SURFACE MAGNETIC RELAXATION - RELATION TO 3He↑ EXPERIMENTS

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SURFACE MAGNETIC RELAXATION - RELATION TO 3He ↑ EXPERIMENTS

H. Godfrin, G. Frossati, B. Hebral, D. Thoulouze

To cite this version:

H. Godfrin, G. Frossati, B. Hebral, D. Thoulouze. SURFACE MAGNETIC RELAXATION - RELA- TION TO 3He ↑ EXPERIMENTS. Journal de Physique Colloques, 1980, 41 (C7), pp.C7-275-C7-280.

�10.1051/jphyscol:1980742�. �jpa-00220180�

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JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n o 7, Tome 41, juiZZet 1980, page C 7 - 2 7 5

SURFACE MAGNETIC RELAXATION - RELATION T O

3 ~ e +

EXPERIMENTS

H. Godfrin, G. F r o s s a t i , B. Hebral and D . Thoulouze

Centre de Recherches sup Zes Trds Basses Tempdratures, C.N.R.S., B.P. 166 X 38042 GrenobZe Cedex, France. (Laboratoire associ6 a' Z'U.S.M.G.)

ABSTRACT p o l a r i z e d can b e ob

: Nuclear r e l a x a t i o n a t t h e w a l l s of e x p e r i m e n t a l c e l l s i s an i m p o r t a n t l i f e t i m e l i m i t a t i o n f o r l i q u i d 3 ~ e . However, maximum s p i n - l a t t i c e r e l a x a t i o n times TI ( i . e . t h e i n t r i n s i c v a l u e s TI bu1@

t a i n e d by d i f f u s i o n l i m i t e d r e l a x a t i o n o r boundary l i m i t e d r e l a x a t i o n . We p r e s e n t NMR measurements on l i q u i d 3 ~ e i n c o n f i n e d g e o m e t r i e s , where t h e l a t t e r p r o c e s s i s dominant. C o a t i n g of t h e w a l l s by 2.7 l a y e r s o f 4 ~ e enhances TI and t h e thermal boundary r e s i s t a n c e by a l m o s t two o r d e r s o f magnitude a t low t e m p e r a t u r e s .

RESUME : La durbe de v i e de 3 ~ e + p e u t s t r e l i m i t b e p a r l a r e l a x a t i o n magnbtique s u r l e s p a r o i s d e s c e l l u l e s e x p b r i m e n t a l e s . Les v a l e u r s maximales du temps de r e l a x a t i o n s p i n r g s e a u (TI i n t r i n s s q u e ) peuvent C t r e o b t e n u e s e n l i m i t a n t e n s u r f a c e ou p a r d i f f u s i o n l a r e l a x a t i o n magngtique. Nous p r b s e n t o n s des mesures de RMN s u r 3 ~ e l i q u i d e e n gbombtrie c o n f i n g e , 02 l a r e l a x a t i o n e s t l i m i t b e e n s u r f a c e . Lorsque l e s s u r f a c e s s o n t r e c o u v e r t e s p a r 2.7 couches de 4He, l e temps de r e l a x a t i o n T I e t l a r g s i s t a n c e de K a p i t z a s o n t augmen- t b e s d ' e n v i r o n deux o r d r e s de grandeur 5 t r S s b a s s e s t e m p b r a t u r e s .

P o l a r i z e d l i q u i d 3 ~ e ( 3 He+) h a s been s t u d i e d The Pomeranchuk method r e q u i r e s p r e c o o l i n g of

t h e o r e t i c a l l y by C. L h u i l l i e r and F. ~ a l o ~ ( ' ) and l i q u i d 3 ~ e ; t h e p o l a r i z a t i o n of t h e s o l i d 3 He C a s t a i n g and N o z i ~ r e s ' ~ ) . Experimental o b s e r v a t i o n o b t a i n e d by compression s h o u l d o n l y depend on t h e of 3 ~ e + was s u b s e q u e n t l y r e p o r t e d by two groups, a t i n i t i a l t e m p e r a t u r e of t h e l i q u i d and on t h e rnagne-

ren noble'^)

and ~ o p e n h a ~ e n ( ~ ) , u s i n g t h e "thermody- t i c f i e l d . However, we have found t h a t h i g h f i e l d narnical t e c h n i q u e t t , (2) w i t h maximum p o l a r i z a t i o n s Pomeranchuk compressions can b e h i g h l y i r r e v e r s i b l e , i n t h e range 10 t o 20 %. F u r t h e r s t u d i e s of 3 ~ e + t h e e f f e c t i v e c o o l i n g power b e i n g v e r y s m a l l ( 5 ) . 1t r e q u i r e h i g h e r p o l a r i z a t i o n s , and hence h i g h l y i s t h e r e f o r e c o n v e n i e n t t o p r e c o o l t h e l i q u i d t o p o l a r i z e d s o l i d 3 ~ e , t h a t c a n b e produced by two t e m p e r a t u r e s below 5 mK ( i n f i e l d s above 3 T) ; methods : d i r e c t c o o l i n g i n a r i g i d o r a g a i n , t h i s r e q u i r e s a l a r g e exchange a r e a which

Pomeranchuck c o o l i n g (4)

.

may s h o r t e n T i .

The f i r s t method i s l i m i t e d by t h e time cons-

-

t a n t f o r c o o l i n g : t h e h e a t c a p a c i t y of s o l i d 3 ~ e

-

i n a magnetic f i e l d i s l a r g e a n d roughly propor-

-

t i o n a l t o (HIT) 2 ( t h e exchange h e a t c a p a c i t y ( J / T ) 2

-

i s s m a l l e r f o r f i e l d s > 2T) and t h e thermal r e s i s -

t a n c e i s l a r g e f o r t h e s m a l l e x c h a n s a r e a s used.

-

Minimum t e m p e r a t u r e s o f 20 mK a t 7 T have b e e n o b t a i n e d ( 3 ) ; t o improve t h e c o o l i n g , a l a r g e r h e a t exchange s u r f a c e would b e needed, b u t t h i s should

-

3

-2

reduce t h e l i f e t i m e o f He+, t h e s p i n - l a t t i c e

2 I ( . .05.1 .2 .5 1 T [Kl-

-

¹ ¹ ^I I I ,

r e l a x a t i o n time T

1 ' FIGURE 1 : Spin d i f f u s i o n c o e f f i c i e n t of l i q u i d

3 ~ e vs t e m p e r a t u r e ( s e e t e x t ) .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980742

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JOURNAL DE PHYSIQUE

We examine h e r e t h e r e l a x a t i o n processes i n 3He, s e p a r a t i n g t h e bulk and s u r f a c e c o n t r i b u t i o n s , and t h e i n f l u e n c e of t h e l a t t e r on t h e h e a t t r a n s f e r .

I n bulk l i q u i d 3 ~ e , s p i n - l a t t i c e r e l a x a t i o n i s due t o t h e modulation of t h e d i p o l a r i n t e r a c t i o n by t h e d i f f u s i v e motion of t h e atoms. T I i s thus c l o s e l y r e l a t e d t o t h e s e l f - d i f f u s i o n c o e f f i c i e n t Ds. The s p i n d i f f u s i o n c o e f f i c i e n t D i s e s s e n t i a l l y e q u a l t o Ds : G a m i n and ~ e i c h ' ~ ) have shown t h a t s p i n - s p i n i n t e r a c t i o n s only c o n t r i b u t e

'L 3 x 1 0 - l ~ cm / s t o t h e t o t a l s p i n d i f f u s i o n coef- 2

'L 2

f i c i e n t , Ds > 6 x cm / s .

Accurate measurements of D have been made i n d i f f e r e n t l a b o r a t o r i e s using NMR

technique^'^'^).

For temperatures T <TF(T 'L < 50 mK i n p r a c t i c e ) , where TF i s the Fermi temperature of l i q u i d 3 ~ e ,

t h e Landau theory of Fermi l i q u i d s p r e d i c t s a T -2

temperature dependence, and D i s not e x a c t l y e q u a l t o D s , b u t i s of t h e same o r d e r of m a g n i t ~ d e ' ~ ) . A t h i g h e r temperatures, D i s understood i n terms of t u n n e x n g of 3 ~ e atoms w i t h high z e r o p o i n t energy:

( 6 ) t h e d i f f u s i o n process i s not t h e r m a l l y a c t i v a t e d

.

D p r e s e n t s a minimum a t T 'L . 7 R, and d e c r e a s e s w i t h i n c r e a s i n g p r e s s u r e s ; Fig. 1 shows a r e d u c t i o n of t h e d a t a of r e f . 6 and 7 t o t h e p r e s s u r e s 10 kPa and 2.2. MPa t h a t w i l l be used t o a n a l y s e T I r e s u l t s .

Bloembergen, P u r c e l l and ~ound(')(BPP) t h e o r y , modified by

orr re^'^),

provides t h e following e x p r e s s i o n f o r t h e s p i n l a t t i c e r e l a x a t i o n time due t o themechanismalready d e s c r i b e d :

where n i s t h e number of s p i n s p e r u n i t volume, y t h e gyromagnetic r a t i o , d t h e d i s t a n c e of c l o s e s t approach (atomic diameter)

.

^{A 1}though t h e a p p l i c a b i - l i t y of t h i s formula i s n o t obvious below t h e degeneracy temperature, i t i s p o s s i b l e t o c o n s i d e r

FIGURE 2 : T i n l i q u i d 3 ~ e : BPP t h e o r y ( 8 ) . ~ e f . 1 4 ( d o t t e d l i n e ) .Dashed l i n e s ( 1 6 ) : raw d a t a (lower c u r v e ) , and c o r r e c t e d d a t a (upper c u r v e ) . Grenoble d a t a ( 3 ) a t 3,5T:

0 SVP + 2.2 MPa.

t h e q u a s i - p a r t i c l e s system a s a c l a s s i c a l monoatomic g a s , t h e e f f e c t s of s t a t i s t i c s being included i n a c o r r e l a t i o n time T >> d/vF (vF = t h e Fermi v e l o c i - t y ) , which can b e o b t a i n e d f r o m t r a n s p o r t measurements :

I 4 2

For a monoatomic gas,

-

^'L ((10)

T~ v 2 d 4 T

3 -12 -2 2

With v % vF 2. 5 x 10 cm 5-1 and -cc ^'^l10 T s K (11).

This simple model i s i n agreement w i t h t h e v a l u e s p r e d i c t e d by BPP. Of c o u r s e , a t h i g h e r tempe-

2,

r a t u r e s (T > 1 K), t h e c o r r e l a t i o n time becomes

-

¹²

r a t h e r c o n s t a n t 'l10 s a s t h e mean f r e e p a t h d e c r e a s e s t o t h e value d.

It has been shown e x p e r i m e n t a l l y t h a t t h e w a l l s of t h e 3 ~ e c e l l can provide an e x t r a - r e l a x a t i o n me-

chanism. The longer measured TI v a l u e s a r e those

o f Romer (13)

( I 2 )

,

Gaines, Luszczynski and Worberg

,

and Horvitz(14! T h e i r smoothed d a t a a t s a t u r a t e d vapour p r e s s u r e (SVP) a r e r e p r e s e n t e d i n f i g u r e 2 , a s w e l l a s Grenoble d a t a a t SVP and 2,2 MPa which extend t h e temperature range t o T << TF. The agreement w i t h BPP theory i s s u r p r i s i n g l y good.

Much s h o r t e r r e l a x a t i o n times were found by

d i f f e r e n t groups ; Low and analysed

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t h e measured T I - ' a s t h e sum of a bulk r e l a x a t i o n

-1 Clf'

frequency T , b =

D

and a w a l l r e l a x a t i o n

-

1

T I W = C2D : - I C l P

y1 ⁼

- +

C 2 ~ [ I] i f i s theSHe d e n s i t y ) D

I n t h i s p i c t u r e , r e l a x a t i o n c e n t e r s ( f o r example paramagnetic i m p u r i t i e s ) a r e supposed t o be l o c a t e d a t t h e w a l l s ; t h e s p i n s must d i f f u s e t o t h e w a l l s , where they a r e immediately r e l a x e d . For a s p h e r e of r a d i u s R, t h e d i f f u s i o n time has been c a l c u l a t e d t o

2

( I 5 ) t h e r e f o r e C 2 =

% .

^For^R^e^{1 cm}

be T~ =

-

₂

R

and D 5 r l g 4 c l s - 1 , -rD 5 IOs, which would dominate t h e measured T I . However, t h e e f f i c i e n c y of t h e w a l l f o r s p i n r e l a x a t i o n i s not one, and can depend on p r e s s u r e , temperature, and 4 ~ e c o o l i n g , a s w i l l be e x p l a i n e d l a t e r .

Figure 2 a l s o shows t h e r e s u l t s of r e f . 16 and t h e T l b v a l u e s o b t a i n e d a f t e r c o r r e c t i o n of w a l l e f f e c t s . The agreement w i t h d i r e c t measurements of T i s good. S i m i l a r p l o t s can be o b t a i n e d a t h i g h e r

1

p r e s s u r e s ( P % 2.2 MPa) ; t h e agreement i s even b e t t e r (owing t o a s m a l l e r w a l l c o n t r i b u t i o n ) .

The c o r r e c t i o n s a r e u s u a l l y made p l o t t i n g ( D T ~ ) - ' vs.DT2 : ( D T ~ ) - ' = C ~ D D - '

-

^{C 2} ^;t h e analy- s i s of Grenoble d a t a p r o v i d e s ( f i g u r e 3 ) :

-6 5 -2 -1

C , = ( 2 , 3 i 0 , l ) 10 cm S g and C 2 = (O,5f ~ ) c m - ~ -6 5 -2 -1

a t SVP, and C I = ( 2 , l

'

0 , I ) x l O cm s g

,

- 2

C2 = ( 0

+

^2)cm a t 2.2 MPa. Wall r e l a x a t i o n i s t h u s n e g l i g i b l e , although T D ?. 2s f o r a c e l l w i t h charac- t e r i s t i c d i s t a n c e s % .06 cm, a t temperatures

5 100 mK. Other experiments(17) have shown a l a r g e i n f l u e n c e of s u r f a c e s f o r t h e same c h a r a c t e r i s t i c d i s t a n c e s ; t h e r e l a x a t i o n i s thus not l i m i t e d by t h e d i f f u s i o n time ; i . e . weak s u r f a c e r e l a x a t i o n i s the b o t t l e n e c k f o r T I , and T >> TD.

NMR measurements on 3 ~ e i n confined geometries, dominated by w a l l r e l a x a t i o n , have been performed i n s e v e r a l l a b o r a t o r i e s , on v a r i o u s s u b s t r a t e s :

(19) z e o l i t e ( 1 8 ) , carbon

particle^(^^'^^),

^aluminium

,

a l u m i n a ( 2 1 ) , v i c o r p i a t i n u m ( 2 1 ' 2 3 ) ,

FIGURE 3 : T I i n bulk l i q u i d 3 ~ e a t 2.2 MPa, 3.5 T and v a r i o u s temperatures, a n a l y s e d w i t h formula [ 11 ( s e e t e x t ) .

mylar f o i l s ( 2 4 ) and g r a f ~ i l ( ~ ~ ' ~ ~ ) . Typical s i z e s a r e i n t h e range 50

A -

10 ; measured T l V s a r e i n t h e range - Is ; t h e d i f f u s i o n time T i s <<T

D 1'

T i s approximately l i n e a r w i t h temperature (19,20, 1

21) f o r T 5 < 300 mK, and reaches a maximum a t T 5 .7 K. The temperature dependence i s s i m i l a r t o t h a t of D-I f o r T 'L > 100 mK, i . e . , s i m i l a r t o t h a t of d i f f u s i o n l i m i t e d r e l a x a t i o n ; t h i s e x p l a i n s t h e s u c c e s s of formula [ I ] f o r e l i m i n a t i n g w a l l c o n t r i - b u t i o n s t o T 1 i n experiments a t T 5 1 K.

F i g u r e 4 shows o u r measurements of T of 3 ~ e 1

confined i n 400

A

alumina powder, 8

u

platinum powder and g r a f o i l , a s w e l l a s t h e r e s u l t s of Kelly and ~ i c h a r d s o n ( ' ~ ) i n 90

A

c a r b o l a c p a r t i c l e s .

A d d i t i o n of 4 ~ e i n c r e a s e s T by almost two 1

o r d e r s of magnitude a t low t e m p e r a t u r e s ( 1 9 * 2 1 ) , but t h e e f f e c t i s small above 1 K. It i s known t h a t 4 ~ e w i l l r e p l a c e 3 ~ e a t t h e s u r f a c e s ( 2 6 y 2 7 ) , owing t o

i t s s m a l l e r zero p o i n t motion. K e l l y and Richardson used ?. 7 l a y e r s 4he c o a t i n g ; w i t h 2.7 l a y e r s we o b t a i n e d the same T I enhancementfhat we r e l a t e d t o t h e s u p p r e s s i o n of a s o l i d 3 ~ e l a y e r on t h e w a l l s . Although t h e r e e x i s t some d i s c r e p a n c i e s on t h e number and c h a r a c t e r i s t i c s of t h e adsorbed s o l i d

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JOURNAL DE P H Y S I Q U E

FIGURE 3

4 : Boundary l i m i t e d T1 of He confined i n

-

8 1 ~ - platinum powder ( P ) , alurnina(A) and G r a f o i l (G) w i t h pure t 3 ~ e (Pt3,A3,G3) and w i t h 2.7 l a y e r s of 4 ~ e (Pt3+4,A3+4, G3+4).

C a d C3+4 : Kelly and Richardson d a t a 3

9

f o r He I n c a r b o l a c w i t h pure 3 ~ e and w i t h % 7 l a y e r s of 4 ~ e .

l a y e r s ( 2 0 y 2 1 ' 2 5 ) , i t i s now c l e a r t h a t r e l a x a t i o n occurs a t a few i n t e r a t o m i c d i s t a n c e s from t h e surface.The lower e f f i c i e n c y of 4 ~ e c o a t i n g f o r r e l a x a t i o n a t temperatures 1 K s u g g e s t s t h a t t h e 2d and 3 l a y e r s s h o u l d b e involved. This i s found from t h e d i f f e r e n c e i n b i n d i n g e n e r g i e s f o r 3 ~ e

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and 4 ~ e measured by Thompson. The r e l a x a t i o n , i n t h i s p i c t u r e , depends on t h e p r o b a b i l i t y o f a d s o r p t i o n p e r c o l l i s i o n w i t h t h e w a l l s . Gamin and ~ e i c h ( ~ ) d e f i n e a p r o b a b i l i t y o f r e l a x a t i o n i n a s i n g l e c o l l i s i o n w i t h t h e w a l l s E ; f o r t h e

"boundary limited". r e l a x a t i o n we a r e c o n s i d e r i n g , they e s t i m a t e TI %

2 ^,

^where^Yi s t h e 3 ~ e volune, S t h e s u r f a c e a r e a of t h e w a l l s , v t h e average

v e l o c i t y of t h e p a r t i c l e s ( v % vF below 1 K ) . That i s , TI %

a ,

w i t h a = t h e c h a r a c t e r i c t i c dimen-

EV

s i o n o f t h e 3 ~ e c e l l . T v a l u e s of f i g u r e 4 show 1 t h a t EUT-', E % f o r alumina and g r a f o i l ,

'L 1 0 - ~ f o r P t , and i s f u r t h e r reduced by % 10 2 w i t h t h e 4 ~ e c o a t i n g . I n t h e experimental c e l l of

r e f . 3, a ^'l.5 x cm, and t h e w a l l s a r e covered by 4 ~ e . Assuming t h a t E i we o b t a i n

TI ^'L

-$

^> ^lo3^S^:t h e w a l l c o n t r i b u t i o n t o t h e r e l a x a t i o n i s s m a l l , although t h e d i f f u s i o n time T~

i s much s h o r t e r t h a n T I . The microscopicmechanisms o f r e l a x a t i o n n e a r t h e w a l l s a r e s t i l l t h e s u b j e c t of experimental and t h e o r e t i c a l s t u d i e s ( s e e 28 and r e f e r e n c e s t h e r e i n ) . The l i q u i d - s o l i d exchange

( i . e . t h e p r o b a b i l i t y of a d s o r p t i o n ) o r t h e s p i n l a t t i c e r e l a x a t i o n time of t h e adsorbed l a y e r s can be r e s p o n s i b l e f o r t h e observed T I .

From t h e experimental p o i n t of view, w i t h t h e s u r f a c e a r e a s >> 1 cmL n e c e s s a r y f o r c o o l i n g down t h e experimental c e l l s , i t is t h e n p o s s i b l e t o use e i t h e r " d i f f u s i o n time l i m i t e d r e l a x a t i o n " o r

"boundary l i m i t e d r e l a x a t i o n " . The f i r s t method has been used i n a Pomeranchuk s e p a r a t i n g t h e

h e a t exchanger from t h e main 3 ~ e volume by a chan- n e l % 1 mm diameter and few mm i n l e n g t h ; t h e c e l l ' s s i z e was ^'L1 cm : d i f f u s i o n times t o t h e s u r f a c e s a r e c a l c u l a t e d t o b e l a r g e r t h a n lo3 se- conds.

We have shown t h a t t h i s c o n d i t i o n i s too

r e s t r i c t i v e , and t h a t "boundary l i m i t e d r e l a x a t i o n "

a l l o w s u s i n g t y p i c a l dimensions of t h e o r d e r o

.

, cm f o r E < which c a n b e achieved w i t h 4 ~ e c o a t i n g of t h e ~ ~ a l l s .

We w i l l not s t u d y h e r e an a d d i t i o n a l r e l a x a t i o n mechanism, p r e s e n t i n l i q u i d 3 ~ e f experiments, which

r e q u i r e s s o l i d - l i q u i d c o e x i s t e n c e movement of t h e s o l i d - l i q u i d i n t e r f a c e (3,4,29)

For l i q u i d 3 ~ e f w i t h l a r g e p o l a r i z a t i o n s , t h e d i f f u s i o n c o e f f i c i e n t w i l l b e i n c r e a s e d by t h e e f f e c t i v e r e d u c t i o n of t h e i n t e r a c t i o n s ( ' ) . Bulk TI w i l l be correspondingly i n c r e a s e d , " d i f f u s i o n l i m i t e d " T e f f i c i e n c y reduced, and "boundary 1 l i m i t e d r e l a x a t i o n " probably remains unchanged.

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The thermal boundary (Ka~itza)(~O) resistance

RK

and the spin-lattice relaxation time TI at ultralow temperatures are closely related, and have been studied theoretically by Be'al-Monod and ~ills(~~). We report measurements of

RK

between sintered silver powders and liquid 3 ~ e in this temperature range.

Figure 5 shows the results of Ahonen et al. (31) for 700 silver powders in contact with pure 3 ~ e :

%

^I¹¹⁰⁰^T-' K~~~W-'. We have measured the Kapitza resistance between 400 A silver powder and dilute 3 ~ e (x3 6%). Above 3 mK, RK 2.35 T - ~ K~ rn2 W-l.

Between 1.6 and 2.5 mK we have found that

%

⁼1.4 x lo4 T - ~ K~ m2w-'. These are the lowest temperatures reported for dilute mixtures. The T-I dependence of RK is similar to that obtained for pure 3 ~ e , suggesting that the same mechanism of heat transfer is involved, the coupling constant being weaker in mixtures due to 4 ~ e coating of the walls. This temperature dependence has recently been observed for 3 ~ e in Pd, with small coverages of 4~e(32). The precooling of Pomeranchuk cells for He+ experiments will then be affected if 4 ~ e 3 coating is used to reduce magnetic relaxation. A compromise must be made to achieve long spin-lattice relaxation times (2. T1 bulk) and a Kapitza resistance leading to short cooling times and low ini- tial temperatures in spite of heat leaks.

In high fields, we have found that the solid at melting pressures produced in a Pomeranchuk cell has an ordering temperature 2. 3 The polari- zation is 2. 70 % for fields 2. 7 T ; the entropy is

< - 2 R 1112. This suggests the possibility of de-

compressing ordered solid ; the final temperature would be lower, increasing the bulk relaxation time.

Finally, it should be pointed out that the microscopic surface properties of 3He, i .e.,

exchange and magnetic relaxation, are being studied in thin layers, for the coverages (

9

2 layers) of interest for the problem of bulk liquid 3 ~ e relaxation at surfaces. (See (33) and references therein).

FIGURE 5 : Kapitza resistance between silver powders and 3 ~ e .

Lower curve : Ahonen et a1. (30), pure 3 ~ e , Ag 700 &

This work

,

^{Ag 400} ^:

+

: pure 3 ~ e . Up er curve : this work, dilute 3 ~ e :

P

T- behaviour below 2.5 mK.

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