Constant Critical Current Density Research Articles

Magnetization and AC loss in a superconductor with an elliptical cross-section and arbitrary aspect ratio

An analytical approximation is developed for the magnetization of an infinitely long superconductor with an elliptical transverse cross-section. The superconductor is modeled in the critical state with a critical current density that is not dependent on the magnetic field. The aspect ratio of the ellipse is varied from one (=circle) to infinitely large. The magnetic field is applied perpendicular or parallel to the broadest face. The analytical expression is compared with a more detailed model that utilizes a numerically optimized contour for the boundary of the saturated zone. The two methods are compared and the maximum error is estimated at 2% for the optimized contour approach and 5% for the analytical approximation. The analytical model is compared with a magnetization loss measurement on a high- T c superconducting tape with an aspect ratio of nearly 20. A good agreement is obtained for a magnetic field pointing perpendicular as well as parallel to the broadest face of the tape. An interesting result for the magnetic behavior determined for the ellipse is that it contradicts with the behavior that is predicted for an infinitely thin strip in perpendicular field. The difference is attributed to the two specific assumptions made in the thin strip model: the constant critical current density distribution across the tape and the magnetic-field profile that does not exclude unsaturated currents in the shielded zone.

Filament bridging and critical current density variation in the cross-section of multifilamentary Bi-2223/Ag tapes

We calculated magnetic fields in the vicinity of model multifilamentary Bi-2223/Ag tapes carrying magnetisation currents with a constant critical current density. The profiles of the perpendicular component of the magnetic field, B/sub mz/, in the lateral direction for the model tape without superconducting interconnections (bridging) and those for the model tape with filament bridging are very different. Experimental results on real tapes qualitatively agree with the calculations. Direct measurements of the filament critical current distribution in 2 of 3 measured tapes showed that the filament critical current, J/sub fc/, was the highest in the tape centre.

Electromigration and Diffusion in Short Al-Ni-Cr Lines

AbstractTo investigate why the formation of electromigration damage in Al lines alloyed with both 0.1 at.% Ni and 0.1 at.% Cr is so effectively suppressed we studied electromigration induced changes in the electrical resistance of short lines. The length of the lines is 4, 6, 8, or 12 µm, the width is 4 µm and the film thickness is 0.3 µm. As previously reported for pure Al lines, depending on current density and sample length, the induced resistance changes fully recover or do not recover after DC stressing for a few hours. The recoverable resistance changes correspond to the build-up or relaxation of mechanical stress and the permanent resistance changes to the formation of a void or hillock. Electron microprobe analysis and resistance measurements after prolonged current stressing provided no evidence for changes in local solute concentration. Therefore diffusion of Al along grain boundaries is regarded as the dominating diffusion process. The activation energy and the pre-exponential factor of this process are determined from the temperature dependence of the relaxation time of the recoverable resistance changes. The activation energy of this process is 0.84±0.03 eV and the pre-exponential factor δD0 = (1.8±0.8)×10−8 cm3/s. At 175 °C the resulting diffusion coefficient is about a factor 70 smaller than that of pure Al. The transition from recoverable to permanent resistance changes is characterized by a constant critical current density -sample length product. It is found that the value of this product for the Al-Ni-Cr lines is two times larger than the value found for pure Al lines. This means that the threshold current density at given sample length for the formation of hillocks or voids is two times larger. Both the slower solvent diffusion and the higher threshold current density contribute positively to a long electromigration lifetime.

Field mapping characterization for axially magnetized, superconducting cylinders in the remanent critical state: theory and experiment

Based on the Bean model with a constant critical current density jc, novel and very precise, analytical approximations for the axial induction component Bz(r) inside and outside of a finite, axially magnetized, circular cylinder with arbitrary aspect ratio in the fully penetrated, remanent critical state are presented. Starting from any mapped field profile the possibility to determine the material parameter jc by means of a global optimum fit procedure is demonstrated. Some characteristic results for melt-textured yttrium barium copper oxide material are outlined. We found that jc determined by vibrating sample magnetometry (VSM) exceeds that from mapping at least by about 50%. This systematic discrepancy is discussed on the basis of two independent effects resulting in a local, space-dependent critical current density: the B-dependence of jc and material inhomogeneities. The first effect becomes important for sample radii in the 1-cm-range, although the Bz-profile remains axially symmetric and well fitted by the Bean model. The second one may lead to asymmetric Bz-profile deformations connected with a decreasing fitting significance. For the first and second effect we estimate the considerable ratio of the absolute maximum to absolute minimum of the local, critical current density of 2 and 4, respectively, which explains the observed discrepancies between the effective jc from mapping and VSM measurements.

Electromigration in Short Al Lines Studied by High-Resolution Resistance Measurement

ABSTRACTElectromigration induced resistance changes in short Al lines have been studied by high-resolution AC bridge measurements. The samples were pure, unpassivated Al lines having a length of 3, 5, 8, 12, 17 or 100 μm, a width of 2 μm, and a film thickness of ∼100 nm. Depending on current density and sample length the induced resistance changes fully recover or do not recover after removal of the DC stressing current. The transition from recoverable to non-recoverable behavior is clear-cut and is characterized by a constant critical current density - sample length product. The value of this product is close to the value of the constant critical current density - sample length product characterizing the occurrence of drift in a drift velocity experiment. Inspection of the lines after current stressing by atomic force microscopy revealed that non-recoverable resistance changes are caused by the growth of a single void, hillock or hillock/void pair. Negative resistance changes correspond to the growth of a hillock and positive resistance changes to the growth of a void. The magnitude of the non-recoverable resistance changes can be very well estimated from the dimensions of the void or hillock. The rate of change of the non-recoverable resistance changes (or the growth rate of a void or hillock) scales linearly with the current density.The characteristic time of the relaxation process of the recoverable resistance scales with the sample length squared. The temperature dependence of the relaxation time shows a good Arrhenius behaviour with an activation energy typical for grain boundary diffusion in Al. The maximum magnitude of the recoverable resistance changes is ΔR/R∼5×10∼-4. The time and temperature dependence of the recoverable resistance changes can be very well explained by the mechanical stress evolution model of Korhonen et al. The evolution of the stress is reflected in changes of the electrical resistance by the piezoresistance effect. A good agreement is found between maximum observed recoverable resistance change and the maximum stress in the line. The good understanding of the resistance changes induced by electromigration in short lines makes this geometry very attractive for studies of fundamental aspects of electromigration in thin film conductors.

Low-temperature magnetization and flux creep studies of a DyBa 2Cu 3O 7 single crystal with a vibrating reed

Magnetization measurements have been performed on a high-temperature DyBa 2Cu 3O 7 superconducting crystal in the magnetic field range 0 T ≤ μ 0 H ≤ 7 T parallel to the c-axis and temperature range 0.1 K ≤ T ≤ 30 K with the vibrating reed technique. No anomalous behavior of the magnetization was observed at the antiferromagnetic transition. The field dependence of the virgin magnetization curve M( H) follows the analytical result for a type-II superconducting strip in perpendicular magnetic field with constant critical current density. We have also measured the time dependence of the magnetization at times 1 s < t ≤ 10 4 s and at a field μ 0 H = 1 T. We obtain for the normalized relaxation rate S = (1/ M irr)d M/d 1n t = 0.02 + T/700 K at T ≤ 20 K. The value S(0) is similar to that observed for very different high-temperature superconductors.

Effect of oxygen and zirconium on the growth and superconducting properties of Nb3sn

The intermetallic compound Nb3Sn is a type II superconductor of interest because of its high superconducting critical current density in high magnetic fields. One technique for forming Nb3Sn is to react a molten tin alloy with a solid niobium-zirconium-oxygen alloy. It was found that the properties of Nb3Sn are directly related to its microstructure, which is in turn directly related to the O: Zr atom ratio in the starting niobium foil. For a niobium alloy foil with an O:Zr atom ratio of 2, the resulting Nb3Sn layer is fine grained and grows linearly with reaction anneal time until the entire Nb-Zr-O alloy core is consumed. This leads to a linear increase in critical current with time and a relatively constant critical current density. For a niobium foil without oxygen, the resulting Nb3Sn grains are large and columnar and grow with a diffusion-limited layer growth rate. The resulting critical current density is low and decreases with reaction time. For a niobium alloy foil with an O:Zr ratio of >0 but <2, fine-grained Nb3Sn is formed initially and grows with a linear layer growth rate, followed by a second layer of large, columnar-grained Nb3Sn growing with a diffusion-limited rate. As a function of reaction anneal time and similar to the grain growth, the critical current initially increases linearly and then decreases.

Type-II-superconductor strip with current in a perpendicular magnetic field.

Current density, magnetic field, penetrated magnetic flux, and magnetic moment are calculated analytically for a thin strip of a type-II superconductor carrying a transport current I in a perpendicular magnetic field ${\mathit{H}}_{\mathit{a}}$. Constant critical current density ${\mathit{j}}_{\mathit{c}}$ is assumed. The exact solutions reveal interesting features of this often realized perpendicular geometry that qualitatively differs from the widely used Bean critical state model: At the penetrating flux front the field and current profiles have vertical slopes; the initial penetration depth and penetrated flux are quadratic in ${\mathit{H}}_{\mathit{a}}$ and I; the initial deviation from a linear magnetic moment is cubic in ${\mathit{H}}_{\mathit{a}}$; the hysteresis losses are proportional to the fourth power of a small ac amplitude; the current density j is finite over the entire width of the strip even when flux has only partly penetrated; in thin films, as soon as the direction of the temporal change of ${\mathit{H}}_{\mathit{a}}$ or I is reversed, j falls below ${\mathit{j}}_{\mathit{c}}$ everywhere, thus stopping flux creep effectively; the Lorentz force can drive the vortices ``uphill'' against the flux-density gradient. These analytical results are at variance with the critical-state model for longitudinal geometry and explain numerous experiments in a natural way without the assumption of a surface barrier.

Irreversibility line and non-linearity in the AC response caused by flux pinning in high- Tc superconductors

We have studied the irreversibility lines (IL) obtained by AC magnetic measurements in the region with notable dependence of the AC susceptibility on the AC field amplitude. The commonly used procedure of taking temperatures of maxima in the imaginary part of AC susceptibility χ″ is shown to be consistent with the definition of the IL as the line of constant critical current density. The data obtained in experiments on melt-grown YBaCuO samples were used to compare this method with two other ones: (a) searching for the appearance of flux pinning in a non-linear flux-flow regime, (b) construction of current-voltage characteristics from AC magnetic measurements. We demonstrated that it is possible to reach good agreement between irreversibility lines acquired under the conditions of a non-linear AC regime by different methods if the current densities and the electrical fields in the sample are comparable.

"Phase diagram" of the vortex-solid phase in Y-Ba-Cu-O crystals: A crossover from single-vortex (1D) to collective (3D) pinning regimes.

We construct a ``phase diagram'' of the vortex-solid phase of Y-Ba-Cu-O single crystals by making a first overall connection of the shape of the magnetic hysteresis M(H,T) with the single-vortex (1D) and collective (3D) pinning regimes. The crossovers between different regimes are visualized by drawing contours of constant critical current density ${\mathit{J}}_{\mathit{c}}$ in the H-T plane. We identify the transition from 1D to 3D pinning, and from the nonlocal into a local behavior of vortex bundles in the collective pinning regime. A direct correlation between the shape of M(H) and the field-dependent thermal relaxation rate is demonstrated. We also identify a signature of the thermal softening boundary at which thermal fluctuations on the scale of the coherence length \ensuremath{\xi} are relevant.

A computer approach to the nonlinear hysteretic problem of electromagnetic field computation in hard superconductors for loss evaluation

The computation of the losses in superconducting wires requires the solution of electromagnetic problems with a complicated constitutive equation of the superconducting material, which is nonlinear with hysteresis, under time-varying conditions. Analytical and numerical procedures which can be found in the literature about this problem present a very limited application range and cannot be applied to cases of practical interest. In the paper a procedure is presented, by which most of the drawbacks are eliminated. The critical state model developed by Bean, Kim et al is used, in both the forms with constant critical current density and with critical current density function of the magnetic field. In this model the magnetic field penetrates the superconductor entering from the boundary by fronts. These fronts cannot reverse their velocity and represent interfaces with unknown geometric shapes. A package has been implemented to solve this problem, some example of field solution are given and the results are discussed.