Physica C 382 (2002) 57–61
www.elsevier.com/locate/physc
Distribution of pinning strength and scaling behavior
in YBCO coated IBAD tape
T. Kiss a,*, M. Inoue a, S. Nishimura a, T. Kuga a, T. Matsushita b, Y. Iijima c,
K. Kakimoto c, T. Saitoh c, S. Awaji d, K. Watanabe d, Y. Shiohara e
a
Department of Electrical and Electronic Systems Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku,
Fukuoka 812-8581, Japan
b
Kyushu Institute of Technology, Iizuka 820-0672, Japan
c
Fujikura Ltd., Tokyo 135-8512, Japan
d
Tohoku University, Sendai 980-8577, Japan
e
Superconductivity Research Laboratory, Tokyo 135-0062, Japan
Abstract
Extended E–J characteristics in a YBCO coated ion beam assisted deposition tape have been studied over a wide
range of perpendicular magnetic field, B, and temperature, T. The statistical distribution of the critical current density,
Jc , and the magnetic transition field have been analyzed within the frame work of the percolation model. It has been
shown that the distribution of pinning strength in the coated tape is much sharper than that in an epitaxial thin film
deposited on a SrTiO3 single crystalline substrate. This result suggests that effective pinning sites are introduced in the
coated tape. Scaling behavior of the pinning force density will also be shown. The present analysis allows us to estimate
the Jc value quantitatively at an arbitrary B, T and electric field criterion.
Ó 2002 Elsevier Science B.V. All rights reserved.
PACS: 74.72.B; 85.25.K; 74.76; 74.60.J
Keywords: YBCO coated conductor; Critical current density; Flux pinning
1. Introduction
YBCO high Tc superconductor is one of the
most promising materials especially for high field
and high current applications. Significant numbers
of studies have been made on various deposition
techniques of YBCO film on flexible metallic
substrates [1–4]. It was shown that critical current
*
Corresponding author. Tel.: +81-92-642-3910; fax: +81-92642-3963.
E-mail address: kiss@sc.kyushu-u.ac.jp (T. Kiss).
density, Jc , more than 106 A/cm2 is attainable on a
metallic substrate by using a bi-axially aligned
substrate obtained by several methods such as ion
beam assisted deposition (IBAD) [1] and rolling
assisted bi-axially aligned textured tape [2]. Moreover, 10-m-class YBCO coated tape as well as
highly oriented long length substrates have been
demonstrated recently [5–7].
It is relevant to study the critical current properties of these YBCO tapes in order to clarify the
feasibility for practical applications, and to realize
practical YBCO conductors. The resistive transition in HTS is strongly influenced by thermal
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 1 1 9 7 - 8
58
T. Kiss et al. / Physica C 382 (2002) 57–61
fluctuations and the wide distribution of pinning
strength. It is necessary to optimize the fabrication
process by making clear the relationship among
critical current properties, crystallinity and fabrication conditions.
In this study, we carried out detailed measurement of extended electric field vs. current density
(E–J) characteristics in a YBCO coated IBAD tape
over a wide range of magnetic field, B, and temperature, T. The measured E–J characteristics
have been analyzed within the framework of the
percolation model. The statistical Jc distribution
and its B-, T-dependence has been discussed.
2. Measurement
A 1 lm thick layer of bi-axially aligned YSZ
was deposited by the IBAD technique on a 100 lm
thick hastelloy substrate. After a 0.1 lm thick
Y2 O3 layer was deposited by sputtering, 1 lm
thick YBCO film was deposited by the laser ablation technique. Finally, a 10 lm thick silver layer
was deposited on top of the YBCO as a protection
layer against thermal instability. The value of the
critical current, Ic , of the 1cm wide tape reached as
high as 85 A at 77 K in self magnetic field. The
critical temperature, Tc , of the tape was 88.7 K.
After etching the sample into a 100 lm wide by
1 mm long bridge shape, we measured the E–J
characteristics in detail over a wide range of B and
T by the four probe method. The magnetic field
was applied perpendicular to the tape surface. The
silver layer near the current terminal was etched
out in order to transfer the current into the superconducting layer in a short distance. The influence of current shunting due to the silver layer
has been determined based on the distributed resistance network model where the leakage resistance per unit length was assumed to be 5 105
X/mm.
3. Results and discussion
Magnetic field dependent E–J characteristics
are shown in Fig. 1. By fitting the percolation
model [8,9] to the measured E–J characteristics, we
Fig. 1. Magnetic field dependent E–J characteristics in YBCO
coated IBAD tape. The influence of the shunt resistance due to
the silver layer was determined by the distributed resistance
model assuming a leakage resistance per unit length, and is
5 105 X/mm. The solid lines are the percolation model while
the points are measured results. The magnetic fields, from right
to left, are 0.3, 0.5, 0.7, 1.0, 1.3, 1.5, 1.7, 2.0, 2.3, 2.5, 2.7, 3.0,
3.3, 3.5, 3.7, 4.0, 4.3, 4.5 T.
estimated the statistical Jc distribution, P ðJc Þ, in
the one dimensional network between the voltage
terminals:
m1
m m Jc Jcm
Jc Jcm
P ðJc Þ ¼
exp J0
J0
J0
for Jc P Jcm ;
¼0
for Jc < Jcm :
ð1Þ
The results are as shown in Fig. 2, where the numerical parameter m was constrained to be 4.4.
The magnetic field dependence of the Jc distribution can be characterized by the scaling of the
minimum value of Jc denoted by Jcm , and the
typical value of Jc denoted by Jk ( Jcm þ J0 ).
Scaling behavior of the corresponding pinning
force density, Fpm Jcm B, is shown in Fig. 3(a) and
(b). The magnetic field dependence of Fpm collapses
into a single curve as a function of reduced magnetic field B=BGL :
c
B
Fpm ¼ ABGL ðT Þf
BGL ðT Þ
d
B
1
for B 6 BGL ;
ð2aÞ
BGL ðT Þ
T. Kiss et al. / Physica C 382 (2002) 57–61
59
Fig. 2. Statistical Jc distribution obtained by the analysis of the
E–J characteristics by using the percolation model.
d
B f
Fpm ¼ ABGL ðT Þ 1 BGL ðT Þ for B > BGL ;
ð2bÞ
where BGL is the percolation transition field, i.e.,
Jcm ¼ 0, and A, f, c, d are numerical parameters.
The maximum value of Fpm , denoted by Fpm max ,
increases in proportion to the power of BGL as
shown in Fig. 3(b) as the temperature decreases.
Similar scaling also holds for Fpk Jk B:
c d
B
B
f
1
Fpk ¼ ABk ðT Þ
Bk ðT Þ
Bk ðT Þ
for B 6 Bk ;
ð3Þ
where Bk is the magnetic field for Jk ¼ 0. Temperature dependence of BGL and Bk are shown in
Fig. 4. The solid lines in Fig. 4 are the analytical
form
"
2 #a
T
BGLðkÞ ðT Þ ¼ BGLðkÞ ð0Þ 1 :
ð4Þ
Tc
The numerical parameters obtained from the
scaling analysis are listed in Table 1.
The difference between BGL and Bk indicates the
variation of pinning strength. It is worthwhile to
compare the results in the coated tape with that of
an epitaxial YBCO thin film deposited on a single
crystalline substrate. The broken lines in Fig. 4 are
the magnetic fields obtained for a 200 nm thick
YBCO film deposited on a SrTiO3 single crystal-
Fig. 3. Scaling behavior of the pinning force density corresponding to the minimum value of Jc denoted by Jcm . (a)
Magnetic field dependence and (b) temperature dependence.
The solid line is the analytical expression given by (2a).
line substrate by the laser ablation technique. As
can be seen, the value of BGL in the coated tape is
almost 50% larger than that of the thin film while
the value of Bk is comparable. This result indicates
that the distribution of the pinning strength in a
perpendicular magnetic field is much sharper in the
coated tape than that in the thin film. Possible
explanations for the enhancement of BGL are (1)
increase of film thickness results in the increase of
correlation volume of flux bundles, therefore, the
60
T. Kiss et al. / Physica C 382 (2002) 57–61
Fig. 4. Temperature dependence of the magnetic fields BGL and
Bk . Solid lines are for the coated tape, whereas the broken lines
are for a 200 nm thick YBCO thin film deposited on a SrTiO3
single crystalline substrate. Solid circles and solid triangles are
measured results for the coated tape and the film, respectively.
Fig. 5. Magnetic field dependence of Jc at various temperatures
with different electric field criteria 1 and 100 lV/cm. The lines
are the analytical expression along with the scaling parameters
while the points are measured results.
Jc ðEc Þ ¼ jJcm j þ
Table 1
Numerical parameters obtained from scaling analysis of YBCO
coated IBAD tape
Quantity
Related parameters
Fpm
A ¼ 2:01 108 , f ¼ 1:80, c ¼ 0:71, d ¼ 1:50,
for B 6 BGL
A ¼ 4:00 107 , f ¼ 1:32, d ¼ 0:75,
for B > BGL
Fpk
BGL ðT Þ and
Bk ðT Þ
A ¼ 4:76 108 , f ¼ 1:80, c ¼ 0:93, d ¼ 1:50
BGL ð0Þ ¼ 49:4, Bk ð0Þ ¼ 74:1, a ¼ 1:53
(for BGL and Bk )
for B > BGL ;
mþ1
Ec J0m þ jJcm jmþ1
qFF
1
mþ1
ð5bÞ
where qFF ¼ 10 lX cm, is shown in Fig. 5. The
electric field criterion, Ec , used to determine the
value of Jc was 1 lV/cm and 100 lV/cm for
the solid lines and the broken lines, respectively.
The analytical expression agreed quantitatively
with the measured results over a wide range of B
and T.
4. Conclusion
minimum pinning strength is enhanced, and (2)
effective pinning sites originated from some defects
in the coated tape make the pinning strength more
uniform. The results of the angular dependence of
BGL support the existence of effective pinning sites
perpendicular to the tape surface [10].
Along with the scaling behavior mentioned
above, we can describe the E–J characteristics at
an arbitrary B, T condition. A comparison between the measured Jc and the analytical expression [2]:
Jc ðEc Þ ¼ Jcm
1
mþ1
mþ1
m
þ
Ec J 0
qFF
for B 6 BGL ;
ð5aÞ
The statistical distribution of the pinning
strength and the scaling behavior of Jc have been
studied from the measured E–J characteristics in a
YBCO coated IBAD tape. It has been shown that
the pinning strength in perpendicular field is much
more uniform in the coated tape than that in an
epitaxial thin film deposited on a SrTiO3 single
crystalline substrate. This result suggests that effective pinning sites have been introduced in the
coated tape and/or increase of the film thickness
enhance the performance of flux pinning. Scaling
behavior of the pinning force density has also been
shown. Along with the scaling parameters, we can
describe the Jc value at an arbitrary conditions of
B, T and E in an analytical form.
T. Kiss et al. / Physica C 382 (2002) 57–61
Acknowledgements
This work was supported by the New Energy
and Industrial Technology Development Organization (NEDO) as Collaborative Research and
Development of Fundamental Technologies for
Superconductivity Applications.
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