Flux pinning in porous type II superconductors

The flux pinning mechanism in porous type II superconductors is investigated by measurements on sintered Nb samples with relatively small values (<5). By careful examination of the metallurgical microstructure it is shown that the porous samples can be regarded as metallurgical model structures. The volume pinning forceP _v is measured as a function ofB, T, and of the microstructure. The results are compared with theories for the pinning mechanism at phase boundaries. Agreement is found with V. V. Shmidt's theory as long as the pore diameter is greater than the superconducting penetration depth. Deviations from this theory are observed nearT _c . The dependence ofP _v on the microstructure, especially on the specific surfaceS _v of pores and on the mean linear pore sized in the formP _v S _v /d, is consistent with the proposed pinning defect model, in which the pinning centers are considered as polyhedrons.This paper is based on thesis D 26, Universität Giessen, 1975. It was presented in part at the International Discussion Meeting on Flux Pinning in Superconductors, Sonnenberg, Germany, 1974.     

Radiation-induced flux pinning in type II superconductors

In monocyrstalline foils of oxygen-doped niobium and niobium—zirconium alloys, statistically distributed or regularly arranged voids were created during irradiation with high-energy ⁵⁸Ni⁺ ions (3.5MeV, up to 8.1 × 10¹⁶ ions/cm²) at temperatures between 750 and 900°C. The voids exhibit a strong interaction with flux lines, which was determined from measurements of the (anisotropic) critical currents as a function of transverse magnetic field, temperature, and defect geometry. The experimentally determined volume pinning forces obey scaling laws and lead to elementary interaction forces between voids and fluxoids that are larger than theoretical values calculated for various possible mechanisms of interaction. The validity of the statistical summation of elementary forces is discussed.Research supported by the U.S. Energy Research and Development Administration, the Deutsche Forschungsgemeinschaft, and the Akademie der Wissenschaften in Göttingen. For numerical computations the facilities of the Gesellschaft für Wissenschaftliche Datenverarbeitung mbH Göttingen were used. This investigation is part of a Habilitation Thesis presented at the University of Göttingen.     

Magnetic pinning in inhomogeneous type II superconductors

The magnetic structure of a vortex in the presence of an anisotropic inhomogeneity distribution is calculated within the London model. The anisotropic supercurrent pattern consists of closed current loops, superimposed on a backflow pattern. The nonvanishing current density at the vortex core gives rise to an intrinsic Lorentz force identical with the pinning force resulting from the spatial variation of the vortex self-energy.     

Flux pinning by thin chromium layers

The flux pinning strength and upper critical field have been measured in multilayered evaporated films composed of thick layers of polycrystalline Pb-18% Bi alloy periodically interleaved with much thinner layers of chromium. The flux pinning strength of a single Cr layer with the applied magnetic field parallel to the layers is estimated to be at least 180 N/m² at a reduced field ofh=H/H _c2=0.7, and is independent of Cr layer thickness. The parallel flux pinning strength drops sharply, however, if the layer spacingd ₁ is reduced to less than 60 nm. The upper critical field with the applied field normal to the layers is slightly elevated for larged ₁ , but is strongly depressed ford ₁ <100 nm; the parallel upper critical field is independent ofd ₁ .This work was supported financially by the U.S. Air Force Office of Scientific Research through grants AFSOR-77-3107 and F44620-74-C-0019. This work benefited from the use of the facilities of the Materials Science Center at Cornell, which is funded by the U.S. National Science Foundation.     

Flux pinning by thin planar defects

Planar defects, specifically grain boundaries, are now recognized as a major source of flux pinning in many materials, including the commercial A-15 superconductors. Unfortunately little theoretical attention has been devoted to the interaction between a planar pinning centre and the flux line lattice (FLL) of a type II superconductor. A Ginzburg-Landau perturbational approach is used here to calculate the pinning force per unit area exerted by a thin isolated planar defect upon the FLL. The pinning force is considered to arise from electron scattering at the defect plane, which creates a perturbation in the Ginzburg-Landau parameter,. The method of approach is of general applicability, however, and is easily adapted to other pinning mechanisms encompassed by the perturbational formalism. Second order terms in the FLL energy are retained, as well as all significant higher order terms in the Fourier transforms both of the superconducting electron density ¦¦², and of ¦¦⁴. It is shown that a large error results, except at very high fields, if the above terms are ignored. The functional dependence of the elementary pinning force on temperature and field are shown to vary somewhat with the nature of the material and the pinning defect.     

Surface superconductivity and pinning sites in type-II superconductors

Surface superconductivity has been investigated by measuring the real and imaginary parts of the magnetic permeability at small, low-frequency magnetic fields. The samples used were cylinders of Ta ₉₂ Nb ₈ , Ta ₉₅ Nb ₅ , and pure niobium which have suffered different bulk and surface treatments. By our measurements we are led to the conclusion that pinning sites at the surface are needed for the existence of surface superconductivity.Experiments carried out at the Clarendon Laboratory, Oxford, England.     

Flux entry fields in amorphous superconductors

We have measured the flux entry fields (lower critical fieldsH _c1) of homogeneous and inhomogeneous extreme type II amorphous superconductors based on zirconium. Samples are prepared by melt quenching at both ambient and elevated substrate temperatures. The degree of homogeneity is classified according to the widths of both inductive and resistive transitions. TheH _c1 (T) curves for powdered homogeneous samples with weak flux pinning are found to be in good agreement with Maki's theory. Taking into account the electron-phonon renormalization effect, we deduce the zero-temperature energy gap values 2_o/k _B T _c to be BCS like. On the other hand, anomalousH _c1 (T) curves are observed in powdered inhomogeneous samples and strips from homogeneous samples parallel to the applied field. Appreciable irreversibility effects are also observed. The latter results are discussed qualitatively in terms of bulk and surface inhomogeneity effects.Research supported by National Science Foundation grant DMR-82-02624.     

Chemical doping and improved flux pinning in Hg-based superconductors

Chemical doping of a small amount (0.020.3) of rhenium (Re) ion into HgBa₂Ca_n–1Cu_nO_y(n=14) has been studied. The flux pinning strength in these Hg-based superconductors is significantly enhanced compared to the undoped parent materials. Neutron diffraction analysis of representative samples (n=3) revealed that Re partially substitutes the Hg-site with octahedrally fully coordinated oxygen atoms, giving rise to the stabilization of Hg(Re)O layer and reduction of this blocking layer thickness. Associated with the expected hybridization of Re-5d and O-2p orbitals and possible metallization of the Hg(Re)O layer, the improved flux pinning behavior is considered to be caused by the decrease of the electromagnetic anisotropy and the enhanced interlayer superconducting coupling strength.     

Flux jumps in internally cooled composite superconductors

This paper is concerned with the stability against flux jumpes of current and temperature distribution in a composite superconductor which has internal cooling channels. The stability and perturbation increments have been found.     

Elementary pinning potential in type II superconductors nearH c2

The elementary pinning potential of a small defect in a type II superconductor is calculated near the upper critical magnetic field. The calculation applies at all temperatures and all background impurity contents of the metal. The pinning potential is found to decay according to the inverse impurity parameter when other impurities are added. A very simple formula for the pinning potential is obtained in the Ginzburg-Landau region. The boundary condition to be imposed on a Ginzburg-Landau theory at small defects is derived.     

Direct mechanical measurement of pinning forces on type-II superconductors

A radially flowing transport current is fed into a disk specimen suspended in a magnetic field perpendicular to the surface, and the torque resulting from the Lorentz forces is measured. Sample and current leads form a closed superconducting circuit. The current induced in this circuit, and thus the torque, can be increased without dissipation until flux flow starts. The torque corresponding to this limit is directly proportional to the pinning force per unit volume. Results for 0.1-mm-thick Nb samples are reported, including the peak effect and a yield phenomenon. The values of the pinning forces are in good agreement with theoretical predictions and of the same order of magnitude as the measurements of other authors.     

Flux vortex dynamics and electric fields in matched pinning systems

The pinning of flux vortices in type II superconductors has been the subject of extensive research. Certain experiments have attempted to investigate this problem by the use of specially prepared pinning structures consisting of regular arrays of pinning centers. In this paper a theory relating to such experiments is described. This theory is based on the existence and properties of defects in an otherwise perfect vortex lattice which is commensurate with a pinning array consisting of a triangular lattice of holes in a superconducting thin film. A quantitative treatment predicts the existence and position of substructure on the critical current versus magnetic field curves in addition to the main peaks previously predicted to occur when the vortex and hole lattices are exactly matched. The theory also qualitatively describes the overall shape of these curves. An analysis of the temperature dependence of this substructure shows broad agreement with existing experimental results. The application of this theory to future experiments should allow a detailed investigation of vortex lattice elasticity and flux flow.     

Fluxoid pinning in superconductors by a periodic array of magnetic particles

We assume a two-dimensional array of ferromagnetic particles on the surface of a thin type-II superconductor in a transverse magnetic field. With a particle at the center of each fluxoid, the pinning forceP and critical current increase J _c due to the particles are calculated. General expressions without arbitrary parameters are given forP and J _c as functions of magnetic field strength and the characteristics of the superconductor and the particles. For broad ranges of conditions values ofP and J _c greater than 10^–7 dyn and 10⁵ A/cm² result and for certain physically realistic sets of conditions,P>10^–6 dyn and J _c>10⁶ A/cm² are predicted. The above effects should be readily observable. An experiment for setting up the assumed conditions is proposed and discussed in some detail.Work supported by the Fonds National pour la Recherche Scientifique.     

Metastability-induced charge and spin fluctuations in 123 type superconductors

Various defects arising from lattice mismatch and coordination incompatibility at the cation sites are known to lend the cuprates a metastable state at temperatures and pressures where they exhibit superconductivity. The present paper considers the metastability induced by coordination incompatibility at Cu(1) sites in oxygen-deficient 123 type systems and looks for their possible effects on charge and spin degrees of freedom. Depending upon the concentration of oxygen vacancies, the resulting unstable charge state at the Cu(1) sites is shown to either temporally fluctuate or spatially equilibrate, providing a mechanism for the 90 K and the 60 K plateaus, with a peak in the former observed in the YBa₂Cu₃O_7-y , samples prepared under thermodynamic equilibrium conditions.     

Flux pinning in superconducting amorphous Zr1−x Co x

The pinning force F_P in amorphous Zr_1–x Co _x (x=0.30; 0.35) is measured as a function of perpendicular field and temperature. The homogeneous samples exhibit a weak flux pinning force of about 10⁴ N/m ³ in the temperature range 2–3 K. The field dependence ofF _P at several temperatures can be explained by a collective pinning model in the Larkin-Ovchinnikov theory in three dimensions. Structural relaxation studies in amorphous ZrCo confirm that bothT _c andF _P are sensitive to a slight isothermal annealing treatment at 220°C for 1 h. The collective flux-pinning characteristics still remain after such a structural relaxation, which allows us to conjecture that these defects are stable against this thermal treatment.     

Flux flow noise power spectra in the presence of local pinning interactions

We derive expressions for the dc flux flow voltage and for the flux flow noise power spectrum in type II superconductors using a model in which flux bundles travel a distance1 less than the sample widthL before being stopped for finite times by local pinning interactions. The frequency dependence of the power spectrum is shown to be identical to our earlier derivation, where we assumed that pinning and release of flux bundles occurred in zero times, an assumption we now show to be incorrect. This frequency dependence has been shown to lead to good agreement for experimentally measured transit times, which have repeatedly been shown to be too short when obtained from models of uninter-rupted flux transit across the sample width. The concept of a pinned fraction arises naturally in our model, and occurs because of two factors; first, in certain regions the Lorentz force is not sufficient to overcome pinning, and second, in regions where flux flow occurs, fluxoids will be held up for brief periods because of interaction with local pinning centers. The expressions for the noise power at zero frequency and the dc voltage are modified by factors that depend on averages of1.Research supported by U.S. ERDA Grant No. E(11–1) 2890.     

Flux pinning in high-Tc superconductive films

Magnetization measurements have been performed onc-axis oriented Y- and Gd-based superconductive films in a wide range of the temperaturesT (4.2–85 K) and magnetic fieldsH (0–8 T) withH c-axis. The influence of flux creep on both the temperature dependence of critical current densityJ _cm and the scaling behavior of flux pinning forceF _p has been discussed in detail. The experimental results show that Y and Gd films have different pinning mechanism. Flux pinning-force peaks in high fields are observed in Gd film at high temperatures and can be considered as evidence for collective pinning.     

Magnetization and critical current of high-temperature superconductors with artificial pinning centers

We present new data on magnetization at T = 4.2 and 77 K for polycrystalline high-temperature superconductors of the Bi₂Sr₂Ca₂Cu₃O_10+δ system containing various amounts of nanodimensional inclusions of tantalum carbide, niobium carbide, or niobium nitride. The introduction of these nanoparticles (≤30 nm in size) leads to an increase in the magnetization and the critical current density. It is established for the first time that the dependence of the normalized critical current on the bulk concentration of indicated dopants is described by the same universal curve. The interval of the optimum dopant concentrations is found, in which the additives lead to the maximum increase in the critical current density.