A METHOD TO MEASURE THE THERMAL CONDUCTIVITY OF DISCS OF ARBITRARY SHAPE, DEMONSTRATED ON A TYPE-II SUPERCONDUCTOR

HAL Id: jpa-00218014

https://hal.archives-ouvertes.fr/jpa-00218014

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A METHOD TO MEASURE THE THERMAL CONDUCTIVITY OF DISCS OF ARBITRARY

SHAPE, DEMONSTRATED ON A TYPE-II SUPERCONDUCTOR

P. Weijenbergh, H. van Beelen

To cite this version:

P. Weijenbergh, H. van Beelen. A METHOD TO MEASURE THE THERMAL CONDUCTIVITY OF DISCS OF ARBITRARY SHAPE, DEMONSTRATED ON A TYPE-II SUPERCONDUCTOR.

Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1194-C6-1195. �10.1051/jphyscol:19786528�.

�jpa-00218014�

JOURNAL DE PHYSIQUE Colloque

C6,

supplgment au no 8, Tome 39, aozit 1978, page C6.1194

A METHOD T O MEASURE T H E THERMAL C O N D U C T I V I T Y O F D I S C S OF ARBITRARY SHAPE, DEMONSTRATED ON A

TYPE-I I

SUPERCONDUCTOR

P.G.P. Weijenbergh and H. Van Beelen

KmerZingh Gnnes Laboratorim der ~ i j k s u n i v e r s i t e i t Leiden, Nieuwsteeg 18, Leiden, The Netherlands

RQsum6.- La mQthode de Van der Pauw pour mesurer la rdsistivitd Qlectrique des disques de forme ar- bitraire est adaptse au cas de la conductibilitd thermique. La mQthode est appliquLe P un Qchantillon supraconducteur de deuxiPme espsce.

Abstract.- Van der Pauw's method to measure the electrical resistivity of discs of arbitrary shape has been converted to the case of thermal conduction. The method has been applied to a type-I1 super- conducting sample.

INTRODUCTION.- In 1958, L.J. Van Der Pauw introdu- ced a method to measure the electrical specific conductivity

o

of singly-connected samples of arbi- trary shape but homogeneous thickness d/i/. This method requires four successive line-shaped contacts A,B,C and D, situated along the circumference of

the sample at arbitrary positions. (See figure 1)

Fig. 1 : The flat sample with four line-shaped con- tacts.

The electrical "resistance"

~ z ! ~ ~

is defined as the potential difference V -V per unit current

D C

flowing from contact A to B through the sample. For infinitesimally small width of the line-shaped con- tacts, the following relation holds generally

If the position of the contacts is chosen so that RM,CD and (el

~ $ 1 ~ ~

are almost equal, equation(1) can be approximated as

temperature gradient) :

It seems that this method is not used before to mea- sure the thermal conductivity A.

EXPERIMENTAL SET-UP.- We tested this method on a type-I1 superconducting sample (Pb+o-In60at.%). The sample was mounted in a vacuum chamber inside a su- perconducting solenoid so that the magnetic field is directed perpendicularly to the broad surface of the sample. By means of small copper strips three thermometers (TA,TC,TD) and three heaters (H A' H

c'%)

are attached to the circumference of the sample whi- le at point B it is thermally anchored to the he- lium bath (see inset figure 2).

EXPERIMENTAL RESULTS.- The curves in figure 2 show the thermal conductivity as a function of the tem- perature in the normal-, superconducting- and mixed- state as measured previously on a rectangular sam- ple using the standard experimental technique/2/.

The points shown in figure 2 are obtained with the four-point method of Van Der Pauw and coincide ni- cely with the curves.

An additional advantage of Van Der Pauw's 2 Ln 2 (2) method is that the errors introduced by the finite

u

=

(e) +R(e) R

nd ~ A B

,

^{CD BC}

,

^DJ size of the contacts are of the order (-)', where L

R is the width of one contact and L the length of Since equation(1) is based on the relation _{. .}

-+ -+ the circumference of the sample. Those errors can

J =

-oh

between the electrical current-density J

be neglected in the present experiment.

and fieldstrength

-$

V, equations (I) and (2) can

As was pointed out by Van Der Pauw, the sa- be immediately converted to the case of thermal

me four contacts can be used to measure the Hall

-

$onduction 2sing the corresponding relaxation

coefficient, which converts to the Righi

-

Leduc

a

^{= -A $T ((a}

-.

the heat-current densitv and

if^

the

coefficient, on the arbitrary shaped sample. These

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786528

coefficients will be proportional to the change of the "resistance" %B,CA per unit magnetic field- strength. This method, however, is not very suita- ble to measure these rather small effects, requi- ring large current-densities, which have to be ap- plied through such small contact areas.

References

/ I / Van Der Pauw,L.J., Philips Research Reports

13 (1958) 1

-

/ 2 / Weijenbergh,P.G.P. and Van Beelen,H., submitted to Physica.

Fig. 2 : Comparison of the results for the thermal conductivity of superconductive Pbso-InBo, obtained by the standard technique (drawn curves) and the present method. The inset shows the circular sample, the slits are made to enlarge the circumference.