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At least 793 records · Page 44

Volumetric energy density impact on mechanical properties of additively manufactured 718 Ni alloy

The 718 Ni-based superalloy has gained enormous attention in the additive manufacturing community for its great weldability, allowing for complex geometries to be formed, and its superb mechanical strength. Here we explore the influence of a wide range of major build parameters on microstructures and mechanical properties of 718 Ni alloys. Volumetric energy density appears to be one of the major parameters that captures the relationship between energy input and measured mechanical properties and microstructures of the alloys. A threshold energy density was identified below which the properties of the additively manufactured specimen degrade substantially. Finally, the influence of energy density on the quality of the built specimen simulated using Flow3D AM correlates well with the experimental results.

36 MATERIALS SCIENCE↗

Stabilizing Ni-rich layered cathode for high-voltage operation through hierarchically heterogeneous doping with concentration gradient

High-nickel LiNi x Mn y Co 1-x-y O 2 (NMC) cathodes have demonstrated superior energy density, yet their stability is compromised under high voltage conditions. To address this, here we propose a strategy of heterogeneous doping with a concentration gradient, specifically through Sr–Zr co-modification. We synthesized Ni-rich NMC particles featuring several micron-sized secondary particles composed of micron-sized primary grains. This design aims to harness the structural robustness of single-crystalline grains and the favorable diffusion kinetics of polycrystalline secondary particles. Systematic characterization using a combination of electrochemical measurements and synchrotron analytics reveals an intriguing pattern of hierarchically heterogeneous Sr–Zr co-doping. It demonstrates a depth-dependent concentration gradient at the secondary particle level and competing dopant segregation over the buried grain boundaries. This unique characteristic creates opportunities for enhancing battery performance, particularly by optimizing precursors and implementing advanced modulation techniques. We also investigate the dissolution and precipitation of the cathode's transition metal cations upon high-voltage cycling. These insights suggest that a tailored compositional variation can be a viable approach to effectively design the next-generation high-Ni NMC cathode materials for high-voltage lithium batteries.

36 MATERIALS SCIENCE↗

Energy and mechanical properties predictions in Fe-Ni binary system by ab initio calculations

Here, the fcc random solid solutions in Fe-Ni binary system were investigated using ab initio calculations. Density functional theory (DFT) was applied along with supercells generated by the Special Quasi-Random Structure (SQS) method to predict the enthalpy of mixing and magnetic and elastic properties. The results were compared with relevant experimental and computational data produced by other groups. The effect of SQS supercell size and relaxation procedure on the predicted properties of the alloys were also studied. Our calculations show that 16-atoms SQS model provides adequate approach to the mixing energy of the alloy. However, calculation of mechanical properties requires larger supercell. Excellent agreement between experimental and calculated elastic properties was found in fcc region of Fe-Ni system.

36 MATERIALS SCIENCE↗

The role of Li doping in layered/layered Na x Li y Ni 0.4 Fe 0.2 Mn 0.4 O 2 intergrowth electrodes for sodium ion batteries

Here, the layered NaTMO 2 (TM = Ni, Fe, Mn) materials with the O3-type structure are attractive as positive electrodes for sodium ion batteries because of their high theoretical capacity. Additionally, Li doping in these materials has been shown to offer substantial enhancements to their electrochemical properties by promoting the formation of intergrowth structures, which are combinations of specific phases. However, the mechanism by which the intergrowth modifies the electrochemical properties is often unclear. Systematic variation of Li content in Na x Li y Ni 0.4 Fe 0.2 Mn 0.4 O 2 (NFM-Li y ) was conducted to identify its role in structural modification and electrochemical performance. Li contents of 0.15 and greater generate a layered/layered Na-O3/Li-O’3 intergrowth structure. 7 Li and 23 Na nuclear magnetic resonance and x-ray absorption spectroscopy identify that when the total solubility for alkali ions in the layered structure is exceeded, Li continues to form the Li-O’3 phase while the excess Na forms residual sodium compounds such as Na 2 O. Higher Li content is associated with improved capacity retention in the initial cycles from the superior stability of the mechanically linked NaO3/Li-O’3 structure that suppresses the P3 to OP2 phase transition during charge. However, high Li contents are associated with increased rates of parasitic side reactions that reduce long-term cycling stability. These side reactions are associated with the instability of the cathode-electrolyte interphase, which can be partially mitigated by atomic layer deposition (ALD) coating with alumina, which significantly enhances the capacity retention and Coulombic efficiency over many cycles. Overall, we find that the layered/layered Na-O3/Li-O’3 intergrowth structure is able to provide structural stability and suppress undesired phase transformations but is overwhelmed by the increased reactivity of the surface if not protected by surface coating.

25 ENERGY STORAGE↗

57 Zn β-delayed proton emission establishes the 56 Ni rp-process waiting point bypass

We measured the 57 Zn β-delayed proton (βp) and γemission at the National Superconducting Cyclotron Laboratory. We find a 57 Zn half-life of 43.6 ± 0.2ms, βp branching ratio of (84.7 ±1.4)%, and identify four transitions corresponding to the exotic β-γ-pdecay mode, the second such identification in the fp-shell. The p/γratio was used to correct for isospin mixing while determining the 57 Zn mass via the isobaric multiplet mass equation. Previously, it was uncertain as to whether the rp-process flow could bypass the textbook waiting point 56 Ni for astrophysical conditions relevant to Type-I X-ray bursts. Our results definitively establish the existence of the 56 Ni bypass, with 14-17% of the rp-process flow taking this route.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Shock-induced phase transitions and stacking fault formation in additively manufactured eutectic high-entropy alloy Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2

Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2 additively manufactured using laser powder bed fusion (LPBF) is among the toughest as-built alloys reported and is a promising candidate for use in extreme environments. However, its behavior under multi-megabar pressure regimes remains unexplored. We used femtosecond in situ X-ray diffraction to investigate the shock response of LPBF Ni40Co20Fe10Cr10Al18W2 under laser-driven shock compression and release. Our results reveal that the initial dual-phase face-centered + body-centered structure transforms to a single face-centered phase over a wide pressure range of 84±10 to 277±55 GPa, followed by a transition to a single body-centered phase at 431±48 GPa. We establish the Hugoniot equation-of-state of LPBF Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2 and compare it to the benchmark alloy AlCoCrFeNi 2.1 , demonstrating the effects of W-doping and increased Al content. High stacking fault probabilities, close to those measured in Au and Ag, are observed upon compression. A portion of the stacking faults are annihilated upon release to ambient pressure.

36 MATERIALS SCIENCE↗

Molecular-level insights into CO 2 activation on Ni(111) from in situ infrared spectroscopy

The activation of CO 2 on nickel surfaces is the first step of various CO 2 conversion processes. Consequently, understanding the surface intermediates formed during this step and their adsorption sites is crucial for elucidating reaction mechanisms. In this study, we employ in situ infrared spectroscopy to investigate the interaction of 1 mbar CO 2 with a model Ni(111) catalyst between 25°C and 300°C. Under these conditions, CO 2 is activated via a direct dissociation into CO and atomic oxygen, while the oxidation state of the Ni(111) surface is primarily determined by residual H 2 and O 2 . The high surface coverage of CO and oxygen at ambient CO 2 pressure induces a competitive adsorption mechanism on the energetically favored hollow sites. This mechanism leads to a temperature-dependent distribution of CO between top and hollow sites, potentially explaining the effect of reaction conditions on the adsorption site of CO intermediates in CO 2 conversion reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unleashing the Potential of Fast Charging Batteries: Leveraging Anion Redox Chemistry in Ni- and Co-Free Cathodes

Designing Li-ion battery cathodes free from critical raw materials such as Co and Ni has a huge technological and societal impact. Though anion redox-based Li-rich oxide cathodes allow designing Co and Ni free cathode compositions, the Li-rich oxides witnessed voltage fade, voltage hysteresis, and irreversible oxygen release despite their high capacity. Conversely, anion redox through highly covalent chalcogenides (S/Se) is emerging due to the improved covalency between metal d and ligand p bands. Here, we investigate the tuning of multi-chalcogen (S/Se) p-band and redox-active metal d-band in a model Li-rich chalcogen composition Li 1.13 Ti 0.57 Fe 0.3 S 2-y Se y (y = 0 - 1) through in-depth electrochemical, X-ray spectroscopy, and DFT-based electronic structure investigations. Introducing the appropriate amount of Se p band character in anion redox sulfides increases interlayer distance and metal - ligand covalency without modifying the original crystal structure, promoting significant electrochemical reversibility through mixed anionic (Se 2- /Se n- , S 2- /S n- , wherein n<2) and cationic (Fe 2+ /Fe 3+ ) redox reactions. Here we show the detailed Fe, S, and Se redox contributions during Li insertion/extraction through X-ray Absorption (XAS) and Hard X-ray Photoemission Spectroscopy (HAXPES) measurements. The orbital tuning approach improves rate capability for more than 10 C charge-discharge rate, exhibiting more than 50% of its original capacity obtained at C/20 rate. The buffer cation in the lattice (Ti 4+ ) remains electrochemically inactive even after significant Se p-band introduction in the sulfide framework. Overall, this work takes advantage of multi-anion redox chemistry to uncover practically demanding fast charging-discharging characteristics in intercalation cathodes. The obtained knowledge of this design can be extended to other oxide and chalcogen cathodes for high performance Li-ion batteries.

25 ENERGY STORAGE↗

Understanding the Beneficial Role of Transition-Metal Layer Na + Substitution on the Structure and Electrochemical Properties of the P2-Layered Cathode Na 2+ x Ni 2– x /2 TeO 6

Layered Na x MO 2 sodium oxide positive electrode materials have experienced renewed interest owing to the current commercial attention on sodium-ion batteries. Although there are many attractive qualities of these materials, they suffer from serious shortcomings owing to Na + ordering and transition-metal layer gliding that cause a plethora of voltage plateaus during cycling. The P2-layered Na 2+x Ni 2–x/2 TeO 6 (0 ≤ x ≤ 0.5) system provides a framework for investigating the effect of dual Na + substitution into the sodium layer and the transition-metal layer of the structure and its effects on the electrochemical properties of the materials. A careful investigation into the synthesis and properties of these materials reveals that the sodium content used during material preparation has a drastic effect on the composition and electrochemical profile of these materials. The sodium substitution disrupts ordering within the transition-metal layer, thereby disrupting Na + ordering in the adjacent sodium layers. Beyond a critical sodium concentration, the layer stacking shifts, and all voltage plateaus of the P2-Na 2 Ni 2 TeO 6 material are no longer observed at 4.4 V versus Na + /Na. These results also question the common belief that additional sodium precursor is required when preparing layered sodium oxide cathodes, providing new guidelines for material synthesis and characterization.

36 MATERIALS SCIENCE↗

Absence of Long-Range Magnetic Ordering in a Trirutile High-Entropy Oxide (Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Ta 1.92 O 6–δ

Functionalities of solid-state materials are usually considered to be dependent on their crystal structures. The limited structural types observed in the emerging high-entropy oxides put constraints on the exploration of their physical properties and potential applications. Herein, we synthesized the first high-entropy oxide in a trirutile structure, (Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Ta 1.92 O 6–δ , and investigated its magnetism. The phase purity and high-entropy nature were confirmed by powder Xray diffraction and energy-dispersive spectroscopy, respectively. X-ray photoelectron spectroscopy indicated divalent Mn, Co, Ni, and Cu along with trivalent Fe. Magnetic property measurements showed antiferromagnetic coupling and potential short-range magnetic ordering below ~4 K. The temperature-dependent heat capacity data measured under zero and high magnetic fields confirmed the lack of long-range magnetic ordering and a possible low-temperature phonon excitation. The discovery of the first trirutile high-entropy oxide opens a new pathway for studying the relationship between the highly disordered atomic arrangement and magnetic interaction. Furthermore, it provides a new direction for exploring the functionalities of highentropy oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The [M 6 (S 2 C 2 Ph 2 ) 6 ] (M = Ni, Pd, Pt) Series: Multielectron Reservoirs That Sustain Ligand-Based Oxidations and Metal-Based Reductions

A complete [M 6 (S 2 C 2 R 2 ) 6 ] series (M = Ni (1), Pd (2), Pt (3); R = Ph), the rarest variety among homoleptic dithiolene transition-metal compounds, has been prepared by reaction between [M(S 2 C 2 Ph 2 ) 2 ] and a M 0 source. The platinum member of this set is the first of its type. Diffraction-quality crystals, grown with high reproducibility by evaporation from PhNO 2 solutions, reveal fully reduced [Ph 2 C 2 S 2 ] 2– dianions and an octahedral M 6 core that is reduced to C 2 symmetry by the fusion of a mononuclear D 2h [M(S 2 C 2 Ph 2 ) 2 ] fragment upon a C 4 -symmetric base. The [Ni 6 (S 2 C 2 Ph 2 ) 2 ] 1– monoanion, prepared by Cp* 2 Co reduction, shows only modest structural differences from its neutral counterpart. In CH 2 Cl 2 , 1 and 2 can undergo two reductions and an oxidation, while 3 sustains two reductions and two oxidations. In benzonitrile, 1 sustains three reversible oxidations at potentials that are shifted appreciably to less positive values. The cathodic processes are shown by density functional theory (DFT) calculations to involve an MO largely of metal–sulfur composition that has contributions throughout the C 4 -symmetric pentametallic base of the assembly, while the oxidations are largely ligand-based and confined to the monometallic [M(S 2 C 2 Ph 2 ) 2 ] cap. The absorption spectra are marked by multiple overlapping bands that produce a continuous, tapering absorption profile of unresolved shoulders and swells.

Ligands↗

Magnetic and EPR Spectroscopic Studies of Thiolate Bridged Divalent Ni, Pd, and Pt Ions Capped with VO(N 2 S 2 ) Metalloligands

Reactions of the metallodithiolate complex VO(bme-dach) (hereafter abbreviated as V, where bme-dach = N,N ′-bis(2-mercaptoethyl)-1,4-diazacycloheptane) with [Pd II (CH 3 CN) 4 ](BF 4 ) 2 and [Pt II (CH 3 CN) 4 ](BF 4 ) 2 yield the V–M–V trimetallic compounds [VPdV](BF 4 ) 2 (2) and [VPtV](BF 4 ) 2 (3). Reaction of a similar metalloligand, VO(bme-daco) (hereafter abbreviated as V′ where bme-daco = N,N′-bis(2-mercaptoethyl)-1,5-diazacyclooctane) with [Ni II (CH 3 CN) 6 ](BF 4 ) 2 afforded the related salt [V′NiV′](BF 4 ) 2 (1). X-ray structural analyses revealed that cations in 1, 2, and 3 adopt a stairstep C 2h structure consisting of two terminal VO(N 2 S 2 ) moieties bridged via thiolate sulfur to the group 10 metal ions. Weak ferromagnetic superexchange coupling (J = 0.282 cm –1 for 1, 0.954 cm –1 for 2, and 1.372 cm –1 for 3) was observed between the two S = 1/2 V IV centers separated by distances in the range of 5.9–6.3 Å, with J values varying following the order Ni < Pd < Pt. Frozen-solution EPR spectra measured on the more soluble [BArF 24 ] − (BArF 24 – = tetrakis((3,5-trifluoromethyl)phenyl)borate) analogues revealed that the [VPtV] 2+ cation exhibits a 15-line hyperfine splitting of 225 MHz at g = 4 in parallel mode, confirming exchange coupling between the two 51 V, I = 7/2 nuclei. Density-functional theory (DFT) calculations indicate an S = 1 ground state for 1–3. These results demonstrate that the choice of paramagnetic metallodithiolate ligand and diamagnetic bridge in such trimetallic species influences the sign and magnitude of magnetic interactions.

anions↗

Temperature-Dependent Speciation of Ni(II) in Molten Chloride, Bromide, and Iodide Salts

Understanding the fundamental speciation and local structure of metal cations─such as nickel, which is present as a corrosion product─in molten salt media is essential for assessing their impact on the thermal and physical properties of salts used for advanced nuclear energy applications. In this study, we employed an integrated approach of combining X-ray absorption spectroscopy (XAS), UV–vis spectroscopy, and ab initio molecular dynamics (AIMD) to investigate the halide-dependent speciation of divalent nickel ions, Ni(II), in LiCl–KCl, LiBr–KBr, and LiI–KI eutectic salt mixtures from room temperature to 600 °C. Our findings show that both halide type and temperature significantly influence the local coordination of nickel in these molten salt systems. A notable aspect of Ni(II) speciation in LiI–KI salts is the formation of a polyiodide species. In conclusion, our findings provide critical insights into metal ion speciation in molten salt systems, enhancing our understanding of the factors that govern the physicochemical properties of these complex fluids.

36 MATERIALS SCIENCE↗

Calorimetric Study of Mixed Phosphates Na 4 M 3 (PO 4 ) 2 P 2 O 7 (M = Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ ) to Evaluate the Electrochemical Trends

Mixed polyanionic compounds have been studied extensively as viable cathode materials for sodium-ion batteries. Mixed phosphates, Na 4 M 3 (PO 4 ) 2 P 2 O 7 (M = Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ ), provide a low barrier for Na-ion diffusion, being advantageous in comparison to phosphates and pyrophosphates. The reported order of sodium extraction is ambiguous and remains unclear. Despite being structurally similar, electrochemical performance differs for all four analogues with different degrees of (de)sodiation, according to the transition element present. High-temperature oxide melt solution calorimetry has been used to establish the relation between thermodynamic phase stability and observed capacity for this series of mixed phosphates. Thermodynamic phase stability largely depends on the kind of structure, type of bonding, and size of the cations present. So, according to our results, the thermodynamic phase stability follows the order Na 4 Mn 3 (PO 4 ) 2 P 2 O 7 > Na 4 Fe 3 (PO 4 ) 2 P 2 O 7 > Na 4 Co 3 (PO 4 ) 2 P 2 O 7 > Na 4 Ni 3 (PO 4 ) 2 P 2 O 7 . The thermodynamic studies serve as guidelines for the selection of compositions with the potential for fabricating advanced cathode materials with maximum performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interaction of Anisole on Alumina-Supported Ni and Mo Oxide Hydrodeoxygenation Catalysts

The conversion of biomass to transportation fuels and value-added chemicals is a promising method to reduce reliance on fossil fuels. Mo-based catalysts have been shown to be highly active in the hydrodeoxygenation of biomass-derived phenolic compounds. The catalyst active phase, surface species, and the effect of adding additional metals is not comprehensively understood. Here we compare the temperature-dependent adsorption behavior of the model compound anisole 2 on an alumina-supported mixed nickel molybdenum oxide catalyst with two reference catalysts of molybdenum oxide and nickel oxide. Raman spectroscopy showed that the catalysts contain significant amounts of molybdates and molybdoaluminates, in addition to NiMoO 4 in the nickel molybdenum catalyst and MoO 3 in the molybdenum-only catalyst. Using transmission infrared spectroscopy under a controlled environment, we find that anisole chemisorbed largely through the oxygen in the methoxy group to form surface-bound phenoxy and methoxy species on all the catalysts. Ambient pressure X-ray photoelectrons spectroscopy measurements of the catalysts in anisole vapor showed reduced Mo atoms are the binding sites. The surface interaction and removal temperature of these species varied with the metal composition. The MoO x component dominated the adsorption behavior in both MoO x and NiMoO x catalysts. The formation of new aromatics, including methylated rings, depended on Ni composition. Upon adding hydrogen to induce the hydrodeoxygenation of anisole, undesirable polynuclear aromatic species were quickly formed on the Mo-based catalysts. In conclusion, these results suggest that the molybdenum oxide controls the adsorption and reactivity of the surface species, with a cooperative effect by Ni.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine Learning Interatomic Potentials for Modeling Framework Flexibility and Water Uptake in NbOFFIVE-1-Ni Metal–Organic Framework

Metal–organic frameworks (MOFs), with their distinctive porous structures and tunable chemical properties, have shown immense promise in the separation and storage of gases. Currently, the accurate simulation of their adsorptive properties remains challenging, especially for systems where the molecules fit very tightly into the pores. Traditional simulation methods often approximate the frameworks as rigid and do not account for the framework flexibility seen in materials such as NbOFFIVE-1-Ni. First-principles molecular dynamics (FPMD) simulations offer the desired accuracy in modeling this flexibility but are limited by their extensive computational demands, rendering them impractical for long simulations. Conversely, classical force field-based simulations offer computational efficiency but lack the necessary accuracy. Here, to break this accuracy-efficiency trade-off, we have developed machine learning interatomic potentials trained on energies and forces from FPMD to model the framework flexibility of NbOFFIVE-1-Ni in the presence of water over nanosecond time scales. Furthermore, by integrating MLIP-driven molecular dynamics (MLIP-MD) with grand canonical Monte Carlo (GCMC) simulations, we further incorporated framework flexibility into adsorption predictions, yielding water adsorption isotherms that better align with experimental data compared to those of conventional GCMC simulations. These advances offer new opportunities for the design and optimization of MOFs in gas storage and separation applications.

adsorption↗

Breaking Simple Scaling Relations through Metal–Oxide Interactions: Understanding Room-Temperature Activation of Methane on M/CeO 2 (M = Pt, Ni, or Co) Interfaces

The clean activation of methane at low temperatures remains an eminent challenge and a field of competitive research. In particular, on late transition metal surfaces such as Pt(111) or Ni(111), higher temperatures are necessary to activate the hydrocarbon molecule, but a massive deposition of carbon makes the metal surface useless for catalytic activity. However, on very low-loaded M/CeO 2 (M = Pt, Ni, or Co) surfaces, the dissociation of methane occurs at room temperature, which is unexpected considering simple linear scaling relationships. This intriguing phenomenon has been studied using a combination of experimental techniques (ambient-pressure X-ray photoelectron spectroscopy, time-resolved X-ray diffraction, and X-ray absorption spectroscopy) and density functional theory-based calculations. The experimental and theoretical studies show that the size and morphology of the supported nanoparticles together with strong metal–support interactions are behind the deviations from the scaling relations. These findings point toward a possible strategy for circumventing scaling relations, producing active and stable catalysts that can be employed for methane activation and conversion.

03 NATURAL GAS↗

Ring Size Effects on the Structures of Sandwich Compounds with a Stoichiometry of C 12 H 12 M (M = Ti–Ni)

Ring size effects on geometries and electronic structures were investigated for the (C n H n )M(C m H m ) (n = 4, 5, or 6; m = 8, 7, or 6; m + n = 12; M = Ti–Ni) systems using density functional theory. The lowest-energy C 12 H 12 M structures for the early transition metals titanium, vanadium, and chromium are the experimentally known singlet (η 5 -C 5 H 5 )Ti(η 7 -C 7 H 7 ), doublet (η 5 -C 5 H 5 )V(η 7 -C 7 H 7 ), and singlet (η 6 -C 6 H 6 ) 2 Cr, respectively. The likewise experimentally known singlet (η 6 -C 6 H 6 ) 2 Ti, doublet (η 6 -C 6 H 6 ) 2 V, and singlet (η 5 -C 5 H 5 )Cr(η 7 -C 7 H 7 ) are the secondlowest- energy structures with only a small energy difference between the two vanadium structures. For the later transition metals, dibenzenemetal complexes are the lowest-energy C 12 H 12 M species with two fully bonded hexahapto benzene rings in the lowest-energy manganese and iron derivatives and one hexahapto and one dihapto benzene ring in the lowest-energy cobalt and nickel derivatives. The lowest-energy (C 5 H 5 )M(C 7 H 7 ) structures for the later transition metals iron, cobalt, and nickel have partially bonded nonplanar C 7 H 7 rings with one or two uncomplexed C=C bonds. The (C 4 H 4 )M(C 8 H 8 ) (M = Ti–Ni) structures with the metal sandwiched between four- and eight-membered rings were found to be much higher in energy than their (C 5 H 5 )M(C 7 H 7 ) and (C 6 H 6 ) 2 M isomers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗