Showing papers in "Physica C-superconductivity and Its Applications in 1988"

Granular and superconducting-glass properties of the high-temperature superconductors

Abstract: The microstructure of bulk samples of the copper-oxide high-temperature superconductors commonly is describable in terms of anisotropic grains of stoichiometric material separated by layers of nonstoichiometric interface material. The granularity strongly influences the electromagnetic properties, especially the transport critical-current density and the magnetization. In this paper, a simple theoretical model for the granularity is introduced and then used to discuss a number of electrodynamic properties (hysteretic magnetization versus magnetic field, zero-field-cooled and field-cooled magnetization versus temperature, ac susceptibility, and flux creep with logarithmic time dependence). Special attention is drawn to the importance of distinguishing between intragranular and intergranular effects.

Models for the modulation in A2B2CanCu1+nO6+2n, A, B=Bi, Sr OR Tl, Ba and n=0, 1, 2

Abstract: A number of models for the modulation in the title compounds are postulated. For the Bi compounds periodic changes are considered due to the following structural models: (a) extra oxygen in the BiO layers, (b) partial substitution of Sr by a vacancy, (c) partial substitution of Bi by Cu, and (d) changes in the orientations of the lone pairs of Bi. Computer calculated images for these models are compared with high resolution images. Also general structural considerations and structural details from the reported subcells are taken into account. It is concluded that the best agreement with experimental data is obtained for the model with extra oxygen in the BiO layers. Several performed experiments, which support this conclusion, are reported and discussed; the most important of which are the existence of solid solutions Bi2Sr2−xBaxCuO6+δ, with x

Electronic structure and properties of Bi2Sr2CaCu2O8, the third high-Tc superconductor

Abstract: Results of a highly precise local density determination of the electronic structure (energy bands, densities of states, Fermi surface and charge densities) of the new high-Tc superconductor Bi2Sr2CaCu2O8 are presented. The calculations employed the full-potential linearized augmented plane wave (FLAPW) method and the subcell structure parameters given by the work of Hazen et al. and Sunshine et al. As in the case of the other Cu-O superconductors, we find a relatively simple band structure at EF and strongly anisotropic highly 2D properties. The Sr and Ca atoms are highly ionic, with the Ca2+ ions serving to insulate the Cu-O planes. The Bi-O planes contribute substantially to N(EF), the density of states at EF, and to the transport properties whereas neither the Sr or Ca do. The N(EF) contribution from the Cu-O planes (∼1.0 states/eV-Cu atom) is lower (per Cu atom) than that found previously for the La-Sr-Cu-O and Y-Ba-Cu-O superconductors. The highly 2D Fermi surface shows regions of strong Cu-O and Bi-O hybridization from which highly anisotropic superconducting energy gaps are predicted. Here, too, an electron-phonon calculation of Tc (using the crude rigid ion approximation) is found to be inadequate. As in the case of YBa2Cu3O7-δ, strongly localized states at EF (arising from Bi-O and Cu-O) may be responsible for charge transfer excitations (excitons) which cause the high Tc.

Studies of oxygen-deficient Ba2YCu3O7−δ and superconductivity Bi(Pb)SrCaCuO

Abstract: Ambient temperature measurements of the crystallographic cell parameters for oxygen deficient Ba 2 YCu 3 O 7−δ prepared by gettered annealing indicate the presence of microscopic differences in the oxygen configuration at fixed δ dependent on annealing temperature. The loss of superconductivity with increasing oxygen deficiency is shown to be due to a step-like increase in length of the plane copper-apical oxygen bond, and not to the orthorhombic to tetragonal transition. The crystal structure of the 84K superconductor Bi 2 Sr 2 CaCu 2 O 8+δ is described, as is the stabilization of 110K superconductivity via partial Pb/Bi substitution with long time annealing.

Compounds and phase compatibilities in the system Y2O3-BaO-CuO at 950°C

Abstract: The subsolidus phase diagram of the system Y2O3-BaO-CuO at 950° C in air has been investigated. In the binary system BaO-CuO the compound Ba2CuO3+δ has been isolated and a new compound with composition in the vicinity of Ba3Cu5O8+δ has been found. In the binary system BaO-Y2O3 it is shown in that the compounds “Ba4Y2O7” and “Ba2Y2O5” are oxycarbonates with composition Ba4Y2O7·CO2 and Ba2Y2O5·2CO2. New compounds that have been identified in the ternary system Y2O3-BaO-CuO are YBa4Cu3O8.5+δ, Y3Ba8Cu5O17.5+δ and a compound with composition close to YBa5Cu Cu2O8.5+δ. The oxygen content and the oxidizing power of these compounds has been measured. The oxygen content depends on the preparation method. Lists of interplanar spacings, relative intensities and h k l indices of these oxygen deficient perovskites as determined from X-ray powder diffraction measurements are presented and possible structures of the unit cells are described. Phase equilibrium relations have been investigated and tie lines in the phase diagram are presented.

Structural anomalies at the disappearance of superconductivity in Ba2YCu3O7−δ: Evidence for charge transfer from chains to planes

Abstract: In systematic studies of oxygen-deficient Ba 2 YCu 3 O 7−δ , we have found that a structural anomaly occurs at the composition where bulk superconductivity disappears. The observed step-like increase in the c lattice parameter, when associated with changes in the atomic positions within the unit cell, indicates that superconductivity is lost due to a charge redistribution from the copper-oxygen chains to the copper-oxygen planes. This is microscopic experimental evidence establishing the role of secondary structural elements in the layered copper-oxide high- T c superconductors.

Stoichiometry of bulk superconducting La2CuO4+δ: A superconducting superoxide?

Abstract: A variety of analytical tools have been combined to show that bulk superconducting La2CuO4+δ has a La to Cu ratio of 2.00 (±0.02) and an oxygen stoichiometry of 4.13 (±0.1). The combination of these analytical results and magnetization data with a model leads us to suggest that the excess charged oxygen is introduced as O-2.

The theory of the measurement of the London penetration depth in uniaxial type II superconductors by muon spin rotation

Abstract: The effect of anisotropy on the measurement, by muon spin rotation, of the London penetration depth in the high- T c uniaxial type II superconductors is considered in detail. Expression are derived which will allow the principal penetration depths, λ 1 (λ ⊥ ) and λ 2 (λ | ), to be determined using meas urements of the μSR line width from single crystals. For polycrystalline, powder or sintered, samples an expression is derived which will allow an effective penetration depth, λ eff , to be determined from the measured μSR line width. Further, it is shown that for all anisotropy ratios, λ 2 /λ 1 , greater than five λ 1 ∼0.81λ eff .

New procedure for determination of [Cu-O]+p charge and oxygen content in high Tc copper oxides

Abstract: The properties of High Tc Superconductors are critically dependent on the degree of oxidation, i.e., on the average [Cu-O]+p charge (or formal oxidation state Cu+2+p of copper). This fact makes it important to accurately characterize High Tc copper oxide samples in term of this key parameter. We describe here a simple and reliable procedure for determining the effective copper oxidation level and, as a result, the oxygen content. Using a modification of standard iodometric titration techniques, our procedure involves the ratio of the results of two titrations: one to determine the copper concentration in the sample and the second to measure the degree of oxidation beyond Cu+. Using this ratio, numerous errors and difficulties are minimized. In addition, the exact stoichiometry of the sample need not be known. Experimental results on YBa2Cu3Oy are discussed which demonstrate the accuracy, reproducibility and reliability of our procedure.

Structural and compositional characterization of polycrystals and single crystals in the Bi- and Tl-superconductor systems: Crystal structure of TlCaBa2Cu2O7

Abstract: The growth of mm-sized crystals in the Tl-Ca-Ba-Cu-O and Bi-Ca-Sr-Cu-O superconductor systems shows the common presence of polycrystals, which can be described as syntactic intergrowth crystals, as well as normal single crystals. Three distinct phases with superconducting transitions at 103 K, 106–108 K and 112–114 K have been grown in the Tl-Ca-Ba-Ca-O system. The newly identified 103 K phase is TlCaBa 2 Cu 2 O 7 which is structurally similar to YBa 2 Cu 3 O 7 but without the presence of chains. Transmission electron diffraction and electron microprobe analysis on several polycrystals show that they are composed of interlayers of these distinct phases grown epitaxially along the c -axis. Crystals have been grown for two phases in the Bi-Ca-Sr-Cu-O system that exhibit transition temperatures at 80 K and at 92 K. Oxygen annealing substantially improves the superconducting properties of most of the crystals.

A note on the symmetry and Bi valence of the superconductor Bi2Sr2Ca1Cu2O8

Abstract: The sub-structure of Bi 2 Sr 2 Ca 1 Cu 2 O 8 can best be described on a non-centric orthorhombic A2aa cell, which permits the oxygen in the BiO plane to move off the center of the Bi square to approach to within 2.2 A of a pair of Bi atoms. Each Bi then has two close oxygens within the BiO plane, and a third at 2.12 A connecting to the CuO layer. The new structure permits the apparent Bi valence to approach 3+ with a more reasonable Bi-O co-ordination than for earlier approximate structural models. This model satisfies the high resolution neutron data of Bordet et al., while agreeing in part with the co-ordination proposed on chemical grounds by von Schnering et al.

The influence of oxygen on the physical properties of the superconducting series Bi2.1(CaχSr1−χ)n+1Cun+4+δ

Abstract: The sensitivity of Tc to oxygen sorption and the Ca to Sr ratio has been studied for the homologous series Bi2.1(CaχSr1−χ)n+1CunO2n+4+δ for n=1, 2 and 3. The n=0 and n=∞ members have been produced as single phase samples but are found to be semiconducting. While single phase n=2 material has been prepared, the n=1 member always displays a small n=2 contribution to the X-ray diffraction pattern. n=3 is only found in multiphase samples. Single phase superconducting samples were equilibrated under a fixed partial pressure of oxygen at temperatures between 300 and 850°C and quenched in liquid nitrogen. It is shown that Tc can be controlled in a reversible and systematic way by varying the oxygen partial pressure and the annealing temperature and consequently the oxygen stoichiometry. The site energy per oxygen sorbed for n=2 is 3.24 eV, only a little less than that for YBa2Cu3O7. However, the volume change on sorption is ten times smaller than that for YBa2Cu3O7, and is manifested as a changing c-axis with the a-axis invariant. This can be interpreted as implying that oxygen sorption occurs within the Bi-O layers. Tc is found to be maximised for a Ca to Sr ratio of 1 to 2 for both n=1 and 2. Thermal expansion data for n=2 material is also reported to illustrate that oxygen sorption does effect the physical properties of these materials.

A comparative study of (BI)polaronic (super)conductivity in high- and low-Tc superconducting oxides

Abstract: A comparative study is made on the conductivity and superconductivity mechanisms in the series of superconducting oxides SrTiO3-δTc⋍0.3 K), BaPb1-xBixO3(Tc⋍12 K), Li1+xTi2-xO4(Tc⋍11 K), La2-xSrxCuO4(Tc⋍40 K), and YBa2Cu3O7-δ (Tc⋍60 K for δ⋍0.3−0.4; Tc⋍90 K for δ⋍0). We claim that all these materials can be viewed as doped semiconductors, where the conductivity is due to doping or self-doping. This procedures mixed-valence conditions for the metal-ions, leading to the formation of small-polarons, namely the combination of the metal atom with its extra charge plus its deformed oxygen coordination. The mobility of the small-polarons is ensured through the mixed-valence charge transfer mechanism. They may be viewed as a dilute gas of charged particles on a lattice, moving in the random fluctuating potential due to the impurities. By varying the concentration of these, small-polarons metal-insulator transitions (probably of the Anderson type) occur in all these materials, which explaines the observed behaviour of the conductivity and points to a universal “minimum conductivity”, σmin⋍102 (Ω cm)−1. The special non-linear (solitonic) features of these mixed-valence small-polarons are pointed out. It is further argued that under special conditions these small-polarons, may combine to form small-bipolarons, and the possible binding mechanism for each of the materials is investigated. The superconductivity may then be explained in terms of a Bose-Einstein condensation of these bipolarons, for which the theory has been developed in the last few years. To substantiate our arguments, a short overview of these theoretical results is given. In addition quite a number of relevant experimental data available in the literature on these compounds is reanalysed in terms of the above concepts.

Stabilizing the high-Tc superconductor Bi2Sr2Ca2Cu3O10+x by Pb substitution

Abstract: The higher-Tc phase of the BiSrCaCu oxide high-Tc superconductor has been stabilized by partially replacing Bi by Pb. The resistance of our best Pb-doped samples falls sharply to zero at 108 K. AC susceptibility data show a single transition to bulk superconductivity with an onset temperature of 108 K. On the basis of X-ray diffraction and EDX data, it is concluded that Pb substitution promotes the growth of the (Bi, Pb)2Sr2Cu3O10+x phase.

The anisotropic superconductivity of RBa2Cu3O7−x (R : Y, Gd and Ho) single crystals

Abstract: Our study of high temperature superconductivity in RBa 2 Cu 3 O 7 − x (R:Y, Gd and Ho) using single crystal samples is reviewed with emphases on the anisotropic transport properties in the superconducting phase as well as the normal phase. Recent transport results obtained by use of a new technique for attaching a number of electrical leads on a small single crystal are also presented.

High-Tc superconductivity induced by ferromagnetic clustering

Abstract: We propose a theoretical model which allows to explain high- T c superconductivity in perovskites. It starts from a Hubbard-type Hamiltonian and from a description of the antiferromagnetic state. We show that when doping with holes immobile ferromagnetic clusters are formed which at higher hole concentrations percolate to metallic lines. The superconductivity occurring along these one-dimensional lines is caused by deformation coupling to Jahn-Teller active optical vibrations. Only a small isotope effect is predicted. The model also explains the spin-glass behaviour for intermediate concentrations and the destruction of superconductivity at high concentrations.

Oxygen vacancy ordering and superconductivity in YBa2Cu3O7−x

Abstract: The superconducting properties of YBa 2 Cu 3 O 7−x have been shown to depend markedly on the overall oxygen stoichiometry and on the ordering of oxygen vacancies on the available sites. YBa 2 Cu 3 O 7−x has been studied in situ by high-temperature neutron powder diffraction in controlled oxygen atmospheres in order to learn the structural properties of the system in thermodynamic equilibrium. Additionally, metastable, oxygen-deficient samples produced by quenching into liquid nitrogen from high temperature and various oxygen partial pressures have been studied at room temperature or low temperature in order to correlate the structural and superconducting properties. Such experiments have shown that a systematic relationship exists between the superconducting transition temperature, T c , the number of oxygen vacancies, and the degree of oxygen vacancy ordering. This brief paper reviews our work in these areas.

Superconductivity and magnetism in the high TC copper oxides

Abstract: The occurrence of long- and/or short-range magnetic ordering in La2−zCuO4−y, La2−xSrxCuO4−y and YBa2Cu3O7−x is reviewed and discussed with respect to the occurrence of high Tc superconductivity in these systems.

Macroscopic theory of superconductors with small coherence length

Abstract: Macroscopic theory for superconductors with small coherence length is developed.

Pressure dependence of the superconducting transition temperature of (Y1−χPrχ)Ba2Cu3O7−δ compounds; Evidence for 4f electron hybridization

Abstract: The effect of nearly hydrostatic pressure to 20 kbar on the superconducting transition temperature Tc of (Y1−χPrχ)Ba2Cu3 O7−δ compounds with 0⩽χ⩽0.5 was determined by means of low frequency ac electrical resistivity measurements. The application of pressure to this system reveals striking effects which appear to be associated with the hybridiazation between Pr 4f and valence band states. In this range of pressure P, Tc increases with P for 0⩽χ⩽0.2, exhibits a maximum at ∼6 kbar for χ=0.3, and decreases rapidly with P for χ⩾0.4, while the initial rate of increase of Tc with pressure (dTc/dP)P=0, increases with χ for 0⩽χ⩽0.3. These results suggest there is a pressure-induced electronic phase transition at ∼6 kbar foir χ=0.3 that shifts to lower values of P for higher values of χ.

Powder X-ray and neutron diffraction study of the superconductor Bi2Sr2CaCu2O8

Abstract: A sample of the new BiO-perovskite superconductor has been synthesized. X-ray diffraction has been used to locate the cations while neutron diffraction has been used to determine the precise oxygen co-ordination. The stricture contains CuO 2 planes with Cu coordinated to four oxygens at 1.92A within the plane, plus more distant oxygen at 2.65A perpendicular to the plane. Two such copper oxide (perovskite) planes are intercalated with planes of BiO. The stricture is described in an Fmmm subcell (5.4A, 5.4A, 30.8A), except for the oxygen within the BiO layers, and to a lesser extent the Bi itself, which require a x5 larger b-axis. The X-ray refinement in Bbmm indicates that this Bi displacement is 0.27A.

Properties of the tetragonal superconductor CaBaLaCu3Ox

Abstract: The compound CaBaLaCu 3 O 6.9 is a tetragonal bulk superconductor with a T c of 80 K. CaBaLaCu 3 O x is isomorphic to tetragonal YBa 2 Cu 3 O x in which the Ca and La ions are both located at the Y- and Ba-site. High temperature X-ray diffraction and thermogravimetric measurements show no indication for “order-disorder” transitions involving the oxygen ions. TEM micrographs of CaBaLaCu 3 O x show no evidence for a / b twinning. The oxygen content and the partial oxygen pressure of CaBaLaCu 3 O x are determined as a function of temperature. The standard enthalpy change for the oxidation reaction, Δ H , is determined as 190.4(0.3) kJ⧸mol O 2 . Transmission electron diffraction patterns show weak but distinct half-order spots indicating an ordering which can be described by a supercell having axes twice as large as the basic unit cell.

A family of non-stoichiometric phases based on Ba2YCu3O7−δ (0≤δ≤1)

Abstract: In the light of recent electron diffraction evidence a reappraisal is made of the problem of non-stoichiometry by oxygen deficiency in high-temperature superconducting Ba 2 YCu 3 O 7−δ . On the basis of the ordered states of the oxygen vacancies detected by that technique, a family of phases is proposed as a better description of oxygen stoichiometry and compositional variations in that material. Five phases appear to exist within the usually considered range 0≤δ≤1. All of these phases, which can be considered as consecutive members of a homologous series differing in oxygen content along the CuO rows running along the b axis, are themselves non-stoichiometric and appear to correspond to well differentiated regions in the characteristic T c versus composition phase diagram found by several authors.

Preparation and neutron diffraction of superconducting “tetragonal” and non-superconducting orthorhombic Tl2Ba2Cu1O6

Abstract: Many different samples of Tl 2 Ba 2 Cu 1 O 6 have been prepared by different heat treatments at relatively low temperature. The material as first prepared is clearly orthorhombic and non-superconducting, but on annealing and quenching, the samples become almost tetragonal with high T c . Various T c values between 3+ O 2- atoms are missing, creating the electron holes apparently necessary for superconductivity. The main difference between the various samples appears to be that the non-superconducting material is orthorhombic, with a well ordered superstructure, while the superconducting material is pseudo-tetragonal, with disordered oxygen within the TlO plane, as for the higher superconducting members of the Tl 2 Ca n Ba 2 Cu n +1 O 2( n +3 ) series. Superconductivity then appears to depend on the precise structural arrangement, and not just on stoichiometry and the number of electron holes.

Optimization of the specific heat jump at Tc and magnetic properties of the superconductor YBa2Cu3O7

Abstract: A number of high-quality polycrystalline YBa 2 Cu 3 O 7 samples were investigated by specific-heat measurements from 30 to 300 K, with emphasis on the second-order transition at T c . The same samples were examined for their Meissner effect, the normal state magnetic susceptibility and crystal structure parameters. A clear correlation was established between the normal state susceptibility and the specific-heat discontinuity Δ C at T c , a fact allowing us to separate the exchange enhanced Pauli contribution. The results impose a constraint on the ratio of the Stoner factor S and the mass renormalization 1 + λ through S /(1 + λ ) = 0.42 A ( λ ), where A ( λ ) = ΔC / γT c . The transition temperature is insensitive even to pronounced variations of the density of states.

Rietveld analysis of Tl2Ba2Can−1CunO4+2n (n=1, 2 and 3) by powder x-ray diffraction

Abstract: Crystal structures of the phases in the Tl-Ba-Ca-Cu-O system determined by powder X-ray diffraction were refined using Rietveld analysis. Three samples having the general composition Tl 2 Ba 2 Ca n −1 Cu n O 4+2 n where synthesized. These were Tl 2 Ba 2 Ca 2 Cu 3 O 10 ( n =3,2223 phase ) with a T c of 116 K, Tl 2 Ba 2 CaCu 2 O 8 ( n =2,2212 phase ) with a T c of 85 K, and Tl 2 Ba 2 CuO 6 ( n =1,2201 phase ) which did not exhibit superconductivity. The results of the Rietveld analysis revealed that as n increased the lattice parameter, a , and the interatomic distance Cu-O(2) became shorter, and the Tl-O and Ba-O layers showed a tendency to become flatter. Possible substitution of about 10% of the Ca-sites with Tl ions in the 2212 and 2223 phases was also suggested.

Electronic structure and properties of the high-Tc superconductors: Tl2Ba2CaCu2O8 and Tl2Ba2Ca2Cu3O10

Abstract: We present results of highly precise local density calculations of the electronic structure of the two high- T c superconductors Tl 2 Ba 2 CaCuO 8 ( T c ≅112 K) and Tl 2 Ba 2 Ca 2 Cu 3 O 10 ( T c ≅125 K), as obtained with the full potential linearized augmented plane wave (FLAPW) method. A relatively simple band structure is found near E F and strong 2D properties are predicted. Again as in the case of the other high- T c materials, Ba and Ca are highly ionic, with the Ca 2+ ions insulating the Cu-O planes. The Tl-O complexes, which are decoupled from the Cu-O planes, produce small electron pockets at E F with predominant O character that contribute to the transport properties. Each Cu-O plane is found to contribute ≃ 1 state/(eV-Cu atom) to the density of states (DOS) at E F , similar to the Bi 2 Sr 2 CaCu 2 O 8 case. Remarkable strong fermi surface nesting is found along the (100) and (010) directions for the 2D Cu-O dpσ bands. Significantly, we show that the usual simple nearest-neighbors only tight-binding model cannot properly describe these states. Crude rigid ion calculations show that a purely electron-phonon mechanism is inadequate to explain the observed high T c . As in the case of the other high- T c superconductors, a charge transfer excitation (excitonic) mechanism appears likely. Interestingly, the partial DOS structure shows that both systems can be viewed as a metal-semiconductor (or metal-semimetal) superlattice indicating a possible relation to the Allender, Bray, and Bardeen model of excitonic superconductivity.

Structure and superstructure of the superconductor Tl2Ca1Ba2Cu2O8 by neutron and electron diffraction

Abstract: Neutron powder diffraction has been used to refine the structure of the high- T c superconductor Tl 2 Ca 1 Ba 2 Cu 2 O 8 to determine the precise oxygen co-ordination and the effective valence of copper. The results are in excellent agreement with the Dupont X-ray structure, confirming the possible substitution of about 9% of the Ca-sites with Tl in our sample. The Tl-sites may be either 3% Tl-deficient or 7% Ca-substituted. The apparent valence of copper is 2.22. Oxygen in the center of the Tl square implies an average valence of less than 3 for Tl, and it is therefore not suprising that this oxygen is desordered toward the mid-point of the shortest Tl-Tl distance. High resolution electron images and diffraction reveal a quite different superstructure to the 5 x 5.4 A superstructure seen in Bi 2 Sr 1 Ca 2 Cu 2 O 8 . Very weak and diffuse superlattice spots may be due to a charge density wave in the TlO plane with period 6 x 3.8 A.

Texture processing of YBa2Cu3O7−x by Joule heat zone melting

Abstract: Joule heat zone melting has been used to produce texture in YBa2Cu3O7−x polycrystalline bars. X-ray diffraction analysis shows the zone melted bars consist of tetragonal YBa2Cu3O7−x, BaCuO2, and CuO. A 900°C homogenization and 600°C anneal in oxygen are found to produce a nominally single phase structure of orthorhombic YBa2Cu3O7−x. SEM examination shows a platelet morphology is produced.

The anisotropic nature of the superconducting properties of single crystal Y1Ba2Cu3O7 − x

Abstract: A series of noncontact magnetic measurements on high-quality single crystals of Y1Ba2Cu3O7 − x have enabled us to demonstrate that the superconducting-state properties of Y1Ba2Cu3O7 − x are those of a conventional, anisotropic superconductor with the anisotropy being associated with the highly conducting Cu O sheets in the Y1Ba2Cu3O7 − x crystal structure The anisotropy in the superconducting state is reflected most strongly in the critical current anisotropy, which is as large as 20 to 1 at low temperatures and low fields and gets arbitrarily large at higher temperatures and higher fields The upper critical field HC2 shows an anisotropy that varies from 6:1 to 10:1 in different crystals of high quality Along the copper-oxygen sheets the upper critical field is enormous, extrapolating to ∼60 Tesla by 77 K and implying a low-temperature Ginzburg-Landau coherence length normal to the layers of 2A− 4A Strong upward curvature is evident in the HC2 data in both orientations of applied field This curvature can be interpreted in terms of thermodynamic fluctuations, and, if this explanation is correct, the critical region is enormous, extending more than 25 K below TC