrahydrofuran < water < methanol. Despite these differences, the reaction pathway does not change; the majority of turnovers occurs via a Langmuir-Hinshelwood mechanism by stepwise addition of sorbed H to sorbed benzaldehyde, first to the carbonyl O and then to the C atom of the formyl group, forming benzyl alcohol. An analysis of the solvation energies shows that both ground and transition states are destabilized by the solvents compared to the same reaction at the gas-solid interface. The destabilization extent of the reacting organic substrates in both states are similar and, therefore, compensate each other, making the net kinetic effects inconsequential. In consequence, the marked reactivity differences arise solely from the differences in the surface stabilization of adsorbed hydrogen adatoms moderated by the four solvents-more weakly bound hydrogen adatoms, because of their solvation by solvent, exhibit higher rates of their hydrogenation reaction in kinetically relevant attack on the C atom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗