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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 12, NO. 1, MARCH 2002 1117
Pinning Strength and Irreversibility Fieldsof Nb–Ti Multifilamentary Composites
with Different Artificial PinsYun Zhu, Osuke Miura, and Daisuke Ito
Abstract—Irreversibility fields and upper critical fields2 for Nb–Ti multifilamentary composites having artificial pin-
ning centers (APC) were investigated to clarify the relationshipbetween their degradation and high-field flux pinning. APC wirespecimens having Nb as strong pins and Ta as weak pins, with thedifferent filament diameter from 1.07 to 0.27 m, were preparedfor measurements. Comparatively large difference betweenand 2 was observed for all of the APC specimens, even for thespecimens with the high flux pinning strength. The temperaturedependence of was explained well by the flux creep theory inwhich the size of superconductors was taken into account. Further-more, magnetic relaxation for the specimens was measured to es-timate the apparent pinning potential 0 . The difference of 0
among the specimens was also explained qualitatively by the fluxcreep theory. These results suggest that the large filament diameterin the bulk limit is quite important to improve the high-field fluxpinning when using APC method more effectively.
Index Terms—Artificial pinning centers, flux creep, flux pinning,irreversibility fields.
I. INTRODUCTION
A RTIFICIAL pinning method is a very important tech-nology not only for increasing critical current density
but also studying flux pinning mechanism for both metallic andoxide superconductors, because it has the excellent ability tochange pin material, volume fraction and pin-shape relativelyfreely. We have been studying the flux pinning propertiesfor several kinds of APC multifilamentary composites, andsuccessfully achieved high for Nb APC composites atmagnetic fields up to 5 T [1], [2]. However, the upper criticalfields and the irreversibility fields degraded withreducing the size of filaments in spite of increase in. Thisdegradation seems to be caused by the mixture of proximityeffect, flux creep and material mixing effect between pins andNb–Ti filaments [3], [4]. Recently, it is pointed out that ther-mally activated flux creep is a dominant cause of degradationof in high superconductors [5]. According to theflux creep theory, it is known that strongly depends onboth the flux pinning strength and the size of superconductors.Previous workers reported a similar restriction of evenfor multifilamentary composites of metallic superconductors
Manuscript received September 25, 2001.Y. Zhu is with the Graduate School of Engineering, Tokyo Metropolitan
University, 1-1 Minamiosawa, Hachioji, Tokyo, 192-0397 Japan (e-mail:[email protected]).
Publisher Item Identifier S 1051-8223(02)04136-2.
TABLE ISPECIFICATION OFSPECIMENS
operated at low temperatures [6], [7]. In order to improveproperties in high fields using APC method, further detailedstudies to clarify the relationship between high-field fluxpinning and the degradation are desired.
In this study, Nb–Ti multifilamentary composites with dif-ferent APC materials and the size of filaments are prepared, andtheir flux pinning properties, temperature dependence ofand , magnetic relaxation are investigated. Moreover, a nu-merical simulation based on the flux creep theory is conductedto compare with the experimental results.
II. EXPERIMENTAL
Nb-50wt.%Ti multifilamentary wires having APC werefabricated by a conventional double stacking method. Sevenround pins with a triangular arrangement were introduced intoeach Nb–Ti filament. Nb as a strong pin and Ta as a weakpin were chosen and the volume fraction of pins inside thefilament was fixed at 17%. To avoid interfilamentary-proximitycoupling, Cu–Ni alloy was used as the matrix material. Thewire specimens with the different filament diameter from 1.07to 0.27 m were prepared. The specification of the specimensis shown in Table I.
Magnetization measurements were carried out using aSQUID magnetometer. – properties were evaluated fromthe magnetization curves using the critical state model atvarious temperatures from 2.5 to 7.5 K and fields up to 7 T.
was defined as the temperature at which the magnetizationat 1 mT changed from a diamagnetic to a paramagnetic state.Temperature dependences of and were estimatedfrom measuring the temperature dependence of magneticmoments under zero-field-cooled and field-cooled conditionsat various magnetic fields. Furthermore, magnetic relaxationdue to the flux creep was measured to estimate the apparentpinning potential using Anderson–Kim model.
1051-8223/02$17.00 © 2002 IEEE
1118 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 12, NO. 1, MARCH 2002
Fig. 1. Magnetic field dependence ofJ andJ of Nb-0.518 from 2.5 Kto 7.5 K. Solid line indicatesJ values while symbols show the experimentalvalues.
TABLE IIPARAMETERS OFJ FOR VARIOUS SPECIMENS
III. RESULTS
A. – Properties
The temperature and magnetic field dependence of the virtualcritical current density in the creep-free case is expressedas
(1)
where, is the upper critical field at 0 K, is a constantand and are pinning parameters.
Fig. 1 shows typical – properties for the Nb-0.518 spec-imen. The pinning parameters are determined to fit with the
values at low temperatures below 3 K. As shown in Fig. 1,the difference between and increases gradually with in-creasing temperatures. Similar tendency is also obtained for allspecimens. The difference betweenand at high temper-atures seems to be caused by the flux creep.
The obtained pinning parameters for all specimens are listedin Table II. The parameter which indicates the mag-nitude of the flux pinning force of the specimen is enhanced bythe pin size decreasing for each APC series. However, it shouldbe noted that of Ta APC specimens is much smallerthan that of Nb APC having the same filament diameter. Thismainly comes from the difference between the magnitudes ofthe elementary pinning force [8].
Parameter decreases gradually with increasing.Therefore, the high-field pinning properties improve somewhat.
Fig. 2. An example of temperature dependence of magnetic moments forNb-0.518 at 0.35 T, measured using ZFC-FC method.
Fig. 3. Temperature dependence ofB andB for Nb APC specimenswith different filament diameter from 0.27to 1.07�m. Dashed line indicatesB (T ) = B (0)(1� T=T ) for Nb-1.07 specimen.
and slightly decrease with reducing the size of pinsfor Nb APC. On the other hand, these values for Ta APC area little smaller than those for Nb APC. This degradation maycome from the proximity effect at the interface between Nb–Tiand pins.
B. Temperature Dependence of and
An example of the temperature dependence of the magneticmoments under zero-field and field-cooled conditions at 0.35 Tfor Nb-0.518 specimen is shown in Fig. 2. was defined asthe temperature at which the slope changed in the paramagneticregion and the irreversibility temperature was determinedas the temperature at which the hysteresis width vanished. Then
and were converted into and , respectively.Temperature dependence of and for Nb APC spec-
imens is shown in Fig. 3. The temperature dependence offor all of the Nb APC specimens is proportional to
near and slightly decreases with reducing the size offilaments. Similar results are obtained for Ta APC specimens.On the other hand, it is observed that the comparatively largedifference between and exists for all of the APC spec-imens. In particular, of Nb-0.270 specimen is about 1 Tsmaller than in spite of having the largest flux pinningstrength.
ZHU et al.: Nb–Ti MULTIFILAMENTARY COMPOSITES WITH DIFFERENT ARTIFICIAL PINS 1119
Fig. 4. Temperature dependence ofB andB for Nb-0.518 and Ta-0.518specimens with the same filament diameter of 0.518�m.
Fig. 5. Magnetic relaxation at 1 T for Nb-0.518 at 3.5 K, 4.5 K and 6.0 K forTa-0.518 at 3.5 K.
Fig. 4 shows the temperature dependence of andfor Nb and Ta APC specimens with the same filament diameterof 0.518 m. It is observed that the difference between and
for the Ta specimen is larger than that for the Nb specimen.The temperature dependence and the difference ofamongthe specimens will be discussed later, compared to the flux creeptheory.
C. Magnetic Relaxation Due to Flux Creep
The time dependence of magnetization due to the flux pinningobeys the well-known logarithmic relaxation with time causedby the thermally activated flux creep
(2)
where and are magnetization at timeand the initialtime , respectively. means the apparent pinning potentialand is the Boltzmann constant. The experimental results forNb-0.518 specimen at various temperatures and 1 T are shownin Fig. 5. The slope of magnetic relaxation becomes graduallysteeper with increasing temperature. Fig. 5 also indicates thedecay result for different specimen of Ta-0.518 at 3.5 K and1 T. The degree of the decay for Ta-0.518 is larger than that
Fig. 6. Temperature dependence of calculatedB and experimentalBfor Nb specimens with different filament diameters from 0.270 to 1.07�m.
for Nb-0.518. This is consistent with the difference of the fluxpinning strength between the specimens.
IV. DISCUSSION
According to the flux creep theory in which the size of su-perconductor is taken in account, the pinning potentialis ex-pressed in terms of and the size of superconductor [5]. Inour case, since the longitudinal correlation length of the fluxoid
is larger than filament diameter, is expressed as
(3)
where is the number of fluxoids in the flux bundle. is aconstant depending on the kind of pinning center. In this workit has been fixed to 4 because of the relatively strong pinningcenters introduced. On the other hand, while the superconductorsize is quite large as a bulk superconductor,is expressed as
(4)
When a sinusoidal washboard potential is assumed, theisestimated from (3) and (4) as follows
(5)
(6)
In the above equations, is the fluxoid spacing and is thedamping oscillation frequency of the flux bundle in the pinningpotential. is a criterion accompanied with an electric field
. In this work, we roughly estimated A/m fromthe width of magnetization and V/m from –properties.
The calculated values compared with experimental re-sults for Nb APC specimens are shown in Fig. 6. The calcu-lated irreversibility lines show good agreement with the ob-
1120 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 12, NO. 1, MARCH 2002
Fig. 7. Temperature dependence of calculatedB and experimentalBfor Nb-0.518 and Ta-0.518.
Fig. 8. Temperature dependence of experimentalU � and calculatedU � forNb-0.518 and Ta-0.518.
served values. The irreversibility line of Nb-0.270 specimen isinferior to the other specimens with large filament diameter inspite of having the highest . and calculated from(6) in the bulk limit for Nb-0.270 specimen are also shown inFig. 6. In low temperatures, the of Nb-0.270 in the bulklimit is about 1 T larger than the experimental , which al-most equals to the calculated from (5). This means that thelarge filament diameter in the bulk limit is quite important toimprove . Fig. 7 indicates the temperature dependence be-tween the observed and the calculated for Nb-0.518 andTa-0.518 specimens. The irreversibility lines are also in agree-ment with the experimental results. This is consistent with thedifference of the flux pinning strength between the specimens.These results suggest that to improve high-field flux pinning,the large filament diameter in the bulk limit is very important aswell as other key factors, such as pin size, volume fraction andpin material.
The apparent pinning potential was estimated from the loga-rithmic decay slope at times from 10to 10 s for Nb-0.518 andTa-0.518 specimens.
According to the Welch’s theory [9] for the case of sinusoidalwashboard potential, the relationship between and isexpressed by
(7)
Temperature dependence of experimental and calculatedfor Nb-0.518 and Ta-0.518 specimens is shown in Fig. 8.
The observed values can be qualitatively reflected bybased on the flux creep theory.
V. CONCLUSION
Irreversibility fields and upper critical fields wereinvestigated for Nb–Ti multifilamentary composites having dif-ferent APC materials and the size of filaments. The temperaturedependence of was nearly proportional to andslightly decreased with reducing the size of filaments due to theproximity effect. Relatively large difference between and
was observed for all of the APC specimens, even for thespecimens with high flux pinning. The temperature dependenceof was explained well by the flux creep theory in which thesize of superconductors was taken into account. The differenceof apparent pinning potential estimated from magnetic re-laxations between specimens was also explained qualitativelyby the flux creep theory. These results suggest that to improvehigh-field flux pinning, the large filament diameter in the bulklimit is crucial as well as other key factors, such as pin size.
REFERENCES
[1] O. Miura, C. Tei, D. Ito, and S. Endo, “Flux pinning scaling behaviorsof ultrafine multifilamentary NbTi superconducting wires with Nb is-land-type artificial pins,”IEEE Trans. Appl. Superconduct., vol. 7, pp.1146–1149, June 1997.
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[6] M. Suenaga, A. Ghosh, Y. Xu, and D. Welch, “Irreversibility tempera-tures of Nb Sn and Nb–Ti,”Phys. Rev. Lett., vol. 66, pp. 1777–1780,Apr. 1991.
[7] H. Matsuoka, S. Otabe, T. Matsushita, and T. Hamada, “Irreversibilityfield in multifilamentary Nb–Ti wires with fine filaments,” inAdvancesin Superconductivity IX (Proc. ISS 96), 1996, pp. 641–644.
[8] Y. Zhu, O. Miura, T. Okubo, D. Ito, and S. Endo, “Flux pinning strengthof different superconducting artificial pins in Nb–Ti multifilamentarycomposites,”IEEE Trans. Appl. Superconduct., vol. 10, pp. 1046–1049,Mar. 2000.
[9] D. O. Welch, “A theoretical comparison of the effects of the shape ofthe pinning potential and a distribution of pinning energies on the ap-parent pinning energy as measured by magnetic flux creep,”IEEE Trans.Magn., vol. 27, pp. 1133–1138, Mar. 1991.