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RESEARCHAND TECHNICALNOTES

T h is p a p e r r e p o r t s o n t h e m e a s u r e m e n t o f t h e s p e ci fi c h e a t o f W a k e f i e l d t h e r m a l

c o m p o u n d f r o m 2 4 0 K

S p e c ific h e a t o f W a k e f i e ld t h e r m a l c o m p o u n d

f r o m 2 t o 4 0 K

J. Sc ott Pa y son a nd L .E. We nge r

K e y w o r d s : s p e c i fi c h e a t ; W a k e f i e l d t h e r m a l c o m p o u n d ; t h e r m a l g r ea s e

Thermal greases are extensively used in this and other

laboratories to thermally anchor samples to substrates.

Using the same substrate repeatedly and knowing the heat

capacity of both the substrate and grease allows for

corrections to the measured heat capacity.

The specific heat of one type of thermal grease, Wakefield

thermal compound, 1 has been previously reported by

Bachmann, et al. 2 and Schwall 3 in the temperature range

of 1 to 10 K. More recently Cort and Naugle 4 have reported

on measurements from 20 to 100 K. In order to close the

gap between 10 and 20 K of these previous measurements,

we have measured the heat capacity of the Wakefield grease

between 2 and 40 K using an adiabatic heat-pulse method , s

An argon annealed copper (OFHC) cup was used as a

sample holder for the grease. The heat capacity of the

empty copper cup and substrate was first measured, then

i 00

T

Fig. 1

4 0 K

iO- I

10-2

10-3

10-4

10-5

0

e e e S

O 0

eX oX X

ii X IKo

o OX= oXQ

tX e

This work

Schwall

Bachmann etal

x Cort and

Nougle

I0 20 30 40

Temperoture, K

Specific heat of

W a k e f i e l d t h e r m a l

compound from 2 to

T h e a u t h o r s a r e a t th e D e p a r t m e n t o f P h y s ic s W a y n e S t a te

U n i v e r s i t y D e t r o i t , M I 4 8 2 0 2 U S A . T h i s r e s e a r c h is s u p p o r t e d i n

p a r t b y t h e N a t i o n a l S c i en c e F o u n d a t i o n ( D M R 7 9 2 1 2 9 8 ) a n d t h e

A l f r e d P . S l o a n R e s e a rc h F o u n d a t i o n . P a p e r re c e i v ed 2 3 J u l y 1 9 8 1 .

3E

0.8

o

S

.6 . , ~

/ .

0.4

X This wor k

V Schwall

y achmon n t l

0 .2 / C = 0 01 46 T 3

/

o I I I I I [

0 I 0 2 0 3 0 4 0 5 0 6 0

Tem perature 2 K2

F i g. 2 S p e c i f i c h e a t o f W a k e f i e ld t h e r m a l c o m p o u n d f r o m 2 t o

7 K p l o t te d a s C/T vs T 2

70

remeasured after adding 2 g of grease. Thus the dif-

ference in these two measurements is due to the heat

capacity of the grease. The specific heat results for the

Wakefield grease are shown in Figs 1 and 2 as well as the

previously reported results. An overall accuracy of 1 is

estimated at the lowest temperatures increasing to 2 at

the highest temperatures. The heat capacity of the grease

represents 40 of the total heat capacity at 4 K and 20

of the total at 40 K.

In comparison to the prior results on the Wakefield thermal

compound, our results are ~ 10 above Bachmann, et al

and ~ 10 below those of Schwall, who suggests that this

difference may arise from di fferent amounts of binder. 6

Above 25 K, our results are in excellent agreement with

those of Cort and Naugle although below 25 K these latest

results are slightly higher and outside the exper imenta l

error. Note also at the lowest temperatures in Fig. 2 that

the specific heat still follows a T 3 temperature dependence

with no observable linear temperature dependence as is

typical of most amorphous systems at very low temperatures. 7

4 4 C R Y O G E N I C S . J A N U A R Y 1 9 82

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T h e p r e s e n t d a t a b e t w e e n 2 a n d 4 0 K h av e b e e n r e p r e s e n t e d

b y l e a s t s q u a r e s f i t ti n g t h e f o l l o w i n g p o l y n o m i a l ,

C p = Z a n t n m J g - 1 K - X ,

? 1 = 3

w h e r e a 3 = 6 . 7 0 6 4 0 x 1 0 - 3 , a 4 = 5 . 1 5 0 7 2 x 1 0 - 3 ,

a s = - 1 . 0 9 7 4 5 x 1 0 - 3 , a 6 = 1 . 0 1 1 8 7 x 1 0 - 4 ,

a 7 = - 5 . 1 3 2 3 3 x 1 0 - 6 , a 8 = 1 . 4 9 0 7 8 x 1 0 - 7 ,

a 9 =

--

2 . 3 7 9 5 0 x i 0 - 9 , a l o = 1 . 6 9 2 9 4 x 1 0 -1 1 . T h e

a v e r a g e d e v i a t i o n i s a p p r o x i m a t e l y 1 .3 , w e l l w i t h i n t h e

e x p e r i m e n t a l e r r o r .

R e f e r e n c e s

1 Wake f ie ld Engineer ing Co . , Wake f ie ld, Mass . 01 880 . The

t h e r m a l g r e a se i s p a r t N o . 1 2 0 - 2

2 B ae h m a n n R . D i S a l vo F . J . Jr . G e b a l l e T . H . G r e e n e R . L .

H o w a r d R . E . K i n g C . N . K i r s e h H . C . L e e K . N . S e h w a l l

R.E., Thom as, H.U., Zub ee k, R.B. Rev Sei [nstr 43 (1972)

2O5

3 S c h w a B ,R.E. Ph.D. thes is (S tanford, 1973)) ) , unpubl ished

4 Co r t , B. , Naugle , D.G. Cryogenics 21 (1981) 313

5 P a y s o n , J . S . , M . S . t h e si s ( W a y n e S t a t e , 1 9 8 1 ), u n p u b l is h e d

6 I n t h e p r e s e n t i n v e st ig a t io n , t h e r m a l c o m p o u n d u s e d d i r e c t l y

f ro m c o n t a i n e r w i th n o b i n d e r

7 Ze l le r , R.C., Pohl , R.O .

Phys Rev

B 4 (1971) 2029;

S t e p h e n s

R . B . , P h y s

Rev

B 8 (1973) 2896

The p resence o f a f ew t en t hs mo l he f i um i n hyd roge n causes anom a l ous vapour p ressu res

as h igh as 10 kPa. This ef fect i s caused by the com bina t ion o f a sma l l co ld ce l l , a s ing le,

l ong f i l l t ube , and t he i nso l ub i l i t y o f he l i um i n l i qu i d hyd rogen . Th i s e f f ec t i s i mp or t a n t

i n t he hand l i ng o f de u t e r i u m- t r i t i um , as rad i oac t ive decay p roduces He 3.

A n o m a l o u s v a p o u r p r e s s u re o v e r l iq u id D - T

P . C l a rk S o ue rs E . M . F e a ro n R . K . S t u m p a n d R . T . T s u g a w a

Key w ords: cryogen ic; deuterium - tritium ; vapour pressure

C r y o g e n i c d e u t e r i u m - t r i t in m ( D - T ) i s o f i n t e r e s t a s a

p o s s i b l e f u e l f o r m a g n e t i c o r i n e r t i a l c o n f i n e m e n t f u s i o n .

C r y o g e n i c D - T w o r k : is b e d e v i l e d b y l i q u i d v a p o u r p r e s s u r e s

t h a t a re h i g h e r th a n e x p e c t e d f r o m t h e s e n s o r t e m p e r a t u r e s .

T h is is a t t r i b u t e d t o e i t h e r t e m p e r a t u r e g r a d ie n t s o r t o

e x c e s s H e 3, t h e d a u g h t e r f o r m e d b y t r i t i u m d e c a y ) T h i s i s

a c c o m p a n i e d b y a H e 3 b l o c k i n g e f f e c t , w h i ch i m p e d e s t h e

l o a d i n g o f t h e c r y o g e n i c c e l l w i th D - T . 2

T h e a p p a r a t u s c o n s is ts o f a r o o m t e m p e r a t u r e g a s s to r a g e

v e s se l a n d a c o l d c e l l c o n n e c t e d b y a l o n g , t h in t u b e . T h e

s t o r a g e v e s s e l h a s a v o l u m e o f a b o u t 1 7 0 0 / ~ m 3 a n d i t s

t e m p e r a t u r e T t i s 2 9 6 t o 2 9 9 K , -+ 0 . 5 K i n a n y g i v e n r u n .

A b a r a tr o n i s m o u n t e d n e x t t o t h e v e s se l t o m e a s u re t h e

s y s t e m p r e s s u r e . T h e s a m p l e c e l l i s s m a l l , w i t h a v o l u m e

V c o f 0 . 3 7 1 / ~ m 3. A g e r m a n i u m s e n s o r , m o u n t e d i n si d e

t h e c o p p e r w a l l o f t h e s a m p l e c e l l, m e a s u r e s t h e t e m p e r a -

t u r e T e , w h i c h i s s e t b e t w e e n 1 9 a n d 2 1 K , + 0 . 0 5 K . T h e

c o n n e c t i n g t u b e h a s a n a v e r a g e in t e r n a l c r o s s se c t i o n a l

a r e a o f 1 . 2 x 1 0 - s m s , a n d i t s l e n g t h v a r i e s f r o m 1 . 7 t o

4 . 5 m . C a l i b r a t io n w i t h H e 3 s h o w s t h a t t h e c o l d t e m p e r a -

t u r e e x t e n d s a b o u t 3 5 m m u p t h e c o n n e c t i n g t u b e . T h e

a p p a r a t u s i s a ll st a in l e s s s t e e l e x c e p t f o r t h e s a m p l e c e l l ,

w h i c h i s c o p p e r a n d K o v a r , w i t h s a p p h i r e v i e w i n g p o r t s .

T h e t e m p e r a t u r e a n d p r e s su r e c a l i b ra t io n h a v e b e e n

p r e v i o u s l y d e s c r i b e d . 2 T h e H 2 a n d D 2 s a m p l e s h a v e k n o w n

q u a n t it ie s o f H e 3 a d d e d ; t h e D - T i s s t o r e d u n t i l t h e d e s i r e d

a m o u n t o f H e 3 is p r e s e n t ( p r o d u c t i o n r a te 0 . 0 1 5 t o o l

The authors are wit h the Lawrence Live rmore National L abor ator y,

Livermore, California 94550, USA. This work was performed under

the auspices of the US Department of Energy under contract

W-7405-Eng-48. Paper received 31 July 1981.

( d a y m o l T ) - I ) . A f t e r e a c h r u n , t h e m i x t u r e i s a n a l y z e d

w i t h a h i gh r e s o l u t i o n m a g n e t ic s e c t o r m a s s s p e c t r o m e t e r .

T h e g a s m i x t u r e i s a d m i t t e d a t 4 0 P a a n d t h e p r e s s u r e

m e a s u r e d b y t h e s p e c t r o m e t e r . T h e h y d r o g e n i s t h e n

r e m o v e d b y a t it a n i u m s u b l im a t i o n p u m p t o a b o u t 0 . 1 P a .

T h e p r e s s u r e o f th e r e m a i n i n g H e 3 i s m e a s u r e d b y t h e m a s s

s p e c t r o m e t e r , w h i c h h a s b e e n c a l ib r a t e d w i th a H e 3

s t a n d a r d . 3 W e e s t i m a t e t h e a c c u r a c y i n d e t e r m i n i n g t h e

a m o u n t o f H e 3 t o b e -+ 1 0 .

T h e s a m p l e g a s i s l o a d e d i n t o t h e s t o r a g e v e s s e l w i t h t h e

v a lv e c lo s e d , a n d t h e r e s t o f t h e s y s t e m i s c o o l e d a n d

e v a c u a t e d . T h e a m o u n t o f s a m p l e g a s i s s e t so t h a t , a t

e v e n t u a l e q u i l i b r i u m , t h e c e l l w i l l b e f i ll e d to t h e t o p

w i t h l i q u i d h y d r o g e n . T h e a p p r o p r i a t e l i q u i d d e n s i ti e s 1

a n d s a t u ra t i o n v a p o u r p r e s s ur e s 4 a r e r e q u i re d , a n d r o o m

t e m p e r a t u r e c h e m i c a l e q u i l ib r i u m i s as s u m e d .

A t t i m e z e r o , t h e v a l v e is e i t h e r f u l l y o r s l i g h tl y o p e n e d .

T h e g a s f l o w s t o t h e c e l l a n d l i q u e f i e s . W i t h t h e v a l v e f u ll y

o p e n a t t i m e z e r o , t h e s e n s o r t e m p e r a t u r e r is e s 0 . 3 t o

0 . 8 K a s t h e h e a t o f l iq u e f a c t i o n i s re l e a s e d . I t s t a b il i z e s

e x p o n e n t i a ll y w i t h a ti m e c o n s t a n t o f a b o u t 0 . 8 s . W h e n

t h e v a lv e is b a r e l y o p e n e d , t h e o b s e r v e d t e m p e r a t u r e r is e

i s 0 . 0 7 t o 0 . 1 4 K .

T h e r e s u l t s o f se v e r a l H e 3 - D 2 ru n s a r e s h o w n i n F i g . 1 . T h e

e x c e s s p r e s su r e is t h e p r e s s u r e a b o v e t h e e x p e c t e d 2 0 K

s a t u r a t i o n v a l u e . T h e p u r e D 2 p r e s s u re ( 0 H e 3 ) d r o p s a s

q u i c k l y as th e c r y o s t a t c a n r e m o v e t h e h e a t o f li q u e f a c t io n .

T h e p r e s s u re s o f th e o t h e r s a m p l e s le v e l o f f a t h ig h e r

p r e s su r e s w h i c h a r e p r o p o r t i o n a l t o t h e a m o u n t o f H e 3

i n i t ia l l y p r e s e n t . W e e x t r a p o l a t e e a c h p r e s s u r e p l a t e a u b a c k

t o t i m e z e r o t o o b t a i n t h e p r e s s u r e P e x . T h i s p l a t e a u

CRYOGENICS . JANUARY 1982 45