Fluxoid Pinning Research Articles

Line defects in crystals and flux pinning in superconductors Scientific work of Reiner Labusch (1935 – 2016)

Reiner Labusch, one of the co-founders of the Conference on Extended Defects in Semiconductors in 1978, and his group made seminal contributions to a fundamental understanding of the electrical and optical properties of dislocations in semiconductors, the fluxon pinning in Type II superconductors, and the solid solution hardening of alloys.With regard to semiconductors, he developed occupation statistics and a band scheme for optical transitions of a half-filled band arising from dangling bonds in the dislocation core that could explain the carrier density in plastically deformed p- as well as n-type germanium and devised experimental setups for photoconductivity measurements avoiding the blurring effect of surface states in Ge and Si and measurements on bundles of single dislocations in CdS and Ge. He extended the band model by introducing empty bands split from the conduction band in the strain field of dislocations. This model is most convincingly confirmed for 90° partial dislocations in Ge by photoconductivity spectra on individual dislocations.Reiner Labusch's theoretical studies on superconductivity include (i) the elastic properties of the fluxoid lattice in type II superconductors, (ii) the nature and properties of fluxoid lattice dislocations and (iii) a rigorous statistical theoretical treatment of the response or, in particular the “pinning”, of the fluxoid lattice to pinning sites/defects in the crystal lattice, and (iv) on the magnetization behavior in type II superconductors of arbitrary shape. This latter rigorous analysis and numerical treatment allowed for the accurate prediction, and a contribution to the understanding of the magnetization properties in disc/platelet samples, including inter alia, the initial fluxoid penetration behavior, fluxoid pinning, and fluxoid lattice transformations relating to the “arrow-head” phenomenon, fluxoid lattice melting and the “intermediate state”.Labusch’s statistical theory of solid solution hardening is based on a fundamental understanding of the interaction of a dislocation moving through a random array of solute atoms or precipitated particles. It yielded an expression for the critical resolved shear stress as a function of the obstacle concentration, the interaction force and range of interaction between the dislocation and a single obstacle, and the dislocation line tension. The analytical result was corroborated by computer simulations which also revealed that the strengthening by extended obstacles in most alloys is beyond the ‘Friedel-limit’ and is adequately described by the ‘Labusch theory’.

Suppression of vortex pinning by field component parallel to the superconducting plane inBi2Sr2CaCu2O8

The response of magnetic fluxoids nearly parallel to the superconducting plane of the layered superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ has been investigated through the ac susceptibility measurement. The fluxoids respond diamagnetically due to pinning when they pierce the superconducting plane to form pancake vortices, but they are released due to melting and become mobile in the high field. The liberation is enhanced by approaching the parallel field direction by the effect of decoupling between planes and finally the vortex pinning is suppressed. The pinning of fluxoids with pancakes and releasing in relation to their lock-in state are presented.

Strong pinning in heat treated YBa2Cu3O7−δ

A number of authors have discussed the pinning of magnetic fluxoids in high temperature superconductors in terms of a cooperative process involving large numbers of defects. In particular, in a recent study of magnetic flux creep in high quality single crystals of YBa2Cu3O7−δ, we showed that an appropriate collective pinning model accurately described the creep in that part of the H-T phase diagram where the creep is controlled by single fluxoid motion. Here we present data on similar crystals given an additional heat treatment at temperatures above 800°C. These crystals exhibit large critical currents that exceed the limit associated with collective pinning, suggesting the influence of strong pinning defects. An analysis of the pinning potential U(j) at large j provides further evidence for strong pinning. We suggest that the heat treatment introduces precipitates of nearly optimum size for pinning, leading to a combination of weak and strong pinning defects.

Radio-frequency acoustic powder echoes in high-T c YBaCuO ceramics around the H-T phase boundary

Intensity of rf acoustic powder echoes are studied around the H-T phase boundary in the superconducting state for powdered samples of YBaCuO prepared by the quench and melt growth (QMG) process and for conventional powder of YBa 2Cu 3O 7−δ. The echoes are fond to vanish at the critical field H C2 rather than the irreversibility field H irr for both of the samples. The intrinsic pinning rather than the pinning of fluxoids to defects seems to be important for the observation of rf acoustic powder echoes in the high-T c YBaCuO ceramics.

High-field superconductivity in Al-O-Pb and Al-O-Pb-Bi sputtered films

The sputter-quenched Al x O y alloys containing lead and bismuth elements, which are insoluble to aluminium; have been found to exhibit a remarkably enhanced upper critical field,H c2, which is higher by about 6 to 66 times than those of pure lead metal and Pb60Bi40 alloy. The sputtered structure consists of amorphous Al x O y and f c c lead or h c pe (lead-bismuth) phases. The lead ande phases disperse homogeneously in the amorphous matrix and their particle sizes and interparticle distances are about 10 to 20 nm and 5 to 20 nm, respectively, for lead ande particles. The superconducting transition temperature,T c, upper critical magnetic field,H c2, at 4.3 K, and residual resistivity at 10 K are 7.74 K, 3.3 T and 2.09 × 105μΩcm, respectively, for (Al-O)92.8 Pb7.2 and 7.45 K, 8.2 T and 1.70 × 106μΩ cm, respectively, for (Al-O)86.2(Pb0.6 Bi0.4)13.8. The remarkable enhancement ofH c2 is interpreted as being mainly due to a remarkable decrease of the coherence length resulting from a large reduction of the effective mean free path of electrons. Additionally, the fluxoid pinning force under applied field has also been markedly enhanced for the duplex structure films than for sputtered lead film, probably because of the change of the dispersed lead phase into a type-II superconductor and an effective fluxoid pinning action at the interface between Al x O y and fine lead particles.

Angle‐resolved XPS studies of oxides at NbN, NbC, and Nb surfaces

AbstractNbN, NbC and Nb are known to be chemically inert with passivating oxides only solvable in HF acid. Despite Nb2O5 as outermost oxide layer, the oxides of Nb compounds show large differences in thickness and in electronic properties. To quantify the differences, angle‐resolved XPS (ARXPS) measurements have been performed. The simultaneous fitting for different angles and preparations of the Nb, C, N and O XPS lines of the oxides yielded the following stoichiometries and distributions: Nb2O5 is the outermost oxide layer on NbN, NbC and Nb, followed by: Nb2N2−xO3+x(x<1) on NbN. Dielectric Nb oxicarbides were not identified for NbC. Underneath the dielectric metallic oxides NbN1−xOx for NbN, NbC1−xOx for NbC and NbO and NbOx for Nb (x<0.5) occur. The oxide growth (a)–(c) is not planar; instead, the oxides serrate the metal surface on an nm scale. The serration is strongest for the soft Nb and smallest for the harder compounds NbN and NbC in parallel to the oxidation rate which is slowest for NbC.The improved oxide quality and better quality of tunnel junctions in comparison with Nb is explained by this first identification of oxinitrides and of reduced serration of NbN (NbC). The first identification of Nb(N, C)1−xOx compounds extending into the metals explains, e.g., regions of depressed superconductivity, leakage current and pinning. The fluxoid pinning is enhanced by dielectric oxides existing for sputtered NbN between the grains and thus explaining the superior superconducting properties of granular NbN.

Effect of annealing on the structure of an amorphous(Mo0.6Ru0.4)82B18alloy

The amorphous metallic glass ${({\mathrm{Mo}}_{0.6}{\mathrm{Ru}}_{0.4})}_{82}$${\mathrm{B}}_{18}$ was annealed for various lengths of time at temperatures up to 650\ifmmode^\circ\else\textdegree\fi{}C. The changes in structure due to these annealing treatments were determined by measurements of superconducting properties (${T}_{c}$,${B}_{c2}$,${J}_{c}$), electrical resistivity (${\ensuremath{\rho}}_{n}$), low-temperature specific heat (electronic coefficient $\ensuremath{\gamma}$), small-angle x-ray scattering (SAXS), and transmission electron microscopy (TEM). At lower annealing temperatures (\ensuremath{\le}450\ifmmode^\circ\else\textdegree\fi{}C) only small changes occurred in the composition-dependent parameters (${T}_{c}$,$\ensuremath{\gamma}$) but large degradations were exhibited in those quantities (${J}_{c}$, fracture strain) sensitive to the defect structure. No evidence of microstructural changes was revealed by SAXS or TEM in this regime. At higher annealing temperatures (or longer times) evidence for the development of, first, phase separation, then, the beginnings of crystallization was found by SAXS and TEM. In this regime larger degradations of ${T}_{c}$ and $\ensuremath{\gamma}$ occurred along with a change in the form of the ${F}_{p}(b)$ curve (i.e., a change in the fluxoid pinning mechanism). The above observations imply annealing-induced long-range compositional variations. The activation energy for the onset of long-range compositional inhomogeneity was determined to be 309 kJ ${\mathrm{mol}}^{\ensuremath{-}1}$ (3.2 eV).

The effects of cold rolling on fluxoid pinning in a superconducting metallic glass

Results exhibiting the influence of cold rolling fluxoid pinning in a metalic glass superconductor (Mo0.6Ru0.4)82B18 are reported. Inhomogeneous deformation up to 20% reduction in thickness does not change either the superconducting transition temperature Tc or upper critical field Hc2 but does degrade the critical current density by as much as 34% from the value in the the as-cast condition. Possible mechanisms for this degradation of Jc are suggested. Pinning by inhomogeneities in composition or density rather than by the simple surface or unresolved second-phase precipitates appears to be likely.

Fluxoid Pinning by Small Nitride Precipitates in Niobium

The magnetic hysteresis of superconducting niobium single crystals containing \ensuremath{\sim}80-\AA{}-diam nitride precipitates was investigated. Introducing precipitates into the samples produced no significant change in the critical-current density ${J}_{c}$ except near the critical fields ${H}_{c1}$ and ${H}_{c2}$. The samples trapped flux below ${H}_{c1}$ and exhibited dramatic peaks in ${J}_{c}$ within 3% of ${H}_{c2}$. These observations are interpreted as clear evidence of a threshold for fluxoid pinning, and reasonable agreement with theory is obtained.

Fluxoid pinning by vanadium carbide precipitates in superconducting vanadium

Abstract : The purpose of this investigation is to study fluxoid pinning in a Type II superconductor. Vanadium was chosen as the superconductor to study because it is obtainable in high purity and its microstructure can be readily controlled. The pinning centers are formed by introducing carbon into the vanadium matrix forming vanadium carbide precipitates. The vanadium carbide precipitates are disc-shaped particles whose thickness is only a few atomic layers. The precipitates are likely to be superconducting when H = 0 by reason of the proximity effect. The vanadium carbide precipitates on the (310) habit planes. According to studies with the transmission electron microscope, the particles are uniformly distributed throughout the specimen. The particle size and number density is changed by aging the specimens for fixed amount of time at 350 C. The present results are based on the study of thirty specimens. A 99.95% pure annealed vanadium specimen was used as a control. The other vanadium specimens contain 0.1 atomic percent to 0.6 atomic percent carbon. As a result of metallurgical analysis, the mean diameters of the particles range from less than 100 A to 2613 A and the number density of the pinning centers range from 3.3 x 10 to the 15 power particles/cc to 4.2 x 10 to the 17th power particles/cc. The measurement of the superconducting properties lead to values of the macroscopic pinning force density ranging from 33400 dynes/cc to 3170000 dynes/cc for T - O K.

Fluxoid pinning in bulk Niobium by voids produced during neutron irradiation

Fluxoid pinning due to voids has been studied in niobium irradiated at temperatures from 460 to 1080°C. T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> decreased slightly and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c2</inf> increased with irradiation temperature indicating possible O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> contamination. The J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> vs H behavior was more complex, with maximum J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> values obtained in the samples irradiated at 790 and 940°C. With the measured superconducting parameters, and data on void size and distribution, our results were quantitatively compared with expressions for void pinning using the statistical theory of Labusch. Of particular interest in this study was the sample irradiated at 790°C which has an ordered void super-lattice.

Study of flux pinning by torque measurements in superconducting Al - 10% at Ag

The influence of magnetic field and temperature on Abrikosov fluxoid pinning in supersaturated Al-10 at % Ag solid solution is investigated by the torque measurement method. The minimum rotation angle of the magnetic field for the breakaway of fluxoids from pinning centres, logarithmic decrement of oscillation attenuation, and oscillation frequency of elastic suspension with the specimen are determined. The magnetic moment of the specimen is also calculated. It is shown that pinning increases with the decomposition of the alloy leading to the formation of γ 1-phase lamels.

Fluxoid pinning in niobium containing small amounts of yttrium or gadolinium

Abstract The fluxoid pinning of niobium containing small amounts of either yttrium or gadolinium (2 at. %) was determined by direct current magnetization measurements on specimens in the heavily-deformed, partially-recovered, and recrystallized conditions. Optical and electron microscopy were used to characterize the samples. Magnetic hysteresis of Nb was increased by the additions of Y or Gd. In the cold-worked condition increased pinning was due to planar sheets and stringers of Y(Gd) produced by the deformation and parallel to the fluxoid axes. The fluxoid pinning was a function of Y(Gd) concentration. In the recrystallized samples the high-angle grain boundaries were the most important pinning sites and the pinning was independent of Y(Gd) content. The Y(Gd) enhanced the pinning effectiveness of grain boundaries by: (1) inhibiting grain boundary migration and thus increasing the grain boundary surface area (decreasing grain size); and (2) reducing preferred orientation in the recrystallized state thus providing greater average grain misorientation, which for Nb with its anisotropic superconducting parameters (K) produces an additional pinning effect.

Losses in laminar composite Nb3Sn at 60 Hz

A detailed study has been made of the ac loss in cylindrical samples of Nb3Sn carrying a transport current at 60 Hz. Samples were prepared by a vacuum codeposition process. At low currents, up to 550 A/cm at 4.2 °K in some samples, the loss is dominated by a surface fluxoid pinning mechanism, varies no faster than the square of the current, and in many cases less rapidly, and is temperature independent. At higher currents, the loss is described by the critical-state model. Formation of the superconductor in cylindrical layers separated by another material provides enhanced bulk fluxoid pinning, thereby increasing the critical current density and decreasing the loss at high currents. The magnitude of the ac loss in this material up to 10–12 °K is comparable to that reported in niobium at 4.2 °K.

Dependence of the pinning of fluxoids on grain boundaries on the direction of magnetic field

The angular dependence of surface pinning on the direction of the Lorentz force is calculated for special types of superconducting grains. Especially, sinusoidal and ellipsoidal grain shapes are considered. The filling of plane with close-packed sinusoidal shapes is evaluated and compared with those of ellipsoidal (or spherical) shapes. From the features of the calculated angular dependences of the pinning some conclusions are suggested for the experimental and structural study of superconducting Nb3Sn tapes prepared by various methods.

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 ΔJ c due to the particles are calculated. General expressions without arbitrary parameters are given forP and ΔJ c as functions of magnetic field strength and the characteristics of the superconductor and the particles. For broad ranges of conditions values ofP and ΔJ c greater than 10−7 dyn and 105 A/cm2 result and for certain physically realistic sets of conditions,P>10−6 dyn and ΔJ 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.

Precipitates and fluxoid pinning in a superconducting Nb-Hf alloy

Abstract The relationship between superconducting fluxoid pinning and precipitate dispersion was investigated in a high-field type II superconducting alloy. The alloy, Nb-38 at. % Hf, is a b.c.c. solid solution above 1200°C; at lower temperatures the equilibrium structure is two-phase: b.c.c. β and Hf-rich h.c.p. a. The quenched alloy was aged at 600°C. The changes in microstructure during ageing were examined by transmission electron microscopy. The attendant changes in superconducting properties—transition temperature (T c) and critical flux gradient (dB/dr)—were measured by an a.c. susceptibility technique. It was found that precipitation at 600°C proceeds by the formation and growth of strained, partially coherent particles in the b.c.c. matrix termed transition alpha, αt. Particle size measurements indicated that growth of at follows a t 1/3 coarsening law after times not longer than ∼ 0·5 hr. Transition temperature measurements substantiate this finding. Measurements of dB/dr showed little change fr...

II quantum oscillations, pinning and the superheating and other critical fields in a low K type II superconducting microcylinder

a.c. susceptibility measurements show the pinning and unpinning of individual fluxoids by the alternating magnetic field. The following critical fields can be identified: H C1 , H C2 , H C3 , and H S (the superheating field). H C2 and H S give consistent K values while H C1 indicates a size effect or supercooling. In accord with theory the ratio H C3 / H C2 is greater than 1.7.

Fluxoid Pinning in Nonideal Type-II Superconductors. I. Force between a Fluxoid and a Lattice Defect

A general expression of the interaction energy between fluxoids and lattice defects is obtained by perturbational calculations of the generalized Ginzburg-Landau equations, which are derived by minimizing the free energy of the mixed state including elastic terms. The present expression is the same as Labusch's obtained only for a special type of lattice defects with a pure shear, but is shown to be applicable to any type of defects. The interaction force between a fluxoid and a lattice defect is derived for some typical types of defects by the use of the present expression of interaction energy, and the results of previous authors are shown to be unsatisfactory, even qualitatively. The present results give the first step for the derivation of a general expression of the so-called “pinning force”, which is the final purpose of this series.

Fluxoid pinning by second phases in a superconducting niobium-zirconium alloy

The effects of second phases on the critical currents of superconducting niobium-zirconium alloys containing a nominal 25 wt % zirconium have been determined by superconducting magnetisation experiments. Heat treatment of annealed and extruded materials in the temperature range 600 to 900° C leads to a cellular decomposition of the high temperature β structure into two isostructural phases, one niobium-rich (β Nb) and the other zirconium rich (β Zr), with an accompanying increase in critical current (at an average field of 20 kOe) up to twelve times the original value. Heat treatment of quenched tubes at 800 or 900° C produces precipitation on sub-boundaries prior to the cellular reaction, this being accompanied by an increase in critical current to at least thirteen times the original value. In this case, however, prolonged heating leads to a fall in critical current which it is suggested is an “overageing” effect.