LT 21

Proceedings of the 21st International Conference on Low Temperature Physics
Prague, August 8-14, 1996
Part $5 - Techniques and applications: Instrumentation

Proposal of Three Terminal Method for Low Temperature Thermal Diffusivity
Measurement
Hiroyuki Fujishiro a, Manabu Ikebe a, Kiminari Nakasatoa and Tomoyuki Naitob
a Faculty of Engineering, Iwate University, 4-3-5, Ueda, Mofioka 020, Japanb Institute for Materials Research, Tohoku University, Aoba-ku, Sendal 980, Japan
We propose a new technique, "three terminal arbitrary heating method" for the thermal diffusivity ct measurement
which at the same time enables one to determine the contact thermal resistance R e between the sample and holder. By
this method, the error in ct due to Re, which becomes progressively consequential at lower temperatures, can beeliminated. The method has been applied to YBa2Cu3OT. b oxide superconductors and the specific heat C has been
accurately determined between 15 to 200K by use of the relation C=r,/ot, where K is the thermal conductivity quasisimultaneously measured with ct.

Heate

1. INTRODUCTION
In low temperature physics and cryogenicengineering, the thermal conductivity K and the thermaldiffusi,)iiy ct are important parameters of thermaltransport. We have proposed an "arbitrary heatingmethod" for the thermal diffusivity ot measurement andhave des'eloped an automated simultaneous measuringsystem of ct and K with an identical experimental setup[1,2]. The measuring temperature range is from 10K to200K using a GM cycle helium refrigerator as acryostat. The specific heat C of various superconductors
was determined from the relahon C=K/ct and the Debye
temperature O D was estimated [3,4]. Since wedetermh~ed the thermal diffusivity ct assuming that thecontact thermal resistance Re at the damped end wasvery small, the estimated C=K/ct was sometimes liable
to errors due to non-negligible R e especially at low
temperatures, ha this paper, we propose a new technique,"three terminal arbitrary heating method" for more
precise thermal diffusivity ot measurement whichenables us to estimate Re as well.
2. EXPERIMENTAL
Fig. 1 shows a schematic view of the sample setup on
the cold stage in a vacuum chamber. One end of thesample was soldered to the cold stage by an In metal and a
metal film resistance heater was attached to the isolatedend of the sample
usingGE7031
varnish.
Au Fe(0.07at.%)-chromel
thermocouples (73p.m indiameter) were used differentially to monitor the threetemperatures Tp T:~ and T 3 at the positions of PI, P2 andP3 which were attached using silver paint. The thermal
conductivity K was also measured under this setup by asteady-state heat flow method using Pl and P3

CzechoslovakJournalof Physics,Vol.46 (1996),Suppl.$5/Sample

Different lalt hermocoupfe

P1dr,--

T2=Ts+ dT

Thermocouple

ICold stage]

Fig. 1. Schematic diagram of tile experimental setup on
the cold stage of a GM refrigerator.
terminals. The determination of the contacf thermal
resistance R c and the thermal diffusivily a wasperfomled as follows: when a heat pulse was applied
from a heater to a sample, time profile of temperature
T(x,t) at a position x is determined by the following
one-dimensional diffusion equation,aT(x,t)
at=aO2Tx,t)
ax"

9(1)

For a certain temperature of the cold stage, the temperature changes Tl0), T2(t ) and % 0 ) at the three measuring
points were recorded 7 times/see after applying the heatpulse. R c is at the clamped end defmed by Re=AT/Q,
where AT is the discontinuous temperature difference andQ is the power passing through the interface [5]. The2761

measured temperature proFde Tz(t) and an arbitrary
resistance Rc were used for boundary conditions of thediffusion equation. In order to determine the optimum aand Rc values systematically, the following calculation
imx~dre was used. For a fixed Ro the maximum
values of the experimentally observed T2(t) and Ta(t)curves and the calculated T2'(t) and T3'(t) ones werereduced to 1 and eighty points in the range from 0.1 to
0.9 of the rising part of the temperature changes were
sampled to obtain the minimum squared time error<At2> between the observed and calculated curves. This
procedure was continuously performed for different Re
values until the a values obtained from T2(t) and 1"30)agreed with each other and thus the optimum ct and Rc
were determined. This method has been applied toYBa2Cu3OT. 5 (YB(X)) oxide superconductor and thespecific heat C has been accurately determined between
15 to 200K.

3. R E S U L T S A N D D I S C U S S I O N
Fig. 2 shows the temperature dependence of thethermal diffusivity a 2 and a 3 of the YBCO sample
which were calculated at the positions of P2 and P3,
respectively (in case of Re=0). The temperaturedependence of the thermal conductivity K was alsoshown in the inset. At higher temperatures, thethermal diffusivities calculated at both positions arealmost the same which indicates Rc is really verysmall at these temperatures, a 2 becomes larger thana 3 with decreasing temperature. This indicates that ct3
at a nearer position from the clamped end was more
influenced than a 2 by Re We performed the iterative
process to decide the optimum a and Re Fig. 3
shows an example of the measured and calculated
temperature changes T3(t), T3'(t) (Rc=0) and T3"(t) (Rc=optimum value). The fitting curve which takes
account of the contact resistance Rc reproduced the1=, ,, n, ,0

....

0 e!

, ....

, ....

. . . . . . . .

----,

99=r~

999|

9912'

999T=30K

0.8
0.6

EIP~

0.4~ 0.2
nO0 ~I02030(sec)

TimeFig. 3 An Example of measured and calculated timevariations of temperature at P3.
experimental data quite satisfactorily. The revised
thermal diffusivity acal was also shown in Fig. 2. Fig.
4 shows the specific heat C2(tUa2), C3(K/Ot3) andrevised Ccal(~acal), together with t he Debye's specificheat CDebye. The levised Ccal taking account of thecontact resistance Rc satisfactorily reproduced theDebye's specific heat CDebye with Oo=430K down tolow temperatures.
300 .

g.

.

oc,L, ~H
2ooH

.

.

.

.

c,,,",Ii. . . .

o:

I-~o ~

0 t . ~ ; ~ ' ~,_100=o,Iso.

.

9.

I.

Temperature

....

.

.

loo.

I

15o.

.

.

.

I

200(K)

Fig.4. The specific heat C vs. temperature T.
.

4. SUMMARY-m 10o,, ~l~clit
9 - ~_ . . . . . . . . . . . . . . . . . .

~,o%

__mA

a= I

9Ora I,141)

109.

9.

I50.

.

.

.

I.

100
Temperature.

.

.

|150.

REFERENCES.

' '20~(K)Fig. 2. Temperature dependence of the thermal
diffusivity a 2 and a 3 (Rc=0) and r 1 (Rcfoptimum).

2762

We propose a "three terminal arbitrary heating
method" for the thermal diffusivity a measurement. By
this method, the error in a due to the contact thermal
resistance Re, which becomes progressively impotant atlower temperatures, can be eliminated.
[1] H. Fujishiro et al.: Cryo. Eng. 28 (1993) 533.
[2] M. Ikebe et al.: J. Phys. Soc. Jpn. 63 (1994) 3107.
[3] H. Fujishiro et al.: Jpn. J. Appl. Phys. 33(1994) 4971.
[4] H. Fujishiro et al.: Physica C235-240 (1994) 825.
[5] C. McMenamin et al.: Cryogenics 33 (1993) 941.

Czech. J. Phys. 46 (1996), Suppl. S5