PROGRESS IN NUCLEAR REFRIGERATION OF 3He

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PROGRESS IN NUCLEAR REFRIGERATION OF 3He

E. Varoquaux

To cite this version:

E. Varoquaux. PROGRESS IN NUCLEAR REFRIGERATION OF 3He. Journal de Physique Collo-

ques, 1978, 39 (C6), pp.C6-1605-C6-1612. �10.1051/jphyscol:19786607�. �jpa-00218102�

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-1605

PROGRESS' I N NUCLEAR REFRIGERATION OF 3He

E. Varoquaux

Institut d'Electronique Fondamentale, Ba.ti.ment 220, Universite Paris Svd, S140S ORSAY, France.

Résumé.- Actuellement 1' 3He liquide peut être refroidi jusque vers 0,3 mK par réfrigération nuclé- aire avec du cuivre. Cet article présente l'état présent de la question.

Abstract.- Nowadays, liquid 3He can be cooled to about 0.3 mK by nuclear refrigeration with copper.

The current state of the art is described in this paper.

INTRODUCTION.- Adiabatic demagnetization of copper is an increasingly popular technique for cooling

3He to below 1 mK. It has already been reviewed by a number of authors /1,2,3,4/. Not only is it a convenient method of refrigeration but it is so far the only one to reach deeply into the microkelvin range. The lowest temperature at present is 300 uK /5/. Early attempts at cooling 3He were reported in

1966 by Osgood and Goodkind /6/ but the method was first successfully put to work in 1973 /7,8/.

Nowadays the combined use of filamentary wire superconducting solenoids and high power dilution refrigerators make nuclear refrigeration both effi- cient and dependable. This paper summarizes recent progress and includes a brief discussion of some of the current problems and of thermometry. It does not include the use of intermetallic compounds, such as Pr Ni , with an enhanced nuclear magnetism, which have also been used to cool 3He below 1 mK /9/.

BASIC RELATIONS.- Nuclear refrigeration relies on the fact that the free energy per unit volume F (T, B ) of a system of nuclear spin S possessing a magnetic moment u = tf y S (see table I for nume- rical values) depends on the applied field B =u H :

a o a

d F = - S dT - ft

^{J B}

(1)

n n a

According to statistical mechanics, the entropy per unit volume S of nuclei with number density N/V = n can be, in the limit B /k„T << 1, written as

a o A(B2 + b2)

S = n k„ Ln (2 S+l) + ... , (2) B 2 T 2

under the simplifying assumption that the various coupling energies of each nuclear spin with its (equivalent) environment (via magnetic dipolar, exchange, quadrupolar interactions ...) can be lum- ped into a single parameter b, the local field. The

quantity A is the Curie constant as seen by deriving the magnetization per unit volume from equations

(!) and (2) :

jj _ *

F

n _ f

T

^n .

T

_ K .

( 3

)

The well-known expression of A is :

A = n S (S+1)(YK)2 /3 kB. (A)

Numerical values are given in table I in units such that Ay is expressed in Kelvin.

If now the field B applied to the thermally isolated spin system is changed from an initial va- lue B. to a final one B, slowly enough so that the process is reversible, then the entropy is conserved.

According to equation (2), the final temperature T reached by the system is related to the initial temperature T. by :

B2 + b2

T = T —

f £ B? + b2 ^

1

This very basic expression holds as long as equation (2) is valid. It has been verified experi- mentally by Hobden and Kurti /10/ who have found b -\, 0.3 mT for their copper nuclear bundle. In badly strained Cu samples, b also includes electric qua- drupole interactions and may be higher than the di- polar contribution by a factor 10 or so.

One can see from equation (5) that adiabatic decrease of the field applied to nuclear spins may lead to substantial reduction of the spin tempera- ture. This reduction is of significance if the nu- clear heat capacity is large. The specific heat per unit volume in a fixed field is obtained from equa- tion (2) :

8S B2 + b2 ...

C = x — 2 - = A -2 (6)

n 3T 2

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786607

JOURNAL DE PHYSIQUE

T a b l e I

T a b l e I : P r o p e r t i e s of some m a t e r i a l s used a t u l t r a - l o w t e m p e r a t u r e : 2 , n a t u r a l abundance ; y/2n gyromagnetic r a t i o i n MHz T - ~ ; S , s p i n ; Q , e l e c t r i c q u a d r u p o l e moment i n cm2; VM, m o l a r vo- lume i n cm3 ; K , K o r r i n g a c o n s t a n t i n s-K ; b , l o c a l f i e l d i n T, e s t i m a t e d from NMR l i n e w i d t h s e x c e p t f o r I n ; A C u r i e c o n s t a n t i n J K ~ - ' m - ~ ; C /T l a t t i c e s p e c i f i c h e a t p e r K e l v i n i n J K-"

mole ; B

,

s u p e r c o n d u c t i n g c r i t i c a l f i e l d i n T ; :IT, t h e r m a l c o n d u c t i v i t y p e r K e l v i n i n W m - ' ~ - ~ , h e a v i l y x e p e n d e n t on p u r i t y and h e a t t r e a t m e n t .

H

3 ~ e

2 7 ~ 1 1 0 0

5 1 ~

The v a r i a t i o n o f C i s s i m i l a r t o t h e high- t i o n (6) y i e l d s : t e m p e r a t u r e t a i l o f a S c h o t t k y anomaly. I n t h e a d i a - B:

+

b 2

+ c o n s t a n t

b a t i c p r o c e s s e x p r e s s e d by e q u a t i o n ( 5 ) , t h e s p e c i - . Hn(Sn'Ba) = (8) f i c h e a t remains c o n s t a n t . T h u s , t h e h e a t c a p a c i t y

The e f f e c t of a t h e r m a l l o a d i s t o r a i s e o f one mole of copper (of molar volume V M = 7.1 cm3

t h e t e m p e r a t u r e of t h e s p i n system from Tf t o T ac- /mole) i n 600 t e s l a p e r K e l v i n (B. = 6 T, Ti =

10

c o r d i n g t o : mK) amounts t o 1 . 2 J / K , which i s l a r g e i n t h e sub-

I 1

m i l l i k e l v i n r a n g e . However, one s h o u l d n o t b e m i s l e d Q = A V (B: + b 2 ) (-

- T)

Tf

t o t h i n k t h a t t h e f i e l d B can b e reduced w i t h impu- B? + b 2 (9)

= A V L Tf

n i t y down t o v a l u e s c l o s e t o b . The a b i l i t y o f t h e T ( I

-

T).

T

?

^f

n u c l e a r system t o cope w i t h an e x t e r n a l h e a t load i s ¹

%

6 3 ~ u 69.1 1 1 . 2 8 p / 2 0 . 1 5 I 7.1 1.28 12.3 67.1 j a . 6 9 5 ; - ¹³⁰⁰

C o o l a n t , NMR t h .

i I

6 5 ~ u j

^30.9

112.09 512 ' 0 . 1 4 i 7.1 j ^{1.25 12.3} i ^77.2 / ^{0.695 j - 1300}

, a n d e x c h a n g e r

,

1 I

i I I

93Nk

)lo0 110.41 /9/2 : 0 . 4 10.9 1 ^0.19 1 ^{I246 7.79}

ⁱ

^{0.25 1}

d e s c r i b e d by i t s t o t a l e n t h a l p y Hn(S, -+ B,), which i s The t o t a l t h e r m a l e n e r g y w i t h which a n u c l e a r

y/2n I S

22.2 51.4

-

by d e f i n i t i o n s u c h t h a t r e f r i g e r a t i o n s t a g e i s a b l e t o cope d e c r e a s e s a s

'

i ^8.7 1 ^0.7 1 1 ^{3.05 i 9.42 /}

1.74 :5/2

l Exchanger

,

I

1.722;1/2

!

- 10.3 I l l

0 1 1

i 0.22 / ^0.646 : - ¹⁰ 1

^Exchanger

i I

dHn = T dSn

-

S . d z a = d [J

en

V dTI]

,

(7) T f , t h e l o w e s t t e m p e r a t u r e of t h e s p i n s .

Q

* ^-L

where S = S V and M = MV. The i n t e g r a t i o n o f equa

n n

/11.09 b/2 0 . 1 4 9 ; 9 . 9 7 / 1 . 8 3 i6.2 : l o 8 : 5 5 0

N M R t h e m c m e t e r

:

100 111.19 1 1 2 i0.3 ' 8.34 ( ^{0.79 i5.7 236} ! 9 . 2 6 : ^0.13

I

I ! 1

^I

j

I

I i

lo9&l 48.6 / 1.981 '112 - 10.3

i 1 1

0 . 1 0.29 i ^{0.646 - 10 i}

^{Exchanger !}

I 1

' l 5 I n / g 5 . 8 ;

^I

9 . 3 1 0 ' ~ / 2 ; 1 . 1 b 4 ' 1 5 . 7 : 0.086 / 2 5 0 0 : 1 3 7 11.69 ; 0.03

5 0 0 i ~ o o l a n t

i ⁱ

^{1 i I}

1 1 7 ~ n 1 7.7 115.77 :1/2 - ! 16.3 / 0.050 ! 1 . 3

i

11.4 i ^{1.78 0.03}

^I

^:

NMR t h .

i

^!

1

19Sn / ^{; 8.7} i ' 15-87 j1/2 i - 1

^I

^{16.3 1 I 0.050 1 . 3} I ^11.6

^{, NMR t h .}

VM

32.43 1/2 - ^136.8 ! - ! -

^{! I}

- 2500 / -

^{Sample at}

⁰

^{Bar ,}

I I ^I

- 1 ^90.7

6.9 33

~ N M R t h .

25.8

I

j ⁱ 1.47

⁶

0.02 , ^{i i}

26.3 1.47 0.02 1 ,

! i

1 9 5 ~ t :

33.7 / 9 . 1 5 3 1 / 2 ; - j 9.10 1 0.030 0.2

K

-

I

-

_EPOXY ^I

I

2 0 3 ~ l i 2 9 . 5 / 2 4 . 3 3 j 1 / 2 / - 17.24

I '

2 0 5 ~ 1

70.5 j 24.57 1/2 / ^- j ^17.24

I

1

0 . 0 0 6 1 2 . 8 0.006 12.8

I

b A

---- ' j

K / T / H a s b e e n u s e d as

I

TIME EVOLUTION OF THE TEMPERATURES.- Let us consi- der the dynamics of this energy transfer and the coupling of the nuclear system to the surroundings.

The nuclear spins are coupled to the conduction electrons by the hyperfine interaction and the lon- gitudinal relaxation of magnetization is governed by a time constant

[

^TJ-I = T,/K. (10)

The temperature Te is the electron tempera- ture and K, the Korringa constant, given in table I, characterizes the behaviour of a pure metal. To the relaxation rate (10) must be added the contribution of ever present magnetic impurities which may be

important. For instance /II/, for c ppm of ?In in Cu far from the Kondo regime (T >> TK 2 mK or B >>

kBTK/pB)

[ T ~- l ~= ~2.5 ~x

lo-"

J _(s) Ba

The evolution with time of the magnetization, linked to the nuclear temperature T by equation (3), is governed by

since the equilibrium value of T is the electron temperature. Since the nuclear enthalpy, given by equation (8), also varies as 1/T the rate of ab-

n'

sorption of energy at fixed field is simply derived from equation ( 12) :

This energy flow is supplied by the electronic system at temperature T to the nuclear system at temperature T

.

It is clearly an extensive quantity as the presence of V indicates explicity'and depends on the intrinsic properties of the refrigerant through the ratio of the Curie constant A to the Korringa constant K. From this stand point alone, it may be seen from table I that indium is the best material for refrigeration. It has indeed been used as such by 0 . G Symko 1121. However, we shall see that other physical parameters are of importance, including the heat conductivity K : this gives the preference to copper.

To see how these other factors enter, let us take two facts into account. Firstly the nuclear stage must be used to cool 3 ~ e . Secondly, there are unavoidable heat leaks both to the stage itself and to the 3 ~ e sample. We shall consider the simplified

model shown in figure 1 . The nuclear spins are lum- ped into one thermal bath with temperature Tn and heat capacity Cn, linked solely to the electron bath

(Te, C ) through a thermal resistance given by equa- tion (13). The conduction electrons receive a heat

Tn S n

Te .ce

^The

he

nuclei el ec. 3 ~ e

T

Fig. 1 : Schematized nuclear stage.

leak Qe, either directly by eddy current heating or through the phonon bath. Although phonons and elec- trons are rather loosely coupled 1131, it is to be expected that most of the heat flowing to the latti- ce will not be reemitted and will end up in the elec- tronic system. The 3 ~ e sa~.ple (THe, CHe) is linked to the electron bath through a resistance RK+q and also recieves a heat input QHe. The thermal resis- tnace RK+R contains two parts, which will be discus- sed later, an interfacial resistance between 3 ~ e and the metal and a bulk resistance of the electrons to heat transport. These resistances both vary as 1/T and can be combined together. The flow of energy between the 3 ~ e bath and the conduction electrons obeys the equation :

From eq. (Z), ( 6 ) , (13) and (14), the evolu- tions of the temperaLures T Te and THe are easily

n'

seen to be governed by the following set of equa- tions :

dTn T - T A V B dB

= C

e n .

n d t n K T- dt (15)

The full solution of this set of non-linear coupled differential equations, as well as those of more sophisticated models /14,15/ may be obtained

numerically on a computer.

QUASI-STATIONARY SOLIJTION : THE IMPORTANT P A M T E R S

.-

However, in order to discern the basic features of operation of a nuclear stage, it suffices to

C6-1608 JOURNAL DE PHYSIQUE

consider t h e q u a s i - s t a t i o n a r y s t a t e obtained a f t e r

(jHe/~K+R

i n eq. (18) becomes t h e dominant term well t h e a p p l i e d f i e l d has been lowered t o B f . The source b e f o r e Ba i s reduced t o v a l u e s comparable t o B _m ^: term dBa/dt i s t h e n zero. Since C i s by f a r t h e t h e performances of a n u c l e a r r e f r i g e r a t o r used t o

n

l a r g e s t h e a t c a p a c i t y i n t h e system, t h e most s i g n i - cool 3 ~ e depend p r i m a r i l y on t h e h e a t l e a k reaching f i c a n t time d e r i v a t i v e i s t h a t of Tn. Neglecting t h e sample and on t h e thermal c o n t a c t t o t h e n u c l e a r t h e o t h e r time d e r i v a t i v e s , we o b t a i n t h e following s t a g e .

n

q u a s i - s t a t i o n a r y s o l u t i o n : The r e c i p e e f o r a s u c c e s s f u l machine i s simple enough : i n c r e a s e A and reduce QHe. Also according ( I 8 ) t o e q u a t i o n ( 9 ) , t h e q u a n t i t y K+R AV B ~ / T ? should be

made adequately l a r g e a s i t governs t h e time during which t h e n u c l e a r s t a g e w i l l s t a y cold. The b e s t way (19) t o i n c r e a s e t h e magnetic energy of a superconducting

magnet i s , a t p r e s e n t , t o i n c r e a s e i t s s i z e . The

These r e l a t i o n s e x p r e s s two simple r e s u l t s : 1) The t o t a l thermal l e a k 'e +

GHe

i s absorbed by t h e n u c l e a r s p i n s which c o n s t i t u t e t h e h e a t s i n k . 2) I n o r d e r t o minimize THe, which i s t h e u l t i m a t e g o a l , b o t h T e and 4 H e / ~ K + R a r e t o be minimized.

The minimum of T i s not obtained f o r B f % O s i n c e i n t h i s l i m i t t h e energy absorbed by t h e r e a r - rangement of t h e Zeeman s u b - l e v e l s a l s o becomes ve-

p r e c o o l i n g temperature T . can be lowered s i g n i f i c a n - t l y below i t s p r e s e n t t y p i c a l v a l u e of 15 mK, down t o 7 mK /16/ o r even lower w i t h improved d i l u t i o n r e f r i g e r a t o r s and h e a t switches. I n a l l , a ten-fold improvement on AV B ? / T ? i s f e a s i b l e b u t , a g a i n , t h i s

1 1

w i l l not n e c e s s a r i l y mean t h a t lower helium tempera- t u r e s w i l l be reached.

Let u s now t u r n t o t h e problem of thermal con- t a c t and i n s u l a t i o n a t u l t r a l o w temperature.

r y s m a l l . D i f f e r e n t i a t i n g e q u a t i o n (19) l e a d s t o t h e

optimum v a l u e s of t h e f i e l d and of t h e e l e c t r o n tem- THERMAL CONTACT.- The t h r e e items of importance f o r p e r a t u r e

Bm

=b

^{(Ge + + b y 2 ,} thermal c o n t a c t a r e :

(20) 1) t h e h e a t p a t h between t h e " a c t i v e " s p i n r e s e r v o i r and t h e h e a t exchanger,

( 2 1 )

2) t h e thermal boundary r e s i s t a n c e between 3He and P u t t i n g t y p i c a l numerical v a l u e s f o r copper t h e m e t a l ,

n u c l e a r s t a g e s , summarized i n t a b l e 11, i n t o equa- 3 ) t h e h e a t c o n d u c t i v i t y w i t h i n t h e l i q u i d .

t i o n s (20) and (21) l e a d s t o optimum f i e l d s of a few By c a r e f u l d e s i g n of t h e h e a t path i n t h e cop- mT and e l e c t r o n i c temperatures of 10-20 11K. The term p e r , i t i s p o s s i b l e (and, a s computation shows, ad-

Table 11

Table I1 : C h a r a c t e r i s t i c s of some n u c l e a r r e f r i g e r a t o r s .

visable) to achieve values of RR smaller than 10/T in [K/w]

.

The electrical resistance RE which cor- responds to RR is given by the Wiedemann-Franz law :

RE = 2.3 x

lo-'

S T

cn1

(22)

A rule of thumb

/g/

is thus to keep

%

^{to a}

quarter of a micro-ohm or below. Such low values can be achieved for mechanical connections /21,22/.

The nuclear stage bundle has to be built with high resistivity ratio (RRR between 300 and 4.2 K) copper wires, since it acts as a heat sink for the total heat load (equations (18) is somewhat oversimplified in this respect). By suitable selection of techni- cal quality copper wire and hea: treatment to 800 K, RRR's of 700 can be obtained /17/. The situation in the sintered material and in the various joints may not be as favourable.

Thc thermal boundary resistance, o r Kapitza resistance, between 3 ~ e and the sintered metal heat exchanger is an even more serious problem. The heat transfer coefficient at the interface is defined as :

hK =

a/

^{A AT}

^,

₍₂₃₎

where Q/A is the power per unit area giving rise to the temperature difference AT. Measured values of h in Pd, Au, Ag, Cu in contact with pure 3 ~ e in the

K

normal Fermi liquid state at low pressure have been collected in figure 2. The high temperature behaviour

Fig. 2 : Boundary heat transfer coefficient versus temperature for Pd, Au, Cu /30/ and Ag 1311.

of hK is the well-established ~ ~ - 1 a w /23/ (50 T~ for Cu, 23 T~ for Au and Ag in W m-'K-'). The low tempe- rature behaviour, as displayed in figure 2, is pro-

portional to T (1.6 x T for Cu, 4.5 x 10-3 T for Ag, 8.2 x T for Au in W m - 2 ~ - 1 . The case of Pd is more complicated). This linear dependence of hK on T is supported by direct measurements of RK+R /3,4,17,18/ on Cu and Ag heat exchanger down to 0.4 mK but it has not been found on Pt wires /24/

nor on Pd heat exchangers / 1 9 / in the superfluid regime. It is interesting to note that, as a first approximation, h /T varies from a metal to another

K

as the electronic Pauli susceptibility, and also that magnetic impurities do not seem to play the crucial rsle that they were once supposed to play.

As can be seen from the numerical values in table 2, the Kapitza resistance is the major obsta- cle for cooling 3 ~ e . Since the amount of liquid which can be cooled is not so stringently restricted,

the best way to partially circumvent this problem is to increase the size of heat exchangers. One may also consider using even more finely divided sinte- red powders. But then, questions must be asked about size effects both in the metal and in the liquid.

Let us leave aside the metal, which is in the form of a sponge and therefore semi-bulky, and take a closer look at the superfluid liquid.

The mean free path of the normal quasi-parti- cles can be derived, in the low temperature limit, from measurements of the longitudinal ringing time /25/ and is plotted as a function of 1/T at various pressures in figure 3. The conduction of heat by

T [ m ~ ]

1 0.7 0.5

0.4

0.3

2

- _E

10

2

I ri -Iv

1 c 2

Fig. 3 : 3 ~ e quasi-particle mean free path (plain line) and characteristic leneth for heat exchange L (dotted line) versus 1/T at various pressures.

fie

arrows mark the base temperatures obtained at Orsay.

C6-1610 JOURNAL DE PHYSIQUE

t h e l i q u i d c o n t a i n e d i n t h e s i n t e r e d powder i s li- mited by s c a t t e r i n g of t h e q u a s i - p a r t i c l e s on t h e w a l l s . Using t h e s i m p l e a p p r o a c h t o t h e low tempe- r a t u r e d i y s i p a t i v e p r o c e s s e s i n s u p e r f l u i d 3 ~ e de- r i v e d by P e t h i c k and Smith 1261, t h i s boundary-limi- t e d h e a t c o n d u c t i v i t y K~ c a n b e e a s i l y e v a l u a t e d i n a powder of mean d i a m e t e r d . It may be s e e n , by w r i t i n g t h e h e a t p r o p a g a t i o n e q u a t i o n i n t h e s i n t e - r e d powder t h a t , f o r f u l l e f f i c i e n c y , t h e s i z e o f t h e h e a t exchanger must be comparable t o o r s m a l l e r t h a n a c h a r a c t e r i s t i c l e n g t h d e f i n e d a s

E s t i m a t e s o f L a t v a r i o u s p r e s s u r e s w i t h d = 2 p, f o r a copper a t exchanger (hK = 1.6 x 1 o - ~ T ) a r e p l o t t e d i n f i g u r e 3 , a s w e l l a s t h e b a s e tempe- r a t u r e s o b t a i n e d i n t h e Orsay machine. We may con- c l u d e t h a t s i z e e f f e c t s a r e p r o b a b l y r e d u c i n g t h e e f f i c i e n c y of o u r h e a t exchangers a t t h e l o w e s t tem- p e r a t u r e s .

HEAT LEAKS.- I f h e a t exchange i s much impeded a t u l t r a l o w t e m p e r a t u r e s , a s s e e n i n f i g u r e 2 , i t might b e e x p e c t e d , a s a c o r o l l a r y , t h a t h e a t i n s u l a t i o n i s improved.

I n a way, t h i s i s indeed s o , a s shown i n f i g u r e 4 where r e c e n t l y measured thermal c o n d u c t i v i t i e s of p o o r l y c o n d u c t i n g m a t e r i a l s have been c o l l e c t e d . It may be e x p e c t e d t h a t t h e s e measurements, c a r r i e d o u t around 100 mK, c a n b e e x t r a p o l a t e d down t o 1 mK : t h e c o n d u c t i o n t h r o u g h s u p p o r t s i s a n e g l i g i b l e f r a c t i o n o f t h e t o t a l h e a t l e a k . What may n o t be e x p e c t e d , however, i s t h a t t h e K a p i t z a h e a t t r a n s - f e r c o e f f i c i e n t h between p u r e 3 ~ e and t h e epoxy

K

w a l l s , which i s about 250 T~ (W m-2~-1) above 20- 30 mK e x t r a p o l a t e s down t o 1 mK. It i s known 1271 t h a t t h e CMN- 3 ~ e boundary r e s i s t a n c e becomes ano- malously low a t u l t r a l o w t e m p e r a t u r e . The odds a r e t h a t a s i m i l a r phenomenon o c c u r s w i t h o t h e r ( n o t n e c e s s a r i l y paramagnetic) m a t e r i a l s and t h a t most of t h e h e a t r e a c h i n g t h e p l a s t i c body of t h e c e l l o r g e n e r a t e d i n i t e v e n t u a l l y ends up i n t h e 3 ~ e sample.

The e x p e r i m e n t a l f a c t s a b o u t h e a t l e a k s a r e t h e f o l l o w i n g s :

-

The observed s t r a y h e a t i n p u t s a r e l a r g e r t h a n e x p e c t e d and c a n n o t , i n g e n e r a l , b e e x p l a i n e d by v i b r a t i o n s , r e s i d u a l exchange g a s , e l e c t r i c a l pick-up, h e a t c o n d u c t i o n through s u p p o r t s , p r e s -

s u r e changes i n t h e f i l l l i n e ,

...,

a l t h o u g h i t i s n o t always e a s y t o have good c o n t r o l of a l l t h e s e f a c t o r s .

F i g . 4 : Heat c o n d u c t i v i t y v e r s u s t e m p e r a t u r e f o r some r e c e n t l y s t u d i e d p o o r l y c o n d u c t i n g m a t e r i a l s :

( 1 ) A1 f o i l , 0.1 mm t h i c k , 5 N p u r i t y i n t h e super- c o n d u c t i n g s t a t e /23/ ; (2) S i l v e r f i l l e d epoxy /32/

(3) S t y c a s t 1266 /35/ ; (4) - S i n t e r e d A1 0 w i t h den- 2 3

s i t y 3.4 /34/ ; (5) N u c l e a r g r a d e g r a p h i t e /34/ ; ( 6 ) Polyimid r e s i n loaded w i t h g r a p h i t e (Dupond Ves- p e l SP 22) / 3 4 / . (7) AGOT g r a p h i t e 1331.

- O f t e n , t h e s e h e a t l e a k s depend on t i m e w i t h t i m e c o n s t a n t s which v a r y from s e v e r a l h o u r s t o seve- r a l weeks. There a r e converging p i e c e s of eviden- c e t h a t some h e a t e v o l v e s from t h e o r g a n i c mate- r i a l s used i n t h e c o n s t r u c t i o n o f t h e n u c l e a t s t a g e 1281 (enamel, e p o x i e s , bonding a g e n t s ,

...

⁾

It may o c c u r t h a t t h e r e s i d u a l e n t r o p y o f t h e s e amorphous s u b s t a n c e s d e c a y s w i t h time through pho- n o n - a s s i s t e d t u n n e l l i n g between a d j a c e n t energy s t a t e s . These p r o c e s s e s a r e a l r e a d y known t o b e r e s p o n s i b l e f o r t h e i r r a t h e r l a r g e anomalous spe- c i f i c h e a t ( t y p i c a l l y 5 x TI ' 3 i n W C ~ - ~ K - ' f o r v i t r e o u s S i 0 2 ) . The i n t e r n a l g e n e r a t i o n of h e a t may a l s o be caused by t h e r e l e a s e of m e c h a n i c a l

s t r a i n s . Yet a n o t h e r s o u r c e o f time-dependent

h e a t l e a k comes from t h e n u c l e a r h e a t c a p a c i t y of ACKNOWLEDGEMENTS.- The a u t h o r i s d e e p l y i n d e b t e d t h e epoxy. A t y p i c a l epoxy c o n t a i n s one mole of t o h i s c o l l e a g u e s f o r t h e i r h e l p and c o l l a b o r a t i o n , p r o t o n s p e r 15 cm3 and h a s a l a r g e C u r i e c o n s t a n t and more p a r t i c u l a r l y t o O l i v i e r Avenel and P e t e r

(Table I ) . The observed thermal r e l a x a t i o n t i m e Berglund who have had t h e main r e s p o n s i b i l i t i e s i n of mylar a f t e r a change of t h e a p p l i e d magnetic t h e n u c l e a r s t a g e c o n s t r u c t i o n .

f i e l d i s 2 t o 3 hours.

THERMOMETRY.- The t o p i c of thermometry i s o f funda- mental importance and would w e l l d e s e r v e s a f u l l -

l e n g t h d i s c u s s i o n . It was l a s t reviewed by Richard- son 1291. Some p r o g r e s s have been made on NMR t h e r - mometry r e c e n t l y w i t h t h e o b s e r v a t i o n by Avenel e t a 1 1171 t h a t t h e Korringa law i n P t e x h i b i t s a n ano- maly below 3 mK. S i m i l a r anomalies i n s i m i l a r P t

samples have a l s o been r e p o r t e d by o t h e r groups 1 1 4 , 301. Taking t h i s anomaly i n t o account and t h e f a c t t h e C u r i e law is a c c u r a t e l y f o l l o w e d , t h e s u p e r f l u i d t r a n s i t i o n t e m p e r a t u r e s T have been measured a t d i f f e r e n t p r e s s u r e s , u s i n g t h e t r a n s v e r s e NMR f e a -

t u r e s a s i n d i c a t o r s o r t h e t r a n s i t i o n . The c u r v e T (P) t h u s o b t a i n e d i s p l o t t e d i n f i g u r e 5 t o g e t h e r w i t h t h o s e of o t h e r l a b o r a t o r i e s . The most r e c e n t measurements seem t o a g r e e w e l l and d e f i n e a t r a n -

s i t i o n l i n e t o 2 t o 3 %.

Fig. 5 : rans sit ion t e m p e r a t u r e i n 3 ~ e v e r s u s p r e s - s u r e :

---

r e f . ( 1 8 ) ,

-

r e f . 1361, Ic, r e f . 1371, o, r e f . 1171.

JOURNAL DE PHYSIQUE

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