Search NASA⌕ Search

SEARCH · Search NASA

Results for “trigonal”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Trigonal symmetry breaking and its electronic effects in the two-dimensional dihalides MX 2 and trihalides MX 3

We study the consequences of the approximately trigonal (D 3d ) point symmetry of the transition metal (M) site in two-dimensional van der Waals MX 2 dihalides and MX 3 trihalides. The trigonal symmetry leads to a 2-2-1 orbital splitting of the transition metal d shell, which is best represented by d orbitals that describe the trigonal rather than Oh symmetry. The ligand-ligand bond length differences (rather than metal-ligand) take the role of a Jahn-Teller-like mode and in combination with interlayer distances and dimensionality effects tune the crystal field splittings and bandwidths. These effects, in turn, are amplified by electronic correlation effects—leading to crystal field splittings of the order of 0.1–1 eV between the singlet and the lowest orbital doublet—as opposed to the often assumed degenerate 3 t 2g states. Our calculations explain why most of the materials in this family are insulating, and why these considerations have to be taken into account in realistic models of them. Further, orbital order coupled to various lower symmetry lattice modes may lift the remaining orbital degeneracies, and we explain how these may support unique electronic states using ZrI 2 and CuCl 2 as examples, and offer a brief overview of possible electronic configurations in this class of materials. By building and analyzing Wannier models adapted to the appropriate symmetry we examine how the interplay among trigonal symmetry, electronic correlation effects, and – d orbital charge transfer leads to insulating, orbitally polarized magnetic and/or orbital-selective Mott states, and we provide a simple framework and numerical tool for others. Our paper establishes a rigorous framework to understand, control, and tune the electronic states in low-dimensional correlated halides. Furthermore, our analysis shows that trigonal symmetry and its breaking is a key feature of the two-dimensional halides that needs to be accounted for in search of novel electronic states in materials ranging from CrI 3 to α–RuCl 3 .

2-dimensional systems↗
DOE OSTI2020

Trigonal polymorph of Li 2 MnO 3

We report the discovery of a trigonal polymorph of the prospective Li ion battery material Li 2 MnO 3 and its synthesis in bulk, single crystal form. Crystal growth of trigonal Li 2 MnO 3 is strongly dependent upon the quality of a polycrystalline LiMnO 2 precursor consumed in the synthesis process. The crystal structure of the new trigonal phase is composed of ordered honeycomb layers of LiO 6 and MnO 6 octahedra segregated by layers of LiO 6 octahedra and represents an ordered stacking variant of the known monoclinic polymorph. Diffuse reflectance spectroscopy reveals a direct optical gap of 2.47 ± 0.11 eV and a series of charge excitations that are well explained by the expected Mn 4+ 3d 3 valence. Density functional theory calculations are in excellent agreement with the spectroscopic measurements and find a near degeneracy in the formation energies of the two polymorphs. Furthermore, our results suggest that the trigonal structure resolves the compositional and structural disorder often manifested in the monoclinic phase.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Trigonal Planar Bis (carbene)Cu(I) Complexes Enable Divergent H 2 Activation with H 2 O for Accelerated Olefin Hydrogenation

CuH-catalyzed olefin hydrogenation is rare compared to those of carbonyl-derived substrates. Olefin insertion into Cu–H to form Cu-alkyl is ubiquitous; however, subsequent H 2 activation remains unknown to our knowledge. Herein, we investigated the transformations of β-H elimination, H 2 cleavage, and catalytic olefin hydrogenation in a series of linear and trigonal planar Cu(I)-alkyl complexes supported by monodentate N-heterocyclic carbene and bidentate naphthyridine- bis (carbene) ligands, respectively. Contrary to unreactive linear species, trigonal planar variants promote β-H elimination, hydrogenolysis, and catalytic hydrogenation of unactivated alkenes at mild temperatures and H 2 pressure. The rare isolation of a naphthyridine- bis (carbene)CuH monomer further affirms two predominant competing pathways for H 2 cleavage of metal–ligand cooperativity at Cu(I)-alkyl or internal electrophilic substitution at Cu(I)-OH. Employing either isolated or in situ generated Cu(I)-OH complex, via protonolysis of alkyl precatalyst by adventitious water, significantly accelerated catalysis compared to that operating primarily by the metal–ligand cooperativity pathway. DFT calculations and energy decomposition analysis on the disparate β-H elimination reactivity between linear and trigonal planar tert-butyl complexes and the mechanism of H 2 activation at a hydroxide complex, indicate that coordination geometry at Cu(I) and properties of the naphthyridine- bis (carbene) ligand are integral to the transformations reported here.

ALMO-EDA↗
DOE OSTI2024

Synthesis and Structural Investigation of Rigid Naphthyridine-Bis(carbene) for Trigonal Planar Coordination of Coinage Metals

Coinage metal complexes, particularly Cu(I) and Au(I), supported by N-heterocyclic carbenes are of broad interest in organometallic synthesis, catalysis, and luminescent materials. The d 10 coinage metals can adopt varied linear, trigonal planar, and tetrahedral geometries. However, two-coordinate, linear Cu(I) and Au(I) complexes supported by sterically demanding monodentate or chelating carbenes are generally observed. In most cases, chelating ligands generate multinuclear species with linear geometries at the corresponding Cu(I) centers rather than mononuclear complexes. In this report, we synthesized two bis(carbene) ligands anchored by a flexible bipyridine and a rigid naphthyridine backbone with tunable proximal and distal steric properties at the wingtips to examine the influence of backbone rigidity and directionality of carbene donors on the formation of trigonal planar coinage metal species. Here, the bipyridine-bis(carbene) (ImPy) 2 ligand exclusively stabilizes dinuclear chloride complexes of Cu(I) and Ag(I), whereas the naphthyridine-bis(carbene) (NBC) stabilizes mononuclear, trigonal planar chloride complexes of Cu(I) and Ag(I) and a dinuclear chloride Au(I) complex.

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

Softening of breathing elastic mode and trigonal elastic mode in the disordered pyrochlore magnet NaCaCo 2 F 7

Cobalt pyrochlore fluoride NaCaCo 2 F 7 is a disordered frustrated magnet that is composed of Co 2+ ions with an effective spin-12 magnetic moment and that exhibits spin freezing below $T_f ~$ 2.4 K. Here, we perform ultrasound velocity measurements on a single crystal of the cubic NaCaCo 2 F 7 . The temperature dependence of the bulk modulus (the breathing elastic mode) exhibits Curie-type softening upon cooling below ~20 K down to $T_f$, which is suppressed by the magnetic field. This Curie-type softening should be a precursor to the enhancement of the strength of exchange disorder via the spin-lattice coupling, which causes the spin freezing. In contrast to the magnetic-field-suppressed Curie-type softening in the bulk modulus, the trigonal shear modulus exhibits softening with a characteristic minimum upon cooling, which is enhanced by the magnetic field at temperatures below ~20 K. This magnetic-field-enhanced elastic anomaly in the trigonal shear modulus suggests a coupling of the lattice to the dynamical spin-cluster state. For NaCaCo 2 F 7 , the observed elastic anomalies reveal an occurrence of magnetic-field-induced crossover from an isostructural lattice instability toward the spin freezing to a trigonal lattice instability arising from the emergent dynamical spin-cluster state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2012

Rhombohedral cubic semiconductor materials on trigonal substrate with single crystal properties and devices based on such materials

Growth conditions are developed, based on a temperature-dependent alignment model, to enable formation of cubic group IV, group II-V and group II-VI crystals in the [111] orientation on the basal (0001) plane of trigonal crystal substrates, controlled such that the volume percentage of primary twin crystal is reduced from about 40% to about 0.3%, compared to the majority single crystal. The control of stacking faults in this and other embodiments can yield single crystalline semiconductors based on these materials that are substantially without defects, or improved thermoelectric materials with twinned crystals for phonon scattering while maintaining electrical integrity. These methods can selectively yield a cubic-on-trigonal epitaxial semiconductor material in which the cubic layer is substantially either directly aligned, or 60 degrees-rotated from, the underlying trigonal material.

Park, Yeonjoon↗
DOE OSTI2020

Copper Clusters Containing Hydrides in Trigonal Pyramidal Geometry

Structurally precise copper hydrides [Cu 11 H 2 {S 2 P(O i Pr) 2 } 6 (C≡CR) 3 ], R = Ph (1), C 6 H 4 F (2), and C 6 H 4 OMe (3), were first synthesized from the polyhydrido copper cluster [Cu 20 H 11 {S 2 P(O i Pr) 2 } 9 ] with nine equivalents of terminal alkynes. Later, their isolated yields were significantly improved by direct synthesis from [Cu(CH 3 CN) 4 ](PF 6 ), [NH 4 ][S 2 P(O i Pr) 2 ], NaBH 4 , and alkynes along with NEt 3 in THF. 1, 2, and 3 were fully characterized by single-crystal X-ray diffraction, ESI-MS, and multinuclear NMR spectroscopy. All three clustershave 11 copper atoms, adopting 3,3,4,4,4-pentacapped trigonal prismatic geometry, with two hydrides inside the Cu 11 cage, the position of which was ascertained by a single-crystal neutron diffraction structure of cluster 1 co-crystallized with a [Cu 7 (H){S 2 P(O i Pr) 2 } 6 ] (4) cluster. Six dithiophosphate and three alkynyl ligands stabilize the Cu 11 H 2 core in which the two hydrides adopt a trigonal pyramidal coordination mode. This coordination mode is so far unprecedented for hydride. The 1 H NMR resonance frequency of the two hydrides appears at 4.8 ppm, a value further confirmed by 2 H NMR spectroscopy for their deuteride derivatives [Cu 11 (D) 2 {S 2 P(O i Pr) 2 } 6 (C≡CR) 3 ]. A DFT investigation allows understanding the bonding within this new type of copper(I) hydrides.

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

Magnetic field induced a b -plane rotation of the Eu magnetic moments in trigonal EuMg 2 Bi 2 and EuMg 2 Sb 2 single crystals below their Néel temperatures

The thermodynamic and electronic-transport properties of trigonal EuMg 2 Bi 2 in ab-plane magnetic fields H x and the A-type antiferromagnetic structure have recently been reported. The Eu magnetic moments with spin S = 7/2 remain locked in the ab plane up to and above the ab-plane critical field $H^{c}_{x}$ = 27.5 kOe at which the Eu moments become parallel to H x . Here additional measurements at low fields are reported that reveal a new spin-reorientation transition at a field H c1 ≈ 465 Oe where the Eu moments remain in the ab plane but become perpendicular to H x . At higher fields, the moments cant toward the field resulting in M ∝ H x up to $H^{c}_{x}$. Similar results are reported from measurements of the magnetic properties of EuMg 2 Sb 2 single crystals, where H c1 ≈ 220 Oe is found. Theory is formulated that models the low-field magnetic behavior of both materials, and the associated anisotropies are calculated. Further, the ab-plane trigonal anisotropy in EuMg 2 Sb 2 is found to be significantly smaller than in EuMg 2 Bi 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Anisotropic magnetism and electronic structure of trigonal EuAl 2 Ge 2 single crystals

Understanding the interplay between magnetic and electronic degrees of freedom is of profound recent interest in different Eu-based magnetic topological materials. Here, we studied the magnetic and electronic properties of the layered Zintl-phase compound EuAl 2 Ge 2 crystallizing in the trigonal CaAl 2 Si 2 -type structure. We report zero-field neutron diffraction, temperature T - and magnetic-field H-dependent magnetic susceptibility χ(T, H), isothermal magnetization M(T, H), heat capacity C p (T, H), and electrical resistivity ρ(T, H) measurements, together with T-dependent angle-resolved photoemission spectroscopy (ARPES) measurements complemented with first-principle calculations. EuAl 2 Ge 2 undergoes second-order A-type antiferromagnetic (AFM) ordering below T N = 27.5(5) K, with the Eu moments (Eu 2+ , S = 7/2) aligned ferromagnetically in the ab plane while these layers are stacked antiferromagnetically along the c axis. The critical fields at which all moments become parallel to the field are 37.5(5) and 52.5(5) kOe for H ∥ ab and H ∥ c, respectively. The H = 0 magnetic structure consists of trigonal AFM domains associated with ab-plane magnetic anisotropy and a field-induced reorientation of the Eu spins in the domains is also evident at T = 2 K below the critical field H c1 = 2.5(1) kOe. The ρ(T) measurements reveal metallic behavior transforming into a slight resistivity increase on cooling towards T N . A pronounced loss of spin-disorder scattering is observed below T N . The ARPES results show that EuAl 2 Ge 2 is metallic both above and below T N , and the Fermi surface is anisotropic with two hole pockets at the zone center and one small electron pocket at each M point. In the AFM phase, we directly observe folded bands in ARPES due to the doubling of the magnetic unit cell along the c axis with an enhancement of quasiparticle weight due to the complex change in the coupling between the magnetic moments and itinerant electrons on cooling below T N . The observed electronic structure is well reproduced by first-principle calculations, which also predict the presence of nontrivial electronic states near the Fermi level in the AFM phase with Z 2 topological numbers 1;(000)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2011

Epitaxial Growth of Cubic Crystalline Semiconductor Alloys on Basal Plane of Trigonal or Hexagonal Crystal

Hetero-epitaxial semiconductor materials comprising cubic crystalline semiconductor alloys grown on the basal plane of trigonal and hexagonal substrates, in which misfit dislocations are reduced by approximate lattice matching of the cubic crystal structure to underlying trigonal or hexagonal substrate structure, enabling the development of alloyed semiconductor layers of greater thickness, resulting in a new class of semiconductor materials and corresponding devices, including improved hetero-bipolar and high-electron mobility transistors, and high-mobility thermoelectric devices.

Park, Yeonjoon↗
DOE OSTI2022

Highly Symmetric, Self-Assembling 3D DNA Crystals with Cubic and Trigonal Lattices

The rational design of nanoscopic DNA tiles has yielded highly ordered crystalline matter in 2D and 3D. The most well-studied 3D tile is the DNA tensegrity triangle, which is known to self-assemble into macroscopic crystals. However, contemporary rational design parameters for 3D DNA crystals nearly universally invoke integer numbers of DNA helical turns and Watson–Crick (WC) base pairs. Here, in this study, 24-bp edges are substituted into a previously 21-bp (two helical turns of DNA) tensegrity triangle motif to explore whether such unconventional motif can self-assemble into 3D crystals. The use of noncanonical base pairs in the sticky ends results in a cubic arrangement of tensegrity triangles with exceedingly high symmetry, assembling a lattice from winding helical axes and diamond-like tessellation patterns. Reverting this motif to sticky ends with Watson–Crick pairs results in a trigonal hexagonal arrangement, replicating this diamond arrangement in a hexagonal context. These results showcase that the authors can generate unexpected, highly complex, pathways for materials design by testing modifications to 3D tiles without prior knowledge of the ensuing symmetry. This study expands the rational design toolbox for DNA nanotechnology; and it further illustrates the existence of yet-unexplored arrangements of crystalline soft matter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Temperature-Dependent Structural Transition in Cu-Intercalated Trigonal CuYbSe 2

Rare-earth delafossites, ARCh 2 ; A = alkali metal, R = rare-earth, Ch = chalcogen which consist of intercalated rare-earth metal dichalcogenides, host frustrated triangular lattices that are fertile ground for exotic phenomena. In most cases, the triangular rare-earth sublattice arises from R-3m (No. 166) structures with three layers of rare-earth metal dichalcogenide octahedra or P6 3 /mmc (No. 194) structures with two such layers, analogous to those found in transition metal dichalcogenides. Substituting the alkali metal with Cu + yields a distinct trigonal crystal symmetry P-3m1 (No. 164) in these structures. This symmetry change alters the coordination environment from ASe 6 octahedra in R-3m AYbSe 2 to CuSe 4 tetrahedra in CuYbSe 2 , resulting in shortened rare-earth to rare-earth separations and significantly reduced interlayer distances. Using X-ray single-crystal diffraction, powder neutron diffraction, resistance, and specific heat measurements, a structural transition slightly below room temperature (258 K) is observed. The low-temperature structure is a lower-symmetry I2/m structure, accompanied by partial Cu-site vacancy ordering. The combination of Cu disorder and the triangular lattice geometry in CuYbSe 2 provides a promising platform for investigating frustrated magnetism and unconventional transport phenomena.

Chemical structure↗
DOE OSTI2022

Surface and Optoelectronic Properties of Ultrathin Trigonal Selenium: A Density Functional Theory Study with van der Waals Correction

Selenium is a crucial earth-abundant and non-toxic semiconductor with a wide range of applications across the semiconductor industries. Selenium has drawn attention from scientific communities for its wide range of applicability: from photovoltaics to imaging devices. Its usage as a photosensitive material largely involves the synthesis of the amorphous phase (a-Se) via various experimental techniques. However, the ground state crystalline phase of this material, known as the trigonal selenium (\textit{t}-Se), is not extensively studied for its optimum electronic and optical properties. In this work, we present density functional theory (DFT) based systematic studies on the ultra-thin $(10\overline{1}0)$ surface slabs of \textit{t}-Se. We report the surface energies, work function, electronic and optical properties as a function of number of layers for $(10\overline{1}0)$ surface slabs to access its suitability for applications as a photosensitive material.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Trigonal Bipyramidal V 3+ Complex as an Optically Addressable Molecular Qubit Candidate

Synthetic chemistry enables a bottom-up approach to quantum information science, where atoms can be deterministically positioned in a quantum bit or qubit. Two key requirements to realize quantum technologies are qubit initialization and read-out. By imbuing molecular spins with optical initialization and readout mechanisms, analogous to solid-state defects, molecules could be integrated into existing quantum infrastructure. To mimic the electronic structure of optically addressable defect sites, we designed the spin-triplet, V 3+ complex, (C 6 F 5 ) 3 trenVCN t Bu (1).We measured the static spin properties as well as the spin coherence time of1demonstrating coherent control of this spin qubit with a 240 GHz electron paramagnetic resonance spectrometer powered by a free electron laser. We found that1exhibited narrow, near-infrared photoluminescence (PL) from a spin-singlet excited state. Using variable magnetic field PL spectroscopy, we resolved emission into each of the ground-state spin sublevels, a crucial component for spin-selective optical initialization and readout. This work demonstrates that trigonally symmetric, heteroleptic V 3+ complexes are candidates for optical spin addressability.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

Topological behavior and Zeeman splitting in trigonal PtBi2-x single crystals

Abstract Transition-metal dipnictide PtBi 2 exhibits rich structural and physical properties with topological semimetallic behavior and extremely large magnetoresistance (XMR) at low temperatures. We have investigated the electrical and magnetic properties of trigonal-phase PtBi 2 -x single crystals with x ~ 0.4. Profound de Haas–van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations are observed. Through fast Fourier transformation (FFT) analyses, four oscillation frequencies are extracted, which result from α, β, γ, and δ bands. By constructing the Landau fan diagram for each band, the Berry phase is extracted demonstrating the non-trivial nature of the α, β, and δ bands. Despite Bi deficiency, we observe the Zeeman splitting in dHvA and SdH oscillations under moderate magnetic field and the moderate Landé g factor (4.97–6.48) for the α band. Quantitative analysis of the non-monotonic field dependence including the sign change of the Hall resistivity suggests that electrons and holes in our system are not perfectly compensated thus not responsible for the XMR effect.

36 MATERIALS SCIENCE↗
DOE OSTI2021

DyFe 2 O 4 : A new trigonal rare-earth ferrite grown by molecular-beam epitaxy

Using epitaxial stabilization, we synthesized single-phase (001)-oriented thin films of DyFe 2 O 4+x on (111) MgAl 2 O 4 substrates by molecular-beam epitaxy. The metastable DyFe 2 O 4 polymorph formed is isostructural to known trigonal ferrimagnetic RFe 2 O 4 phases with space group $R\bar{3}m$, where R = Ho to Lu. The epitaxial DyFe 2 O 4 thin films have two in-plane orientation relationships: [100] DyFe 2 O 4 || [$2\bar{1}1$] MgAl 2 O 4 plus a twin variant related by a 60° in-plane rotation. DyFe 2 O 4 is not bulk stable and has never been synthesized before. Indeed, it has been predicted to be on the edge energetically of what may be possible to stabilize. The fact that the RFe 2 O 4 phase is stable for all elements leading up to dysprosium (Ho–Lu) leads us to believe that DyFe 2 O 4 could be a “remnant metastable phase,” one which, given the right thermodynamic conditions, could become the lowest free energy phase. We find that although we are able to get structurally very close to $R\bar{3}m$ DyFe 2 O 4 , the films are not stoichiometric as they have an increased c lattice parameter, indicative of extra oxygen as is sometimes seen in other RFe2O4 phases. The unintended surplus oxygen opens questions regarding what may be achievable using such tricks as epitaxial stabilization to access metastable phases and whether this indeed constitutes “remnant metastability.”

36 MATERIALS SCIENCE↗
DOE OSTI2019

Magnetic anisotropy and entropy change in trigonal Cr 5 Te 8

We present a comprehensive investigation of the anisotropic magnetic and magnetocaloric properties of quasi-two-dimensional weak itinerant ferromagnet trigonal Cr 5 Te 8 single crystals. Magnetic-anisotropy-induced satellite transition T * is observed at low fields applied parallel to the ab plane below the Curie temperature ( T c ~ 230K). T * is featured by an anomalous magnetization downturn, similar to that in structurally related CrI 3 , which possibly stems from an in-plane antiferromagnetic alignment induced by out-of-plane ferromagnetic spins canting. Magnetocrystalline anisotropy is also reflected in magnetic entropy change Δ S M ( T , H ) and relative cooling power. Furthermore, given the high Curie temperature, Cr 5 Te 8 crystals are materials of interest for nanofabrication in basic science and applied technology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

$A$-type antiferromagnetic order and magnetic phase diagram of the trigonal Eu spin-$\frac{7}{2}$ triangular-lattice compound $\mathrm{EuSn_2As_2}$

The trigonal compound EuSn 2 As 2 was recently discovered to host Dirac surface states within the bulk band gap and orders antiferromagnetically below the N´eel temperature T N = 23.5(2) K from neutron-diffraction measurements. Here the magnetic ground state of single-crystal EuSn 2 As 2 and the evolution of its properties versus temperature T and applied magnetic field H are reported. Included are the zero-field single-crystal neutron diffraction measurements versus T, magnetization M(H, T), magnetic susceptibility χ(H, T) = M(H,T)/H, heat capacity C p (H, T), and electrical resistivity ρ(H, T) measurements. The neutron-diffraction and χ(T) measurements both indicate a collinear A-type antiferromagnetic (AFM) structure below T N , where the Eu 2+ spins S = 7/2 in a triangular ab-plane layer (hexagonal unit cell) are aligned ferromagnetically in the ab plane whereas the spins in adjacent Eu planes along the c axis are aligned antiferromagnetically. The χ(H ab , T) and χ(Hc, T) data together indicate a smooth crossover between the collinear AFM alignment and an unknown magnetic structure at H ≈ 0.12 T. Dynamic spin fluctuations up to 60 K are evident in the χ(T), Cp(T) and ρ(H, T) measurements, a temperature that is more than twice T N . The ρ(H, T) is consistent with a low-carrier-density metal with strong magnetic scattering and does not reflect a contribution of the topological state of the material as reported earlier by ARPES measurements. This observation is consistent with previous ones for other topological insulators where the chemical potential is above the Dirac point so that ARPES readily detects the surface states, whereas resistivity measurements do not. Finally, the magnetic phase diagrams for both H ∥ c and H ∥ ab in the H-T plane are constructed from the T N (H), χ(H, T), Cp(H, T), and ρ(H, T) data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗