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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011

Anisotropic Thermal Conductivity of Silver Sheathed
Bi2223 Superconducting Tape
Tomoyuki Naito, Hiroyuki Fujishiro, and Jun Fujikami

Abstract—Anisotropic thermal conductivity,, of a silver
sheathed Bi2223 (Bi2223/Ag) tape was determined for three typ, width, and thickness.
ical directions; the lengthof the tape along the -direction was measured directly and thosealong the - and -directions were estimated by measuring stackedofsamples in which several Bi2223/Ag tapes were soldered.
the tape along the - and -directions was 250
at77 K and almost coincided with each other. On the other hand,of the tape along the -direction was about one order of magnitude smaller than those along other directions. The measured
curves were analysed using an equivalent heat current circuit. Results show that the applied heat flows through the Ag parts
for three directions. The amount of the Ag parts being in the routeof the heat current depends on the direction.
Index Terms—Anisotropy, equivalent heat current circuit, silver
sheathed Bi2223 tape, thermal conductivity.

AI. INTRODUCTIONSILVER sheathed Bi2223 (Bi2223/Ag) superconducting
tape has been developed to achieve a long length cablewith higher critical current density . Recently, a Bi2223/Ag
tape with high critical current, , over 200 A at 77 K in theself-field was reported [1], [2], which gives us an opportunity
to use the tape practically in power applications such as cables
and high-field coil magnets. In the applications, it is importantto estimate the thermal stability. We can calculate the amountof the heat intrusion and the heat exhaust through the tape, ,using the thermal conductivity,, by the following relation,Here, and are the cross section and the length of the tapeand and are the temperatures at both sides of the tape. In awinding coil, the heat might flow both along the length directionof the tape and along the radial direction of the coil, which is perpendicular to the thickness direction of the tape. We measured, of a double-pancake
the anisotropic thermal resistance,
value
coil using Bi2223/Ag tape and pointed out that theManuscript received August 02, 2010; accepted October 25, 2010. Date ofpublication November 22, 2010; date of current version May 27, 2011.
T. Naito and H. Fujishiro are with the Faculty of Engineering, Iwate
University, Morioka 020-8551, Japan (e-mail: tnaito@iwate-u.ac.jp; fujishiro@iwate-u.ac.jp).
J. Fujikami is with Sumitomo Electric Industries Ltd., Osaka 554-0024, Japan(e-mail: fujikami-jun@sei.co.jp).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2010.2090326

Fig. 1. Photograph of the cross section of the Bi2223/Ag tape. (White region)
Ag parts and (black region) Bi2223 filaments.

of the tape along the thickness direction is important to analyseprecisely the thermal transport along the radial direction [3].
of the Bi2223/Ag tapes have been usually meaHowever,sured only along the length direction [4]–[6], because the thickby a steady-stateness of the tape is too thin to measureheat flow method.
In this paper, we measured and estimated the thermal conductivity of the Bi2223/Ag tape along three directions, thealong the length direction
length, width and thickness.
was measured using a single tape, and those along the width
and thickness directions were estimated using stacked bundles
which consisted of several Bi2223/Ag tapes. We discuss theanisotropic heat flow in the Bi2223/Ag tape using an equivalentheat current circuit.
II. EXPERIMENTAL DETAILS
A. Sample Preparation
Bi2223/Ag tapes were ‘Type H’ tapes of DI-BSCCO family
produced at Sumitomo Electric Industries, Ltd. by the powderin tube (PIT) method with the controlled overpressure (CT-OP)
sintering technique [7]. The details of the fabrication process
have been described elsewhere [7]. Fig. 1 shows a photographof the cross section of the Bi2223/Ag tape. The white region
represents the Ag sheath and the black one, the Bi2223 filaments. The “Ag-ratio” defined by
was estimated to
be about 1.8 from the photograph, whereandwere
the volume of the Ag sheath and Bi2223 filaments, respectively.
of the Bi2223/Ag tape was determined along three typical directions, the length , width
and thickness , inthe following. As described in Fig. 2(a),along the -direction was measured directly using a single Bi2223/Ag tape,which was abbreviated as the -sample. To estimateof thetape along the - and -directions, two stacked bundles wereprepared by joining several Bi2223/Ag tapes using a commercial solder (LFM-48), as described in Fig. 2(b) and (c), whichwere named - and -sample, respectively. The dimensions ofthe samples are summarized in Table I.
B. Method of Thermal Conductivity Measurement, of each sample was measured
Thermal conductivity,
by a steady-state heat flow method. One end of the sample wassoldered to a copper-block as a heat sink. A small metal chip

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NAITO et al.: ANISOTROPIC THERMAL CONDUCTIVITY OF SILVER SHEATHED BI2223 SUPERCONDUCTING TAPE

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TABLE ISPECIFICATIONS OF THE SAMPLES

Fig. 3. Temperature dependence of the thermal conductivity
for thelength , width , and thickness samples. The thick lines represent the(see text). The reported
curvescalculated thermal conductivityof Ag-0.09at%Au alloy [8] and Bi2223 polycrystal [9] are also plotted.
Fig. 2. Schematic illustration of (a) the single Bi2223/Ag tape for the measurealong the length direction ( -sample) andment of the thermal conductivityof the tape (b) along the width
the stacked bundles for the estimation of( -sample) and (c) along the thickness direction ( -sample).

resistor (5was adhered to the other end of the sample as aheater using GE7031 varnish. is given as

where
is the applied heat flow,
the temperature difference and the distance between the two thermocouples, andis the cross section of the sample.
was measured using
two chromel-constantan thermocouples (76in diameter)
and was maintained at about 0.5–0.7 K by controlling the electric current applied to the chip resistor. The temperature of thesample stage was controlled using a Gifford-McMahon cycle
helium refrigerator and 30 W heater. To eliminate the radiation
loss, was measured below 200 K.
III. RESULTS
Fig. 3 presents the temperature dependence of the thermal
conductivity,, of three samples.
of the -sample
slightly decreases with decreasing temperature, begins toincrease below 60 K, and becomes maximum of about 800
around 18 K, which is similar toofBi2223/Ag tape reported previously [4]–[6].
of the-sample almost coincides with that of the -sample. For the-sample,could not be measured below 40 K because of

the limit of the heater power. The temperature dependence ofof the -sample is similar to that of other two samples.
However the absolute value ofof the -sample is about
one order of magnitude smaller than that of other samples. Thethickness of the solder layer between the tapes is found to be
extremely thin from the photograph (not shown here) and thevalue of the solder (LFM-48) [4] is rather larger thanthat of the -sample. Therefore, the smallvalue of the-sample does not originate from the solder layers.
IV. DISCUSSIONAs described in Fig. 1, the Bi2223 filaments distribute separately in the Ag sheath. The path of the heat current is rather
complicated. We simply assume that the applied heat flows
through both Ag and Bi2223 parts in parallel and suggest asimple model, in which all the Bi2223 filaments were virtually
collected at the center of the tape in the cross section as shownin Fig. 4(a). The dimensions of the tape and the Bi2223 region
along each direction were defined in the figure. The equivalentheat current circuits for the -sample and both - and -samples
are represented in Fig. 4(b) and (c), respectively. Here,,and
are the thermal resistances of the whole tape,
the Ag region and the Bi2223 filaments, respectively;
isgiven by. In general, the absolute value ofof Bi2223 is about two orders of magnitude smaller than that ofhigh-purity Ag, as shown in Fig. 3. The purity of the Ag sheathin the Type H tape was estimated to be about 99.9% from themeasurement [4]. In this study, we use the reported

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011

Fig. 4. (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.
,, andare the thermal resistances of the whole tape,
The equivalent heat current circuit for (b) the -direction and (c) both - and -directions.
the Ag region, and the Bi2223 filaments, respectively.

of Ag-0.09at%Au alloy [8] as. Thevalue of thepolycrystalline Bi2223 [9] is used as, becauseof Bi2223 single crystal has not been reported. Consequently,
the heat current path including Bi2223 in series can be ignored
because of. Thermal conductivity along the-direction,, can be calculated by the following relation,

In Fig. 3, the calculatedis also presented.
of the-sample is well reproduced byfor,except for around the peak structure at low temperature. The
value is the same as the filling factor of the superconductor,, which is defined by the volume ratio of Bi2223 filaments to the whole tape and is roughly estimated to be 0.36,
because Ag-ratio
was 1.8. The slight difference
insuggests the small amount of Ag, about 15% of total Agparts, does not contribute to the thermal transport. This might
originate from the complicated heat path in the core region.
of the tape along the -direction andalong
the -direction, respectively, are given by

andThe similar fitting procedure was adopted forand -samples, and thenandtained independently.
multiplied byof the were ob-equals to 0.45. The resultant value is consistent with thevalue determined by the analysis for the -sample, which supports the validity of our model. Consequently, we can conclude
that the measuredof the ‘stacked’ - and -samples correspond to those of the tape along - and - directions, because thethickness of the solder layer between the tapes is negligibly thinand the contact thermal resistance is ignored. The mechanismof the thermal transport for the -direction almost the same asthat for the -direction. The value ofmeans that theapplied heat flows through only about 4% of the total Ag region
for the -direction. The volume ratio of the edges of the tapeto the whole tape,, is roughly estimated to be 5%
from Fig. 1. Therefore,
is a plausible value andwe can conclude for the -direction that the routes of the applied
heat are both edges of the tape. We succeeded in explaining theanisotropic thermal conductivity of the Bi2223/Ag tape in thewide temperature range between 50 and 200 K by the simplified heat-flow model.
V. CONCLUSION
We have determined the temperature dependence of thethermal conductivity,, of a silver sheathed Bi2223(Bi2223/Ag) tape along three typical directions, the length,width and thickness. To estimateof the tape along thewidth and thickness directions, we prepared two stacked bundles consisting of several Bi2223/Ag tapes.
of the tapealong the length and width directions was 250
at77 K and coincided with each other. On the other hand,of the tape along the thickness direction was about one order ofmagnitude smaller than that of others, although the temperaturedependence was almost similar. The measuredof thesamples can be regarded as theof the tape along the threedirections. The measured
was well reproduced by thecalculated
based on the equivalent heat current circuit.
For three directions, the applied heat flows through the Ag
sheath, the amount of which depends on the direction.

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