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Submitted on 1 Jan 1978
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THERMAL CONTACT IN LIQUID 3He DOWN TO
0,4mK
D. Edwards, J. Feder, W. Gully, G. Thas, J. Landau, K. Muething
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplement au n° 8, Tome 39, aout 1978, page C6-260
THERMAL CONTACT IN LIQUID 3H
eDOWN TO 0.4mK+
D.O. Edwards, J.D. Feder, W.J. Gully, G.G. Ihas, J. Landau and K.A. Muething
Physios Department; The Ohio State University Colymbus, Ohio, U.S.A. 45210
Résumé.- Des mesures du temps d'équilibre thermique et de la chaleur spécifique de l'^He liquide dans un cryostat à désaimantation nucléaire indiquent que la conductance Kapitza du palladium est proportionnelle à la chaleur spécifique du liquide dans l'état super-fluide B ou dans l'état normal.
Abstract.- Measurements of the thermal time constant at the heat capacity for liquid 3He in a nuclear cooling cryostat indicate that the "anomalous" Kapitza boundary conductance to Pd sinter is proportional to the heat capacity of the liquid in both the normal and superfluid phases.
Our cryostat is of fairly standard design / ] / and a very brief description has been given ear-lier 111. For this paper the heat exchanger is of primary concern. It contains 10 cm3 of sintered 2 micron Pd powder /3/ with an estimated surface area of 25m2. The Pd powder was first sintered at 800°C
while packed in coconut charcoal which provided a reducing atmosphere. Afterwards the heat exchanger was reheated to 600°C in a clean hydrogen atmosphere and cooled under vacuum to anneal and purify the sinter. In test pieces this treatment resulted in resistivity ratios of 100 or more, but in the actual heat exchanger the ratio was found to be only 15. Even with this ratio there is a negligible thermal resistance in the sinter at low temperatures. The Pd is in the form of four rings 10 mm deep by 17 mm diameter sintered around copper posts of 6.3 mm dia-meter. This arrangement was designed to promote con-tact between Pd and Cu because of the large contrac-tion on sintering, but the diameter of the posts was too large since there was a tendency for radial cracks to appear in the sinter.For one ring this problem was so severe as to have broken good contact between it and its copper post, reducing the effec-tive area to 19 in2. The electrical resistances of the sinter rings and of their contacts to the Cu were measured at various temperatures both before and after the nuclear cooling experiments. These measurements are useful in showing that the important
thermal resistances at very low temperatures are not in the metals.
The 3He sample space consists of ~ 10 cm3 in the
heat exchanger and about 7 cm3 distributed in four
"towers". The sample and bundle can be precooled to ~ 26 mK while the bundle is in a field of 80kg. The sample and heat exchanger are in a region com-pensated to less than 30 gauss. The heat leaks after demagnetization are not time-dependent and are approximately 5 nW to the bundle and 0.3 nW into the helium. The temperature of the 3He sample is measured by a commercial pulsed Pt nmr thermo-meter, the Instruments for Technology PLM3(2) which can be self-calibrated using the Korringa relation. The cell also contains a Straty Adams pressure gauge to compare the temperature scale with the melting curve. The nmr solenoid is ma-gnetically isolated from the main solenoid by a superconducting tube.
The cryostat was first tested with 3He con-taining about 0.1 % of '•He. This correspond to ~ 2 layers of "*He on the surface of the sinter. The lowest temperature teached was 0.7 mK. The 3He
thermal time constants observed at SVP and at 3 bars are shown in figure 1. Above about 5 mK the
time constant is internal to the 3He and is due to the fairly long heat paths between different parts of the 3He sample. Below 5 mK the time constant is
determined by the product of the 3He heat capacity
and the Kapitza resistance to the heat exchanger. It was possible to measure the approximate 3He heat capacity below 1.5 mK because of the long thermal relaxation time between the impure 3He and
the heat exchanger. The heat capacity was obtained in the conventional way by measuring the tempera-ture rise due to a pulse of heat.
This work was supported by the US National Science Foundation, grant number DMR-19546-AO1
F i g . 1 : Time c o n s t a n t s f o r t h e r e l a x a t i o n of t h e l i q u i d 3 ~ e temperature t o t h a t of t h e n u c l e a r r e f r i g e r a t o r . The p r e l i m i n a r y d a t a a t 3 b a r s a r e shown i n f i g u r e 2. The r e s u l t s i n d i c a t e t h a t t h e r a t i o of t h e d i s c o n t i n u i t y t o t h e normal h e a t c a p a c i t y , AC/C i s s m a l l e r t h a n expected : of t h e o r d e r of
-
2 t o 2.5, i n agreement w i t h t h e measurements of S h i e l d s and Goodkind /4/ which were a l s o made w i t h o u t u s i n g a h e a t s w i t c h .F i g . 2 : The h e a t c a p a c i t y of 3 ~ e a t 3 b a r s .
For t h e impure 3 ~ e , t h e time c o n s t a n t s between 5 mK and 2.5 mK a t 3 b a r s a r e c o n s i s t e n t with an o r d i n a r y T~ Kapitza conductance which, p e r
u n i t a r e a , corresponds t o h K = 30 w a t t ~ m ~ ~ ~ ) ~ ~ i n good agreement w i t h p r e v i o u s measurements /S/ f o r
Pd. Below 2.5 mK t h e time c o n s t a n t l e v e l s o u t , i n - d i c a t i n g an "anomalous" conductance which i s pro- p o r t i o n a l t o T i n t h e normal l i q u i d and t o approxi-
mately 'T3 i n t h e s u p e r f l u i d B phase below Tc=l .25mK When t h e impure 3 ~ e was r e p l a c e d by 3 ~ e c o n t a i n i n g l e s s t h a n 30 ppm of ' ~ e , t h e Kapitza r e s i s t a n c e was decreased by roughly a f a c t o r of 7, s o t h a t t h e lowest a t t a i n a b l e temperature w i t h our h e a t l e a k of
-
0.3 nWwas below 0.4 mK. I t might be supposed t h a t t h e l i m i t i n g r e s i s t a n c e i n t h i s c a s e i s t h a t of t h e l i q u i d 3 ~ e whose c o n d u c t i v i t y i s reduced by boundary s c a t t e r i n g i? t h e p o r e s of t h e s i n t e r . A c a l c u l a t i o n of t h i s e f f e c t , based on gas flow measurements through a sample of t h e s i n - t e r , i n d i c a t e s t h a t although t h e reduced conducti- v i t y i s p r o p o r t i o n a l t o t h e h e a t c a p a c i t y i t i s too l a r g e by two o r d e r s of magnitude t o e x p l a i n t h e thermal time c o n s t a n t . We t h e r e f o r e conclude t h a t we a r e a g a i n o b s e r v i n g a Kapitza conductance which i s p r o p o r t i o n a l t o t h e h e a t c a p a c i t y of t h e l i q u i d i n b o t h t h e normal and s u p e r f l u i d phases. The ma- g n i t u d e of t h i s conductance p e r u n i t a r e a , h k = ( 5 X I O - ~watt/^%^)^
i s much s m a l l e r than t h a t measured e a r l i e r on Pd f o i l /5/ and i t i s about t h e same a s t h a t found f o r Cu and Ag s i n t e r s i n o t h e r n u c l e a r c o o l i n g experiments 121.Re£ e r e n c e s
/ l / Ahonen, A . I . , Berglund, P.M., H a i k a l a , M.T., Krusius, M., Lounasmaa, O.V., and Paalanen, M.A., Cryogenics
5
(1976) 9./ 2 / "Physics a t U l t r a l o w Temperatures", Proceedings of t h e I n t e r n a t i o n a l Symposium a t Hakone, J a Japan, September 5-9, (1977) 280.
131 Leico I n d u s t r i e s I n c . 250 W. 57th S t . , New York New York.
/41 S h i e l d s , S.E. and Goodkind, J . M . , J.Low Temp. Phys.
