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At least 595 records · Page 33

Double-Layer Kagome Metals Pt 3 Tl 2 and Pt 3 In 2

The connectivity and inherent frustration of the kagome lattice can produce interesting electronic structures and behaviors in compounds containing this structural motif. Here we report the properties of Pt 3 X 2 (X = In and Tl) that adopt a double-layer kagome net structure related to that of the topologically nontrivial high-temperature ferromagnet Fe 3 Sn 2 and the density wave hosting compound V 3 Sb 2 . We examined the structural and physical properties of single crystal Pt 3 Tl 2 and polycrystalline Pt 3 In 2 using X-ray and neutron diffraction, magnetic susceptibility, heat capacity, and electrical transport measurements, along with density functional theory calculations of the electronic structure. Our calculations show that Fermi levels lie in pseudogaps in the densities of states with several bands contributing to transport, and this is consistent with our Hall effect, magnetic susceptibility, and heat capacity measurements. Although electronic dispersions, characteristic of simple kagome nets with nearest-neighbor hopping, are not clearly seen, likely due to the extended nature of the Pt 5d states, we do observe moderately large and non-saturating magnetoresistance values and quantum oscillations in the magnetoresistance and magnetization associated with the kagome nets of Pt.

36 MATERIALS SCIENCE↗

Charge Transport Characteristics of Molecular Electronic Junctions Studied by Transition Voltage Spectroscopy

The field of molecular electronics is prompted by tremendous opportunities for using a single-molecule and molecular monolayers as active components in integrated circuits. Until now, a wide range of molecular devices exhibiting characteristic functions, such as diodes, transistors, switches, and memory, have been demonstrated. However, a full understanding of the crucial factors that affect charge transport through molecular electronic junctions should yet be accomplished. Remarkably, recent advances in transition voltage spectroscopy (TVS) elucidate that it can provide key quantities for probing the transport characteristics of the junctions, including, for example, the position of the frontier molecular orbital energy relative to the electrode Fermi level and the strength of the molecule–electrode interactions. These parameters are known to be highly associated with charge transport behaviors in molecular systems and can then be used in the design of molecule-based devices with rationally tuned electronic properties. This article highlights the fundamental principle of TVS and then demonstrates its major applications to study the charge transport properties of molecular electronic junctions.

36 MATERIALS SCIENCE↗

First-Principles Calculations of Thermoelectric Transport Properties of Quaternary and Ternary Bulk Chalcogenide Crystals

Chalcogenide crystals have a wide range of applications, especially as thermoelectric materials for energy conversion. Thermoelectric materials can be used to generate an electric current from a temperature gradient based on the Seebeck effect and based on the Peltier effect, and they can be used in cooling applications. Using first-principles calculations and semiclassical Boltzmann theory, we have computed the Seebeck coefficient, electrical conductivity, electronic thermal conductivity, power factor, and figure of merit of 30 chalcogenide crystals. A Quantum Espresso package is used to calculate the electronic properties and locate the Fermi level. The transport properties are then calculated using the BoltzTraP code. The 30 crystals are divided into two groups. The first group has four crystals with quaternary composition (A 2 BCQ 4 ) (A = Tl; B = Cd, Hg; C = Si, Ge, Sn; Q = S, Se, Te). The second group contains 26 crystals with the ternary composition (A’B’Q 2 ) (A’ = Ag, Cu, Au, Na; B’ = B, Al, Ga, In; Q = S, Se, Te). Among these 30 chalcogenide crystals, the results for 11 crystals: Tl 2 CdGeSe 4 , Tl 2 CdSnSe 4 , Tl 2 HgSiSe 4 , Tl 2 HgSnS 4 , AuBSe 2 , AuBTe 2 , AuAlTe 2 , AuGaTe 2 , AuInTe 2 , AgAlSe 2 , and AgAlTe 2 are revealed for the first time. In addition, temperature-dependent transport properties of pure and doped AgSbSe 2 and AgSbTe 2 crystals with dopant compositions of AgSb 0.94 Cd 0.06 Te 2 and AgSbTe 1.85 Se 0.15 were explored. These results provide an excellent database for bulk chalcogenides crucial for a wide range of potential applications in renewable energy fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Compositionally Complex Alloys: Some Insights from Photoemission Spectroscopy

Photoemission spectroscopy (PES) is an underrepresented part of current and past studies of compositionally complex alloys (CCA) such as high-entropy alloys (HEA) and their derivatives. PES studies are very important for understanding the electronic structure of materials, and are therefore essential in some cases for a correct description of the intrinsic properties of CCAs. Here, we present several examples showing the importance of PES. First, we show how the difference between the split-band structure and the common-band structure of the valence band (VB), observed by PES, can explain a range of properties of CCAs and alloys in general. A simple description of the band crossing in CCAs composed from the early and late transition metals showing a split band is discussed. We also demonstrate how a high-accuracy PES study can determine the variation in the density of states at the Fermi level as a function of Cu content in Ti-Zr-Nb-Ni-Cu metallic glasses. Finally, the first results of an attempt to single out the contributions of particular constituents in Cantor-type alloys to their VBs are presented. The basic principles of PES, the techniques employed in studies presented, and some issues associated with PES measurements are also described.

36 MATERIALS SCIENCE↗

Large Nernst Effect and Thermodynamics Properties in Weyl Antiferromagnet

The noncollinear antiferromagnet Mn3Sn exhibits a large anomalous Hall effect (AHE) driven by a large Berry curvature despite the vanishingly small magnetization. Theoretically, the large Berry curvature in antiferromagnets is predicted to be induced by the time-reversal breaking Weyl state in momentum space. Here, we comprehensively study the thermal conductivity, specific heat, thermoelectric power S(T), and thermomagnetic power S ji (T) in single crystals of Mn 3 Sn. Mn 3 Sn exhibited a large spontaneous anomalous Nernst effect (ANE) at room temperature; in particular, the signal magnitude of Mn 3 Sn exceeded 0.6 µV/K, which is comparable to that of ordinary ferromagnets. The large ANE results from the magnetic Weyl states near the Fermi level E F and likely shares its origin with the AHE. Moreover, the possibility of Nernst-type thermoelectric modules was evaluated by analyzing the basic thermal and electric physical properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tunable graphene-based infrared reflectance filter having patterned nanoantenna layer and unpatterned graphene layer

An actively tunable optical filter can control the amplitude of reflected infrared light. The filter exploits the dependence of the excitation energy of plasmons in a continuous and unpatterned sheet of graphene, on the Fermi-level, which can be controlled by conventional electrostatic gating. An exemplary filter enables simultaneous modification of two distinct spectral bands whose positions are dictated by the device geometry and graphene plasmon dispersion. Within these bands, the reflected amplitude can be varied by over 15% and resonance positions can be shifted by over 90 cm−1. Electromagnetic simulations verify that tuning arises through coupling of incident light to graphene plasmons by a nanoantenna grating structure. Importantly, the tunable range is determined by a combination of graphene properties, device structure, and the surrounding dielectrics, which dictate the plasmon dispersion. Thus, the underlying design is applicable across a broad range of infrared frequencies.

Beechem, III, Thomas Edwin↗

Fundamentals of SrCoO 3-δ Based Oxygen Deficient Perovskites as Cathodes for Solid Oxide Fuel Cells

The local structure and oxygen stoichiometry in oxide systems have a profound impact on oxygen electrocatalysis encountered in metal-air batteries and solid oxide fuel cells (SOFCs). However, this knowledge is often obtained under conditions different from the real working conditions of the material, resulting in misinterpretation and misunderstanding. This PhD dissertation aims to obtain the structure and oxygen-stoichiometry information of a class of perovskite oxides under their real working conditions in solid oxide fuel cells. Several perovskite oxides were selected for the study: Sr 0.9 Y 0.1 CoO 3-δ (SYC10), Sr 0.9 Y 0.3 CoO 3-δ (SYC30), SrCo 0.9 Nb 0.1 O 3-δ (SCN10) and SrCo 0.9 Ta0.1O 3-δ (SCT10). The local crystal structure and oxygen stoichiometry of these materials were systematically characterized with in-situ neutron diffraction (ND). The oxygen stoichiometry was also measured by thermogravimetric analysis (TGA) and iodometric titration methods. To establish the correlation among structure, oxygen stoichiometry and oxygen reduction reaction (ORR) activity, high temperature electrochemical impedance spectroscopy, oxygen permeation and single cell testing were also performed. In chapter 2, SYC10 is described to have a more symmetrical structure and $V_o^{··}$ distribution, and higher $V_o^{··}$ concentration than SYC30. Molecular orbital energy analysis based on the local structure of the ORR-active Co1-polyhedra indicates SYC30 has a higher Fermi level relative to O-2p energy level in the active Co1-polyhedra, and thus a higher motional enthalpy for $V_o^{··}$ migration. However, the ORR activity of Y-doped SrCoO 3-δ (SCO) are found uncompetitive with other popular catalysts. In chapter 3 and 4, systematic structural studies are presented for Nb and Ta-doped SCO, namely SCN10 and SCT10, respectively. The methodology of unrevealing the structure-activity relationships in chapter 2 is also found applicable to SYC10, SCN10 and SCT10 as presented in chapter 5. The electrochemical tests indicate that SCT10 is the best catalyst due to its excellent thermal and electrochemical stability. In chapter 6, SCT10 is evaluated in a real solid oxide fuel cell in the form of nanoscaled SCT10 layer coating on the commercial (La 0.6 Sr 0.4 ) 0.95 Co 0.2 Fe 0.8 O 3-δ (LSCF). The bilayer structured cathode shows excellent properties of coarsening-resistant, Sr-segregation-free and high ORR-activity.

Yang, Tianrang↗

Voltage-Dependent Barrier Height of Electron Transport through Iron Porphyrin Molecular Junctions

Electron transport through iron porphyrin (FeP) molecules self-assembled on a gold (Au) substrate was investigated using conductive atomic force microscopy (AFM) to measure current–voltage (I–V) characteristics. In the direct tunneling region (|V| ≤ 0.1 V), the Simmons model was used to characterize the electron transport. Furthermore, the energy barrier between the Fermi energy level of Au and the highest occupied molecular orbital (HOMO) level of the FeP molecule was determined to be between 0.3 and 0.6 eV; the range of the electron attenuation coefficient was 0.6–0.8 Å–1. Instead of a constant barrier height, a voltage-dependent barrier height was adapted to simulate the experimental I–V curves over the entire voltage range (|V| ≤ 2 V) using the Simmons model for the intermediate case. The voltage-dependent barrier height is supported by a previously predicted response of molecular-projected self-consistent Hamiltonian orbitals. The dependence showed that the HOMO level relative to the Fermi energy level of the Au electrode decreased as the bias voltage increased. To verify the deposition of the FeP on the Au substrate, Raman spectroscopy and AFM analysis were performed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantifying Charge Carrier Localization in PBTTT Using Thermoelectric and Spectroscopic Techniques

Chemically doped poly[2,5-bis(3-alkylthiophen-2-yl)thieno[3,2- b ]thiophene] (PBTTT) shows promise for many organic electronic applications, but rationalizing its charge transport properties is challenging because conjugated polymers are inhomogeneous, with convoluted optical and solid-state transport properties. Herein, we use the semilocalized transport (SLoT) model to quantify how the charge transport properties of PBTTT change as a function of iron(III) chloride (FeCl 3 ) doping level. We use the SLoT model to calculate fundamental transport parameters, including the carrier density needed for metal-like electrical conductivities and the position of the Fermi energy level with respect to the transport edge. We then contextualize these parameters with other polymer-dopant systems and previous PBTTT reports. Additionally, we use grazing incidence wide-angle X-ray scattering and spectroscopic ellipsometry techniques to better characterize inhomogeneity in PBTTT. Our analyses indicate that PBTTT obtains high electrical conductivities due to its quickly rising reduced Fermi energy level, and this rise is afforded by its locally high carrier densities in highly ordered microdomains. Ultimately, this report sets a benchmark for comparing transport properties across polymer-dopant-processing systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Edge‐Driven Fringe‐Field Effects, Reduced Screening, and Bandgap Widening in Graphene Nanoribbons Enable Single‑Molecule Sensitivity

Graphene nanoribbons (GNRs) offer promising platforms for single‐molecule sensing due to their quasi‐1D channels and discrete electronic states, providing superior sensitivity toward molecular perturbations. While prior studies emphasize smoother edges as essential for optimal performance, the potential benefits of controlled edge roughness remain largely unexplored. Additionally, most investigations focus on GNR arrays, leaving critical edge‐ and width‐dependent factors, including fringe fields, bandgap widening, interactions between adsorbing molecules and GNR atoms, density of states (DOS) suppression, and electrostatic screening lengths, and their collective impact on sensitivity, poorly understood. Here, in this work, we fabricated field‐effect transistors using individual GNRs (widths: 200–20 nm) and characterized their response to molecular adsorption with perfluorooctanoic acid as the model analyte. Narrower ribbons displayed significantly enhanced sensitivity, yielding a coverage‐normalized response of 116 ± 10 mV per molecule in 20 nm‐wide GNRs (from calibrated ensemble Dirac‐point shifts). Experimental and theoretical analyses reveal that this heightened sensitivity arises from stronger fringe fields, width‐dependent quantum confinement effects, reduced DOS, and increased edge roughness that facilitates molecular anchoring, enhanced orbital overlap, and improved charge transfer efficiency. Our findings challenge the conventional assumption that smoother edges inherently enhance sensor performance, demonstrating that controlled edge disorder substantially boosts molecular sensitivity in GNR sensors.

36 MATERIALS SCIENCE↗

Elucidating Design Rules toward Enhanced Solid-State Charge Transport in Oligoether-Functionalized Dioxythiophene-Based Alternating Copolymers

This study investigates the solid-state charge transport properties of the oxidized forms of dioxythiophene-based alternating copolymers consisting of an oligoether-functionalized 3,4-propylenedioxythiophene (ProDOT) copolymerized with different aryl groups, dimethyl ProDOT (DMP), 3,4-ethylenedioxythiophene (EDOT), and 3,4-phenylenedioxythiophene (PheDOT), respectively, to yield copolymers P(OE3)-D, P(OE3)-E, and P(OE3)-Ph. At a dopant concentration of 5 mM FeTos 3 , the electrical conductivities of these copolymers vary significantly (ranging between 9 and 195 S cm –1 ) with the EDOT copolymer, P(OE3)-E, achieving the highest electrical conductivity. UV–vis–NIR and X-ray spectroscopies show differences in both susceptibility to oxidative doping and extent of oxidation for the P(OE3) series, with P(OE3)-E being the most doped. Wide-angle X-ray scattering measurements indicate that P(OE3)-E generally demonstrates the lowest paracrystallinity values in the series, as well as relatively small π–π stacking distances. The significant (i.e., order of magnitude) increase in electrical conductivity of doped P(OE3)-E films versus doped P(OE3)-D or P(OE3)-Ph films can therefore be attributed to P(OE3)-E exhibiting both the highest carrier ratios in the P(OE3) series, along with good π–π overlap and local ordering (low paracrystallinity values). Furthermore, these trends in the extent of doping and paracrystallinity are consistent with the reduced Fermi energy level and transport function prefactor parameters calculated using the semilocalized transport (SLoT) model. Observed differences in carrier ratios at the transport edge (c t ) and reduced Fermi energies [η(c)] suggest a broader electronic band (better overlap and more delocalization) for the EDOT-incorporating P(OE3)-E polymer relative to P(OE3)-D and P(OE3)-Ph. Ultimately, we rationalize improvements in electrical conductivity due to microstructural and doping enhancements caused by EDOT incorporation, a structure–property relationship worth considering in the future design of highly electrically conductive systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Emergent quasi-two-dimensional metallic state derived from the Mott-insulator framework

Recent quasi-two-dimensional (quasi-2D) systems with judicious exploitation of the atomic monolayer or few-layer architecture exhibit unprecedented physical properties that challenge the conventional wisdom on condensed matter physics. Here we show that the infinite layer SrCuO 2 (SCO), a topical cuprate Mott insulator in bulk form, can manifest an unexpected metallic state in the quasi-2D limit when SCO is grown on TiO 2 -terminated SrTiO 3 (STO) substrates. The sheet resistance does not conform to Landau's Fermi liquid paradigm. Hard x-ray core-level photoemission spectra demonstrate a definitive Fermi level that resembles the hole doped metal. Soft x-ray absorption spectroscopy also reveals features analogous to those of a hole doped Mott insulator. Based on these results, we conclude that the hole doping does not occur at the interfaces between SCO and STO; instead, it comes from the transient layers between the chain-type and the planar-type structures within the SCO slab. In conclusion, the present work reveals a metallic state in the infinite layer SCO and invites further examination to elucidate the spatial extent of this state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Significantly increased Raman enhancement on defect-rich O-incorporated 1T-MoS 2 nanosheets

Improving charge transfer is the key to the performance of non-noble metal semiconductor-based surface enhanced Raman scattering (SERS) substrates. In this work, the O-incorporated 1T-MoS 2 nanosheets with rich sulfur defects (ID-MoS 2 ) are obtained by simple calcination of 1T-MoS 2 nanosheets in air atmosphere. Using rhodamine 6G (R6G) as typical probe molecules, ID-MoS 2 nanosheets show ultrahigh Raman enhancement effects with an enhancement factor of 1.24 × 10 7 due to sulfur defects and O incorporation in the 1T-MoS 2 lattice. First-principle density functional theory calculations suggest that the existence of sulfur defects and O incorporation significantly increase the Fermi energy level (E f ) and electronic density of states of ID-MoS 2 . Furthermore, O incorporation can enhance the interactions between the substrate and the adsorbed molecules through electrostatic and hydrogen bonding. All these improve the charge transfer resonance and result in the remarkable SERS activity of ID-MoS 2 nanosheets. This is the first study on the increasing SERS performance of semiconductor substrates by simultaneously employing defect and dopant incorporation. This study provides an approach to optimize the performance of semiconductor-based SERS substrates.

36 MATERIALS SCIENCE↗

Know the enemy: 2D Fermi liquids

Highlights: • Regime of validity of the Fermi liquid theory in 2D interacting Fermi systems has been investigated. • Phase diagram for hydrodynamic and ballistic regimes in the frequency–temperature space has been obtained. • Temperature correction to quasiparticle effective mass has been calculated. • 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation have been discussed. We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency–temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Direct Evidence of Charge Transfer upon Anion Intercalation in Graphite Cathodes through New Electronic States: An Experimental and Theoretical Study of Hexafluorophosphate

Graphite intercalation compounds continue to be central to technologies for electrochemical energy storage from anodes in established Li-ion batteries to cathodes in beyond Li-ion concepts paired with multivalent anodes. When used as a cathode, graphite intercalates a variety of anions with PF 6 - being among the most common. Paired with Li intercalation at the anode, the corresponding dual carbon battery yields high energy and power densities. Given the available choice of anions as intercalants, it is important to elucidate how the graphite structure accommodates them in order to tailor the molecular species to maximize charge and reversibility. However, the changes in electronic structure of the host graphite lattice upon anion intercalation are poorly understood compared to cations, which represent a fundamentally different reaction. Herein, PF 6 -intercalated graphite has been studied using techniques sensitive to electronic structure, namely, X-ray Raman spectroscopy (XRS), X-ray absorption near-edge spectroscopy (XANES), and X-ray emission spectroscopy (XES). Complementary full-potential, all-electron density functional theory calculations yielded excellent agreement with the spectra, thus providing insight into charge compensation in the graphite lattice. In particular, a pre-$π^*$ feature emerged in XRS/XANES, which is direct evidence of the removal of charge from the host lattice to compensate the intercalated anions, leading to an overall lowering of the Fermi energy level. This is expected to be characteristic of many intercalants in anion-intercalated graphite. The unambiguous identification of the origin of the pre-$π^*$ spectral feature, which is frequently seen in graphitic systems, is of broad interest to the spectroscopy of graphitic systems beyond the practical implications of anion-induced changes in the electronic properties for real devices.

36 MATERIALS SCIENCE↗

Improving Strain-localized GaSe Single Photon Emitters with Electrical Doping

Exciton localization through nanoscale strain has been used to create highly efficient single-photon emitters (SPEs) in 2D materials. However, the strong Coulomb interactions between excitons can lead to nonradiative recombination through exciton–exciton annihilation, negatively impacting SPE performance. Here, we investigate the effect of Coulomb interactions on the brightness, single photon purity, and operating temperatures of strain-localized GaSe SPEs by using electrostatic doping. By gating GaSe to the charge neutrality point, the exciton–exciton annihilation nonradiative pathway is suppressed, leading to ∼60% improvement of emission intensity and an enhancement of the single photon purity g (2) (0) from 0.55 to 0.28. The operating temperature also increased from 4.5 K to 85 K consequently. In conclusion, this research provides insight into many-body interactions in excitons confined by nanoscale strain and lays the groundwork for the optimization of SPEs for optoelectronics and quantum photonics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tailoring the Surface of Metal Halide Perovskites to Enable the Atomic Layer Deposition of Metal Oxide Contacts

Replacing organic contact layers with inorganic counterparts, such as metal oxides, is one strategy for improving long-term device stability in metal halide perovskite solar cells. Often, the methods used to deposit metal oxide thin films are incompatible with metal halide perovskites, creating challenges for the fabrication of contacts above the perovskite absorber layer. In this study, we utilize a one-step, solution treatment of the top surface of Cs 0.25 FA 0.75 Pb(Br 0.20 I 0.80 ) 3 to create a thin (~1 nm) overlayer of lead sulfide (PbS) to protect the underlying perovskite during subsequent deposition. X-ray characterization of the surface region shows that the PbS overlayer limits undesirable changes to the perovskite structure and stoichiometry during atomic layer deposition (ALD) of SnO 2 . This protection enables ALD growth of SnO 2 electron contacts on top of the perovskite without an organic transport layer (e.g., C 60 ), resulting in a solar cell with a power conversion efficiency of 5.8%. This result is a marked improvement over devices with ALD SnO 2 grown directly on the perovskite without a PbS overlayer, which produce no power output. Furthermore, the interface characterization and device results in this study highlight some of the key challenges associated with ALD metal oxide growth on perovskite materials and can help inform the future design of inorganic contact layer deposition in solar photovoltaic technologies.

36 MATERIALS SCIENCE↗

Tunable n- and p-Type Behavior of Ruddlesden–Popper and Dion–Jacobson 2D Perovskites

Interfacial band alignment in two-dimensional (2D)/three-dimensional (3D) perovskite heterostructures is important for maximizing separation, extraction, and collection of charge carriers, which, in turn, stabilize the perovskite layer during solar cell operation. Despite the wide use of 2D spacer cations for stabilizing perovskite solar cells, spacer cation exchange across the 2D/3D interface induces structural transformation and degradation in performance and stability. We have now examined the electrochemical and photoelectrochemical behavior of 2D Ruddlesden–Popper (RP) and Dion–Jacobson (DJ) perovskites to assess the impact of binding configuration on the interfacial charge separation and their operational stability. In-situ open circuit potential (OCP) responses of 2D perovskites under light illumination, paired with redox couples (ferrocene/ferrocenium), reveal different semiconducting polarizabilities of BA-RP (n-type) and BDA-DJ (p-type). The tunability of the Fermi energy level in 2D perovskites discussed in this study offers insight into the design of 2D/3D interfaces for optimizing charge transfer and enhancing charge neutrality and stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗