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Cryogenics 49 (2009) 429–432

Contents lists available at ScienceDirect

Cryogenics
journal homepage: www.elsevier.com/locate/cryogenics

Thermal conductivity of single and multi-stacked DI-BSCCO tapes
Tomoyuki Naito a,*, Hiroyuki Fujishiro a, Yuichi Yamada babFaculty of Engineering, Iwate University, Morioka 020-8551, Japan
Sumitomo Electric Industries, Ltd., 1-1-3 Shimaya, Konohana-ku, Osaka 554-0024, Japana r t i c l e

i n f oArticle history:
Received 20 October 2008
Received in revised form 23 May 2009
Accepted 16 June 2009

Keywords:
High Tc superconductors (A)Thermal conductivity (C)Transport properties (C)a b s t r a c t
We have measured the temperature dependence of the thermal conductivity, jðTÞ, for DI-BSCCOâ tapes
fabricated by Sumitomo Electric Industries, Ltd., which are ðBi; PbÞ2 Sr2 Ca2 Cu3 O8þx tapes sheathed with Ag
or Ag–Au alloy. The jðTÞ of the tape sheathed with Ag (residual resistance ratio (RRR) = 15) decreases
with decreasing temperature and starts to increase rapidly below 60 K, with a maximum at around
15 K. On the other hand, the jðTÞ of the tape sheathed with Ag–5.4 wt%Au alloy has a very low value that
decreases monotonically with decreasing temperature. At around 77 K, the absolute values of jðTÞ forboth tapes were about 260 W m1 K1 and 80 W m1 K1 , respectively. The jðTÞ of a stacked sample,
in which six DI-BSCCO tapes sheathed with Ag are soldered, was also measured. The measured jðTÞwas fairly well reproduced by the estimated jðTÞ, which was calculated using the measured jðTÞ ofthe single tape and solder.
Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction
A superconducting tape consisting of ðBi; PbÞ2 Sr2 Ca2 Cu3 O8þx
(Bi2223) superconductor and an Ag sheath, called Bi2223/Ag, hasbeen studied by many researchers and companies. Sumitomo Electric Industries, Ltd. has developed a new sintering technique with acontrolled overpressure (CT-OP) [1], which enables us to fabricate
the Bi2223/Ag tape without voids and with an extremely small
amount of non-superconducting phases. Recently, using this method, a Bi2223/Ag tape with a high critical current over 200 A at 77 K
and under the self-ﬁeld was successfully manufactured [2]. Moreover, it has a higher modulus of elasticity than conventional
Bi2223/Ag tape [3]. Therefore, it was named Dynamically Innovative BSCCO ðDI-BSCCOâ Þ.
The critical current over 200 A allows for the possibility of using
the tape practically in superconducting devices such as high-ﬁeld
coil magnets and power cables in liquid N2 . In this case, however,
we must correctly estimate the amount of heat leakage throughthe tape [4]. The heat leakage Q leak through the tape between the
low and high temperature sides, T low and T high , respectively, is generally given by

Q leak ¼

SL

Z T high
T lowjðTÞdT;

where jðTÞ is the temperature dependence of the thermal conductivity, L the length and S the cross section of the tape. The absolute* Corresponding author.
E-mail address: tnaito@iwate-u.ac.jp (T. Naito).
0011-2275/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cryogenics.2009.06.005

value and the temperature dependence of jðTÞ strongly depend on
the sheath material, the sheath/Bi2223 ratio and the fabrication
process [4–7]. As far as we know, the jðTÞ of DI-BSCCO has not beenreported.
In this paper, we report the temperature dependence of thethermal conductivity, jðTÞ, for two types of DI-BSCCO tapes. The
thermal conductivity was also measured for a stacked sample consisting of six tapes that were joined by a commercial solder, andthe jðTÞ obtained for the stacked sample was compared with thejðTÞ calculated using the measured thermal conductivities of boththe single tape and the solder.

2. Experimental
DI-BSCCO tapes were fabricated by the powder in tube (PIT)
method with the CT-OP sintering technique. The details of sample
preparation have been described elsewhere [1]. Two types of DIBSCCO tapes (types H and G) were studied. A stacked sample
was also prepared, consisting of six type H tapes that were joinedby the commercial solder (LFM-48). Hereafter, we refer to thissample as type H6. The sheath material of type H is Ag. We estimate the purity of Ag using a residual resistance ratio (RRR), because the thermal conductivity of the metal strongly depends on
the purity. Fig. 1 shows the temperature dependence of the reduced resistance R=R(11.5 K) for Ag of type H tape. The value of
RRR was estimated to be about Rð300KÞ=Rð11:5 KÞ ¼ 15. The inset
of Fig. 1 shows the RRR vs. impurity content for high purity copper,
which is reported in Ref. [8]. Assuming that a similar relation isrealized for silver, the purity of Ag used for type H tape is roughlyAuthor's personal copy

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T. Naito et al. / Cryogenics 49 (2009) 429–432

Fig. 1. Temperature dependence of the reduced electrical resistance,
RðTÞ=R(11.5 K), for Ag of type H tape. Inset shows the residual resistance ratio(RRR) vs. impurity content for Cu, which is derived from Ref. [8]. The arrow roughly
indicates the impurity content for RRR = 15.

Fig. 2. Photograph of the cross section of type H tape. Black and white regions
represent the Bi2223 ﬁlaments and Ag region, respectively.

estimated to be 99.9% by extrapolating the curve, which is indicated by the arrow in the ﬁgure. The sheath material of type G tapeis an Ag–5.4 wt%Au alloy. Fig. 2 is a picture of the cross section of
the type H tape. From this picture, the sheath/Bi2223 ratio of type
H tape was estimated to be about 1.8. The sheath/Bi2223 ratio of
the tape of type G was almost the same value. Table 1 summarises
the speciﬁcations of the DI-BSCCO tapes.
The thermal conductivity along the surface of the tape, i.e.,along the ab plane of the Bi2223 ﬁlament, was measured by a conventional steady-state heat ﬂow method [9]. The experimental setup is schematically illustrated in the inset of Fig. 3. One end of thetape was soldered to the copper stage, and a small metal chip resistor (1 kX) was adhered to the other end of the tape as a heaterusing GE7031 varnish. The j is estimated by the relation

j¼

Q L
 ;
DT S

where Q is the applied heat ﬂow, DT is the temperature difference, L
is the distance between the thermocouples, and S is the cross section of tape. DT was measured using two Chromel–Constantan thermocouples (76 lm in diameter) that were adhered to the sample
with GE7031 varnish. The upper thermocouple was set at a distanceof about 5 mm from the heater, and L was typically about 10 mm.
The length of each tape was about 25 mm. Q was generated by ﬂowing current to the chip resistor and was automatically controlled tomaintain a DT of 0.5–0.8 K. The electrical resistivity was measured

Table 1
Speciﬁcations of the DI-BSCCO tapes.

Sheath material
T c (K)
Cross section (mm2)
Width (mm)Thickness (mm)Sheath/Bi2223 ratio*

Type H

Type G

Type H6

Ag (RRR = 15)
110.8
0.935
4.25
0.22
1.8

Ag–5.4 wt%Au
111.0
0.994
4.14
0.24
1.8

Ag (RRR = 15)
111.0
5.88
4.42
1.33*
–

Including the thickness of solder layers.

Fig. 3. Temperature dependence of the thermal conductivity, jðTÞ, for the two
types of DI-BSCCO tape (type H, type G). The broken lines represent the electron
thermal conductivity, jel , for each sample. The experimental setup is schematicallyillustrated in the inset, where the coordinate axes represent the crystallographic
axes of Bi2223.

by a four-probe method with a typical current density of about 3 A/
cm2. The temperature of copper stage was controlled using a Gifford–McMahon cycle helium refrigerator from 5 to 300 K. To eliminate radiation loss, the thermal conductivity was measured below
250 K.
3. Results and discussion
3.1. Thermal conductivity for single tapes
Fig. 3 shows the temperature dependence of the thermal conductivity, jðTÞ, for types H and G DI-BSCCO tapes. The jðTÞ of type
H tape decreases slightly with decreasing temperature from 250 K
to 100 K. It increases moderately between 100 K and 60 K, starts toincrease rapidly below 60 K, and has a peak around 15 K. The peakvalue is approximately 800 W m1 K1 . On the other hand, the jðTÞof the type G tape decreases monotonically with decreasing temperature. The absolute value of j for the type G tape near 77 K isabout one third of that for type H tape. No anomaly appears at
the superconducting transition in either sample. The shape of thejðTÞ curve for type H tape is similar to that for a high-purity metallic conductor. The thermal conductivity for a part of the sheath,jsheath , can be estimated from the relation

jtape ¼ fsc j2223 þ ð1  fsc Þjsheath ;where jtape and j2223 are the thermal conductivities for the wholetape and the Bi2223 ﬁlaments, respectively, and fsc is the volume ratio of the Bi2223 parts to the whole tape, the value of which isroughly estimated to be 0.36 for type H tape using the sheath/
Bi2223 ratio (=1.8). Using this relation, the peak value of jsheathfor type H tape is approximately estimated to be 1200 W m1 K1 .
Here, we use the reported values of j2223 for polycrystalline
Bi2223 [9]. This value approximately corresponds to that for Ag–
0.09 at%Au alloy [10], indicating that the purity of Ag for type H tapeis better than 99.9%. This value is consistent with the purity estimated from the value of RRR in Section 2. Consequently, we canconclude that the sharp peak in jðTÞ for type H tape originates fromthe nature of the high-purity metal. On the other hand, the smallvalue of jðTÞ for type G tape is often observed in a solid solution.
The behaviours of jðTÞ observed here resemble those of other
Bi2223 tapes sheathed with silver-based alloys [4–7].
In a conducting solid, the thermal conductivity generally consists of contributions from both phonons and electrons, jph andjel . Using the electrical resistivity, jel is roughly estimated by theAuthor's personal copy

T. Naito et al. / Cryogenics 49 (2009) 429–432

431

Fig. 4. Temperature dependence of the electrical resistivity, qðTÞ, for the two typesof DI-BSCCO tape (type H, type G).

Wiedemann–Franz
(W–F)
law,
jel ¼ L0 T=q,
where
L0 ð¼ 2:45  108 WX K2 Þ is the Lorenz number. Fig. 4 shows thetemperature dependence of the electrical resistivity, qðTÞ, for types
H and G DI-BSCCO tapes. The critical temperature, T c , as determined by zero electrical resistivity, was about 111 K for both samples, demonstrating the high quality of the superconducting part of
Bi2223. Both qðTÞ curves show a good linear dependence on T
above T c . The absolute value of qðTÞ for type G tape is somewhat
larger than that of type H, because the sheath metal of the former
is a solid solution Ag–Au alloy (Ag–5.4 wt%Au alloy). Considering
the linear dependence on T of the qðTÞ and the W–F law, the jel
is expected to be independent of temperature. As a result, the values of jel for each sample are estimated to be about 240 (type H)
and 110 W m1 K1 (type G), which are shown as the broken lines
in Fig. 3. These values are comparable to the measured jðTÞ values,
indicating that the dominant heat carriers are electrons. In the normal state, the applied current mainly ﬂows through the metal
sheath, because the resistivities of the metal sheaths are considerably smaller than that of Bi2223; for instance, the reported value ofq at 150 K for Bi2223 polycrystal is about 500 l X cm [9] and thatfor pure silver is 0:5 l X cm [5]. On the other hand, the j values ofpolycrystalline Bi2223 below 150 K were reported to be smaller
than approximately 3 W m1 K1 [9]. The qðTÞ of polycrystalline
Bi2223 also shows the metallic linear dependence on T, and therefore jel was estimated to be about 0:8 W m1 K1 [9] in the normal
state, which is approximately 20% of the total j, meaning that thedominant heat carriers are phonons in Bi2223. Consequently, inboth the superconducting and normal states, the contribution of
the Bi2223 ﬁlaments to the heat transport is negligibly small,and most of the applied heat is carried by electrons through themetal sheath. We previously reported that the behaviour of thejðTÞ of the Bi2223/Ag–Au tape is quite similar to that of the Ag–
Au alloy [5], which is consistent with the present results.

Fig. 5. (a) Temperature dependence of the thermal conductivities, jðTÞ’s, for the DIBSCCO tape sheathed by Ag (H), the sixfold sample (H6), and the solder (LFM-48).
The calculated jðTÞ values for the sixfold sample (H6 cal) are also shown. The inset
shows a schematic image of the heat ﬂow in the stacked sample, where thecoordinate axes represent the crystallographic axes of Bi2223. (b) The estimatedjðTÞ for the sixfold type G sample (G6), the measured jðTÞ for the single tape (typeG) and the solder (LFM-48) are shown.

jðnÞ ¼

Q ðnÞ L;DT SðnÞ

where Q ðnÞ is total applied heat ﬂow and SðnÞ is the cross section of
the stacked sample. The schematic image of heat ﬂow through thestacked sample is demonstrated in the inset of Fig. 5a. The stacked
n-fold sample consists of n pieces of tape and ðn  1Þ layers of solder. Here, we denote the heat ﬂow and the thermal conductivity forthe single tape as Q ð1Þ and jð1Þ and those for the solder as Q sol andjsol , respectively. In this conﬁguration, the equivalent circuit is parallel to that of the heat transport. Thus, the Q ðnÞ is given as

Q ðnÞ ¼ nQ ð1Þ þ ðn  1ÞQ sol :Since the DT and L are the same for all parts, jðnÞ is written as

3.2. Thermal conductivity of a stacked samplejðnÞ ¼ ðjð1Þ  nSð1Þ þ jsol  Ssol Þ=SðnÞ ;Fig. 5a shows the temperature dependence of the thermal conð1Þ
ð6Þ
ductivities, jmes ðTÞ, jmes ðTÞ and jsol
mes ðTÞ, for the single tape (typeH), sixfold sample (type H6) and solder (LFM-48), respectively.
ð1Þjð6Þ
mes ðTÞ almost coincides with jmes ðTÞ. The absolute value ofð6Þ
sol
jmes ðTÞ is somewhat smaller than both jð1Þmes ðTÞ and jmes ðTÞ, but increases very slowly with decreasing temperature from 250 K toaround 40 K. Below 40 K, it increases somewhat rapidly withdecreasing temperature.
We attempted to estimate the jðTÞ value for n-fold sample
using those of the single tape and the solder. The total thermal conductivity, jðnÞ , is written with the relation

where Ssol is the sum of cross section for the solder part, i.e.,
Ssol ¼ SðnÞ  nSð1Þ . In this case, Ssol was estimated to be
0:27 mm2 (=S(6) - 6  S(1)), which is approximately 5% of the total
cross section of type H6 tape. We also calculated the thermal conð6Þ
ductivity of type H6 tape, which is denoted as jcal and depicted inð6Þð6Þ
Fig. 5a. jcal ðTÞ nearly corresponds to the measured jmes ðTÞ, meaningthat the thermal conductivity of the n-fold sample can be estimatedusing those of the single tape and the solder.
Using this relation, the jðTÞ’s of type G (single tape) and the solð6Þ
der give the jcal of a sixfold sample of type G tape, which does notexist at present. Here, the value of Sð6Þ for the stacked sample ofAuthor's personal copy

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T. Naito et al. / Cryogenics 49 (2009) 429–432

type G tape is calculated by assuming that the Ssol value is the sameð6Þ
ð1Þas that for type H6 tape. The estimated jcal ðTÞ and measured jmes
ð6Þfor type G tape are shown in Fig. 5b. jcal ðTÞ is almost equal to
ð1Þ
sol
jð1Þ
mes ðTÞ, but is larger than jmes ðTÞ below 20 K, because jmes ðTÞ isð1Þ
somewhat larger than jmes ðTÞ at T < 20 K. Weiss et al. [7] reported
that the jðTÞ of a stacked sample consisting of triple Bi2223/Ag–
5 wt%Au tapes and solder is larger than that of the single tape below 50 K, which shows that our estimation for type G tape is reasonable. Consequently, we conclude that the thermal
conductivity of the multi-stacked sample can be estimated using
those of the single tape and the solder.
4. Summary
The thermal conductivity, jðTÞ, as a function of temperature for
two types of DI-BSCCO tapes was measured. The jðTÞ for DI-BSCCO
sheathed with Ag of RRR = 15 (type H) decreases with decreasing
temperature, starts to increase below 60 K, and has a large peakaround 15 K, at which the peak value is about 800 W m1 K1 . On
the other hand, for DI-BSCCO sheathed with Ag–5.4 wt%Au alloy(type G), jðTÞ decreases monotonically with decreasing temperature. The magnitude of jðTÞ for the type G tape is somewhat smaller than that of the type H tape.
The jðTÞ for a stacked sample consisting of six pieces of DIBSCCO tape sheathed with Ag was measured, which can be compared to the calculated jðTÞ using the measured jðTÞ of the single
tape and the solder. The measured and calculated jðTÞ agree wellwith each other. The jðTÞ for the stacked sample was also esti-

mated for a DI-BSCCO tape sheathed with Ag–Au5.4 wt% alloy.
These results are applicable to other multi-stacked superconducting tapes for cryogenic engineering.
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