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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Magnetic structure, excitations and short-range order in honeycomb Na 2 Ni 2 TeO 6

Na 2 Ni 2 TeO 6 has a layered hexagonal structure with a honeycomb lattice constituted by Ni 2+ and a chiral charge distribution of Na + that resides between the Ni layers. In the present work, the antiferromagnetic transition temperature of Na 2 Ni 2 TeO 6 is confirmed at TN˜ 27 K, and further, it is found to be robust up to 8 T magnetic field and 1.2 GPa external pressure; and, without any frequency-dependence. Slight deviations from nominal Na-content (up to 5%) does not seem to influence the magnetic transition temperature, TN. Isothermal magnetization curves remain almost linear up to 13 T. Our analysis of neutron diffraction data shows that the magnetic structure of Na 2 Ni 2 TeO 6 is faithfully described by a model consisting of two phases described by the commensurate wave vectors vec kc, (0.5 0 0) and (0.5 0 0.5), with an additional short-range order component incorporated in to the latter phase. Consequently, a zig-zag long-range ordered magnetic phase of Ni 2+ results in the compound, mixed with a short-range ordered phase, which is supported by our specific heat data. Theoretical computations based on density functional theory (DFT) predict predominantly in-plane magnetic exchange interactions that conform to a J1-J2-J3 model with a strong J3 term. The computationally predicted parameters lead to a reliable estimate for TN and the experimentally observed zig-zag magnetic structure. A spin wave excitation in Na 2 Ni 2 TeO 6 at E ˜ 5 meV at T = 5 K is mapped out through inelastic neutron scattering experiments, which is reproduced by linear spin wave theory calculations using the J values from our computations. Our specific heat data and inelastic neutron scattering data strongly indicate the presence of short-range spin correlations, at T > TN, stemming from incipient antiferromagnetic clusters.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A Metastable CaSH 3 Phase Composed of HS Honeycomb Sheets that is Superconducting Under Pressure

Evolutionary searches have predicted a number of ternary Ca–S–H phases that could be synthesized at pressures of 100–300 GPa. P6 3 /mmc CaSH 2 , Pnma CaSH 2 , Cmc2 1 CaSH 6 , and I$\bar{4}$CaSH 20 were composed of a Ca–S lattice along with H 2 molecules coordinated in a “side-on” fashion to Ca. The H–H bond lengths in these semiconducting phases were elongated because of H 2 σ → Ca d donation, and Ca d → H 2 σ* back-donation, via a Kubas-like mechanism. P$\bar{6}$m2 CaSH 3 , consisting of two-dimensional HS and CaH 2 sheets, was metastable and metallic above 128 GPa. The presence of van Hove singularities increased its density of states at the Fermi level and concomitantly the superconducting critical temperature, which was estimated to be as high as ~100 K at 128 GPa. Furthermore, this work will inspire the search for superconductivity in materials based upon honeycomb HX (X = S, Se, Te) and MH 2 (M = Mg, Ca, Sr, Ba) layers under pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ferrimagnetic spin waves in honeycomb and triangular layers of Mn{sub 3}Si{sub 2}Te{sub 6}.

A detailed analysis of the ferrimagnetic ground state of Mn 3 Si 2 Te 6 has been performed using inelastic neutron scattering. Although the proposed valence of the nominal Mn 2+ ions would have quenched orbital angular momentum, a significant exchange anisotropy exists in Mn 3 Si 2 Te 6 . This apparent exchange anisotropy is a manifestation of a weak spin-orbit coupling in the layered material. We employ a detailed simulation of the spin-wave spectrum coupling traditional refinement of dispersion parameters to image analysis techniques, while including Monte Carlo simulations of the instrumental resolution to accurately identify the exchange couplings to the third nearest neighbor. An independent validation of our results is made by comparing our final Hamiltonian to heat capacity measurements.

Sala, G.↗
DOE OSTI2020

Determining Compression Characteristics of Honeycomb Material - 19674

The objective is to determine compression test characteristics of stainless steel honeycomb material to be able to represent honeycomb structures accurately in analytical models used to simulate hypothetical accident scenarios of shipping packages. Honeycomb is a material used primary in the aerospace industry due to its high strength-to-weight ratio. Because it doesn't have a shelf life and can withstand high heats, it is an excellent candidate for a structural material in package designs. Honeycomb has orthotropic material properties. The honeycomb currently being evaluated is made of metal ribbons spot welded together to form hexagon pattern between metal plates. The hexagon ribbons are brazed to the metal plates. The complexity of the honeycomb significantly lengthens the simulation time, which is further complicated when the brazing, welding, and imperfections of the material is considered. This means to affectively represent the honeycomb in simulation programs, such as Abaqus, the material needs to be approximated as a uniform orthotropic material. This requires material properties in each of the three directions, T, W, and L. The T direction is defined as the 'strong' direction, perpendicular to the honeycomb sheet. The L direction is parallel the ribbon and the W direction is perpendicular to the ribbon. Honeycomb has 3 different compression stages. Stage 1 is the initial compression where the honeycomb maintains its structural integrity and does not permanently deform from loads from normal operations. Stage 2 is when the initial buckling causes irreversible damage to the honeycomb. Stage 2 is the one we are most interested in because it absorbs the most energy from a hypothetical accident scenario. During Stage 2, the honeycomb fails layer-by-layer, indicating that the more layers, the longer material crushing is sustained, and thus the more energy that is absorbed. Stage 3 is final compression, similar to compressing solid metal. During stage 3 the stress increases with a diminishing rate of elongation and the honeycomb is completely failed where the plates between the honeycomb core sandwich the crushed honeycomb ribbon. The stress-strain graph bellow shows compression test of 3 different samples in the T direction. The red lines divide the three stages. The far left is Stage 1, the middle stage 2, and the right stage 3. The data collected is displayed in the table below. The expressions in the table represent the regression formula that represents each stage of the compression on a stress-strain graph. Stage 1 is assumed to intersect with the origin; data for stage 3 for the crush in W and L directions where unable to be gathered due to the nature of failure for those directions. Stage 1 and 2 are linear regressions while stage 3 is a degree 2, to best match the curve. Linear regression is used on stage 2 because ultimately that represents the energy absorbed. With more data, a degree n x 2 regression would be a more appropriate regression for stage 2, where n is the number of layers. The table below is the approximation of each scenario and stage. Each stage starts and ends at the intersection of the next stage. There where two main objectives for these tests: firstly to understand how honeycomb performs under extreme compression, and secondly to be able to numerically represent the honeycomb structure. Both of these where completed to varying degrees. It is important understood how the honeycomb fails. If it is crushed in the T direction it retains its integrity even after being crushed, however when crushed in the L and W crush direction, if it fails, it disintegrates, and loses all integrity. Also, the more layers the more time the material spends in stage 2. Failure is started by buckling, thus if there is any imperfection, the stress will not spike but transition straight into stage 2. The data collected and aggregated can be used for initial simulation of honeycomb used in packages. The initial testing has set the ground work for more data to be collected in order to verify results and to allow more confidence in the simulation results. This is only the initial data collected. The next steps is to continue to collect more data to verify results and to test more variants of honeycomb, with different brazing, layers, and shape.

36 MATERIALS SCIENCE↗
DOE OSTI2025

THE DESIGN OF RADIAL HONEYCOMB LATTICES FOR IMPACT ENERGY ABSORPTION IN RADIOACTIVE MATERIALS PACKAGES

In this research we present a variation on the corrugation technique of honeycomb lattices, for cylindrical honeycombs, making them much easier to design for impact energy absorption in radioactive materials packages. This variation, termed radial honeycomb lattices, eliminates the residual strain and saddle effect. The use of honeycomb lattices provides advantages over the typically used foams. While foams are effective at absorbing impact energy, they can burn, their material properties are difficult to control, they can degrade over time, and procurement of raw materials can be dependent on timing of manufacturer batch runs. While the weaknesses of foam are strengths for honeycomb lattices, lattices have a different set of problems. Typically, when cylindrical honeycomb lattices are manufactured, they are manufactured flat, wrapped around a mandrel of the desired radius, and then brazed. This approach introduces residual strains, resulting in the saddle effect, which limits both the radial thickness and cylinder length. The radial honeycomb lattice approach presented here makes the design of thicker and longer cylinder honeycombs possible. To address these issues, we propose a honeycomb lattice which changes in cross-section from the inner to the outer radius of the cylinder. This causes the lattice to automatically wrap into a cylinder as it exits the corrugating gears. The theoretically bounding case, of a square cross-section at the inner radius, transitioning through a hexagon, to a diamond cross-section at the outer radius, results in a maximum thickness of approximately 41% of the inner radius. Full mathematical derivations, implemented in computer code, allow for the design of an entire radial honeycomb lattice, including the corrugating gears. To accomplish this only the radial thickness, inner cross-section shape, cell size, and nominal gear radius need to be specified, making the design of these lattices very efficient. Radial honeycomb lattice prototypes have demonstrated that the honeycomb does indeed wrap into a cylinder as intended, without the saddle effect, and can therefore be used to create thick-walled cylinders of any length. These design improvements make cylindrical honeycomb lattices much more accessible as a design element for radioactive materials packages

Johnson, William R. [Savannah River National Labor↗
DOE OSTI2024

Structural Distortions and Short‐Range Magnetism in a Honeycomb Iridate Cu 3 ZnIr 2 O 6

Layered honeycomb iridates receive significant attention in the materials chemistry and physics fields due to the relevance of their crystal structures to the Kitaev model of a quantum spin liquid (QSL). In quest of liquid‐like magnetic ground state signatures, first‐generation alkali metal iridates A 2 IrO 3 ≡ A 3 [AIr 2 ]O 6 (A = Li, Na) and second‐generation iridates T 3 [AIr 2 ]O 6 ( T = Cu, Ag, H) are developed. T 3 [AIr 2 ]O 6 is synthesized from A 3 [AIr 2 ]O 6 via metathesis reactions replacing alkali ions located between honeycomb layers. Herein, the next level of chemical and structural complexity is introduced by synthesizing the honeycomb iridate, Cu 3 ZnIr 2 O 6 , in which alkali ions between and within the honeycomb layers are both selectively exchanged with two different transition metals. Analysis of powder X‐Ray diffraction data reveals corrugation of the honeycomb layers in Cu 3 ZnIr 2 O 6 that hinders complete magnetic frustration and results in a spin glass behavior observed from magnetization and specific heat data. Thus, Cu 3 ZnIr 2 O 6 represents yet another model, which broadens understanding of intricate relationships between intralayer distortions and magnetism of prospective Kitaev QSL compounds.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Honeycomb-Lattice Mott Insulator on Tantalum Disulphide

Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5$\textit{d}$ electrons. Iin this work, we engineer a well-known triangular lattice 2D Mott insulator 1$\textit{T}$ – TaS 2 into a honeycomb lattice utilizing an adsorbate superstructure. Potassium (K) adatoms at an optimum coverage deplete one-third of the unpaired $\textit{d}$ electrons and the remaining electrons form a honeycomb lattice with a very small hopping. Ab initio calculations show extremely narrow $Z_2$ topological bands mimicking the Kane-Mele model. Electron spectroscopy detects an order of magnitude bigger charge gap confirming the substantial electron correlation as confirmed by dynamical mean field theory. It could be the first artificial Mott insulator with a finite spin Chern number.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Exotic edge states of C 3 high-fold fermions in honeycomb lattices

A generalization of the graphene honeycomb model to the case where each site in the honeycomb lattice contains a n -fold degenerate set of eigenstates of the C 3 symmetry has been recently proposed to describe several systems, including triangulene crystals and photonic lattices. These generalized honeycomb models are defined by ( n a , n b ) , the number of C 3 eigenstates in the a and b sites of the unit cell, resulting in n a + n b bands. Thus, the (1,1) case gives the coventional honeycomb model that describes the two low-energy bands in graphene. Generalizations, such as (2,1), (2,2), and (3,3) display several nontrivial features, such as coexisting graphenelike Dirac cones with flat bands, both at zero and finite energy, as well as robust degeneracy points where a flat band and a parabolic band meet at the Γ point. Here we explore the edge states of this class of crystals, using as reference triangulene crystals, and we find several types of edge states absent in the conventional (1,1) honeycomb case, associated to the nontrivial features of the two-dimensional bands of the high-fold case. First, we find dispersive edge states associated to the finite-energy flat bands, that occur both at the armchair and zigzag termination. Second, in the case of noncentrosymmetric triangulene crystals that lead to a S = 1 Dirac band, we have a bonding-antibonding pair of dispersive edge states, localized in the same edge so that their energy splitting is reduced as their localization increases, opposite to the conventional behavior of pairs of states localized in opposite edges. Third, for the (3,3) case, that hosts a gap separating a pair of flat conduction and valence bands, we find nondispersive edge states with E = 0 in all edge terminations. Published by the American Physical Society 2024

Madail, L. (ORCID:0000000208457748)↗
DOE OSTI2021

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↗
DOE OSTI2023

Introducing the monoclinic polymorph of the honeycomb magnet Na 2 Co 2 TeO 6

Recent theoretical studies have suggested that the low-energy Hamiltonian of honeycomb cobaltate systems could be dominated by anisotropic Kitaev interactions. Motivated by the theory, a honeycomb layered material Na 2 Co 2 TeO 6 with a hexagonal unit cell has been studied and found to exhibit antiferromagnetic (AFM) ordering at 27 K with two spin reorientation transitions at 15 and 5 K. Here we report a monoclinic polymorph of Na 2 Co 2 TeO 6 , also with honeycomb layered structure but with a single AFM transition at 9.6 K and without spin reorientation transitions at lower temperatures. Here, using neutron diffraction, we identify an in-plane zigzag AFM order in the ground state with the spins canted out of the honeycomb planes and ferromagnetically coupled between them. The zigzag order is suppressed by a magnetic field of 6T. The lower critical temperature and field, positive Curie-Weiss temperature, and out-of-plane canting of spins in the monoclinic Na 2 Co 2 TeO 6 suggest enhanced frustration in this polymorph compared to the hexagonal one.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum Disordered State of Magnetic Charges in Nanoengineered Honeycomb Lattice

Abstract A quantum magnetic state due to magnetic charges is never observed, even though they are treated as quantum mechanical variables in theoretical calculations. Here, the occurrence of a novel quantum disordered state of magnetic charges in a nanoengineered magnetic honeycomb lattice of ultra‐small connecting elements is demonstrated. The experimental research, performed using spin resolved neutron scattering, reveals a massively degenerate ground state, comprised of low integer and energetically forbidden high integer magnetic charges, that manifests cooperative paramagnetism at low temperature. The system tends to preserve the degenerate configuration even under large magnetic field application. It exemplifies the robustness of disordered correlation of magnetic charges in a 2D honeycomb lattice. The realization of quantum disordered ground state elucidates the dominance of exchange energy, which is enabled due to the nanoscopic magnetic element size in nanoengineered honeycomb. Consequently, an archetypal platform is envisaged to study quantum mechanical phenomena due to emergent magnetic charges.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

N-doped honeycomb-like porous carbon towards high-performance supercapacitor

Biomass-derived porous carbon with developed pore structure is critical to achieving high performance electrode materials. In this work, we report a grape-based honeycomb-like porous carbon (GHPC) prepared by KOH activation and carbonization, followed by N-doping (NGHPC). The obtained NGHPC exhibits a unique honeycomb-like structure with hierarchically interconnected micro/mesopores, and high specific surface area of 1268 m2/g. As a supercapacitor electrode, the NGPHC electrode exhibits a remarkable specific capacitance of 275 F/g at 0.5 A/g in a three-electrode cell. Moreover, the NGHPC//NGHPC symmetric supercapacitor displays a high energy density of 12.6 Wh/kg, and excellent cycling stability of approximately 95.2% capacitance retention after 5000 cycles at 5 A/g. The excellent electrochemical performance of NGHPC is ascribed to its high specific surface area, honeycomb-like structure and high-content of pyrodinic-N (36.29%). It is believed that grape-based carbon materials show great potential as advanced electrode materials for supercapacitors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum anomalous Hall insulator phases in Fe-doped GaBi honeycomb

We discuss electronic and magnetic properties of the Fe-doped GaBi honeycomb using first principles calculations. Our analysis shows that the pristine GaBi honeycomb transitions from being a two-dimensional quantum spin Hall (QSH) insulator to a quantum anomalous Hall (QAH) insulator when it is doped with one Fe atom in a 4 × 4 GaBi honeycomb. Additionally, the QAH phase in Fe-doped GaBi is found to be robust in that it maintains its Chern number (C = 1) under fairly large strains (~ 4%) and supports a gap as large as 112 meV at 2.21% strain. The QAH phase is also retained when the Fe-doped GaBi is placed on a CdTe substrate, suggesting that Fe-doped GaBi films could be useful for spintronics applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Crystal structure, magnetism, and specific heat of lightly depleted layered honeycomb oxides, Na$_2$(Ni$_{2-x}$D$_x$)TeO$_6$ ($D$ = Mg, Ga, Co; 0.10 ≤ $x$ ≤ 0.25)

Layered oxides, in which transition metal atoms form a honeycomb lattice, are known for complex magnetic phase diagrams. In this work we study the doped compounds, Na$_2$(Ni$_{2-x}$D$_x$)TeO$_6$, $D$ = Mg, Ga, and Co (0.10 ≤ $x$ ≤ 0.25), to understand how chemical dilution at the nickel site influences the stability of magnetic exchanges within the honeycomb layer of the parent, Na$_2$ Ni$_2$ TeO$_6$. Here, the studied compounds were found to crystallize in $P6_3/mcm$ space group common to P2 type layered oxides. In general, the lattice parameters and the unit cell volume expanded with increased doping. The oxidation states determined from X-ray photoelectron spectroscopy were consistent with bond valence sum estimates, that confirmed the presence of Ni$^{2+}$, Mg$^{2+}$, Ga$^{3+}$, Co$^{2+}$ in our samples. Irrespective of magnetic or non-magnetic doping, the magnetic phase transition temperature ($T_N$) of the doped compounds were reduced from that of Na$_2$ Ni$_2$ TeO$_6$ or Na$_2$ Co$_2$ TeO$_6$, and lay between 21.7 K and 26.8 K. The effective paramagnetic moments extracted from Curie–Weiss analysis were in the range 3.17 μ B to 3.84 μ B and the Weiss temperatures were between $-15$ K and $-25$ K, suggesting antiferromagnetism. Mg- and Ga-doped compounds showed free spin formation, indicated by Curie–Weiss tails in their magnetic susceptibility. Our results suggest emergence of short-range magnetic correlations in Na$_2$(Ni$_{2-x}$D$_x$)TeO$_6$, enhanced due to the depletion of the Ni honeycomb lattice.

75 - CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY A↗
DOE OSTI2025

Synthesis and Characterization of Metastable Cobalt Honeycomb KCoAsO 4

The Kitaev model has served as a long-sought-after target in the realization of a quantum spin liquid that could host Majorana Fermions. Such non-Abelian anyons could revolutionize quantum computing if properly implemented to overcome decoherence. A 3d 7 electronic configuration, like Co 2+ , has been explored by theory and experimental work to design Kitaev materials. Here, in this study, we report the synthesis of a new cobaltate honeycomb material KCoAsO 4 . The compound is synthesized through a low-temperature solution route and crystallized in space group R¯3 with lattice parameters a = 5.0394(1) and c = 28.6790(1) as determined by neutron powder diffraction. The crystal structure follows motifs similar to those of the honeycomb compound BaCo2(AsO 4 ) 2 but presents differing magnetic behavior. Magnetization/heat capacity measurements on the powder show antiferromagnetic transition T N = 14 K. Two lower-temperature transitions are present in susceptibility at low field that resemble spin reorientations. Magnetization data as a function of field have curvature indicative of metamagnetic behavior below the magnetic ordering temperature, with the magnetic ordering suppressed upon application of a higher magnetic field. Computational studies suggest the presence of a weak nearest-neighbor Kitaev term, K 1 , consistent with related honeycomb cobaltates. Together, the data suggest that this material should present a new platform for developing Kitaev quantum spin liquids.

cobaltate↗
DOE OSTI2021

Ground state in proximity to a possible Kitaev spin liquid: The undistorted honeycomb iridate Na x IrO 3 (0.60 ≤ x ≤ 0.80)

Here, we report the results of our study of a recently synthesized honeycomb iridate Na x IrO 3 (0.60 ≤ x ≤ 0.80). Single-crystal Na x IrO 3 adopts a honeycomb lattice noticeably without distortions and stacking disorder inherently existent in its sister compound Na 2 IrO 3 . The oxidation state of the Ir ion is a mixed valence state resulting from a majority Ir 5+ (5d 4 ) ion and a minority Ir 6+ (5d 3 ) ion. Na x IrO 3 is a Mott insulator likely with a predominant pseudospin =1 state. It exhibits an effective moment of 1.1 μB/Ir and a Curie-Weiss temperature of –19 K but with no discernible long-range order above 1 K. The physical behavior below 1 K features two prominent anomalies at T h = 0.9 K and T l = 0.12 K in both the heat capacity and AC magnetic susceptibility. Intermediate between T h and T l lies a pronounced temperature linearity of the heat capacity with a large slope of 77 mJ /mole K 2 , a feature expected for highly correlated metals but not at all for insulators. These results along with a comparison drawn with the honeycomb lattices Na 2 IrO 3 and (Na 0.2 Li 0.8 ) 2 IrO 3 point to an exotic ground state in proximity to a possible Kitaev spin liquid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗