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At least 307 records · Page 17

Toughening of Boron Carbide Composites by Hierarchical Microstructuring

Due to a unique combination of properties including high hardness, low density, chemical and thermal stability, semi-conductivity, and high neutron absorption, boron carbide (B4C) is a potential candidate for various applications involving extreme environment. However, B4C’s current application is limited because of its low fracture toughness. In this study, a hierarchical microstructure design with features including TiB2 grains and graphite platelets was used to toughen B4C by simultaneously utilizing multiple toughening mechanisms including crack deflection, bridging, and micro-crack toughening. Using field-assisted sintering technology (FAST), B4C composites with dense and hierarchical microstructure were fabricated. Previously, the fracture toughness of fabricated B4C composites was measured at micro-scale using micro-indentation to have up to 56% improvement. In this work, the B4C composites’ fracture toughness was characterized at macro-scale using four-point bending methods and compared with previous results obtained at micro-scale. Micromechanics modeling of fracture behaviors for B4C-TiB2 composites was also performed to evaluate the contributions from experimentally observed toughening mechanisms. From four-point bending tests, B4C composites reinforced with both TiB2 grains (~15 vol%) and graphite platelets (~8.7 vol%) exhibited the highest fracture toughness enhancement from 2.38 to 3.65 MPa∙m^(1/2). The measured values were lower than those obtained using micro-indentation but maintained the general trends. The discrepancy between the indentation and four-point bending test results originated from the complex deformation behaviors triggered by the high contact load during indentation tests. Through micromechanics modeling, introduced thermal residual stress due to thermal expansion mismatch between B4C and TiB2, and weak interphases at B4C-TiB2 boundaries were identified as the main causes for experimentally observed toughness enhancement. These results proved the effectiveness of hierarchical microstructure designs for B4C toughening and can provide reference for the future design of B4C composites with optimized microstructures for further fracture toughness enhancement.

composites↗

DECOVALEX-2023: Task G, SAFENET Final Report

DECOVALEX Task G deals with fracture mechanics at several scales using a combined approach of experimental work, related model development, benchmarking and experimental analysis. Fig. 0.1 provides a graphical abstract for Task G. The experimental basis for the related mechanical (M), hydro-mechanical (HM), and thermo-mechanical (TM) processes comes from the rock mechanics laboratories of Universities of Freiberg (TUBAF) and Edinburgh, as well as the Korea Institute of Civil Engineering and Building Technology (KICT). The experimental work in the rock laboratories is closely linked to the underground research laboratories (URLs) Reiche Zeche (Germany), KURT (Korea), and Mont Terri (Switzerland). The scientific key questions are related to fracture permeability evolution under THM conditions, anisotropy effects on fracturing processes, and thermal fracture slip, which are being addressed in specific steps of the task. A large variety of numerical methods have been developed and applied for experimental analysis, ranging from continuum to discontinuum approaches. A detailed comparison of mechanical and hydro-mechanical processes is given in the section 3 via the benchmarking exercises. As a result of DECOVALEX-2023 Task G we further improved our understanding and predictability of fracturing processes under THM conditions. This was based on robust numerical simulation methods and in-depth experimental analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Experimental gastric ulcers induced by immobilization and electric shock of rats and their pharmacotherapy

The mechanism of development of experimental gastric ulcers, induced in rats by combined immobilization and electric shock, was analyzed pharmacologically with peripheral neurotropic agents. It is concluded that: (1) The most marked preventive effect in the development of the experimentally induced gastric ulcers was displayed by agents capable of blocking the ascending activation system of the reticular formation. (2) Sympathetic fibers, which disrupt the trophism of the gastric wall, form the efferent portion of the reflex arc. (3) Gastric secretion does not appear to be the primary cause of ulceration.

Zabrodin, O. N.↗

A comparative study of the effectiveness of empirical potentials for molecular dynamics simulations of borosilicate glasses

Despite their practical importance, atomistic modeling of B 2 O 3 containing glasses have been challenging due to the lack of reliable empirical potentials. Fortunately, a few recent developments have shown promises to simulate these glasses where the boron coordination has complex and non-linear dependence on glass composition. This work aims to provide an evaluation of the effectiveness of three recently developed potentials by a systematic study of a series (~20) of sodium borosilicate glasses with constant K (ratio of [SiO 2 ]/[B 2 O 3 ]) =2 and varying R (ratio of [Na 2 O]/[B 2 O 3 ] ranging from 0.1 to 4) values and several sodium boroaluminosilicate glasses. A comparative assessment was established on the basis of the short- and medium-range structure features, such as boron N 4 values, total correlation functions, bond angle distribution, oxygen speciation, and mechanical properties using experimental or well-established models as criteria. Furthermore, this work provides insights on the choices of empirical potentials for MD simulations of borosilicate glasses and gives directions of future potential development and refining.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Modeling the Environment-Dependent Kinetics of Oxygen Reduction Reaction – a Continuum Model for Electric Double Layer

Here, for proton-exchange-membrane fuel cells (PEMFCs) to achieve broad commercialization, improved energy-conversion efficiency with minimal Pt-based electrocatalyst is required. Because the sluggish rate of oxygen reduction reaction (ORR) limits the efficiency of PEMFCs, the efficiency improvement requires a better understanding of ORR kinetics and mechanism to design better catalyst. To understand the ORR mechanism, theoretical and experimental analyses have been conducted. While previous studies reasonably explained the catalyst-dependent activity on single crystal catalysts in 0.1 M perchloric acid solution, the explicit effect of electrolyte and related microenvironments is not thoroughly understood. The change in the electrolyte alters the electric-double-layer (EDL) structure and thus the local microenvironment at the electrode/electrolyte interface. Thus, the structure of the EDL should be carefully analyzed to uncover the electrolyte-dependent reaction kinetics. In this talk, we propose a multiscale continuum model to predict the EDL structure and examine the effect of perchloric acid concentration on ORR activity on Pt (111). The model includes Density Potential Functional Theory (DPFT) for electron density and Modified Poisson Boltzmann equation for species’ density and electric potential. Also, the interaction between adsorbents and electric field is taken into account by minimizing the grand potential. After model validation with experimentally measured double-layer capacity data as a function of applied potential and concentration, the effect of the perchloric acid concentration (0.02 M – 0.2 M) on ORR activity is analyzed and discussed. It is shown that the model reproduces the specific activity obtained in the experiments when assuming the oxygen adsorption is limiting the rate, which can be attributed to the large energetic barrier for solvent reorganization. Then, extension of the model to PEMFC ionomer electrolytes will be introduced. Overall, the model framework and findings provide insights into the ORR mechanism and guidance on how to tailor catalyst materials for increased PEMFC performance.

30 DIRECT ENERGY CONVERSION↗

Hypersonic Boundary-Layer Transition on Blunted Cones at Angle of Attack

Experimental studies of cones at several high-speed facilities have demonstrated that, for small nosetip bluntness, transition onset over a circular cone moves upstream along the leeward side and downstream along the windward side, but this trend may be reversed at large bluntness values, where transition onset moves downstream along the leeward side and upstream along the windward side. A theoretical and numerical investigation is performed to characterize the effects of nose bluntness on disturbance amplification over the circular cone for several angles of attack, with the goal of understanding the potential physical mechanisms behind the experimental observations. The three-dimensional laminar basic states over a 1.5 m long, 7-degree half-angle cone with 9.525 mm nosetip radius are computed for selected angles of attack values and freestream conditions that are selected to match the Mach 10 experiments conducted within the Hypervelocity Wind Tunnel 9 at the Arnold Engineering Development Complex (AEDC). The solutions at a freestream unit Reynolds number of 17.1 million per meter are used to perform detailed instability analyses for angles of attack equal to 0, 1, 3, and 5 degrees. Results indicate that the linear amplification of stationary crossflow waves along inflection lines may begin to influence transition along the acreage of the cone for angles of attack equal to or larger than 5 degrees. The measured trend in transition front with respect to increasing angle of attack is found to be consistent with the predicted increase in the amplification factors for Mack mode disturbances along the streamline trajectories. The increase in Mack mode amplification along the windward ray for higher angles of attack is shown to be the result of a progressively earlier entropy-layer swallowing. Computations also indicate that the transition amplification factor along the windward ray is not constant and increases with the angle of attack and that the transition #-factors along the leeward ray are rather small. The nonmodal analysis for zero degrees angle of attack shows that entropy-layer disturbances with appreciably strong energy growth can coexist with Mack mode instabilities at the measured transition location.

boundary layer transition↗

Hypersonic Boundary-Layer Transition on Blunted Cones at Angle of Attack

Experimental studies of cones at several high-speed facilities have demonstrated that, for small nosetip bluntness, transition onset over a circular cone moves upstream along the leeward side and downstream along the windward side, but this trend may be reversed at large bluntness values, where transition onset moves downstream along the leeward side and upstream along the windward side. A theoretical and numerical investigation is performed to characterize the effects of nose bluntness on disturbance amplification over the circular cone for several angles of attack, with the goal of understanding the potential physical mechanisms behind the experimental observations. The three-dimensional laminar basic states over a 1.5 m long, 7-degree half-angle cone with 9.525 mm nosetip radius are computed for selected angles of attack values and freestream conditions that are selected to match the Mach 10 experiments conducted within the Hypervelocity Wind Tunnel 9 at the Arnold Engineering Development Complex (AEDC). The solutions at a freestream unit Reynolds number of 17.1 million per meter are used to perform detailed instability analyses for angles of attack equal to 0, 1, 3, and 5 degrees. Results indicate that the linear amplification of stationary crossflow waves along inflection lines may begin to influence transition along the acreage of the cone for angles of attack equal to or larger than 5 degrees. The measured trend in transition front with respect to increasing angle of attack is found to be consistent with the predicted increase in the amplification factors for Mack mode disturbances along the streamline trajectories. The increase in Mack mode amplification along the windward ray for higher angles of attack is shown to be the result of a progressively earlier entropy-layer swallowing. Computations also indicate that the transition amplification factor along the windward ray is not constant and increases with the angle of attack and that the transition #-factors along the leeward ray are rather small. The nonmodal analysis for zero degrees angle of attack shows that entropy-layer disturbances with appreciably strong energy growth can coexist with Mack mode instabilities at the measured transition location.

Boundary Layer Transition↗

CFD Fuel Slosh Modeling of Fluid-Structure Interaction in Spacecraft Propellant Tanks with Diaphragms

Liquid sloshing within spacecraft propellant tanks causes rapid energy dissipation at resonant modes, which can result in attitude destabilization of the vehicle. Identifying resonant slosh modes currently requires experimental testing and mechanical pendulum analogs to characterize the slosh dynamics. Computational Fluid Dynamics (CFD) techniques have recently been validated as an effective tool for simulating fuel slosh within free-surface propellant tanks. Propellant tanks often incorporate an internal flexible diaphragm to separate ullage and propellant which increases modeling complexity. A coupled fluid-structure CFD model is required to capture the damping effects of a flexible diaphragm on the propellant. ANSYS multidisciplinary engineering software employs a coupled solver for analyzing two-way Fluid Structure Interaction (FSI) cases such as the diaphragm propellant tank system. Slosh models generated by ANSYS software are validated by experimental lateral slosh test results. Accurate data correlation would produce an innovative technique for modeling fuel slosh within diaphragm tanks and provide an accurate and efficient tool for identifying resonant modes and the slosh dynamic response.

Sances, Dillon J.↗

Understanding the low-temperature chemistry of 1,2,4-trimethylbenzene

1,2,4-trimethylbenzene is an important representative aromatic component of gasoline/diesel/jet fuels and thus it is necessary to understand its low-temperature chemistry. In this paper, ignition delay times (IDTs) of both 1,2,4-trimethylbenzene (124TMB) and its blends with n -heptane were measured at engine-like conditions using both a high-pressure shock tube and a rapid compression machine for fuel in ‘air’ mixtures at pressures of 10 and 30 atm and at temperatures in the range 600 – 1100K. The experiments in this study show for the first time that 124TMB presents a two-stage ignition behavior at engine relevant conditions. Blending n -heptane with 124TMB can significantly increase mixture reactivity at temperatures below 1000K. A new detailed mechanism has been developed to simulate the experimentally measured IDT data. The mechanism can capture well the two-stage ignition behavior as well as the ignition delays at different pressures, equivalence ratios over a wide temperature range, for both pure fuels and their blended mixtures. Flux analyses show that the benzylic radicals (formed via H-atom abstraction from the methyl groups ortho-sites on 124TMB) can add to O 2 forming $\mathrm{R\dot{O}_2}$ radicals, which can isomerize to $\dot{Q}$OOH by intramolecular H-atom transfer from the ortho- methyl group and these $\dot{Q}$OOH radicals undergo a second addition to O 2 . This is analogous to the chain branching reaction pathways of alkanes. The chain branching reaction pathways are responsible for the first-stage heat release of 124TMB. In conclusion, the competitions between chain branching and both chain propagating and chain termination reaction pathways lead to a less pronounced negative temperature coefficient (NTC) behavior for 124TMB oxidation, compared to two-stage ignition behavior observed for alkanes and other fuels.

1,2,4-trimethylbenzene↗

Nuclear–Electronic Orbital General Rate Theory: Predicting Hydrogen Kinetic Isotope Effects in the Deep Tunneling Regime

Hydrogen transfer is a critical component of many chemical and biological processes. The ratio of rate constants for hydrogen and deuterium transfer defines the H/D kinetic isotope effect (KIE), which is a powerful tool for elucidating hydrogen transfer mechanisms. Interpretation of experimental H/D KIEs relies on accurate and affordable computational methods. However, due to their light mass, hydrogen and deuterium can undergo tunneling, which is challenging to describe in multidimensional molecular systems. Herein, we introduce the nuclear–electronic orbital general rate theory (NEO-GRT), which enables the efficient prediction of H/D KIEs based on full-dimensional molecular quantum chemistry calculations. The NEO-GRT approach describes the hydrogen transfer rate constant with a general expression that spans the vibrationally adiabatic and nonadiabatic hydrogen tunneling regimes. The input quantities are computed using NEO density functional theory, which treats the transferring hydrogen or deuterium nucleus quantum mechanically on the same level as the electrons. We investigate two intramolecular proton transfer reactions in organic molecules at temperatures down to 50 K to evaluate the performance of NEO-GRT by comparison to transition state theory and ring-polymer instanton theory. The KIEs computed with NEO-GRT agree with those calculated using ring-polymer instanton theory for the full-dimensional molecular systems at the same level of electronic structure theory. This agreement indicates that NEO-GRT captures the deep hydrogen tunneling effects, in contrast to transition state theory, which neglects such effects. Given its relatively low computational cost, NEO-GRT is a promising approach for predicting H/D KIEs in large organic and organometallic systems.

Hydrogen↗

Effects of Fe atoms on hardening of a nickel matrix: Nanoindentation experiments and atom-scale numerical modeling

Significant hardening effect due to Fe concentrations in Ni-based alloys with face-centered-cubic structure has been studied by using a combined experimental and atomistic-based computational approach via nanoindentation tests. The obtained experimental load–displacement data for the [0 0 1] crystal orientation reached a qualitative good agreement with molecular dynamics simulations results, leading to strong evidence that the main strengthening factors are associated to sluggish dislocation diffusion, reduced defect sizes and the nucleation of tetrahedral stacking faults. Here, interstitial type prismatic dislocation loops mainly formed by $\frac{1}{6}$$\langle$1 1 2$\rangle$ Shockley dislocations are nucleated during the loading process, where their interaction leads to the formation of pyramidal shaped stacking fault which are mainly created by $\frac{1}{3}$$\langle$1 0 0$\rangle$ Hirth dislocations lines. Observing both types of defects coexisting in the same plastic deformation zone by both approaches. Reported mechanical data, measured experimentally and interpreted numerically, are also in accordance with microstructural SEM and TEM investigations.

36 MATERIALS SCIENCE↗

Tensile Properties of Polymeric Matrix Composites Subjected to Cryogenic Environments

Polymer matrix composites (PMC s) have seen limited use as structural materials in cryogenic environments. One reason for the limited use of PMC s in cryogenic structures is a design philosophy that typically requires a large, validated database of material properties in order to ensure a reliable and defect free structure. It is the intent of this paper to provide an initial set of mechanical properties developed from experimental data of an advanced PMC (IM7/PETI-5) exposed to cryogenic temperatures and mechanical loading. The application of this data is to assist in the materials down-select and design of cryogenic fuel tanks for future reusable space vehicles. The details of the material system, test program, and experimental methods will be outlined. Tension modulus and strength were measured at room temperature, -196 C, and -269 C on five different laminates. These properties were also tested after aging at -186 C with and without loading applied. Microcracking was observed in one laminate.

Whitley, Karen S.↗

Direct Evidence of Photoinduced Charge Transport Mechanism in 2D Conductive Metal Organic Frameworks

Conductive metal organic frameworks (MOFs) represent a promising class of porous crystalline materials that have demon-strated potential in photo-electronics and photocatalytic applications. However, the lack of fundamental understanding on charge transport (CT) mechanism as well as the correlation of CT mechanism with their structure hampered their further development. Herein, we report the direct evidence of CT mechanism in 2D Cu-THQ MOFs and the correlation of temporal and spatial behaviors of charge carriers with their photoconductivity by combining three advanced spectroscopic methods including time resolved optical and X-ray absorption spectroscopy and terahertz spectroscopy. In addition to Cu-THQ, the CT in Cu/Zn-THQ after incorporating Zn2+ guest metal was also examined to uncover the contribution of through space pathway as the presence of the redox inactive 3d10 Zn2+ is expected to perturb the long range in-plane CT. We show that the hot carriers in Cu-THQ generated after photoexcitation are highly mobile and undergo fast localization to a lower energy state (cool carriers) with electrons occupying Cu center and holes in ligands. The cool carriers, which have super long lifetime (> 17 ns) are responsible for the long-term photoconductivity in Cu-THQ and transport through O-Cu-O motif with negligible contribution from interlayer ligand π-π stacking as incorporation of Zn2+ in Cu-THQ significantly reduced photoconductivi-ty. These unprecedent results not only demonstrate the capability to experimentally probe CT mechanism but also provide important insight in the rational design of 2D MOFs for photoelectronic and photocatalytic applications.

14 SOLAR ENERGY↗

Effects of Zn and Ca on the deformation texture evolution of Mg–Zn–Ca alloys at elevated temperatures

This work utilized crystal plasticity simulations and experimental thermo-mechanical processing to examine how Zn and Ca content affects texture evolution in Mg–Zn–Ca alloys during simulated hot rolling. Four different compositions were studied: unalloyed Mg and three Mg alloys of ZX0p50 (Mg- 0.5 wt% Zn- 0.1 wt% Ca), ZX30 (Mg-3 wt% Zn- 0.1 wt% Ca), and ZX31 (Mg-3 wt% Zn- 0.3 wt% Ca). Multi-pass Gleeble experiments simulated hot rolling using plane strain conditions. Unalloyed Mg developed a strong basal texture, while the addition of Zn and Ca significantly weakened the texture in ZX30 and ZX31; this reduction was not seen in ZX0p50. Notably, ZX31 exhibited a split basal texture aligned with the rolling direction. Crystal plasticity simulations revealed that the weaker basal texture in ZX30 and ZX31 resulted from reduced activation of basal and twinning modes compared to unalloyed Mg and Zx0p50. Increased Zn and Ca content raised the ratios of basal to pyramidal critical resolved sheer stress (CRSS) and twin to pyramidal CRSS, enhancing pyramidal slip activity and weakening the basal texture. Extension twinning played a critical role in texture development during the first deformation pass. In unalloyed Mg and ZX0p50, twinning led to a strong basal texture, while ZX30 and ZX31 had weak basal textures that increased only slightly with further deformation. The split basal poles simulated in ZX31 were consistent with the experimental findings, highlighting the interplay between alloy composition and texture evolution.

Crystal plasticity finite element↗

Theoretical and experimental quantification of Suzuki segregation enthalpy and strengthening mechanisms in a binary alloy

Solute segregation to planar defects in metallic alloys has been shown to drastically alter mechanical properties. While various works using first-principles and thermodynamic calculations have studied the fundamental driving forces for solute segregation via the Suzuki criterion, planar defect energy, or a comparison of energies of the HCP-like phase and FCC matrix, a quantitative experimental and computational comparison of equilibrium composition and segregation enthalpies has not yet been reported. In this work, we predict the equilibrium composition and segregation enthalpy to intrinsic stacking faults in a Ni-60Co (at.%) alloy and compare the results to two independent experimental methods. We observed that Co segregates to the innermost two planes of the intrinsic stacking fault, and we found that the experimental segregation enrichment, measured from transmission electron microscopy energy dispersive X-ray spectroscopy, of the faults is 6.8 at.% Co, which is 2.2 at.% less than the predicted value at the same temperature. We also find that the segregation enthalpy measured from the composition profile is −21.1 ± 6.4 meV/atom and separately from differential scanning calorimetry segregation enthalpy is −33.2 meV/atom, whereas the predicted enthalpy is −31 ± 1 meV/atom. Based on these results, we determine that segregation occurs very rapidly, within 8 min at temperatures as low as 36% of the homologous solidus temperature. Furthermore, this analysis provides an overview of the possible dislocation mechanisms responsible for strengthening effects due to solute segregation, and concludes that changes in room temperature hardness from local phase transformation is likely tied to post-segregation room temperature equilibrium partial separation distance.

Ab initio calculation↗

Toward the Prediction and Control of Glass Transition Temperature for Donor–Acceptor Polymers

Semiconducting donor–acceptor (D–A) polymers have attracted considerable attention toward the application of organic electronic and optoelectronic devices. However, a rational design rule for making semiconducting polymers with desired thermal and mechanical properties is currently lacking, which greatly limits the development of new polymers for advanced applications. Here, polydiketopyrrolopyrrole (PDPP)-based D–A polymers with varied alkyl side-chain lengths and backbone moieties are systematically designed, followed by investigating their thermal and thin film mechanical responses. The experimental results show a reduction in both elastic modulus and glass transition temperature (Tg) with increasing side-chain length, which is further verified through coarse-grained molecular dynamics simulations. Informed from experimental results, a mass-per-flexible bond model is developed to capture such observation through a linear correlation between Tg and polymer chain flexibility. Using this model, a wide range of backbone Tg over 80 °C and elastic modulus over 400 MPa can be predicted for PDPP-based polymers. This study highlights the important role of side-chain structure in influencing the thermomechanical performance of conjugated polymers, and provides an effective strategy to design and predict Tg and elastic modulus of future new D–A polymers.

36 MATERIALS SCIENCE↗

Lattice-Distortion-Enhanced Yield Strength in a Refractory High-Entropy Alloy

Severe distortion is one of the four core effects in single-phase high-entropy alloys (HEAs) and contributes significantly to the yield strength. However, the connection between the atomic-scale lattice distortion and macro-scale mechanical properties through experimental verification has yet to be fully achieved, owing to two critical challenges: 1) the difficulty in the development of homogeneous single-phase solid-solution HEAs and 2) the ambiguity in describing the lattice distortion and related measurements and calculations. Here, a single-phase body-centered-cubic (BCC) refractory HEA, NbTaTiVZr, using thermodynamic modeling coupled with experimental verifications, is developed. Compared to the previously developed single-phase NbTaTiV HEA, the NbTaTiVZr HEA shows a higher yield strength and comparable plasticity. The increase in yield strength is systematically and quantitatively studied in terms of lattice distortion using a theoretical model, first-principles calculations, synchrotron X-ray/neutron diffraction, atom-probe tomography, and scanning transmission electron microscopy techniques. These results demonstrate that severe lattice distortion is a core factor for developing high strengths in refractory HEAs.

36 MATERIALS SCIENCE↗

Synchrotron Photoionization Study of the Diisopropyl Ether Oxidation

Abstract Scientific evidence has shown oxygenates help to reduce dangerous pollutants arising from burning fossil fuel in the automotive sector. For this reason, their use as additives has spread widely. The aim of this work consists in providing a comprehensive identification of the main primary oxidation products of diisopropyl ether (DIPE), one of the most promising among etheric oxygenates. The Cl‐initiated oxidation of DIPE is examinated by using a vacuum ultraviolet (VUV) synchrotron radiation at the Advanced Light Source (ALS) of the Lawrence Berkeley National Laboratory (LBNL). Products are identified on the basis of their mass‐to‐charge ratio, shape of photoionization spectra, adiabatic ionization energies, and chemical kinetic profiles, at three different temperatures (298, 550, and 650 K). Acetone, propanal, propene, and isopropyl acetate have been identified as major reaction products. Acetone is the main primary product. Theoretical calculations using the composite CBS‐QB3 method provided useful tools to validate the postulated reaction mechanisms leading to experimentally observed species. The formation of other species is also discussed.

Giustini, Andrea↗