Physica C 484 (2013) 159–162

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Physica C
journal homepage: www.elsevier.com/locate/physc

Anisotropic thermal transport in Bi2223/Ag superconducting tape withsandwiched structure
Tomoyuki Naito a,b,⇑, Hiroyuki Fujishiro a,b, Goro Osabe c, Jun Fujikami caDepartment of Materials Science and Engineering, Faculty of Engineering, Iwate University, Morioka 020-8551, Japan
Soft-Path Engineering Research Center (SPERC), Faculty of Engineering, Iwate University, Morioka 020-8551, Japanc
Sumitomo Electric Industries Ltd., Osaka 554-0024, Japanba r t i c l e

i n f oArticle history:
Accepted 19 March 2012
Available online 28 March 2012
Keywords:
Bi2223/Ag tape
Thermal conductivity
Anisotropy
Equivalent heat current circuita b s t r a c t
The thermal conductivity, j(T), of the Bi2223/Ag tape reinforced by metal tapes (stainless steel (SS) or
copper-based alloy (CA)) from both side was evaluated along the length (l) and width (w) directions.
j(T) along the l-direction was measured directly using a single tape and that along the w-direction
was estimated from the j(T) measured for a stacked bundle which consists of several sandwiched
Bi2223/Ag tapes. We analyzed the obtained j(T) curves using an equivalent heat current circuit, andfound that the heat transports along both directions were nearly the same and that the route of heat-ﬂow
depended on the species of the reinforcing metal. The absolute values of j(T) at 77 K along the l- and wdirections for the Bi2223/Ag-SS tape were 174 and 140 W m1 K1 and those for the Bi2223/Ag-CA tapewere 206 and 206 W m1 K1, respectively, the values of which were approximately 30–40% and 10–15%
smaller than those of the standard Bi2223/Ag tape.
Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction
Recently, the critical current, Ic, of a superconductive Bi2223
sheathed with silver (Bi2223/Ag) tape exceeded 200 A at 77 K under the self-ﬁeld [1]. Therefore, the Bi2223/Ag tapes are promisingmaterials to fabricate the coil, transformer and so on. Thermal conductivity, j(T), is one of the important physical properties for theestimation of the thermal stability for the superconducting applications. We have measured the j(T) of various Bi2223/Ag tapes[2–4]. Recently, we reported j(T) of the Bi2223/Ag tape along three
typical directions, the length (l), width (w) and thickness (t) [5].
The j(T) values along the l- and w-directions were almost identicalwith each other and the heat ﬂew mainly through the Ag sheath.
On the other hand, the magnitude of j(T) along the t-direction
was about one order of magnitude smaller than those along otherdirections, because of the small cross section of Ag path. In addition
to the thermal stability for the applications, it is necessary to enhance the mechanical strength of the Bi2223/Ag tapes. To achieve
higher mechanical strength, the Bi2223/Ag tape is usually sandwiched by thin metal tapes, such as stainless steel, brass, bronze
and so on. In this case, j(T) of the sandwiched Bi2223/Ag tapealong the l-direction depends on the species and thickness of thereinforcing metal tape [4]. However, the anisotropic j(T) of the⇑ Corresponding author at: Department of Materials Science and Engineering,
Faculty of Engineering, Iwate University, Morioka 020-8551, Japan. Tel./fax: +81 19
621 6362.
E-mail address: tnaito@iwate-u.ac.jp (T. Naito).
0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.physc.2012.03.043

Bi2223/Ag tape with sandwiched structure had not been
investigated.
In this paper, we measured the j(T) of the Bi2223/Ag tape withsandwiched structure along the l-direction and estimated j(T)along the w-direction from the j(T) measured for the stacked bundle which consists of several sandwiched Bi2223/Ag tapes. The
anisotropic heat ﬂow in the Bi2223/Ag tape with sandwiched
structure is discussed using an equivalent heat current circuit.

2. Experimental procedure
2.1. Sample preparation
Bi2223/Ag tapes were fabricated by the powder in tube (PIT)
method with the controlled overpressure (CT-OP) sintering technique at Sumitomo Electric Industries, Ltd. The details of the fabricating process was described elsewhere [6]. A standard Bi2223/Ag
tape (Type H) reinforced by sandwiching from both surfaces using
thin metal tapes and the solder (LFM-48) was named Type HT. In
this study, two Type HT tapes reinforced by stainless steel (SS)
20 lm in thickness or the copper-based alloy (CA) 50 lm in thickness were prepared and named Types HT-SS or HT-CA, respectively.
As shown in Fig. 1a, j(T) along the l-direction was measured
directly using the single Type HT tape, which was abbreviated as
the l-sample. j(T) along the w-direction was estimated from themeasured j(T) of the stacked bundle. The bundle, which wasnamed w-sample, was prepared by joining several Type HT tapes

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T. Naito et al. / Physica C 484 (2013) 159–162

Reinforcing
metal tape

l
w

Qapp

t
Bi2223/Ag tapeQapp(a) l -sample(b) w-sample

Fig. 1. Schematic illustration of (a) the single Bi2223/Ag tape with sandwiched structure for the measurement of the thermal conductivity, j(T), along the length direction (lsample) and (b) the stacked bundle for the estimation of j(T) of the tape along the width direction (w-sample).

using the solder (LFM-48), as described in Fig. 1b. As reported previously [5], the thermal contact resistance at the solder layer between the Bi2223/Ag tapes in the w-sample can be ignored.
Therefore, we regard the measured j(T) of the w-sample as j(T)along the w-direction.

2.2. Thermal conductivity measurement

κ (W m-1K-1)

Thermal conductivity, j(T), was measured by a steady-state heat
ﬂow method. One end of the sample was thermally attached to a

10

3

10

2

(a)

Ag-0.09at%Au alloy

LFM-48(solder)
Stainless Steel (SS)

10

1

κ

κ

HT-SS
10

l-samplew-sample

0

0

50

100

150

200

heat sink. A small metal chip resistor (1 kX) was adhered to theother end of the sample as a heater using GE7031 varnish. A constant current was applied to the heater, and then the constant temperature gradient, grad T, was measured. j is given as j = q/grad T,
where q is the heat ﬂux per unit cross section and grad T is given by
the temperature difference DT divided by the distance L between
the two thermocouples. The temperature of the sample was controlled using a Gifford–McMahon cycle refrigerator and 30 W heater. To eliminate radiation loss, j was measured below 200 K.
3. Results
Fig. 2a and b shows the temperature dependence of the thermal
conductivity, j(T), of the Types HT-SS and HT-CA samples, respectively. j(T) reported for Ag–0.09 at%Au alloy [7] and j(T)’s measured for the solder (LFM-48), the SS tape and the CA tape arealso shown. j(T) of the l-samples for both HT-SS and HT-CA slightly
decreases with decreasing temperature, starts to increase below
70 K, and takes a maximum of about 500–550 W m1 K1 around
14 K. Absolute value and temperature dependence of j(T) dependon the species of the reinforcing material. j(T) of the w-sample
for Type HT-SS somewhat rapidly decreases with decreasing temperature and deviates from j(T) of the l-sample. The peak in j(T)of the w-sample is suppressed to one third of that of the l-sample.
For Type HT-CA, j(T) of the w-sample almost corresponds to that of
the l-sample from 200 K down to 40 K. Its maximum appeared below 20 K is about half of that of the l-sample.

T(K)4. Discussion10(b)Ag-0.09at%Au alloy3

κ (W m-1K-1)

Copper Alloy (CA)102

To clarify the anisotropic heat transport in the Type HT tapes,
we examine the contribution of each constitutional part to the heattransport. An equivalent heat current circuit is considered in thefollowing procedure. When the applied heat, Q, ﬂows in the
Bi2223/Ag tape sandwiched by metal tapes, Q is given as

Q ¼ Q s þ Q m þ Q sol ;LFM-48(solder)

10

1

κ
HT-CA
10

where, Qs, Qm and Qsol are the heat ﬂow through the Bi2223/Ag, metal tape and solder layer, respectively. Since the DT and L are thesame for all the parts, the total thermal conductivity, jtot, can be
estimated byκl-samplew-sample

jtot ¼

0

0

50

100

150

200

T(K)
Fig. 2. Temperature dependence of the thermal conductivity, j(T), of the length (l)and width (w) samples for (a) Type HT-SS and (b) Type HT-CA. The thick lines
represent the calculated thermal conductivities jcal(T) (see text). The reported j(T)curve of Ag–0.09 at%Au alloy [7] and the measured j(T) curves of the solder (LFM48), the stainless steel (SS) tape 20 lm in thickness and the copper-based alloy (CA)tape 50 lm in thickness are also shown.

js  Ss þ jm  Sm þ jsol  Ssol
Stot;

where, js, jm and jsol are the thermal conductivities and Ss, Sm and
Ssol are the cross sections for each part. As schematically shown in
the left of Fig. 3a, the Bi2223 ﬁlaments distribute ﬁnely in the Ag
sheath, which complicates the route of the heat current. To simplify
the equivalent heat current circuit, we virtually collected the Bi2223
parts at the center of the cross section as shown in the right of Fig. 3a.
The dimensions of the Bi2223/Ag tape and Bi2223 region were deﬁned in the ﬁgure. The equivalent heat current circuits of Bi2223/

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T. Naito et al. / Physica C 484 (2013) 159–162
lw

w
Bi2223/Ag
tape

t

t

l
b

a
Reinforcing
metal tape

Solder
Bi2223

Solder

Ag

Ag

Bi2223(a)Reinforcing
metal tape

Rs
Rs
RAg

R2223

Rm

RAg

Rsol

RAg
R2223

Rm

Rsol

RAg

l-direction
w-direction

(b)

(c)

Fig. 3. (a) Schematic image of a model for the equivalent heat current circuit. The dimensions of the tape and the virtually collected Bi2223 region are illustrated. The
equivalent heat current circuit for (b) the l-direction and (c) the w-direction. Rs surrounded by the broken line, RAg, R2223, Rm and Rsol are the thermal resistances of the Bi2223/
Ag tape, the Ag region, the Bi2223 ﬁlaments, the reinforcing metal and the solder, respectively.

Table 1
Ratio of the amount of the heat-ﬂow among the Ag, reinforcing material and solder layer for the l- and w-directions of Types HT-SS and HT-CA tapes at 100 K.
Type HT-SS

l-direction
w-direction

Type HT-CA

Ag (%)

SS (%)

Solder layer (%)

Ag (%)

CA (%)

Solder layer (%)

95
92

1
1

4
7

59
62

38
31

3
7

Table 2Absolute value of the thermal conductivity at 77 K, jabs(77 K) along the l- and wdirections for Types H [5], HT-SS and HT-CA tapes.

jabs(77 K) (W m1 K1)l-direction
w-direction

Type H

Type HT-SS

Type HT-CA

240
220

174
140

206
206

Ag, Rs’s, along the l- and w-directions, respectively, are shown in Figs.
3b and c. Here, Rs surrounded by the broken line, RAg, R2223, Rm and
Rsol are the thermal resistances, R = (L/jS), of the Bi2223/Ag tape,
the Ag region, the Bi2223 ﬁlaments, the reinforcing metal and thesolder, respectively. Using the thermal conductivity of Ag andBi2223, jAg and j2223, j of the Bi2223/Ag tape along the l-direction,jsðlÞ , can be calculated by the following relation,jðlÞ
s ¼ jAg  1 


 
ab
ab
þ j2223 :
wt
wt

Since the absolute value of j2223 [8] is known to be about two orders of magnitude smaller than that of jAg, j2223 can be ignored.
The measured j(T) of both l-samples is well reproduced by the calculated j, jcal, using the equivalent heat current circuit shown in
Fig. 3b, except for around the peak structure at low-temperature,
as demonstrated in Fig. 2. The obtained (ab/wt) values, which correspond to the ﬁlling factor of the superconducting tape, fs, are 0.48
and 0.51 for the Types HT-SS and HT-CA samples, respectively.
The fs is deﬁned as the ratio of the volume of the Bi2223 ﬁlamentswith the Bi2223/Ag tape, V2223/Vs. The fs value of the Bi2223/Ag tapeused here was estimated to be approximately 0.36 from the pictureof the cross section [2]. The difference in fs between the ﬁtting results and the actual value indicates that the small amount of Ag,
about 12–15% of total Ag region, does not act as the heat path.
For Type HT-SS, the ratio of the amount of the heat-ﬂow among
the Ag, SS and solder parts at 100 K is estimated to be approximately 95:1:4, meaning that most of the applied heat ﬂows throughthe Ag region. On the other hand, the ratio for Type HT-CA is59:38:3. Therefore, we cannot ignore the contribution of the CA region to the thermal transport, which originates from the high thermal conductive CA. For the w-direction, the thermal conductivity ofðwÞ
the Bi2223/Ag, js , can be written asjðwÞ¼ jAg ðTÞ  1 
s


b
;
t

because of jAg  j2223. The similar analysis was done for j(T) of thew-samples for both Types HT-SS and HT-CA. The obtained b/t value
for Type HT-SS is 0.54 and that for Type HT-CA is 0.51, the values ofwhich are quite similar to the ab/wt values determined independently by the analysis for the l-direction. The b/t value represents
the cross sectional ratio of Bi2223 region to the Bi2223/Ag tape,S2223/Ss, and then corresponds to the ﬁlling factor. The good agreement between the ab/wt and b/t values suggests that the nature ofheat transport of the w-direction is nearly the same as that of the ldirection. For the w-samples, the ratio of the amount of the heatﬂow among the Ag, reinforcing material and solder parts at 100 K
are estimated approximately 92:1:7 for the Type HT-SS and
62:31:7 for the Type HT-CA. These ratios are comparable with thosefor the l-direction, which also supports the conclusion above. The
percentage of the contribution of each constitutional part to theheat transport is summarized in Table 1.

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The absolute values of j(T) at 77 K, jabs (77 K), along the l- andw-directions for Type HT-SS are 174 and 140 W m1 K1 and thosefor Type HT-CA are 206 and 206 W m1 K1, respectively. jabs
(77 K) along the l- and w-directions for the standard Type H wereabout 240 and 220 W m1 K1, respectively [5]. The j(T) values of
the Type HT series are smaller than that of the Type H tape, whichis caused by the low thermal conductive reinforcing metal in comparison with the silver sheath. The obtained results are summarized in Table 2.

SS, about 90–95% of the applied heat ﬂew through the silver sheathand the contribution of the stainless steel to the thermal transport
was negligibly small. On the other hand, the amount of the heatﬂow in the copper-based alloy was estimated to be approximately
30–40% of the total applied heat in the Bi2223/Ag-CA. The absolutevalue of j(T) for the Bi2223/Ag-SS and Bi2223/Ag-CA tapes wereapproximately 30–40% and 10–15% smaller than that of the standard Bi2223/Ag tape.
References

5. Summary
We have determined the temperature dependence of thermal
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Bi2223/Ag tape. To obtain j(T) along the w-direction, we prepareda stacked bundle in which several sandwiched Bi2223/Ag tapes
were soldered. j(T) along both l- and w-directions are nearly identical with each other, however the pronounced peak structure observed in the l-direction was strongly suppressed in the wdirection. The calculated j(T) using the equivalent heat current circuit reproduced the measured j(T) successfully. In the Bi2223/Ag-[1] S. Yamade, N. Ayai, J. Fujikami, S. Kobayashi, E. Ueno, K. Yamazaki, M. Kikuchi, T.
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