Extended Bean Model Research Articles

Improvement of the Superconducting Properties of GdBa2Cu3O7-δ with Nano-Sized Ferrite Addition

We have been investigating the effect of (CoFe2O4)x and (ZnFe2O4)x (x is the wt%) nano-sized ferrites on the superconducting (SC) properties of the high-Tc SC compound GdBa2Cu3O7-δ (Gd123) prepared by the conventional solid-state reaction technique. In this work, the magnetic hysteresis for pure Gd123 samples and samples added with nano-sized ferrites was measured using a superconducting quantum interference device (SQUID) magnetometer using a dc field up to 30,000 Oe. The magnetic Jc was estimated using the extended Bean model. While a clear increase in Jc values with the addition of (CoFe2O4)x nano-sized ferrites is observed, a less clear positive effect on the Jc values is observed with the addition of (ZnFe2O4)x nano-sized ferrites. These results indicate an improvement of grain connectivity, decrease of voids between the grains, and decrease of porosity in Gd123 compound resulting from CoFe2O4 addition consistent with the mechanical properties measured before. (CoFe2O4)x nano-sized ferrite addition has thus resulted in an improvement in the SC properties of Gd123 high-Tc SC compound making it more convenient for applications.

Crack problem in superconducting cylinder with exponential distribution of critical-current density

The general problem of a center crack in a long cylindrical superconductor with inhomogeneous critical-current distribution is studied based on the extended Bean model for zero-field cooling (ZFC) and field cooling (FC) magnetization processes, in which the inhomogeneous parameter η is introduced for characterizing the critical-current density distribution in inhomogeneous superconductor. The effect of the inhomogeneous parameter η on both the magnetic field distribution and the variations of the normalized stress intensity factors is also obtained based on the plane strain approach and J-integral theory. The numerical results indicate that the exponential distribution of critical-current density will lead a larger trapped field inside the inhomogeneous superconductor and cause the center of the cylinder to fracture more easily. In addition, it is worth pointing out that the nonlinear field distribution is unique to the Bean model by comparing the curve shapes of the magnetization loop with homogeneous and inhomogeneous critical-current distribution.

Enhanced Critical Current Density of FeF2 Added YBa2Cu3O7−δ

The effect of nanosized FeF2 (∼120 nm) addition on the critical current density, Jc, of YBa2Cu3O7−δ was studied. YBa2Cu3O7−δ superconductor was prepared by the solid-state reaction method with addition of 0 to 0.10 wt% FeF2 additions. The magnetization critical current density, Jcm (at 77 K), was estimated from the extended Bean model by using vibrating sample magnetometer (VSM) measurements. The transport critical current density, Jct, was measured using the four-point probe method with the 1 µV/cm criterion. The onset transition temperature, \(T_{\mathrm{c}\mbox{-}\mathrm{onset}}\) showed a maximal value at 92 K for 0 to 0.03 wt% additions. Jc increased with FeF2 addition up to 0.03 wt%. Addition of FeF2 of more than 0.03 wt% suppressed \(T_{\mathrm{c}\mbox{-}\mathrm{onset}}\) and Jc. The inter-grain current density was enhanced by two orders of magnitude on 0.03 wt% FeF2 addition. In addition to the condensation energy associated with their core, the full vortex magnetic energy by addition of nanosized FeF2 enhanced Jc in the system.

Microstructure and Superconductive Property of MgB<sub>2</sub>/Al Composite Materials

MgB2 has the higher critical temperature of superconducting transition (TC : 39K) among the intermetallic compound superconductive materials, however, MgB2 is hard for practical use because of its unworkable and lower critical current density (JC) in a high magnetic field than Nb-based superconductive materials. We have developed the original method of three-dimensional penetration casting (3DPC) to fabricate the MgB2/Al composite materials. In the composite material we made, MgB2 particles dispersed to the matrix uniformly. Thus, these composite materials can be processed by machining, extrusion and rolling. The TC was determined by electrical resistivity and magnetization to be about 37～39K. In this work, we made composite material with ground MgB2 particle with the purpose of extruding thinner wires of composite material, successfully produced φ1mm wire and changed the matrix from pure Al to Al-In alloy. JC of composite materials with the matrix of Al-In alloy was calculated from the width of the magnetic hysteresis based on the extended Bean model. The result was better than that of MgB2/Al composite material without Indium. Microstructures of these samples had been confirmed by SEM observation.

Microstructure and Superconductive Property of MgB2/Al Composite Materials

MgB2has the higher critical temperature of superconducting transition (TC: 39K) among the intermetallic compound superconductive materials, however, MgB2is hard for practical use because of its unworkable and lower critical current density (JC) in a high magnetic field than Nb-based superconductive materials. We have developed the original method of three-dimensional penetration casting (3DPC) to fabricate the MgB2/Al composite materials. In the composite material we made, MgB2particles dispersed to the matrix uniformly. Thus, these composite materials can be processed by machining, extrusion and rolling. TheTCwas determined by electrical resistivity and magnetization to be about 37～39K. In this work, we made composite material with ground MgB2particle with the purpose of extruding thinner wires of composite material, successfully produced φ1mm wire and changed the matrix from pure Al to Al-In alloy.JCof composite materials with the matrix of Al-In alloy was calculated from the width of the magnetic hysteresis based on the extended Bean model. The result was better than that of MgB2/Al composite material without Indium. Microstructures of these samples had been confirmed by SEM observation.

Magnetic Properties of YBCO Single-Crystal Grown on Y2O3 Layer by a Cold Top-Seeding Method

In this work, single-crystal samples 20 mm in diameter were grown by a cold top-seeding method. In order to study the effect of an Y2O3 buffer layer, a compacted precursor was located in a crucible on a buffer layer of freely poured Y2O3 powder. The YBCO bulk samples were carefully prepared in the same chemical composition. In order to examine the homogeneity of the samples, rectangular specimens were cut from a sample. The structural orientation of the specimens was measured by a X-ray diffractrometer (XRD). The microstructure was observed with a Scanning Electron Microscope (SEM). The magnetic properties were measured using a Vibrating Sample Magnetometer (VSM) at 77 K with the applied magnetic field parallel to the c-axis. As a result only (00l) peaks were observed in X-ray diffraction data, indicating that all specimens are highly oriented with the c-axis perpendicular to the top surface. Also the cut samples exhibited very fine Y211 inclusion distributed in the bulk sample observed in SEM micrographs. The critical current density Jc (A/cm2) has been estimated by the extended Bean model. The maximum value of the critical current density at 77 K is 5.2×104 A/cm2 in a self-field. The trapped magnetic field measurements of the samples were performed by using Hall probe scanning device with static field of 0.5 T at 77 K. The single-domain sample exhibits a trapped field of 1140 G at 77 K.

Superconducting Properties of MgB<SUB>2</SUB> Particle Impregnated with Mg-Based Alloys

The three-dimensional penetration method combined with semi-solid casting (SS-3DPC) was utilized to prepare magnesium diboride (MgB2) powder composite materials with various host materials of Mg, Mg-3%Al, Mg-3%Al-1%Zn, Mg-9%Al, and Mg-9%Al-1%Zn. X-ray diffraction measurements indicated predominant peak patterns of MgB2 and a host alloy, implying that the host material tightly bonded MgB2 grains without melting the MgB2 powder. This was confirmed by SEM images. Measured electrical resistivity and magnetization versus temperature showed clear signals of superconducting transition temperature of 27∼38 K for all the samples cut out from the billets. Magnetic hysteresis loop observed at 5 K enabled us to estimate a critical current density (Jc) based on the extended Bean model. Additions of aluminum and zinc elements to magnesium host-matrix were found to enhance Jc and increase residual resistivity (ρ0) suggesting that aluminum and zinc have an effect on pinning magnetic flux flow for Jc enhancement, and scattering conduction electrons for increase of ρ0.

Structural characterization and superconducting properties of MgB2 prepared by SHS-method

Self-propagating high-temperature synthesis (SHS) of bulk MgB2 superconductor from Mg-2B powder blend is reported. This reaction proceeds violently at 100 A under a protective atmosphere. Since the heat of reaction of Mg and B was not enough for chain reaction, then (Ti + C) mixed powders were used as the ignition agent to assist the reaction (Mg + 2B). In this case, the combustion front moved without any difficulty. The diffraction lines of the product can be indexed to a hexagonal MgB2 phase, with lattice constants a = 3.0845 A, and c = 3.5259 A. For comparison, the direct synthesis of (Mg + 2B) mixture was carried out at (800°C–1000°C). It can be found, that high-temperature sintering (1000°C) will induce the formation of impurities. The MgB2 grains are fine, well compacted and more homogenous. The structure of materials was studied using XRD, FESEM and EDX. M-H curvatures were measured under the magnetic fields between −80 kOe and 80 kOe. J c was calculated from width of magnetization hysteresis loops based on the extended Bean Model.

Critical current anisotropy in non-sintered metal-clad MgB 2 tapes

Ag/MgB 2, Cu/MgB 2 and SS/MgB 2 (stainless) tapes were fabricated by the oxide powder-in-tube method. X-rays diffraction studies showed the formation of moderate c-axis texturing in the MgB 2 core, which increases with the sheath strength and correlates with the core microhardness. Magnetization hysteresis loops of the tapes were measured for applied magnetic field ( H) parallel and normal to the tape plane, in a wide range of H (0–5 T) and temperature (5–25 K). The critical current density ( J cm), calculated using the extended Bean model, indicates the possible current limitation due to inter-particle links. Significant anisotropy in J cm is observed. The “parallel” J cm is one order of magnitude higher than the “normal” J cm which is of the same order of magnitude as transport J c in non-sintered tapes. This anisotropy is assumed to be originated from the weak large-scale connectivity (deformation-induced crack formation) in densified MgB 2 core after the rolling process.

Flux dynamic behaviour of a melt-textured YBa2Cu3O7-δsample

The flux dynamics behaviour of a melt texturedYBa2Cu3O7-δ sample was studied by measuring the sweeping ratedependence of magnetization at different temperatures. First, J(T,B) curveswere obtained from the extended Bean model in order to discuss themagnetization dependence on the sweeping rate. Then the curves of ln E-ln J and the thermal excited potential U0(T,B) were derived fromthe magnetic measurements. Thereby the magnetic response of this sample,especially the influence of the field sweeping rate to the second peak wasanalysed. Thus, the peak effect of this sample and the factorsaffecting the magnitude and position of the second peak were discussed.

Study of flux dynamics in NdBCO single crystal before and after heavy ions irradiation

The magnetic properties in NdBCO single crystal fabricated by flux growing method in controlled oxygen atmosphere have been investigated using both SQUID magnetometer and magneto-optical (M-O) technique before and after heavy ions irradiation. An external magnetic field was applied parallel to the sample c-axis up to 7 T at different temperatures. Critical current densities were obtained using the extended Bean model from the hysteresis loops as measured by SQUID. The M-O images were collected using a special facility equipped with a superconductor magnet able to reach 8 T. The indicator film was produced in ISTEC. The M-O images were associated to the data obtained by analysing the magnetization curves. It was found that the irradiation strongly affects the magnetic behaviour. The direct and detailed visualization of the field behaviour provided by magneto optical images allows a more precise understanding of the magnetization loops.

The ac loss near the glass-liquid transition temperature in high-Tc superconductors - an extended Bean model

The ac loss in high-Tc superconductors near the glass-liquid transition temperature Tg is studied numerically and theoretically. It is found that the ac loss in a slab sample under a dc bias magnetic field depends remarkably on the angular frequency, , which cannot be described by the usual critical state model using the critical current density Jc defined with the electric field criterion. However, it is shown that the ac loss including the flux flow loss is described quantitatively by the well known expression based on the Bean critical state model, where Jc is replaced by the effective critical current density Jce(). The applicability of the present expression is also discussed.

Comparative study of global and local magnetization measurements on single crystalline high-Tc superconductors

The mixed state of several (RE)Ba2Cu3O7−δ single crystals (RE=Y,Yb) was investigated by various measuring techniques. Using an 8 T SQUID magnetometer as a reference, we compare the current densities evaluated from global magnetization measurements (SQUID, torque and VSM) and from a local technique (Hall probe array). Taking the specific time scales of the various measurements into consideration, we obtain excellent agreement at all temperatures from 5 to 77 K. Magneto-optical images of the flux density gradients confirm that the current densities can be calculated on the basis of an extended Bean model. The established correspondence between global and local techniques is of fundamental relevance for future experimental work on the subject.

High-resolution magneto-optical imaging of critical currents in YBa 2Cu 3O 7− δ thin films

Magneto-optical investigation of flux penetration into type-II superconductors allows the determination of the local critical current density j c by inversion of the Biot–Savart law. Due to the required computational effort, in the past, this method was limited to low spatial resolution of the current density. In this paper, we present a fast inversion scheme using Fast-Fourier-Transformation, which allows high spatial resolution imaging of current distributions. Due to the nonlocal relation between magnetic field and current density, it is necessary to use a method that images field and current distribution of superconductors as a whole, and enables high resolution at the same time. To demonstrate the power of our method, the local current density in a YBa 2Cu 3O 7− δ square and disk are imaged with high resolution and described in detail for increasing and decreasing external magnetic fields. At low fields, the dependencies of j c( B) on the local magnetic field B and of the average j c (magnetic moment) on the applied magnetic field show significant differences. Finally, we directly image the local current density near macroscopic defects in a square and a disk. The observed current distributions near defects significantly differ from the predictions of an extended Bean model.

Magneto optical characterizations of flux dynamics in NdBaCuO bulk superconductors

We investigated the magnetic flux dynamics of NdBaCuO (NdBCO) bulk superconductors produced by the Oxygen-Controlled-Melt-Growth (OCMG) method using the Magneto-Optical (M-O) technique at various low temperatures. An external magnetic field was applied both parallel ( H t| c) and perpendicular ( H ⊥ c) to the c-axis of the sample. While for H t| c the flux motion was isotropic, for H ⊥ c anisotropic penetration and expulsion of the flux lines were directly visualized. In the configuration H ⊥ c the flux lines were observed to move in and out of the sample predominantly parallel to the a- b planes. The flux behavior was also correlated to the microstructure. Particularly, the microcracks along the basal plane were found to provide a channel for easy flux motion. The anisotropic behavior of the flux front reflects the anisotropy in the critical current density J c. The different components of J c were independently calculated from the M-O data directly analyzing the magnetic induction profiles. These J c values were consistent with those estimated interpreting the magnetization hysteresis measurements within the framework of the extended Bean model.

Magnetization hysteresis loops of the granular high- Tc superconductors in the AC measurements

In this paper, with some improvements to the conventional AC response technique, we report experimentally on the M- H hysteresis loops at different temperatures and frequencies when applying an AC field H = h osin( σt) to the granular superconductor of YBa 2Cu 3O 6.4. Two kinds of hysteresis loops are found with different shapes in different AC field frequencies. Based on the simple Bean model and the extended Bean model, considering the influence of the intergranular lower critical field, we derived the expressions of the magnetization in the AC case, which are in good agreement with the M- H curves measured by our experiments.

Magnetic properties and critical currents in Tl-based high-Tcsuperconducting single crystals

${\mathrm{Tl}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$ (Tl-2223) and (TlPb)(SrBa${)}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{8}$ (Tl-1223) single crystals were investigated by superconducting quantum interference device magnetometry in fields up to 8 T (H\ensuremath{\parallel}c axis). The samples were subjected to sequential reactor neutron irradiation up to a fluence of 24\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}2}$ (E>0.1 MeV). The superconducting transition temperature ${\mathrm{T}}_{\mathrm{c}}$, the magnetization, and the irreversibility lines were measured before and after each irradiation step. Because of the wide range of magnetic fields and temperatures, where the magnetization is totally reversible, especially in Tl-2223, the basic mixed-state parameters, such as the critical magnetic fields and the characteristic lengths, could be evaluated. In the irreversible range, the critical current densities were calculated from the hysteresis loops using an extended Bean model. We find that ${\mathrm{J}}_{\mathrm{c}}$ is strongly enhanced by the radiation-induced defects, e.g., by a factor of 52 in Tl-2223 at 40 K and 1 T. The irreversibility lines are shifted to higher fields and temperatures, but remain always below those of unirradiated Tl-1223, even at the highest neutron fluence. In Tl-1223, the critical current densities are moderately enhanced. The irreversibility line is at the same position or even higher than that of Y-123 and is moderately shifted to higher fields and temperatures after irradiation. The experimental results are discussed in terms of flux pinning and dimensionality.

From Bean's model to the H-M characteristic of a superconductor: some numerical experiments

We present a series of two-dimensional simulations in transverse field as validation of a simple finite difference method for the computation of fields inside superconductors described by an extended Bean model.

Remanent magnetization of ceramic and single-crystal high-T c superconductors in tilted magnetic fields

Dependence of the remanent magnetization (Mr) anisotropy on the structure and shape of the superconductor and on the magnetizing procedure was studied for a number of high-Tc superconductor ceramics and single crystals. The experiments were done by means of a vibrating-sample magnetometer with a rotatable sample holder. It was found that the main contribution to the anisotropic behavior of Mr is due to the surface screening currents, and therefore the anisotropy is subject to variation when sample shape is changed. The question is resolved, why the effective demagnetization factors for decoupled ceramic samples are different from those calculated in the inscribed-ellipsoid approximation. Influence of inhomogeneous grain magnetization and global bulk currents on the angular dependencies of Mr in ceramic samples is investigated. The evolution of remanence in YBCO single crystals with an increase of the magnetizing field is described within an extended Bean model.

Scaling properties of the magnetization curves of the neutron-irradiated YBa 2Cu 3O y crystal prepared by melt-textured growth method

The magnetization curves of neutron-irradiated YBa 2Cu 3O y crystal prepared by melt-textured method were measured from 5 K to 85 K for H‖ C. The virgin magnetization curves, the complete hysteresis loops and the critical current density all exhibit scaling behavior. A new scaling law for the volume pinning force was observed. The scaling behavior observed was explained in terms of the extended Bean model.