Critical Current Distributions of Recent Bi-2212 Round Wires
Shaon Barua, Daniel S. Davis, Yavuz Oz, Jianyi Jiang, Eric E. Hellstrom, Ulf P. Trociewitz, David C. Larbalestier
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b THIS ARTICLE HAS BEEN ACCEPTED FOR PUBLICATION IN A FUTURE ISSUE OF IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 1
Critical Current Distributions of Recent Bi-2212Round Wires
Shaon Barua, Daniel Davis, Yavuz Oz, Jianyi Jiang,
Senior Member, IEEE,
Eric E. Hellstrom,
Senior Member, IEEE,
Ulf P. Trociewitz,
Senior Member, IEEE, and David C. Larbalestier,
Fellow, IEEE
Abstract —Bi Sr CaCu O + x (Bi-2212) is the only high-field,high-temperature superconductor (HTS) capable of reaching acritical current density J c (16 T, 4.2 K) of 6500 A · mm − in thehighly desirable round wire (RW) form. However, state-of-the-art Bi-2212 conductors still have a critical current density ( J c )to depairing current density ( J d ) ratio around 20 to 30 timeslower than that of state-of-the-art Nb − Ti or REBCO. Previously,we have shown that recent improvements in Bi-2212 RW J c are due to improved connectivity associated with optimizationof the heat treatment process, and most recently due to atransition to a finer and more uniform powder manufacturedby Engi-Mat. One quantitative measure of connectivity may bethe critical current ( I c ) distribution, since the local I c in a wirecan vary along the length due to variable vortex-microstructureinteractions and to factors such as filament shape variations,grain-to-grain connectivity variations and blocking secondaryphase distributions. Modeling the experimental V − I transitionmeasured on a low resistance shunt as a complex sum of voltagecontributions of individual filament and wire sub-sections allowsa numerical extraction of the I c distribution from the d V / dI treatment of the V − I curves. Here we compare ∼ I c distributions of Bi-2212 RWs with recent state-of-the-artvery high- J c Engi-Mat powder and lower J c and older Nexansgranulate powder. We do find that the I c spread for Bi-2212 wiresis about twice the relative standard of high- J c Nb − Ti well below H irr . We do not yet see any obvious contribution of the Bi-2212anisotropy to the I c distribution and are rather encouraged thatthese Bi-2212 round wires show relative I c distributions not toofar from high- J c Nb − Ti wires. Index Terms —Bi-2212, Critical current distribution, HTS.
I. I ntroduction R CENT advances in the critical current density ( J c ) ofpowder-in-tube Bi-2212 round wires have generatedgreat interest for their use in high field magnet technology[1]. An irreversibility field ( H irr ) of more than 100 T at Manuscript receipt and acceptance dates will be inserted here. The work issupported by the US DOE O ffi ce of High Energy Physics under grant numberDE-SC0010421 and by the NHMFL, which is supported by NSF under AwardNumber DMR-1644779, and by the State of Florida, and is amplified by theU.S. Magnet Development Program (MDP). (Corresponding author: ShaonBarua) S. Barua is with the Applied Superconductivity Center, National HighMagnetic Field Laboratory, Tallahassee, FL 32310, USA and also with FloridaState University (e-mail: [email protected]).D. S. Davis, Y. Oz, J. Jiang, E. E. Hellstrom, and U. P. Trociewitz arewith National High Magnetic Field Laboratory, Florida State University,Tallahassee, FL 32310, USA.E. E. Hellstrom, and D. C. Larbalestier are with the National High MagneticField Laboratory, Florida State University, Tallahassee, FL 32310, USA andalso with the Department of Mechanical Engineering, FAMU-FSU College ofEngineering.Digital Object Identifier 10.1109 / TASC.2021.3055479 − Ti and Nb Sn are limited by theirmuch lower irreversibility fields of ∼
11 T and ∼
25 T (at4.2 K) [2], [3]. Although its J c (16 T, 4.2 K) = · mm − far exceeds the Future Circular Collider (FCC) specificationof J c (16 T, 4.2 K) = · mm − , J c for state-of-the-artBi-2212 is still lower than 1% of the depairing current density[4] ( J d ∼ H c /λ ∼ × A · mm − , where the thermodynamiccritical field H c ∼ λ ) ofBi-2212 ∼
240 nm), as opposed to the 20 – 30% valuesachieved with Nb − Ti or REBCO. Our recent comprehensivesurvey of many Bi-2212 wires made between 2009 and 2019has shown that while J c defined by I c / A , where A is the totalBi-2212 cross-section, varied by almost a factor of 6 theyactually all had almost identical normalized J c ( H ), leading usto conclude that very similar vortex pinning properties wereshared by all wires and that | J c | was determined by the e ff ectivefilament connectivity [6]. Filament connectivity is a ff ectedby multiple factors on many length scales, including fila-ment cross-section variations before reaction and post-reactiondefects such as, cracks, voids, blocking secondary phases,and grain-to-grain connectivity variation. Moreover, cuprategrain boundary J c drops exponentially with increasing grain-boundary misorientation angle. Indeed, grain misorientationhas historically been the main impediment to the realizationof high J c in cuprate HTSs [1]. Although the quasi-biaxialtexture produced by the RW Bi-2212 heat treatment process isbelieved to mitigate this high angle grain boundary limitation[7], the c - axis rotation of the highly anisotropic Bi-2212grains results in an inherent J c variation along the lengthof each filament. Another commonly observed wire defectis variation of the filament cross section due to the highlynon-uniform grain growth characteristics of Bi-2212 from theliquid state. More recently we have seen that the grain textureand filament structure in Bi-2212 RWs are strongly dependenton powder type [4], heat treatment parameters [8], and wirediameter [9].The I c distribution is a potential quantitative measure ofthis complex connectivity variation. We are motivated bythe possibility that this distribution can identify avenues forimproving I c and perhaps for wire production quality control.Recently, a transition to finer powder made by Engi-Mat hasmore than doubled J c in state-of-the-art Bi-2212 wires [4]compared to earlier wires made with Nexans granulate powder. HIS ARTICLE HAS BEEN ACCEPTED FOR PUBLICATION IN A FUTURE ISSUE OF IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 2
TABLE IS ample S pecifications Sample Material Powder Sheath Manufacturer Diameter No. of Filling J c (5 T, 4.2 K)Material [mm] Filaments Factor [A · mm − ]pmm180410 Bi-2212 Engi-Mat Ag–0.2 wt.% Mg B-OST 1.0 85 ×
18 0.201 7115pmm100913 Bi-2212 Nexans Ag–0.2 wt.% Mg B-OST 0.8 37 ×
18 0.221 4085Nb – Ti Nb–47 wt.% Ti Cu Supercon Inc. 0.6 54 0.436 3280
To extract the I c distribution of our wires, we employed themethod previously employed to characterize the I c distributionfrom V − I characteristics of Nb − Ti and Nb Sn wires usinga normal shunt to make d V / dI analysis possible [10]–[13].We should note that the shunt resistance of the normal metalmatrices of Cu in Nb − Ti and Ag in Bi-2212 are rather similar,both having residual resistivity ratio (RRR) >
100 [14], [15].II. E xperimental
Two Bi-2212 RWs with the same nominal powder compo-sition of Bi . Sr . Ca . Cu . O x but very di ff erent powdersand time of fabrication were selected. The pmm100913 andpmm180410 wires were fabricated in 2010 and 2018 byBruker-Oxford Superconducting Technology (B-OST) usingNexans granulate (lot 77) and Engi-Mat (LXB 116) powder.Both powders were state-of-the-art at the time. Double restackmultifilamentary wires were made by the Powder-In-Tube(PIT) process using powder-filled pure Ag tubes and an outersheath of Ag–0.2 wt.% Mg alloy. The heat treatment of 1.5 mspiral wires was done at 50 bar over-pressure with an oxygenpartial pressure of 1 bar [4]. Wires were then soldered ontoa brass ITER-like barrel [16] and the V − I characteristics ofmultiple 10 cm sections of each sample were measured usingstandard four-probe transport measurement methods at 4.2 Kin magnetic fields up to 15 T. The peak applied currents werewell above the standard 1 µ V · cm − criterion limit far intothe flux flow regime, so as to obtain the full I c distribution.A standard Nb–47 wt.% Ti wire of high J c manufactured bySupercon Inc. was also measured. Detailed specifications ofthe samples are listed in Table I. A. Measurements of the Critical Current Distribution
Traditional four-probe transport measurements reveal onlythe lower end of the I c distribution. In a well-optimizedmaterial like Nb − Ti where current is believed to flow uni-formly, magnetization and transport measurements typicallyagree well when corrections for electric field ( E ) di ff erencesare made (and filament sausaging is avoided). Bi-2212 ismore complex: the current path is percolative and uncertainwith a fractional occupancy of as little as 1% [6]. Moreover,most transport measurements typically characterize only ∼ − Ti and Nb Sn it appears that a relatively high criterionof 1 µ V · cm − reliably predicts the quench performance ofeven potted magnets [17], making it interesting to explore the V − I transition at both lower and higher E values.An early method that was successfully used to character-ize the I c distribution of Nb − Ti and Nb Sn wires used a substantial normal metal shunt to avoid conductor burn out[11], [18]. The method models the I c distribution as a seriesarray of many short longitudinal sections of varying I c [13],[19]. As the applied current exceeds the local critical current( i c ) of a section, the section transitions from a pinned to aflux flow state. Since the flux flow resistivity is two to threeorders of magnitude higher than the silver matrix and the highconductance barrel [11], almost all the excess current is carriedby the normal matrix and shunt without excessive heatingand depinning of vortices in the superconductor. As originallyformulated by Baixeras and Fournet [10], the voltage across asub-element with critical current i c as a function of appliedcurrent I is given by a series distribution of variable i c elements: V ( I , i c ) = R ( I − i c ) (1)The normal method of degradation of I c in Nb − Ti is byonset of filament sausaging which fits the series i c arraymodel well but almost all other practical superconductorshave more complex series-parallel current paths. Plummerand Evetts [18] extended this analysis to filamentary Nb Snconductors, where the normal bronze matrix can have higherohmic dissipation than flux flow in the Nb Sn filaments(bronze Cu is always poisoned by the residual Sn content,typically 0.15 – 1 at.% meaning that its RRR is < Sn distribution,arriving at the same equation as Baixeras and Fournet. Intheir model, the I c distribution was assumed to be Gaussiandue to many variations of grain size, local Sn content andfilament uniformity, none of which were well controlled oreasy to measure. In this more general case of a wire withmany filaments, varying vortex pinning and varying activecross-section, the distribution of i c values is both parallel andseries and complex. Denoting the desired distribution φ ( i c ) asthe probability distribution density of i c in the wire suggestsuse of a Gaussian function since many independent factorsare locally determining the local i c values. Taking R e ff as thee ff ective resistance of the normal currents in the stabilizer andshunt, integrating over all possible i c values gives the followingexpression for the total voltage measured across the wire at agiven applied current I : V ( I ) = R e ff Z I ( I − i c ) φ ( i c ) di c (2) φ ( I ) = √ πσ exp − ( I − µ ) σ (3) d V ( I ) dI = R e ff φ ( I ) = R e ff √ πσ exp − ( I − µ ) σ (4) HIS ARTICLE HAS BEEN ACCEPTED FOR PUBLICATION IN A FUTURE ISSUE OF IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 3 Di ff erentiating V ( I ) twice with respect to I yields R e ff · φ ( I ),which allows extraction of the I c distribution and R e ff . Toreduce noise, a Savitzky-Golay filter was used to smooth thedata before calculating the second derivative [11], [20] byregression fitting a second order polynomial to a typical combsize ( m ) of 7 – 15 V − I points, the analytical derivative beingdetermined from the coe ffi cient at the center of a group of2 m + ff ect local critical current are thoughtto be randomly distributed and uncorrelated, the distributionof i c plausibly converges to a Gaussian as predicted by thecentral limit theorem [13], [18], [21], [22] enabling extractionof distribution parameters, such as the mean I c ( µ in (4)) andthe standard deviation ( σ ). B. The Fraction of Superconductor in Flux Flowf D ( I ) represents the fraction of superconductor wire in theflux flow state at a given current and this was calculatedfrom d V / dI at I c determined by both 0.1 µ V · cm − and1 µ V · cm − criteria according to: f D ( I ) = Z I φ ( i c ) di c (5) C. Critical Current Measurements of Short (4.5 cm) Samples
To compare regular measurements on short samples to thosedetermined on the shunted barrel samples, 10 cm long wiresof Bi-2212 were heat treated along with each spiral sample.Transport critical currents I c were measured using the four-probe method at 4.2 K in perpendicular magnetic fields up to15 T using both 0.1 µ V · cm − and 1 µ V · cm − criteria. Theresistive transition index ( n value) was calculated by fittingthe V − I curve from 0.6 – 20 µ V · cm − .III. R esults Fig. 1(a) shows the I c distribution of a 10 cm section of thehigher- J c Engi-Mat wire at 5 T and 14 T. The basic features aresimilar in all measured samples. Both 5 T and 14 T curves areslightly asymmetric due to an extended high current tail but itis also evident that the 14 T I c distribution is sharper than the5 T distribution. Two separate lines mark the short sample I c position based on 0.1 µ V · cm − and 1 µ V · cm − criteria. The I c of the higher- J c Engi-Mat short sample at 1 µ V · cm − is1078 A at 5 T and 782 A at 14 T compared to the distributionanalysis mean I c ∼ ± σ ∼ ± σ/µ ∼ ± J c Nexans wire shows mean I c ∼ ± σ ∼ ± σ/µ ∼ ± I c distribution of theSupercon Nb − Ti wire at various fields. At 5 T, it has I c ∼ ± σ ∼ ± σ/µ ∼ ± − Ti wire distribution width is significantly lower thanboth Bi-2212 samples at fields well below H irr but does crossthe Engi-Mat Bi-2212 wire close to H irr . Further details of thedistribution parameters are listed in Table II.
400 600 800 1000 1200 14000.00000.00050.00100.00150.0020 Engi-Mat d V / d I [ m V (cid:215) A - ] Current, I [A] I c ( . m V (cid:215) c m - ) = A I c ( . m V (cid:215) c m - ) = A
14 T 5 T I c ( . m V (cid:215) c m - ) = A I c ( . m V (cid:215) c m - ) = A Bi-2212(a) d V / d I [ m V (cid:215) A - ] Current, I [A]
Nb Ti . m V (cid:215) c m - . m V (cid:215) c m - . m V (cid:215) c m - . m V (cid:215) c m - . m V (cid:215) c m - . m V (cid:215) c m - . m V (cid:215) c m - . m V (cid:215) c m - (b) Fig. 1. Critical current distribution of (a) pmm180410 (Engi-Mat) wire at5 T (circle) and 14 T (diamond) at 4.2 K, (b) Nb − Ti wire at 5 T (circle),7 T (square), 8 T (star), and 9 T (diamond) at 4.2 K. Two separate lines aredrawn in the distribution plot for each field to delineate the short sample I c based on 0.1 µ V · cm − (black dotted line) and 1 µ V · cm − (red dotted line)criterion. Solid black lines represents the Gaussian distribution. Fig. 2(a) shows J c ( H ) for Engi-Mat, Nexans and Nb − Tiwires. The power law fit of J c ( H ) from 3 T to 15 T for bothBi-2212 wires is shown in the inset of Fig. 2(a).Fig. 2(b) shows σ/µ of the I c distribution for Engi-Mat,Nexans, and Nb − Ti wires with error bars of one standarddeviation calculated from multiple sections of the spiral oneach barrel. For Nb − Ti, σ/µ increases monotonically withfield from 0.034 ± ± − Ti, H / H irr is always significantly lower than unity. At 10 T, Nexans andEngi-Mat wires show σ/µ ∼ − Ti. The fractional energy dissipation( f D ) and the ratio of short sample critical current to meancritical current ( I c /µ ) are listed in Table II. The f D ( I c ) of theEngi-Mat wire, where I c using the 1 µ V · cm − electric fieldcriterion on the 4.5 cm long sample shows that 60 – 65%of the superconductor has transitioned from the flux pinning HIS ARTICLE HAS BEEN ACCEPTED FOR PUBLICATION IN A FUTURE ISSUE OF IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 4
Engi-Mat C r iti ca l C u rr e n t D e n s it y , J c [ k A (cid:215) mm - ] Applied Field, m H [T]NexansNb-Ti H ^ wire axis (a) J c / J c ( T , . K ) Applied Field, m H [T] y = 2.066 x - 0.259
Fitting: 3 T to 15 Ty = 2.190 x - 0.286
Fitting: 3 T to 15 T R e l a ti v e S t a nd a r d D e v i a ti on , s / m Applied Field, m H [T]Engi-MatNb-TiNexans(b)
Fig. 2. (a) Critical current density evaluated at 1 µ V · cm − , and (b)relative standard deviation of I c distribution as a function of applied fieldfor pmm180410 (square), pmm100913 (circle), and Nb − Ti (diamond) wiresat 4.2 K. The power law fit from 3 T to 15 T for both Bi-2212 wire is shownin the inset. Dashed lines are guides for the eye. to the flux flow state. In contrast, the more conservative0.1 µ V · cm − criterion corresponds to 22 – 27% in flux flow.In the lower- J c Nexans wire f D ranges from 43 – 50% at I c (1 µ V · cm − ), while the conservative ( I c µ V · cm − )criterion yields ∼
15 – 19%. For the Nb − Ti wire, f D increasedfrom 14% to 69% with an increasing magnetic field. The I c /µ ratio of Engi-Mat, Nexans, and Nb − Ti wires are ∼ ∼ iscussion In this work, we have compared the I c distribution oftwo Bi-2212 RWs made by B-OST prepared with newerand better and older and worse quality powders from Engi-Mat and Nexans. We were motivated to better understandthe conclusion of Brown et al. [6] that the magnitude of J c in Bi-2212 wires was almost completely determined by thee ff ective connectivity of the current path which we interpretedto be very small since the ratio J c / J d is of order 1% orless. Even if the vortex pinning in Bi-2212 is weak (it is also not yet clarified and may just be due to cation defectfluctuations within the Bi-2212 structure), such a low ratio of J c to J d implies that the long range current path may occupya small fraction of the total cross-section. In the absence ofdetailed measurements of J c at the filament level (we havedone this earlier for sections of Bi-2223 filament and foundvalues of J c several times the average [23]), we started thiswork to see if the distribution of J c values extracted from d V / dI measurements would o ff er a better understanding ofthe di ff erences between representative wires made with theformer champion Nexans and the more recent champion Engi-Mat powders with about a factor of 2 di ff erence in the filament J c defined by the measurement of I c divided by the fullydensified Bi-2212 cross-section.In analyzing the data we take the common view [12], [21],[22], [24] that the local I c along the wire is controlled bymultiple independent factors that justify a Gaussian approxi-mation consistent with the central limit theorem [18]. Gaussiandistributions have earlier been measured in Nb Sn [13], [18],[19] with σ/µ values of 0.15 at 15 T, about 0.6 H irr . Here weshow that a high- J c Nb − Ti has a significantly smaller σ/µ of ∼ ∼ H irr ), although it does rise significantlyabove 0.1 at 8 T close to H irr . Both Nb − Ti and Nb Sn areisotropic with respect both to vortex pinning and to H c2 [25],[26]. Given the meandering c - axis along the filament, weexpect that some grains will have very favorable orientationsfor H c2 and some quite unfavorable. Not yet being clear whatthe strong pinning centers are in Bi-2212, we cannot yet apriori say whether the high H c2 ab - plane orientation hasstronger pinning than the c - axis orientation but we mightexpect that the d V / dI would be broadened on the high I c side by this anisotropy.Indeed, we found that our two Bi-2212 wires showedGaussian behavior over about three quarters of their I c dis-tribution but also possessed a notable non-Gaussian extendedtail beyond about 150% of the mean I c . Such a tail was alsoseen in studies of Bi-2223 tapes [27]. Since both Bi-2223and Bi-2212 are strongly anisotropic cuprates and both havepercolative current paths, broader transitions and some non-Gaussian behavior is not unexpected, particularly at higher I c values that may correspond to grains with higher H c2 values. Qualitatively then the non-Gaussian high-side tail hasa plausible physical basis, even if we are very far from beingable to access the whole range of i c of grains with stronglyvarying orientations.It is worth pointing out that the Bi-2212 distributions yieldmean critical current values µ within a few percent of themeasured short ( ∼ I c (1 µ V · cm − ) results, with adissipation fraction f D rather independent of field, whereas forNb − Ti f D increases from 15% to 68% between 3 T and 10 Twith µ moving from above to below I c . This corresponds to adecrease in dissipation from ∼
200 mW · cm − at 3 T to only10 mW · cm − at 10 T at a 1 µ V · cm − criterion, in the contextof the low enthalpy margin of Nb − Ti, on the order of 1 –10 mJ · cm − . The higher dissipation occurring at lower fieldscauses LTS conductors to quench rapidly when even a fractionof the distribution is normal, as seen by the higher n valuesof their transitions. By contrast, for Bi-2212, the dissipation HIS ARTICLE HAS BEEN ACCEPTED FOR PUBLICATION IN A FUTURE ISSUE OF IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 5
TABLE IIP arameters D erived F rom T he C ritical C urrent D istribution Sample † Magnetic Mean, µ Standard Relative Std. R e ff+ Critical n value f D ( I c ) a f D ( I c ) b I c ++ µ Field Deviation, σ Deviation, σ/µ
Current, I c ++ [T] [A] [A] [ µ Ω · cm − ] [A] [%] [%]pmm180410 3 1210.6 96.6 0.080 0.023 1242.5 26.6 22.8 61.9 1.03(Engi-Mat) 5 1039.8 99.3 0.095 0.028 1078.8 26.7 30.5 64.2 1.047 947.6 91.2 0.096 0.027 982.6 25.6 28.7 64.1 1.049 881.3 84.4 0.096 0.027 916.5 26.2 29.6 63.7 1.0410 859.6 85.7 0.100 0.028 888.9 25.7 29.5 63.1 1.0311 834.0 85.7 0.103 0.028 863.3 25.2 29.1 62.6 1.0413 793.8 85.9 0.108 0.029 814.1 25.0 24.9 60.9 1.0314 774.2 84.3 0.109 0.029 799.7 22.2 30.6 62.1 1.03pmm100913 5 448.2 59.1 0.132 0.030 445.2 17.4 16.5 49.6 0.99(Nexans) 10 376.6 53.5 0.142 0.032 377.2 18.8 18.6 47.8 1.0015 336.2 50.1 0.149 0.032 328.0 15.2 13.3 43.8 0.98Nb – Ti 3 589.7 20.3 0.034 0.047 556.1 50.2 1.7 14.3 0.945 394.9 18.6 0.047 0.048 382.8 62.6 8.1 30.5 0.977 233.0 13.8 0.059 0.048 230.1 58.6 18.6 43.9 0.998 154.9 12.0 0.077 0.048 155.2 55.2 23.6 53.5 1.009 82.1 11.2 0.136 0.048 84.4 44.5 36.1 59.9 1.0310 25.1 3.1 0.125 0.049 26.9 15.8 21.3 68.5 1.07 † Distribution is measured for multiple sections of the spiral sample at each field. Here average results of the fitting parameters are listed. + Each voltage tap in pmm180410, pmm100913, and Nb − Ti samples is 10 cm, 20 cm, and 30 cm apart, respectively. ++ Critical current is calculated from a 4.5 cm short sample based on 1 µ V · cm − criterion at 4.2 K. a f D ( I c ) is calculated based on short sample I c at 0.1 µ V · cm − criterion. b f D ( I c ) is calculated based on short sample I c at 1 µ V · cm − criterion. changes are much less, ∼
160 – 100 mW · cm − from 3 –14 T for the Engi-Mat wire, and the enthalpy margin is twoorders of magnitude larger, leading to more uniform f D and n values. At higher fields the margin decays only gradually forBi-2212, which still has over 10 times more margin at 30 Tthan Nb − Ti has at 5 T.The relative standard deviation ( σ/µ ) is a significant pa-rameter which considers both the breadth and the mean of the I c distribution. Previous investigations of the I c distribution oftechnological conductors yielded σ/µ ∼ Sn,Nb − Ti, and Bi-2223 [11], [13]. However, Warnes et al. alsoreported an enhanced σ/µ ∼ − Ti wire at 4 T (reduced field, H / H irr ∼ ∼ σ/µ value with strong filament sausaging. Here we measured the I c distributions of Bi-2212 wires up to 15 T but since this isonly 10 – 15% of H irr , the complete H / H irr dependence of σ/µ in our wires is not known. Hence, we believe that it is moreappropriate to compare the low field σ/µ values of Nb − Tito our Bi-2212 wires. The relative broadening width near theirreversibility field seen in the Nb − Ti probably results fromlarge fluctuations in the e ff ective vortex pinning near H irr asthe elementary pinning forces generated by the dense α -Tivortex-pins become proximity coupled to the superconducting β -phase matrix [28].In line with our original conjecture, we did find a markeddi ff erence in σ/µ between the Engi-Mat (pmm180410) andNexans (pmm100913) wires. It is evident (see Fig. 2(b)) thatthe older and lower- J c Nexans wire has about 40% higher σ/µ ( ∼ et al. [6], manywires made with Nexans, Engi-Mat and other powder sets had the same normalized J c ( H ) characteristics, even though themagnitude of J c varied by almost 6. We conclude that thee ff ective percolative connectivity of wires is what is reallycontrolling the J c magnitude. The modern fine particle Engi-Mat powder has more uniform characteristics than the earliergeneration Nexans powder as demonstrated experimentally byJiang et al. [4]. We conclude that much of the ∼ J c improvement is due to improved filament connectivity of theEngi-Mat powder [4]. Thus, we conclude that the 30% lower σ/µ in our Engi-Mat sample compared to the lower- J c Nexanssample is due to improved connectivity associated with themuch finer and more uniform Engi-Mat powder.As noted above, the Nexans σ/µ values are very similarto that of a severely sausaged Nb − Ti wire [11]. Knowingthat Nexans powder has many hard particles of varying sizewhich distort the filament structure, it is plausible to comparethe degraded connectivity of Bi-2212 wire made with Nexanspowder to sausaged Nb − Ti wire [11]. However, we do notconclude that filament sausaging is the sole reason for thedegraded σ/µ of our Nexans sample. It is interesting that aBi-2223 wire ( µ ∼ σ ∼ σ/µ ∼ σ/µ [27]. Many other factors are alsostill in play, one being degraded grain-to-grain connectivitythat is certainly present in both Bi-2212 and Bi-2223.Although better connected than the Nexans powder wire, thehigher- J c Engi-Mat powder wire has a ∼ σ/µ ,and an almost 50% smaller n value compared to our high- J c Nb − Ti wire. Based on the experimental evidence it can beexpected that I c of Bi-2212 RWs could be increased furtherif the σ/µ can be minimized by identifying and addressingconnectivity limitations. To this end, we believe that the σ/µ HIS ARTICLE HAS BEEN ACCEPTED FOR PUBLICATION IN A FUTURE ISSUE OF IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 6 value can be used as a quantitative parameter for conductorquality control. V. C onclusion
In fact, the I c distribution, though wider for Bi-2212 than foroptimized Nb–47 wt.% Ti, is not a great deal larger, in spiteof Bi-2212 being strongly anisotropic along each filament,possessing current-blocking regions, and having highly non-uniform filament shapes. The much lower- J c Nexans wire hasthe same normalized vortex pinning (same normalized J c ( H )curve) and a broader σ/µ , suggestive of poorer connectivity.The relative standard deviation of Engi-Mat wire is ∼ ff ectivefilament connectivity can be quantified from the d V / dI measurement. We believe that measurements like these canbe a useful tool in further understanding of how best to raise J c in Bi-2212 conductors.A cknowledgment We acknowledge the help of G. Bradford, V. S. Gri ffi n, andE. Miller of the National High Magnetic Field Laboratory.R eferences [1] D. C. Larbalestier, J. Jiang, U. P. Trociewitz, F. Kametani, C. Scheuer-lein, M. Dalban-Canassy, M. Matras, P. Chen, N. C. Craig, P. J.Lee, and E. E. Hellstrom, “Isotropic round-wire multifilament cupratesuperconductor for generation of magnetic fields above 30 T,” NatureMaterials , vol. 13, no. 4, pp. 375–381, 2014.[2] H. Miao, Y. Huang, S. Hong, and J. A. Parrell, “Recent advancesin Bi-2212 round wire performance for high field applications,”
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