Physica C 357±360 (2001) 785±788

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Thermal contact resistance between high-Tc
superconductor and copper
Hiroyuki Fujishiro *, Tatsuya Okamoto, Koichi Hirose
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan
Received 16 October 2000; accepted 17 January 2001

Abstract
The thermal contact resistivity (Wc ) through the connection between a high-Tc superconductor and a copper block
was measured from 10 to 200 K for various connecting methods using In solder, silver paste, epoxy resin and varnish asadhesives. Wc was measured by a steady state heat ¯ow method and with a three-terminal non-steady state method bywhich the thermal diusivity a was also determined simultaneously. It was found that Wc seriously depended on theconnecting method and increased with decrease in temperature. The measured Wc values by both steady and non-steadymethods were roughly consistent with each other. The proposed three-terminal non-steady state method was proved to
be a useful method to determine both a and Wc . Ó 2001 Elsevier Science B.V. All rights reserved.
PACS: 44.30.+v; 66.60.+aKeywords: Thermal contact resistivity; Thermal diusivity; Superconducting connection; Adhesives

1. Introduction
In the ®eld of the cryogenic engineering and low
temperature physics, the thermal contact resistance (TCR) through the connection between twomaterials is an important parameter. For applications of high-Tc superconductors as power current leads to a cryocooled superconducting magnet(SCM), for example, it is necessary to electricallyconnect a high-Tc superconductor with copper
leads. In such a case, TCR between them is as
important as the thermal conductivity of the highTc superconductor itself to estimate the amountand velocity of the heat intrusion in order to avoid*

Corresponding author. Tel./fax: +81-19-621-6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).

the quenching of SCM [1]. In case of applying astandard non-steady state heat ¯ow techniques forthe thermal diusivity a measurement, the TCRs
between the thermometer and the sample and between the sample and the heat sink seriously
damage the accuracy of the measurements. In thiscase, TCR results in the time lag of temperaturechange T t of the sample and the determined atends to be estimated lower than the true one.
The thermal contact resistance is de®ned byRc  DT =Q (K/W), where DT is the discontinuous
temperature dierence at the interface of the twomaterials and Q is the heat power passing throughthe interface [2]. The thermal contact resistivity Wc
can be de®ned by Wc  Rc S (mm2 K/W), where S isthe contact area. Even if the two materials areconnected using a speci®ed adhesive, the Wc T value cannot be decided uniquely because Wc T 0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 3 6 4 - 1

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depends on the surface roughness of the interface,
the thickness of the adhesive, the mechanicalpressure in the connection and so on. Wc increases
with decreasing temperature and is usually verysmall at the room temperature [2]. Therefore, there
is not so much investigation concerning Wc T 
except for the Kapitza resistance at very low temperatures [3].
In this paper, we measured the thermal contact
resistivity Wc between the YBa2 Cu3 O7 polycrystal(YBCO) and the copper metal by steady statemethod between 10 and 200 K for several connecting methods. We also estimated Wc by thethree-terminal non-steady state method previously
proposed by us [4], in which the thermal diusivity
a is simultaneously determined. The Wc values
obtained by both methods were compared eachother.

the GM cycle helium refrigerator, were connectedusing various adhesives (silver paste (DUPONT4922N), In solder (99.9999% purity), epoxy resin(Stycast: 2850-GT) and varnish (GE-7031)). The
connecting surfaces were polished using a #1000
emery paper and were rinsed out. The thickness of
the used adhesive was estimated to be as thick as100 lm. AuFe(0.07 at.%)±chromel thermocouples with 76 lm / in diameter were used to monitor the temperatures at P1 , P2 and P3 which wereattached using the silver paste [5]. The wholesample chamber was evacuated to <10 5 Torr toprevent heat leak by remnant gas. With the continuous heat power Q applied to the slender
YBCO sample (2:5  3:0  30:0 mm3 ), the temperature jump DT at the interface was estimated by
the extrapolation from the temperature rises at P1 ,P2 and P3 in the steady state.

2. Experimental

3. Results and discussion

Fig. 1 shows an experimental setup around thesample for the determination of Wc . YBCO
(Tc  92 K, d  5:80 g/cm3 ) and the copper block,
both of which were situated on the cold stage ofFig. 2 shows a ¯ow chart for the simultaneousdetermination of the thermal contact resistivity Wc
and the thermal diusivity a using the three-terminal non-steady state method [4]. When a heatFig. 1. The schematic view of the experimental setup for the determination of the thermal contact resistivity Wc . The temperaturepro®le in the steady state heat ¯ow method is also shown.

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787
2Fig. 2. A ¯ow chart of the simultaneous determination of theoptimum thermal contact resistivity Wcopt and thermal diusivity aopt using the three-terminal non-steady state method.

pulse is applied from a heater into a sample under
the identical experimental setup in Fig. 1, the time
variation of temperature T x; t is described by the
one-dimensional diusion equation. For a certain®xed temperature of the cold stage, the temperature changes T1 t, T2 t and T3 t at three measuring points were recorded 14 times/s after
applying the heat pulse. The observed temperaturerise DT2 t at P2 and DT3 t at P3 were reduced by
the maximum value (DT2 max and DT3 max ) and therising part of the DT2 t and DT3 t curves wascompared with the solutions of the diusion
equation, DT20 t and DT30 t. For a ®xed contact
resistance value Wc , the calculations were performed using T1 t as the boundary conditions forvarious diusivity values a2 and a3 . a2 and a3 ,which correspond to the diusivities of the sample
monitored at points P2 and P3 , were determinedfrom the minimum squared time error hDti between the measured and the calculated ones. This
procedure was successively performed for various
Wc values until the a2 and a3 values agreed witheach other and the optimum aopt and Wcopt weredetermined. The fundamental concept of thismethod is that the thermal diusivity of a materialmust be unique even if it is monitored at dierent
points of a sample.
Fig. 3 shows the temperature dependence of thethermal contact resistivity Wc for various connecting methods which was determined by a steadystate method. The Wc values seriously depended on
the connecting method; the order of Wc values
using the various adhesives was GE-varnish >Stycast > In solder > Ag-paste. This order of themagnitude in Wc is consistent with that of thethermal resistivities ( 1=j) of the adhesives. For
example, the thermal conductivity j of In metal,
Stycast (2850-GT) and varnish (GE-7031) is 780,
15 and 4 mW/cm K at 300 K, respectively. The
measured Wc values may include the thermal resistivity of the adhesives besides the intrinsic
Wc . The Wc increase with decreasing temperature
was gradual in the high temperature regime andbecame very steep at lower temperatures below
40 K.

Fig. 3. The temperature dependence of the thermal contact
resistivity Wc T  for various connecting methods which wasdetermined by a steady state method. Wc determined by thenon-steady state method was also plotted in the case of Stycast(2850-GT) adhesive.

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H. Fujishiro et al. / Physica C 357±360 (2001) 785±788

ductor and a copper block was measured by boththe steady state method and the non-steady statemethod proposed by us. The Wc values estimatedby both methods are nearly consistent with eachother. The observed Wc values may include theeect of the thermal resistivity ( 1=j) of the adhesive materials besides the intrinsic thermal contact resistivity. In the industrial applications andthe basic thermal researches at low temperatures,the quantitative measurement of the thermal contact resistivity for several connections is important,which should be investigated more systematicallyin the future.
Fig. 4. The temperature dependence of the thermal diusivities
a2 and a3 (Wc  0) and the optimum aopt (Wc  Wcopt ) for theconnection using Stycast (2850-GT).

Fig. 4 shows the temperature dependence of thethermal diusivities a2 , a3 (in case of Wc  0) andthe optimum aopt which was determined simultaneously with the optimum thermal contact resistivity Wcopt for the connection using Stycast(2850-GT). The thermal diusivity a2 (Wc  0) estimated at P2 is always larger than a3 (Wc  0)
estimated at P3 because the in¯uence of Wc on the aestimation is more reduced for the measuring point
separated further from the contact interface. The
corrected aopt under the condition of a2  a3 using
an optimum Wcopt should more precisely reproduce
the true value of diusivity. Wcopt determined bythis technique was also plotted in Fig. 3. The Wcoptvalues are nearly consistent with those determinedby steady state method. However, Wcopt cannot be
estimated at T < 40 K because the thermal diusivities (a2 ; a3 ) and the Wc values are too large andare out of the validity limit of the re®nement
process shown in Fig. 2.
In summary, the thermal contact resistivity
Wc T  at the connection of a high-Tc supercon-

Acknowledgements
The authors wish to thank Prof. M. Ikebe ofIwate University for valuable discussions. Thiswork is partially supported by a grant-in-aid for
Scienti®c Research from the Ministry of Education, Science, Sports and Culture (no. 09555018),and Japan Science and Technology Corporation
under the Joint-research Project for Regional Intensive in the Iwate Prefecture on ``Developmentof practical applications of magnetic ®eld technology for use in the region and in everyday
living''.

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