Damian P. Hampshire

The scaling law for the strain dependence of the critical current density in Nb3Sn superconducting wires

Comprehensive measurements are reported of the critical current density (JC) of internal-tin and bronze-route Nb3Sn superconducting wires as a function of magnetic field (B?23?T), temperature (4.2?K ?T?12?K) and axial strain (?1.6%??I?0.40%). Electric field?temperature characteristics are shown to be equivalent to the standard electric field?current density characteristics to within an experimental uncertainty of ~20?mK, implying that JC can be described using thermodynamic variables. We report a new universal relation between normalized effective upper critical field (BC2*(0)) and strain that is valid over a large strain range for Nb3Sn wires characterized by high upper critical fields. A power-law relation between BC2*(0,?I) and TC*(?I) (the effective critical temperature) is observed with an exponent of ~2.2 for high-upper-critical-field Nb3Sn compared to the value ?3 for binary Nb3Sn. These data are consistent with microscopic theoretical predictions and suggest that uniaxial strain predominantly affects the phononic rather than the electronic properties of the material. The standard Summers scaling law predicts a weaker strain dependence than is observed. We propose a scaling law for JC(B,T,?I) based on microscopic theory and phenomenological scaling that is sufficiently general to describe materials with different impurity scattering rates and electron?phonon coupling strengths. It parametrizes complete datasets with a typical accuracy of ~4%, and provides reasonable predictions for the JC(B,T,?I) surface from partial datasets.

Experiments concerning the connective nature of superconductivity in YBa2Cu3O7

Samples of YBa2Cu3O7 have been prepared with rather sharp inductive transitions having in the best cases breadths of 7 K and midpoint Tc values of 88 K. The resistive Tc midpoints are 92–95 K with transition widths of ±1–2 K. Flux shielding at 4.2 K is normally 100% and flux expulsion at 4.2 K reaches 95%. However, even small fields of order 1 mT decouple some 15%–20% of the volume, allowing flux to enter the samples. Resistive Hc2 measurements suggest that Hc2(0) varies from 300 T, depending on the criterion chosen. ac susceptibility measurements suggest that Hc2(0) is ∼60 T. Magnetization current densities are relatively high (150–200 A/mm2 at 1–10 T at 4.2 K) but measured transport current densities are small (≤1 A/mm2). Magnetization current densities at 77 K are about two orders of magnitude lower. The samples were seen to be heavily twinned by light microscopy (scale of 1–5 μm) and by transmission electron microscopy (scale of ∼250 nm). It is concluded that these measurements are consistent w...

A probe for investigating the effects of temperature, strain, and magnetic field on transport critical currents in superconducting wires and tapes

A variable-temperature probe has been developed to study the effect of strain on the transport properties of superconducting wires and tapes in high magnetic fields. The strain is applied to the wire by soldering it to a thick coiled spring and twisting one end of the spring with respect to the other. Strain can be applied reversibly from −0.7% to +0.7%. Measurements can be performed either in (pumped) cryogen or under vacuum. When immersed in liquid helium at 4.2 K, the probe can carry at least 200 A. From 6 to 16 K, with thin (low-loss) current leads the temperature of the sample is stable to ±45 mK for currents around 15 A, and to ±100 mK for currents around 25 A. With thick current leads, ±10 mK stability is achieved for currents up to 85 A. Full details of the probe design are described. Results obtained for a bronze processed niobium–tin multifilamentary wire are presented.

Improved critical current characteristics in 1-2-3 oxide superconductors: weak flux pinning and percolative aspects

The authors have fabricated bulk samples of high-Tc oxide superconductors with narrow inductive Tc transitions ( approximately 3 K) and low resistivities ( rho (100 K):250-1000 mu Omega cm). They find such samples to have improved transport critical current density (Jct) properties. Although Jct decreases rapidly with increasing field for fields <1 T, Jct is then approximately independent of field over the range 2-15 T at 4.2 K; at 77 K the field dependence is also much reduced. Jct is about the same whether the applied current is parallel to or perpendicular to the applied field. The high-field values of Jct are, however, still small (<or approximately=50 A cm-2), but are much higher than previous samples in which S-N-S tunnelling controlled Jct, reducing it to less than 1 A cm-2 in fields of approximately 1 mT at 77 K. DC magnetisation data demonstrate that the local critical current density within the individual grains is as high as 107 A cm-2 in fields up to 20 T at 4.2 K. The evidence that the low Jct is the result of easy flux shear along the grain boundaries, as well as that suggesting percolative processes operate, is discussed.

Weak links and the poor transport critical currents of the 123 compounds

Abstract The results of recent transport measurements, DC and AC magnetization measurements, and investigations of the grain boundary morphology and composition of 123 compounds which have been conducted by our group are described. The samples studied have low normal state resistivities (200–600 μΩcm at 100 K) and largely magnetic-field-independent transport critical current densities (J ct ) in the range 2–10 T at temperatures of 4–77 K, indicating that they are of relatively high quality. Nevertheless, the J ct values measured on these samples are still very low (4–100 A/cm 2 , 2–20 T, 4.2 K), and the large values of J cm /J ct (J cm is the magnetization critical current density) determined for these specimens indicate that weak links still limit J ct . Critical current measurements have been made under different relative orientations of applied field, crystal axes, and measuring current on sintered textured samples (c axes of all of the grains nearly parallel). Anisotropy of J cm similar to that observed in single crystals was found. By comparing the ratio J cm /J ct for different orientations of B relative to the c axis, it is concluded that local composition variations must act as efficient pinning centers at 4.2 K. A very low and strongly-field-dependent J cm for B ⊥ c at 77 K suggests, however, that these 4.2 K pinning centers become weak links at 77 K. Evidence is presented for the occurrence of weak links at regions internal to the grains. Detailed microstructural investigations using conventional and analytical transmission electron microscopy and scanning Auger microanalysis on fracture surfaces did not provide any definitive information about the nature of the weak links.

An in depth characterization of (NbTa) 3 Sn filamentary superconductor

Further to our programme of investigations of new, technical superconductive materials which are of interest to designers of practical devices, we present the results of a detailed study of the critical parameters of the ternary addition A.15 material (Nb7.Sw/oTa) 3 Sn manufactured by Vacuumschmelze GMBH, Hanau F.R.G. The basis of the results we report is a comprehensive Jc(B, T) characterization within the range, O<B<15.5T, 2K<T<Tc, with particular emphasis on the temperature in the region of Tc. From these data we extract the relevant information relating to the flux pinning behaviour of the material and discuss its implications. The techniques and apparatus used broadly follow those reported previously although some refinements and improvements we have developed will be described.

Critical current scaling laws for advanced Nb3Sn superconducting strands for fusion applications with six free parameters

This paper presents comprehensive measurements on three advanced ITER internal-tin Nb3Sn strands manufactured by Oxford Superconducting Technology (OST), Outokumpu Superconductors (OKSC) and Luvata Italy (OCSI) for fusion applications. The engineering critical current density (JC )a t 10μ Vm −1 and the index (n) characterized over the range 10‐100 μ Vm −1 are presented as a function of magnetic field (B 15 T in Durham and B 28 T at the European high-field laboratory in Grenoble), temperature (2.35 K T 14 K) and intrinsic strain (−1.1% eI 0.5%). Consistency tests show that the variable strain JC data are homogeneous (±5%) along the length of the strand, and that there is a good agreement between different samples measured in Durham and in other laboratories (at zero applied strain). Limited strain cycling (fatigue) tests demonstrate that there is no significant degradation in the critical current density in the strands due to cyclic mechanical loads. JC is accurately described by the scaling law that was derived using microscopic and phenomenological theoretical analysis and n is described by the modified power law of the form n = 1 + rI s C ,w herer and s are approximately constant. Using variable strain high magnetic field data at 2.35 K for the OCSI sample, it is demonstrated that these laws can be extended to describe data below 4.2 K. For these advanced strands, thirteen, nine and six free parameter fits to the data are considered. When thirteen or nine free parameters are used, the scaling laws fit the data very accurately. The accuracy with which the scaling law derived from fitting data taken at 4.2 K alone fits all the variable temperature data if calculated errors in fitting JC are shown to be primarily determined by uncertainties in TC. It is shown that six free parameter fits can successfully be used when, as with these advanced strands, the strain dependence of the normalized effective upper critical field at zero temperature is accurately known—this approach may provide the basis for comparing partial JC(B, T ,e )data on other similar strands from different laboratories. The extensive data presented here are also parametrized using an ITER scaling law recently proposed for characterizing Nb3Sn strands and the strengths and weaknesses of that approach are discussed.

A scaling law for the critical current density of weakly- and strongly-coupled superconductors, used to parameterize data from a technological Nb3Sn strand

There is currently no consensus on how best to parameterize the large volume of data produced in measuring the magnetic field (B), temperature (T) and strain (e) dependence of the engineering critical current density (JE(B, T, e)) for A15 superconducting strands. For the volume pinning force (FP) and the upper critical field BC2(T, e), we propose given b = B/BC2(T, e) and t = T/TC(e) where TC(e) is the critical temperature. FP (or JE(B, T, e)) includes three strain-dependent variables α(e), BC2(0, e) and TC(e) and four constants, n, p, q and v. The form is different to that proposed by Summers et al by a factor T2C(e). We suggest that the form is sufficiently general to describe superconductors whether the electron–phonon coupling is weak or strong and find that α(e) is proportional to where Δ(e) is the superconducting gap and γ(e) is the Sommerfeld constant. Comprehensive JE(B, T, e) data are presented for a modified jelly-roll (MJR) Nb3Sn conductor that are consistent with the form proposed with n ≈ 5/2, p = ½, q = 2 and v = 1.374. Hence the scaling law proposed leads to a critical current density for the MJR Nb3Sn given by Comparison with data in the literature suggests that α(e) ≈ 3 × 10−3μ0γ(e). Furthermore, the volume pinning force (FP(S/C)) within the Nb3Sn superconducting filaments alone can be described in terms of superconducting parameters in the form where κ(T, e) is the Ginzburg–Landau parameter.

The strain and temperature scaling law for the critical current density of a jelly-roll Nb3Al strand in high magnetic fields

The engineering critical current density (JE) and the index of transition, N (where E = αJN), of a Nb3Al multifilamentary strand, mass-produced as a part of the Fusion programme, have been characterized as a function of field (B), temperature (T) and strain (e) in the ranges B ≤ 15 T, 4.2 K ≤ T ≤ 16 K and −1.79% ≤ e ≤ +0.67%. Complementary resistivity measurements were taken to determine the upper critical field (BC2(T, e)) and the critical temperature (TC(e)) directly. The upper critical field defined at 5%ρN, 50%ρN or 95%ρN, is described by the empirical relation BC2ρN(T, e) = BC2ρN(0, e)[1 −(T/TCρN(e))ν]. The upper critical field at zero Kelvin and the critical temperature are linearly related where BC2ρN (0, e) ≈ 3.6TCρN (e) − 29.9, although strictly BC2ρN (0, e) is a double-valued function of TCρN (e). JE was confirmed to be reversible at least in the range −0.23% < e < 0.67%. The JE data have been parameterized using the volume pinning force (FP) where FP = JE × B = A(e)BC2n (T, e)bp (1 − b)q and b = B/BC2(T, e). A(e) is taken to be a function of strain otherwise the maximum value of FP (found by varying the field) was a double-valued function of BC2 when the temperature was fixed and the strain varied. To achieve a very high accuracy for the parameterization required by magnet engineers (~1 A), the data were divided into three temperature–strain ranges, BC2(T, e) described by the empirical relation and the constants p, q, n and ν and the strain-dependent variables A(e), BC2(0, e) and TC(e) treated as free-parameters and determined in each range. A single scaling law that describes most of the JE data has also been found by constraining BC2(T, e) using the resistivity data at 5%ρN where ν = 1.25, n = 2.18, p = 0.39 and q = 2.16. When BC2(T, e) is constrained at 50%ρN or 95%ρN, the scaling law breaks down such that p and q are strong functions of temperature and q is also a strong function of strain. Good scaling provides support for identifying BC25%ρN (T, e) as the characteristic (or average) upper critical field of the bulk material. The JE data are also consistent with a scaling law that incorporates fundamental constants alone, of the Kramer-like form where the Ginzburg–Landau (GL) parameter κ is given by the relation γ is the Sommerfeld constant and t = T/TC(e). At an applied field equal to the upper critical field found from fitting the Kramer dependence (i.e. at BC2(T, e)), the critical current is non-zero and we suggest that the current flow is percolative. The functional form of FP implies that in high fields the grain boundary pinning does not limit JE, this is consistent with JE-microstructure correlations in other superconducting materials.

The critical current density of grain boundary channels in polycrystalline HTS and LTS superconductors in magnetic fields

We provide evidence that a single mechanism—flux flow along channels—can explain the functional form of the critical current density (Jc) in the low-temperature superconductor Nb3Sn and in the high-temperature superconductors (HTS) YBa2Cu3O7−δ (YBCO) and (Bi,Pb)2Sr2Can−1CunOx (BiSCCO) in low and high magnetic fields. In this paper, we show that standard flux pinning theories, used for the past four decades to describe Jc in low-temperature superconductors (LTS), cannot explain the strain dependence of Jc in YBCO because Jc is a function of strain but the average superconducting properties are not. We conclude that in the polycrystalline samples presented here, the channels are grain boundaries that are narrow and metallic in Nb3Sn and YBCO but wide and semiconducting in BiSCCO. In Nb3Sn, strain alters Jc by changing the superconducting properties of the grains, whereas in YBCO, strain alters Jc by changing the properties of the grain boundaries.