MEASUREMENTS OF THE THERMAL BOUNDARY RESISTANCE BETWEEN 3He AND SILVER FROM 0,4 TO 10 mK.

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MEASUREMENTS OF THE THERMAL BOUNDARY

RESISTANCE BETWEEN 3He AND SILVER FROM

0,4 TO 10 mK.

A. Ahonen, O. V . Lounasmaa, M. Veuro

To cite this version:

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JOURNAL D E PHYSIQUE

Colloque

C6,

supplement au n"

8,

Tome

39,

aout

1978,

page

C6-265

MEASUREMENTS OF THE THERMAL BOUNDARY RESISTANCE BETWEEN 3H

e

AND SILVER FROM 0.4 TO 10 mK.

A.I. Ahonen , O.V. Lounasmaa, and M.C. Veuro

Low Temperature Laboratory, Helsinki University of Technology, SF-02150, Espoo IS, Finland

Résumé.- Nous avons mesuré de 0.4 à 10 mK la résistance de contact thermique entre l'3He à

pression nulle et une poudre d'argent frittée. Nous trouvons une loi de variation en 1/T. Abstract.- The thermal boundary resistance between silver sinter and 3He at zero pressure

has been found to have a 1/T temperature dependence from 0.4 to 10 mK.

As a by-product of tests on our nuclear re-frigerator /1/ we have measured the thermal boundary resistance between silver sinter and liquid 3He at zero pressure in the temperature range from 0.4 to 10 mK. The work thus extends to both the normal and the superfluid regions of the liquid, with the tran-sition temperature T =1.1 mK. Our data are of interest in theoretical investigations of the Kapit-za resistance and in the construction of refrigera-tors for cooling superfluid 3He below 1 mK.

The experiments were performed in the 3He cell of our nuclear demagnetization refrigerator. The silver sinter inside the silver cell body was made of 0.07 um diameter powder /2/ of 99.6 % purity. The total surface area was found with the BET method to be A = 12.9 m2, corresponding to a characteristic surface area of 1.3 m2 per gram of

sinter. The silver powder was first presintered at 200°C for 20 min. The resulting material, ground to a rough powder, was then packed into the 8 mm deep and 2 mm wide grooves in the cell body by exerting a pressure of 200 bar. The final sintering was done by heating the cell to 220°C in about 15 min. and then cooling quickly back to room temperature.

The temperature of the 3He sample was

deter-mined by measuring the nuclear magnetic susceptibi-lity of 1 9 5Pt by pulsed NMR techniques. The

tempe-rature scale was calibrated by the spin-lattice relaxation time of the platinum powder at 2 mK and it was also checked against the superfluid transi-tion temperature T . The applied magnetic field was 28 mT during all our experiments.

The thermal resistance was measured by apply-ing a heat current <3, typically between 0.1 and

10 nW, to 3!Ie by means of a Speer carbon resistor ground to a thin slab of less than 1 mm thickness. R = AT/Q, where AT is the temperature increment due to the heat flux, is the total thermal resistance between*3He and the nuclear stage. In order to

ex-tract the Kapitza boundary resistance R^, the ther-mal resistance of the long cell support was separa-tely measured and subtracted. R^ was found to be responsible for 75 % of the total heat barrier between the 3He and the rest of the cryostat.

Figure 1 shows our results. The best data are below 1 mK, where the heat capacity of the nu-clear stage was largest and consequently the tempe-rature drift, due to external heat leaks, was smal-lest.

5 0 i ' | ' ' ' i | 1 1 > 1 ) I . , , ,

rfmK)

Fig. 1 : The thermal boundary resistance L as a function of temperature.

At the high temperature end of our measurements the rapid temperature drift made precise determinations Present address : Department of Physics, Cornell

University, Ithaca, New York 14853, USA

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of AT difficult, leading to scatter of the data. The Kapitza resistance is observed to have a 1/T dependence over the whole temperature region investigated; the line drawn into figure 1 fits the equation = 86/T K~/w. Above 1 mK this beha- viour is expected /3/

,

but the observation of the same temperature dependence below the superfluid transition at 1.1 mK is somewhat surprising.

The absolute magnitude of the boundary resistance, R@T = 1100 ~ 2 m * / ~ , is four times larger than that found by Andres and Sprenger 131. The probable reason for this discrepancy is that our sinter is made of much smaller particles than the

5

5 pm powder employed in Reference 131. The heat conductivity of our sinter is presumably poo- rer than that of a sinter made of larger particles.

The thermal conductivity of bulk liquid 3 ~ e is good in the low millikelvin region but inside the sinter, with the voids much smaller than the mean free path of the 3 ~ e quasiparticles, the heat conductivity is greatly reduced 141. A temperature gradient can thus develop across liquid 3 ~ e confi- ned inside the relatively deep sintered regions. Therefore, the effective surface area in our cell may be smaller than the measured A = 12.9 m2.

The lack of any sign of change in the tem- perature dependence of RK in the superfluid B phase is astonishing because the nuclear spin of the 3 ~ e atom is assumed to be involved in the energy transfer process across the liquid 3He-metal interface. The nuclear spin properties of 3 ~ e change drasti- cally in the superfluid; in the B phase the thermal boundary conductance is expected to decrease faster than

in

the normal phase

151.

A'simple explanation for the observed beha- viour of

$

is that the liquid inside the sinter may not undergo the superfluid transition at all. The pare size of our sinter, a 0:l pm, is of the same order of magnitude as the coherence length of the superfluid and, therefore, the transition may be suppressed. If this is the case, the use of sinter made of very fine particles is advantageous for cooling liquid 3 ~ e below 1 mK. In this way one

could benefit from the smaller boundary resistance of the' normal liquid inside the sinter while inves- tigating the superfluid in the open areas of the experimental cell.

On the other hand, if the thermal boundary resistance between 3 ~ e and a metal has the same temperature dependence in the normal and in the

superfluid B phase, a revision of current theories on the heat transfer mechanism at a liquid 3 ~ e - metal interface is needed.

Reference

/ l / Veuro, M.C., Ph.D.Thesis, Acta Polytechnica Scandinavica (to be published in April 1978). See also paper XXX at this Conference.

/ 2 / Purchased from Vacuum Metallurgical Co.,Shonan- building 1-12-10 Ginza, Chuo-ku, Tokyo, Japan. /3/ Andres, K. and Sprenger, W.O., Proc. 14th Int.

Conf. on Low Temp.Phys.

1

(1975) 123. /4/ Befts, D.S., Brewer, D.F., and Hamilton,R.S.,

J. Low Temp. Phys.

16

(1974) 331.