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At least 19 records

Design and Beam Test Results for the 2-D Projective sPHENIX Electromagnetic Calorimeter Prototype

sPHENIX is a new experiment under construction for the Relativistic Heavy Ion Collider at Brookhaven National Laboratory which will study the quark-gluon plasma to further the understanding of quantum chromodynamics (QCP) matter and interactions. A prototype of the sPHENIX electromagnetic calorimeter (EMCal) was tested at the Fermilab Test Beam Facility in Spring 2018 as experiment T-1044.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Charge-4e Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene

We show that unconventional nematic superconductors with multicomponent order parameter in lattices with three- and sixfold rotational symmetries support a charge-4e vestigial superconducting phase above T c . The charge-4e state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is nonsuperconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-4e state over the nematic phase, as it acts as a random mass to the former but as a random field to the latter. Furthermore, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-4e superconducting phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The Use of Long-wave Infrared Cameras for Hazardous Waste Remediation - 20457

For over fifty years, infrared cameras have been used in military applications, nondestructive testing, condition monitoring, and predictive maintenance. As infrared cameras continue to become more sophisticated and less expensive, they are providing value in an ever-increasing variety of unique applications, including hazardous waste remediation. This paper describes several instances of how infrared cameras have been used within the US Department of Defense and the US Department of Energy in support of waste remediation projects, including the author's recent use of an infrared camera in support of the Calcine Retrieval Project at the Idaho National Laboratory. Infrared cameras provide images of infrared radiation, or heat energy, which is otherwise invisible to the unaided eye. Infrared radiation is part of the electromagnetic spectrum, which includes visible light. But unlike visible light, infrared has wavelengths longer than the human eye can detect. Infrared is emitted by everything with a temperature above absolute zero (-273 deg. C, or -459 deg. F); the higher the temperature, the greater the infrared thermal radiation, or heat, that is emitted. Even objects that feel cold to us, like ice, emit thermal radiation and can be imaged by infrared cameras. These cameras are typically used to look for abnormally hot or cold spots on a component or target area under normal operating conditions. The method provides a rapid, wide-area, noncontact technique for identifying problems associated with a temperature differential. All infrared cameras can provide qualitative thermal information by displaying relative differences in temperatures within a two-dimensional image. More expensive infrared cameras can also provide quantitative information where an absolute temperature value is assigned to each pixel associated with the displayed two-dimensional image. Proper camera calibration and a solid understanding of heat transfer and thermography techniques are required when using an infrared camera to obtain quantitative information. Case studies outlined in this paper include the rapid, non-intrusive detection of hazardous decontamination solution within one-ton shipping containers at Pine Bluff Arsenal, the non-intrusive identification of residual elemental sodium within the cooling loops of the Experimental Breeder Reactor II (EBR-II) reactor at the Idaho National Laboratory, process monitoring of heat exchanger melt-and-drain efforts during EBR-II decommissioning, and the remote detection of internal steel supports within calcine storage bins prior to bin penetration. For each use of thermography, the author describes a summary of the waste remediation effort, the infrared camera used, the thermal imaging technique employed, and the results obtained. The paper concludes with a discussion on common mistakes to avoid for similar applications of thermography. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Spin reorientations in structurally metastable, disordered, and hexagonal Cr 7 ⁢Te 8

Vapor deposited two-dimensional Cr 7 ⁢Te 8 displays unusual temperature dependent Hall effect properties, including a room-temperature anomalous Hall effect, sign reversals of the Hall resistivity on cooling, and a peak in the Hall resistivity at low temperatures. The two-dimensional Cr 7⁢ Te 8 heterostructures that form the basis of these measurements are hexagonal in structure. We study the magnetic and structural properties of bulk Cr 7 ⁢Te 8 synthesized by quenching from 1000⁢°C with the goal of relating the magnetic, structural, and electronic properties. This quenched phase is metastable, hexagonal, and displays different magnetic properties from the slow-cooled and more thermodynamically stable monoclinic phase. High-resolution x-ray diffraction of the quenched hexagonal phase finds a first-order transition to a lower symmetry monoclinic phase on heating above ∼550 K. Magnetic susceptibility measurements of the quenched hexagonal phase reveal ferromagnetic ordering above room temperature, along with the two distinct transitions at ∼220 K and ∼70 K. Through neutron diffraction studies, we find the ∼220 K anomaly is a spin reorientation transition of the ferromagnetically aligned magnetic moments and the ∼70K feature represents a transition from a high-temperature ferromagnet to a low-temperature antiferromagnet. We suggest that these magnetic transitions are related to changes in the unit-cell dimensions and are connected to the temperature-dependent Hall resisitivity studied in two-dimensional heterostructures. This implies a link between structural, magnetic, and electronic properties in the “pseudo” two-dimensional chromium tellurides.

Chemical synthesis↗

Li x (C 5 H 5 N) y Fe 2– z Se 2 : A Defect-Resilient Expanded-Lattice High-Temperature Superconductor

Two-dimensional iron chalcogenide intercalates display a remarkable correlation of the interlayer spacing with enhancement of the superconducting critical temperature (T c ). In this work, synchrotron X-ray absorption (XAS; at the Fe and Se K-edges) and emission (XES; at the Fe Κβ) spectroscopies allow one to discuss how the important rise of T c (~44 K) in the molecule-intercalated Li x (C 5 H 5 N) y Fe 2-z Se 2 relates to the electronic and local structural changes felt by the inorganic host upon doping (x). XES shows that widely separated layers of edge-sharing FeSe 4 tetrahedra carry low-spin moieties, with a local Fe magnetic moment slightly reduced compared to the parent β-Fe 2-z Se 2 . Pre-edge XAS expresses the progressively reduced mixing of metal 3d-4p states upon lithiation. Doping-mediated local lattice modifications, probed by conventional T c optimization measures (cf. the anion height and FeSe 4 tetrahedra regularity), become less relevant when layers are spaced far away. On the basis of extended X-ray absorption fine structure, such distortions are compensated by a softer Fe network that relates to Fe-site vacancies, alleviating electron-lattice correlations and superconductivity. Density functional theory (DFT) guided modification of the isolated Fe 2-z Se 2 (z, vacant sites) planes, resembling the host layers, identify that Fe-site deficiency occurs at low energy cost, giving rise to stretched Fe sheets, in accordance with experiments. Here, the robust high-T c in Li x (C 5 H 5 N) y Fe 2-z Se 2 , arises from the interplay of electron-donating spacers and the iron selenide layer's tolerance to defect chemistry, a tool to favorably tune its Fermi surface properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Flat bands and ferrimagnetic order in electronically correlated dice-lattice ribbons

In this work, we study ribbons of the dice two-dimensional lattice (that we call “dice ladders”) known to have nontrivial topological properties, such as Chern numbers 2. Our main results are two fold. (1) Analyzing the tight-binding model in the presence of Rashba spin-orbit coupling and an external magnetic field, we observed that dice ladders qualitatively display properties similar to their two-dimensional counterpart all the way to the limit of only two legs in the short direction. This includes flat bands near the Fermi level, edge currents and edge charge localization near zero energy when open boundary conditions are used, two chiral edge modes, and a nonzero Hall conductance. (2) We studied the effect of Hubbard correlation U in the two-leg dice ladder using Lanczos and density matrix renormalization group techniques. We show that by increasing U the flat bands split without the need of introducing external fields. Moreover, robust ferrimagnetic order develops. Overall, our work establishes dice ladders as a promising playground to study the combined effect of topology and correlation effects, one of the frontiers in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Metastable piezoelectric group-IV monochalcogenide monolayers with a buckled honeycomb structure

Multiple two-dimensional materials are being naïvely termed stable on the grounds of displaying phonon dispersions with no negative frequencies and of not collapsing on molecular dynamics calculations at fixed volume. But, if these phases do not possess the smallest possible structural energy, how does one understand and establish their actual meta stability? To answer this question, twelve two-dimensional group-IV monochalcogenide monolayers (SiS, SiSe, SiTe, GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, and PbTe) with a buckled honeycomb atomistic structure—belonging to symmetry group P3m1—displaying an out-of-plane intrinsic electric polarization are shown to be metastable by three independent methods. First, we uncover a coordination-preserving structural transformation from the low-buckled honeycomb structure onto the lower-energy Pnm2 1 (or Pmmn for PbS, PbSe, and PbTe) phase to estimate energy barriers E B that must be overcome during such structural transformation. Using the curvature of the local minima and E B as inputs to Kramers escape formula, large escape times are found, implying the structural metastability of the buckled honeycomb phase (with the exception of PbS and PbSe, these phases display escape times ranging from 700 years to multiple times the age of the universe and can be considered “stable” for practical purposes in that relative sense). The second demonstration is provided by phonon dispersion relations that include the effect of long-range Coulomb forces and display no negative vibrational modes. The third and final demonstration of structural metastability is furnished by room-temperature ab initio molecular dynamics for selected compounds. Here, the magnitude of the electronic band gap evolves with chemical composition. Different from other binary two-dimensional compounds such as transition metal dichalcogenide monolayers and hexagonal boron nitride monolayers which only develop an in-plane piezoelectric response, the twelve group-IV monochalcogenide monolayers with a buckled honeycomb structure also display out-of-plane piezoelectric properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A perspective on two-dimensional van der Waals opto-spin-caloritronics

Two-dimensional (2D) van der Waals magnetic semiconductors displaying controllable ferromagnetism at room temperature form atomically sharp interfaces with various substrates. Such heterostructures create platforms for understanding spin-dependent phenomena across interfaces and surfaces for high-performance technological applications. Combining these 2D magnets with light and the spin Seebeck effect (SSE) in-state-of-the-art thermo-opto-spin studies forms a new paradigm in the field of spin-caloritronics that harnesses light as the new heat. In this Perspective, we detail how to exploit recent advances in 2D van der Waals materials to boost the SSE and propose a new strategy for optically controlled SSE in 2D magnetic semiconductor-based heterostructures with the intent to establish the research thrust of “opto-spin-caloritronics.”

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Colloquium : Physical properties of group-IV monochalcogenide monolayers

The state-of-the-art knowledge of ferroelectric and ferroelastic group-IV monochalcogenide monolayers is surveyed. These semiconductors feature remarkable structural and mechanical properties, such as a switchable in-plane spontaneous polarization, soft elastic constants, structural degeneracies, and thermally driven two-dimensional structural transformations. Additionally, these 2D materials display selective valley excitations, valley Hall effects, and persistent spin helix behavior. After a description of their Raman spectra, a discussion of optical properties arising from their lack of centrosymmetry (such as an unusually strong second-harmonic intensity, large bulk photovoltaic effects, photostriction, and tunable exciton binding energies) is provided as well. Here, the physical properties observed in these materials originate from (correlate with) their intrinsic and switchable electric polarization, and the physical behavior hereby reviewed could be of use in nonvolatile memory, valleytronic, spintronic, and optoelectronic devices: these 2D multiferroics enrich and diversify the 2D material toolbox.

2D ferroelectrics↗

Chirality Transfer to the Magnetic Sublattice in the Hybrid Perovskite (R)-/(S)-3-Fluoropyrrolidinium Copper(II) Chloride

Incorporating chiral organic cations into organic–inorganic hybrid materials has been shown to enable the inorganic sublattice to display chiroptical properties. We report a new two-dimensional magnetic (S = 1/2) chiral metal halide perovskite, (R)- and (S)-(C 4 H 9 FN) 2 CuCl 4 (where (C 4 H 9 FN) + is 3-fluoropyrrolidinium), which consists of Cu–Cl inorganic layers separated by (C 4 H 9 FN) + organic cations. The presence of the chiral (C 4 H 9 FN) + organic cation induces the formation of chiral magnetic order, even though the inorganic sublattice itself is nearly structurally centrosymmetric. We also report the racemic variant, containing an equal amount of (R)- and (S)- cations, which shows no evidence of chiral magnetic order. When the magnetic susceptibility is measured perpendicular to the inorganic Cu–Cl layer propagation direction, an antiferromagnetic phase transition at Néel temperature T N = 2.23 K is observed in both the chiral and racemic materials, and the existence of the magnetic phase transition is supported by specific heat capacity measurements. Field-induced magnetic chirality is observed through the existence of a second-order magnetoelectric effect in the chiral variant, while no magnetoelectric signal is observed for the racemic material, indicating the absence of magnetic chirality. Our findings demonstrate that materials exhibiting chiral magnetic order can be created through the incorporation of a chiral cation into an organic–inorganic hybrid magnetic material, potentially allowing for the design of tailored materials that combine chiral magnetism with other desirable optical and electronic properties that come from structural chirality.

Cations↗

Excitons in two-dimensional metal-halide perovskites

Georgia Tech School of Chemistry and Biochemistry Special Summer Seminar Series, Prof Carlos Silva; While polarons --- charges bound to a lattice deformation induced by electron-phonon coupling --- are primary photoexcitations at room temperature in bulk metal-halide hybrid organic-inorganic perovskites (HOIP), excitons --- Coulomb-bound electron-hole pairs --- are the stable quasi-particles in their two-dimensional (2D) analogues. Here we address the fundamental question: are polaronic effects consequential for excitons in 2D-HIOPs? Based on our recent work, we argue that polaronic effects are manifested intrinsically in the exciton spectral structure, which is comprised of multiple non-degenerate resonances with constant inter-peak energy spacing. We highlight measurements of population and dephasing dynamics that point to the apparently deterministic role of polaronic effects in excitonic properties. We contend that an interplay of long-range and short-range exciton-lattice couplings give rise to exciton polarons, a character that fundamentally establishes their effective mass and radius, and consequently, their quantum dynamics. Given this complexity, a fundamentally far-reaching issue is how Coulomb-mediated many-body interactions---elastic scattering such as excitation-induced dephasing, inelastic exciton bimolecular scattering, and multi-exciton binding---depend upon the specific exciton-lattice coupling within the structured excitation lineshape. We measure the intrinsic and density-dependent exciton dephasing rates of the multiple excitons and their dependence on temperature by means of two-dimensional coherent excitation spectroscopy. We find that diverse excitons display distinct intrinsic dephasing rates mediated by phonon scattering involving different effective phonons, and contrasting rates of exciton-exciton elastic scattering. These findings establish specifically the consequence of distinct lattice dressing on exciton many-body quantum dynamics, which critically define fundamental optical properties that underpin photonics and quantum optoelectronics.

solar cells, metal-halide perovskites, excitons, p↗

2020 Vehicle Technology Office Annual Progress Report from Jianchao Ye

Traditional batteries are composed of two-dimensional films that are stacked and/or rolled. Thin film batteries display high power density while their thick film counterparts show good energy density, but it has proven difficult to concurrently achieve both within these planar form factors. In addition, conventional Li-ion batteries based on liquid organic electrolytes or gel polymer electrolytes have raised severe safety concerns due to the intrinsic flammable properties of the organic electrolytes.

25 ENERGY STORAGE↗

VTO_2021_APR_LLNL_Ye

Traditional batteries are composed of two-dimensional films that are stacked and/or rolled. Thin film batteries display high power density while their thick film counterparts show good energy density, but it has proven difficult to concurrently achieve both within these planar form factors. In addition, conventional Li-ion batteries based on liquid organic electrolytes or gel polymer electrolytes have raised severe safety concerns due to the intrinsic flammable properties of the organic electrolytes. They are also not ideal for the use of high energy density metallic lithium (Li) anodes due to Li dendrite growth, or sulfur cathodes due to shuttling effects that result in fast capacity fade. There is an urgent need to develop safe, high-performance solid-state batteries (SSBs) with advanced electrolyte and separator technologies. Although in recent years a series of superionic conductors have been developed for electrolytes and separators, their performance does not satisfy demanding criteria due to large impedance from poor solid electrolyte-electrode contact and questionable electrochemical and mechanical stability. Unlike the well-established roll-to-roll fabrication of conventional Li-ion batteries, the processing of SSBs is unique due to the brittleness of solid-state electrolytes (SSEs). The commercially available or lab-developed SSE discs are usually very thick (hundreds of micrometers to millimeters) to overcome their brittle nature, which unfortunately increases the cell impedance and accounts for the majority of the overall cell weight and volume, leading to dramatically decreased power and energy densities. In this project, we will investigate 3D printing techniques to overcome safety, fabrication, mechanical, and electrochemical issues in SSBs. 3D printing builds complex structures in a layer-by-layer fashion, which allows rapid production of hierarchical architectures, gradient and multi-material structures, and multi-component assemblies. 3D printing is an emerging area that could fundamentally transform energy storage devices. For example, 3D printing can produce batteries with arbitrary form factors to fit a product’s specific volume requirements and can create interwoven electrode arrangements over a wide range of length scales to improve transport and increase power density for a given energy density. For SSBs, 3D printing may dramatically reduce the separator thickness from ~1 mm (by hydraulic pressing) to tens of micrometers or less. In addition, the interfacial contact area between the electrolyte and the electrode may be increased via 3D interdigitated designs. Hence, we expect a significant reduction of the overall cell impedance and enhancement of both energy and power densities of SSBs by harnessing an array of 3D printing technologies being developed at Lawrence Livermore National Laboratory (LLNL).

25 ENERGY STORAGE↗

Hierarchical domain structures in buckled ferroelectric free sheets

Flat elastic sheets tend to display wrinkles and folds. From pieces of clothing down to two-dimensional crystals, these corrugations appear in response to strain generated by sheet compression or stretching, thermal or mechanical mismatch with other elastic layers, or surface tension. Extensively studied in metals, polymers and, — more recently — in van der Waals exfoliated layers, with the advent of thin single crystal freestanding films of complex oxides, researchers are now paying attention to novel microstructural effects induced by bending ferroelectric-ferroelastics, where polarization is strongly coupled to lattice deformation. Here we show that wrinkle undulations in BaTiO3 sheets bonded to a viscoelastic substrate transform into a buckle delamination geometry when transferred onto a rigid substrate. Using spatially resolved techniques at different scales (Raman, scanning probe and electron microscopy), we show how these delaminations in the free BaTiO3 sheets display a self-organization of ferroelastic domains along the buckle profile that strongly differs from the more studied sinusoidal wrinkle geometry. Moreover, we disclose the hierarchical distribution of a secondary set of domains induced by the misalignment of these folding structures from the preferred in-plane crystallographic orientations. Our results disclose the relevance of the morphology and orientation of buckling instabilities in ferroelectric free sheets, for the stabilization of different domain structures, pointing to new routes for domain engineering of ferroelectrics in flexible oxide sheets.

36 MATERIALS SCIENCE↗

Ultrathin Plasmonic Tungsten Oxide Quantum Wells with Controllable Free Carrier Densities

Localized surface plasmon resonances (LSPR) of nanostructures can be tuned by controlling their morphology, local dielectric environment, and free carrier concentration. We report the colloidal synthesis of an ~3 tungsten–oxygen (W-O) layer thick (~1 nm), two-dimensional (2D) WO 3-x nanoplatelets (NPLs) (x ≈ 0.55–1.03), which display tunable near-infrared LSPR properties and additionally high free electron density (N e ) that arises predominantly from the large shape factor of 2D NPLs. Importantly, the W to O composition ratios inferred from their LSPR measurements show much higher percentage of oxygen vacancies than those determined by X-ray diffraction analysis, suggesting that the aspect ratio of ultrathin WO 3-x NPLs is the key to producing an unprecedentedly large Ne, although synthesis temperature is also an independent factor. We find that NPL formation is kinetically controlled, whereas thermodynamic parameter manipulation leads to N e values as high as 4.13 × 10 22 cm –3 , which is close to that of plasmonic noble metals, and thus our oxide-based nanostructures can be considered as quasi-metallic. The unique structural properties of 2D nanomaterials along with the high N e of WO 3-x NPLs provide an attractive alternative to plasmonic noble metal nanostructures for various plasmon-driven energy conversions and design of photochromic nanodevices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nanophotonic waveguide chip-to-world beam scanning

A seamless chip-to-world photonic interface enables broad advancements in optical ranging, display, communication, computation and quantum information science. The ideal solution enables two-dimensional scanning of a diffraction-limited beam from anywhere on a photonic integrated circuit to a large number of resolvable spots. Current beam-scanning technologies are limited by a fundamental trade-off: photonic-integrated-circuits with diffractive optics offer scalability but have poor mode quality, whereas inertially limited micromechanical scanners provide high-quality beams but lack scalable integration. Here we report a photonic ski-jump—a nanoscale waveguide monolithically integrated on a piezoelectric cantilever—to overcome these limitations. It passively curls ~90° out-of-plane within a less-than-0.1 mm 2 footprint, emits a submicrometre, broadband diffraction-limited beam, and exhibits kilohertz-rate mechanical resonances with quality factors of over 10,000. Fabricated in a volume complementary metal–oxide–semiconductor (CMOS) foundry, our device enables scalable two-dimensional beam scanning. Driven on-resonance at CMOS-level voltages, it achieves a footprint-adjusted spot rate of 68.6 mega spots s –1 mm–², exceeding state-of-the-art micro-electro-mechanical systems mirrors by more than 50-fold, which is sufficient for one million pixels at 100 Hz from an approximately 1.5 mm diameter footprint. We demonstrate full-colour image and video projection, and single-photon initialization and readout from silicon vacancy centres in diamond. Finally, by demonstrating uniformity across a 64 ski-jump array, we establish a pathway to achieving greater than one gigaspot resolution at kilohertz rates within a sub-5-cm-diameter footprint, creating a seamless optical pipeline between integrated photonic processors and the free-space world.

Displays↗

Strong-field nonsequential double photoionization using virtual-detector theory with path summation

We present an ab initio study of the nonsequential strong-field ionization dynamics of a model two-electron atom with helium character. Single- and double-ionization events are characterized and displayed using detector signals extracted at different points in the two-electron two-dimensional space. The double photoelectron momentum distribution is calculated via coherent path-summation over virtual-particle trajectories. A comparison is made between the momentum distributions obtained with the virtual-detector method, the Schrödinger wave function, and the time-dependent surface flux method developed by Tao and Scrinzi [New J. Phys. 14, 013021 (2012)]. Insights into different ionization and electron recollision pathways are gained from detailed virtual-particle tracking and energy-time readouts. Furthermore, this study demonstrates the extension of virtual-detector theory to strong-field multielectron quantum dynamics and highlights the importance of the evolving quantum phase in quasiclassical electron propagation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

From n- to p-type material: Effect of Metal Ion on Charge Transport in Metal-Organic Materials

An intriguing new class of two-dimensional (2D) materials based on metal–organic frameworks (MOFs) has recently been developed that displays electrical conductivity, a rarity among these nanoporous materials. The emergence of conducting MOFs raises questions about their fundamental electronic properties, but few studies exist in this regard. Here, we present an integrated theory and experimental investigation to probe the effects of metal substitution on the charge transport properties of M-HITP, where M = Ni or Pt and HITP = 2,3,6,7,10,11-hexaiminotriphenylene. The results show that the identity of the M-HITP majority charge carrier can be changed without intentional introduction of electronically active dopants. We observe that the selection of the metal ion substantially affects charge transport. Using the known structure, Ni-HITP, we synthesized a new amorphous material, a-Pt-HITP, which although amorphous is nevertheless found to be porous upon desolvation. Importantly, this new material exhibits p-type charge transport behavior, unlike Ni-HITP, which displays n-type charge transport. These results demonstrate that both p- and n-type materials can be achieved within the same MOF topology through appropriate choice of the metal ion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗