NUCLEAR SPIN-LATTICE RELAXATION IN LIQUID Li-Na, Li-Mg AND Li-Pb ALLOYS

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NUCLEAR SPIN-LATTICE RELAXATION IN LIQUID Li-Na, Li-Mg AND Li-Pb ALLOYS

P. Heitjans, G. Kiese, H. Ackermann, B. Bader, W. Buttler, K. Dörr, F.

Fujara, H. Grupp, A. Körblein, H.-J. Stöckmann

To cite this version:

P. Heitjans, G. Kiese, H. Ackermann, B. Bader, W. Buttler, et al.. NUCLEAR SPIN-LATTICE

RELAXATION IN LIQUID Li-Na, Li-Mg AND Li-Pb ALLOYS. Journal de Physique Colloques,

1980, 41 (C8), pp.C8-409-C8-413. �10.1051/jphyscol:19808101�. �jpa-00220196�

JOURNAL DE PHYSIQUE CoZZoque C 8 , suppL6ment au n08, Tome 4 1 , aoCt 1980, page C8-409

NUCLEAR SPIN-LATTICE RELAXATICN IN L I Q U I D L i - N a , Li-Mg AND L i - ? b ALLOYS

P. H e i t j a n s , G . K i e s e , H . A c k e r m n n , B. Bader, W . I l u t t l e r , K. X r r , F. F u j a r a , H . Grupp A . K i i r b l e i n and H . - J . Stackmann.

Fachbereich Physik, Universi tiit Marburg, Germany, and Ins t i tu t Laue-Langevin, Crenob Ze, France;

Phys. Ins

t..

Universi t a t Hei&Zberg, Germany.

-

¹

A b s t r a c t . The n u c l e a r s p i n - l a t t i c e r e l a x a t i o n r a t e T l o f ' ~ i i n l i q u i d Li-Na, Li-Mg and Li-Pb a l l o y s h a s been measured by means o f t h e asymmetric B-decay r a d i a t i o n o f p o l a r i z e d ' ~ i (T1 = 0.8s) n u c l e i a s a f u n c t i o n o f t e m p e r a t u r e T and s o l u t e c o n c e n t r a t i o n c . T;' i s dominated by m a i n e t i c h y p e r f i n e i n t e r a c t i o n w i t h c o n d u c t i o n e l e c t r o n s . The r e d u c e d r a t e ( T I T )

-'

depends s l i g h t l y on T

i n a way which, f o r Li-Na and Li-Mg, i s s i m i l a r t o t h a t r e p o r t e d f o r t h e e l e c t r i c a l r e s i s t i v i t y . The T dependence o f t h e l i q u i d s t r u c t u r e i s assumed t o b e t h e main r e a s o n f o r b o t h t h e s e f i n d i n g s .

( T ~ T ) - ' / ~ v a r i e s a b o u t l i n e a r l y w i t h c i n Li-Na and Li-Mg and o b e y s t h e K o r r i n g a r e l a t i o n ( T , T ) - ' / ~ = c0nst.K i n Li-Na, where t h e K n i g h t s h i f t K i s known, o v e r t h e e n t i r e c - r a n g e . I n Li-Pb, however, ( T ~ T ) - ' / ~ h a s a marked minimum n e a r c = 20 a t Z Pb which can be a s c r i b e d t o t h e compound f o r m i n g t e n d e n c y o f L i and Pb i n t h e m e l t . Comparison w i t h r e c e n t Knight s h i f t measure- mentsshows t h a t t h e measured r a t e i s s i g n i f i c a n t l y enhanced o v e r t h e K o r r i n g a r a t e around c = 2 0 a t % . The r e s u l t f i t s i n t o t h e scheme p r o p o s e d by Warren which r e l a t e s t h e enhancement t o t h e e l e c t r i c a l c o n d u c t i v i t y i n t h e s t r o n g s c a t t e r i n g regime.

1 . INTRODUCTION

I n r e c e n t y e a r s a n i n c r e a s i n g number o f i n v e s - and I V . The measurements have b e e n done on t h e t i g a t i o n s o n l i q u i d l i t h i u m a l l o y s h a s b e e n done. 0 - a c t i v e n u c l i d e 8Li (T = 0.E.s) by a decay-

1 12

They a r e a t t r a c t i v e f o r t h e i r b a s i c p r o p e r t i e s which r a d i a t i o n d i s t r i b u t i o n t e c h n i q u e t o be b r i e f l y r a n g e from f r e e - e l e c t r o n t o s e m i c o n d u c t i n g b e h a v i o u r o u t l i n e d below. The T;' r e s u l t s f o r 8 ~ i w i l l b e a s w e l l a s f o r t h e i r p o t e n t i a l a p p l i c a t i o n e . g . i n d i s c u s s e d and compared w i t h 7 ~ i - ~ n i g h t s h i f t d a t a c o n n e c t i o n w i t h e n e r g y g e n e r a t i o n and s t o r a g e . which a r e known f o r Li-Na [ I ] and r e c e n t l y a l s o C u r r e n t e x p e r i n e n t a l s t u d i e s o f L i a l l o y s i n c l u d e f o r Li-Pb (van d e r M a r e 1 , p r i v a t e communication) measurements o f e l e c t r i c a l r e s i s t i v i t y , d i f f r a c t i o n from c o n v e n t i o n a l n u c l e a r m a g n e t i c r e s o n a n c e (NMR) d a t a and thermodynamic q u a n t i t i e s . A w e l l known measurements. R e f e r e n c e w i l l a l s o be made t o + t h e r p o s s i b i l i t y f o r s t u d y i n g m e l t s m i c r o s c o p i c a l l y i s e x p e r i m e n t a l i n f o r m a t i o n s u c h a s r e s i s t i v i t y , t o measure K n i g h t s h i f t s K and n u c l e a r s p i n - l a t t i c e

r e l a x a t i o n r a t e s T;'. While K n i g h t s h i f t d a t a on ' ~ i i n some l i q u i d L i a l l o y s have become a v a i l a b l e i n t h e l a s t few y e a r s [ 1-31 t h e r e seem t o be no

- I

c o r r e s p o n d i n g T I measurements up t o now. However, a s f a r a s r e l a x a t i o n by m a g n e t i c h y p e r f i n e i n t e r - a c t i o n w i t h t h e c o n d u c t i o n s - e l e c t r o n s i s c o n c e r n e d ,

-

¹

T I d a t a when combined w i t h K v a l u e s p r o v i d e a d d i - t i o n a l i n f o r m a t i o n o n t h e m i c r o s c o p i c dynamics o f t h e e l e c t r o n s . I f t h e e l e c t r o n s a r e f r e e , ~ - l s h o u l d

1 c o r r e s p o n d t o t h e r e l a x a t i o n r a t e c a l c u l a t e d from K by means o f t h e K o r r i n g a r e l a t i o n [ 4 ] . On t h e o t h e r h a n d , i f t h e e l e c t r o n s e x h i b i t a tendency t o

localize,^;'

w i l l b e enhanced o v e r t h e K o r r i n g a r a t e a's h a s b e e n e x p l a i n e d by Warren [ 5 ] i n a g r e e - ment w i t h b t t ' s pseudogap model [ 6 ] .

I n t h e f o l l o w i n g we r e p o r t T-I measurements i n 1

l i q u i d Li-Na, Li-Xg and Li-Pb a s examples f o r b i n a r y a l l o y s o f L i w i t h s i m p l e m e t a l s from g r o u p I , I1

n e u t r o n d i f f r a c t i o n and thermodynamic d a t a . 2. EXPERIHENTAL

The e x p e r i m e n t h a s been performed a t t h e High F l u x R e a c t o r G r e n o b l e u s i n g t h e in-beam NMR s p e c t r o - m e t e r S 6 . The 8 L i n u c l e i were produced and p o l a r -

i z e d i n s i t u by c a p t u r e o f p o l a r i z e d n e u t r o n s i n 7 ~ i c o n s t i t u t i n g t h e l i t h i u m component o f t h e a l l o y s . The L i p o l a r i z a t i o n was m o n i t o r e d v i a t h e 8 a s y m e t r y o f t h e 0 - r a d i a t i o n , b e i n g measured by d e t e c t o r s a t 0 and 180" w i t h r e s p e c t t o a n e x t e r n a l m a g n e t i c f i e l d . The s p i n - l a t t i c e r e l a x a t i o n t i m e T o f 8 L i was measured w i t h o u t a p p l i c a t i o n o f a

I

r a d i o f r e q u e n c y f i e l d s i m p l y by r e c o r d i n g t h e t r a n - s i e n t asymmetry a f t e r n e u t r o n - a c t i v a t i o n p u l s e s . The method and i t s a p p l i c a t i o n i n g e n e r a l and i n s t r u m e n t d e t a i l s a r e d e s c r i b e d i n [ 7 1 and [ 8 1 .

The s a m p l e s were p r e p a r e d from i s o t o p i c a l l y p u r e (99.99 %) 7 L i and 4N Na, Mg and Pb, r e s p e c - t i v e l y . The c o n s t i t u e n t s were m e l t e d t o g e t h e r and

m

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808101

JOURNAL DE cg-410

s e a l e d i n s t a i n l e s s s t e e l c o n t a i n e r s (6x4x0.5 cm 3 ) by w e l d i n g i n s i d e a g l o v e box u n d e r argon atmos- p h e r e .

3 . FXSULTS AND DISCUSSION

The s p i n - l a t t i c e r e l a x a t i o n r a t e T-I of ' ~ i 1

was measured a t s o l u t e c o n c e n t r a t i o n s c r a n g i n g from 0 t o a b o u t 60 a t % Na, Mg and Pb, r e s p e c t i v e l y , and a t t e m p e r a t u r e s T from above t h e l i q u i d u s up t o a b o u t 1000 K . The e x t e r n a l m a g n e t i c f i e l d was k e p t c o n s t a n t a t B = 339 mT.

Regarding f i r s t t h e t e m p e r a t u r e dependence, T- I was found t o i n c r e a s e w i t h i n c r e a s i n g T i n t h e

1

t h r e e s y s t e m s a t a l l c o m p o s i t i o n s . A p o s s i b l e ex- c e p t i o n m i g h t be Li-Pb a t c o n c e n t r a t i o n s around

22 a t % Pb where t h e l i q u i d u s h a s i t s a b s o l u t e maximum [ 9 ] and t h e t e m p e r a t u r e r a n g e i n t h e m e l t p r e s e n t l y a c c e s s i b l e w i t h o u r f u r n a c e i s t o o s m a l l t o d e t e r m i n e t h e T d e p e n d e n c e . A p o s i t i v e s l o p e o f

- I

T I ^{V S .} T may be r e g a r d e d a s a n i n d i c a t i o n t h a t

-

1

T, i s dominated by m a g n e t i c h y p e r f i n e i n t e r a c t i o n w i t h c o n d u c t i o n e l e c t r o n s . A q u a d r u p o l a r r e l a x a t i o n r a t e due t o a t o m i c m o t i o n i s e x p e c t e d t o d c c r e a s e w i t h i n c r e a s i n g T ( s e e e .g. [ 101 )

.

Q u a d r u p o l a r r e l a x a t i o n o f 8 L i which, a p r i o r i , i s handicapped by i t s s m a l l q u a d r u p o l e moment and a s m a l l S t e r n h e i m e r a n t i s h i e l d i n g f a c t o r was found t o be c o m p l e t e l y n e g l i g i b l e i n pure Li [ I 1,121 and i s n o t e x p e c t e d t o be v e r y s i z e a b l e i n t h e l i q u i d a l l o y s e i t h e r . T h i s a s s u m p t i o n i s based p a r t l y on t h e known s i z e o f t h e d i f f u s i o n - i n d u c e d q u a d r u p o l c c o n t r i b u - t i o n i n s o l i d Li-Mg a l l o y s j u s t below t h e s o l i d u s t e m p e r a t u r e [ 13,141.

I n t h e c a s e o f m a g n e t i c r e l a x a t i o n by f r e e , n o n i n t e r a c t i n g s - e l e c t r o n s t h e r a t e , n o r m a l i z e d t o t h e t e m p e r a t u r e , s h o u l d obey t h e K o r r i n g a r e l a - t i o n 141

w i t h t h e s t a n d a r d e x p r e s s i o n f o r t h e K n i g h t s h i f t

8.1~

K = - R X P

3 p F '

Here R i s t h e a t o m i c volume,

X

t h e P a u l i s p i n P

s u s c e p t i b i l i t y p e r u n i t volume and PF = <1$(0) 12> F t h e p r o b a b i l i t y d e n s i t y o f t h e c o n d u c t i o n e l e c t r o n s a t t h e n u c l e u s , a v e r a g e d o v e r t h e Fermi s u r f a c e . The c o n s t a n t So i s g i v e n by So = ( y e h n ) 2 ( ~ / 4 ~ ~ g ) , where y and yn a r e t h e g y r o m a g n e t i c r a t i o s o f a n e l e c t r o n and t h e n u c l e u s , r e s p e c t i v e l y

( S = 1 . 2 0

.

^{s .} f o r ' ~ i ) . ^~

According t o (1) ( T ~ T ) - ' s h o u l d b e e s s e n t i a l l y i n d e p e n d e n t o f t e m p e r a t u r e . E x p e r i m e n t a l l y , however, ( T ~ T ) - ' was found t o depend s l i g h t l y o n T i n e a c h a l l o y i n a c h a r a c t e r i s t i c way. T h i s i s shown i n F i g . I f o r Li-Na and Li-Mg : d ( T l T ) - ' / d T , b e i n g o f t h e o r d e r o f + s-'K-' a t h i g h L i c o n t e n t ,

0 2 0 40 6 0 80 0 20 40 60 80 100

at%Na d % M g

F i g . I . Temperature d e r i v a t i v e of t h e r e d u c e d s p i n - l a t t i c e r e l a x a t i o n r a t e ( T ~ T ) - ' of ' ~ i v e r s u s con- c e n t r a t i o n i n l i q u i d Li..Na and Li-Mg.

lo4

I I I I I I I -

i n c r e a s e s i n Li-Na b u t becomes z e r o o r s l i g h t l y n e g a t i v e i n Li-Mg when g o i n g t o h i g h e r s o l u t e con- c e n t r a t i o n s . A s i m i l a r b e h a v i o u r i s known f o r t h e t e m p e r a t u r e d e r i v a t i v e o f t h e e l e c t r i c a l r e s i s t i v - i t y d p / d t i n Li-Na ( F i g . 1 i n [151) and i n Li-Mg ( F i g . 5 i n [ 1 6 1 ) . I n t h e s e s y s t e m s , c o n t r a r y t o t h o s e where t h e n e a r l y - f r e e - e l e c t r o n (NEE) model i s n o t v a l i d ( s e e below),T1 i s n o t d i r e c t l y r e l a t e d t o p. A c o r r e l a t i o n between d ( T I T ) - ' / d T ( o r d ( T I T ) - l i 2 / d T ) and dp/dT c a n , however, b e imagined i n d i r e c t l y v i a t h e dependence on s t r u c t u r e f a c t o r s . I n a p s e u d o p o t e n t i a l - c a l c u l a t i o n o f t h e s - e l e c t r o n d e n s i t y PF, t h e p o s i t i v e d ( T I T ) - / d T v a l u e f o r p u r e L i I shown i n F i g . 1 h a s i n f a c t b e e n e x p l a i n e d e s s e n - t i a l l y by t h e T dependence o f t h e e x p e r i m e n t a l s t r u c t u r e f a c t o r 1171. F o r t h e a l l o y s a s i m i l a r c a l c u l a t i o n u s i n g p a r t i a l s t r u c t u r e f a c t o r s i s n o t y e t a v a i l a b l e . As f o r t h e r e s i s t i v i t y , o n t h e o t h e r hand, t h e g e n e r a l b e h a v i o u r o f dp/dT,mentioned a b o v e , c o r r e s p o n d s q u a l i t a t i v e l y t o what i s e x p e c t e d i n t h e frame o f t h e Faber-Ziman t h e o r y f o r s y s t e m s i n v o l v i n g mono- and d i v a l e n t m e t a l s [ l a ] . Without a c t u a l c a l c u l a t i o n s , i t i s d i f f i c u l t t o d e c i d e w h e t h e r t h e o r y o n t h e s e grounds a c c o u n t s a t l e a s t q u a l i t a t i v e l y f o r t h e c o r r e l a t i o n o f t h e experimen- t a l r e s u l t s .

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dependence o f T i 1 . I n Li-Na and Li-Mg a n a p p r o x i - m a t e l y l i n e a r i n c r e a s e and d e c r e a s e , r e s p e c t i v e l y , o f t h e q u a n t i t y ( T T ) - ' / ~

,

which a c c o r d i n g t o ( I )

1

s h o u l d be p r o p o r t i o n a l t o K , was found. The s l o p e s d ( ~ ~ T ) - ~ / ~ / d c o f t h e s t r a i g h t l i n e s i n F i g . 2, o b t a i n e d by a f i t , a r e + 1.8 ( 4 ) . 1 0 -4 and

- 2 . 3 ( 1 ) . 1 0 - ~

,-'I2 .

K - I / ~

.

( a t % ) - I f o r Li-Na and Li-Mg, r e s p e c t i v e l y .

The d a t a f o r Li-Na a t 673 K can be compared w i t h 7 ~ i Knight s h i f t d a t a a t t h e same tempera- t u r e

111.

The K o r r i n g a p r o d u c t T I T K~ t u r n s o u t t o be a b o u t c o n s t a n t o v e r t h e e n t i r e c o n c e n t r a t i o n r a n g e . T h i s g i v e s e v i d e n c e t h a t r e l a x a t i o n o f ' ~ i i n Li-Na i s i n d e e d due t o m a g n e t i c h y p e r f i n e c o u p l i n g w i t h q u a s i f r e e e l e c t r o n s . T h e r a t i o S /T T K~ a n o u n t s

0 1

t o 0 . 6 3 o n t h e a v e r a g e , i . e . i s s m a l l e r t h a n 1 which i s g e n e r a l l y found f o r normal m e t a l l i c s y s t e m s and c a n b e a s c r i b e d t o t h e i n f l u e n c e of e l e c t r o n - e l e c - t r o n i n t e r a c t i o n ( s e e e . g . 119,201 )

.

F e i t s m a e t a 1 [ I ] , u s i n g t h e i r Knight s h i f t d a t a and known v a l u e s f o r t h e s p i n s u s c e p t i b i l i t i e s and a t o m i c volumes o f L i and Na, have a l r e a d y p o i n t e d o u t t h a t a c c o r d i n g t o

P ( c = 100 a t % ) K(100)

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XP)Li

F -

P F ( 0 ) -

imj---.

( 3 )

(' %),a

t h e d e n s i t y of F e r m i - s u r f a c e e l e c t r o n s e x p e r i e n c e d by a L i n u c l e u s i n f i u r e tJa i s a b o u t 40% l a r g e r t h a n i n pure L i . A s i m i l a r r e s u l t i s o b t a i n e d when t h e p r e s e n t ( T I T ) - ' / * d a t a a r e u s e d . I t i s i n t e r e s t i n g t o n o t e t h a t w h i l e (Xp)Li and (Xp)Na (2.01 and 1 . 1 10 -6 c g s volume u n i t s , r e s p . [211) d i f f e r by a f a c t o r o f a l m o s t two t h e s u s c e p t i b i l i t i e s p e r atom Xp A = 0 % a r e a b o u t t h e same f o r p u r e L i and p u r e Na. Thus, i f one assumes t h a t f o r i n t e r m e d i a t e c o n c e n t r a t i o n s t h e s u s c e p t i b i l i t y p e r atom i s g i v e n by l i n e a r i n t e r p o l a t i o n , i . e . X; i s c o n s t a n t , t h e l i n e a r c o n c e n t r a t i o n dependence o f I< and (T T) -1/2

I

r e f l e c t s a l i n e a r l y v a r y i n g s - e l e c t r o n d e n s i t y P F ( c ) . I n t h e c a s e of Li-118 no Knight s h i f t d a t a i n t h e l i q u i d seem t o b e a v a i l a b l e f o r comparison.

I n t e r p r e t i n g t h e :Tll.)-li2 d a t a a g a i n i n t e r n s o f e q s . ( I ) and ( 2 ) and a d o p t i n g t h e s e m i e m p i r i c a l v a l u e (XP)M

2

1 . 6 c g s volume u n i t s [ 2 2 ] , t h e r a t i o

g

PF( 1 0 0 ) / P F ( 0 ) %O.S c a n be derived.Though i t seems n o t v e r y l i k e l y i t c a n n o t b e c o m p l e t e l y r u l e d o u t t h a t t h e l i n e a r c o n c e n t r a t i o n dependence o f ( T ~ T ) - " ~ i s f o r t u i t o u s and r e s u l t s from t h e s u p e r - p o s i t i o n o f a concave-shaped m a g n e t i c h y p e r f i n e c o n t r i b u t i o n and some e x t r a r e l a x a t i o n r a t e . I n a n y

c a s e i n s o l i d Li-Pqg t h e '1.i Knight s h i f t a c c o r d i n g t o Lynch e t a l . [ 2 3 ] shows a d e e p minimum a t a b o u t 5 0 a t % Efg (1231, F i g . 2 ) . On t h e o t h e r hand, t h e i r v a l u e i n t h e r a n g e o f low tlg c o n t e n t which i s f o r 6 atXMg and which can be compared w i t h o t h e r a u t h o r s ' r e s u l t s [ 2 4 , 2 5 , 1 3 1 a p p e a r s t o be much t o o s m a l l . T I measurements on 8 ~ i i n s o l i d Li-Plg c o v e r - i n g t h e whole c o n c e n t r a t i o n r a n g e a r e i n p r o g r e s s . W h i l e , a t l e a s t i n t h e l i q u i d s t a t e , Li-Plg seems t o b e a f a i r l y good NFE a l l o y , s t r u c t u r e and thermo- dynatcic d a t a [ 3 5 ] show some d e v i a t i o n from i d e a l s o l u t i o n b e h a v i o u r .

I n Li-Pb, c o n t r a r y t o Li-Na and Li-E:g, ( T T r 1 l 2 I i s f a r from b e i n g l i n e a r i n t h e c b n c e n t r a t i o n . A s shown i n F i g . 3 which r e f e r s t o T=1000K

2

0 20 40 6 0 8 0 0 2 0 CO 60 80 100

at %No at

%Mg

F i g . 2 . ^, C o n c e n t r a t i o n dependence o f ( T , T ) - ' / ~ o f

8 ~ l n l i q u i d Li-Na and Li-Mg a t T 1 = 673 and 900K, r e s p e c t i v e l y . The c o n t i n u o u s l i n e s r e p r e s e n t l i n e a r f i t s .

Li-Pb

,lo-**

1 I I I I I I I

0 20

40 60 80

100

at %Pb

- l / 2 F i g . 3. C o n c e n t r a t i o n dependence o f (TIT) of

* ~ i i n l i q u i d Li-Pb a t T = 1000 K.

Li - Na

Li-Mg

JOURNAL DE PHYSIQUE

r a p i d l y f a l l s o f f from i t s v a l u e i n p u r e L i t o a minimum n e a r c = 20 a t % Pb and i n c r e a s e s s l i g h t l y f o r h i g h e r c o n c e n t r a t i o n s . T h i s b e h a v i o u r o f t h e n u c l e a r r e l a x a t i o ~ i r a t c i s p a r a l l e l e d i n a n o m a l i e s of a number of m a c r o s c o p i c p r o p e r t i e s . The e l e c t r i - c a l c o n d u c t i v i t y 1261 h a s a pronounced d i p w i t h a minimum v a l u e n e a r c = 20 a t % Pb of a b o u t

2000 ~ - ' c m - ' and t h u s , i n a c e r t a i n c o n c e n t r a t i o n r a n g e , i s s m a l l e r t h a n t h e lower l i m i t f o r t h e

-1 -I v a l i d i t y of t h e NFE model of r o u g h l y 3000 f? cm [61. Neutron d i f f r a c t i o n measurements [271 r e - v e a l e d marked s h o r t - r a n g e o r d e r around 20 a t % Pb which i s c h a r a c t e r i z e d by a p r e f e r e n c e f o r u n l i k e n e a r e s t n e i g h b o u r s and a r e d u c t i o n o f t h e i r d i s - t a n c e a s comparcd w i t h t h e mean d i s t a n c e o f t h e p u r e components. The p h y s i c o c h e m i c a l p r o p e r t i e s d e r i v e d from measurements o f e . g . t h e d e n s i t y [281, v e l o c i t y o f sound [ 2 8 ] , e l e c t r o m o t i v e f o r c e 1291 and t h e e n t h a l p y o f m i x i n g [ 3 0 ] a l s o d e v i a t e c o n s i d e r a b l y from t h e i d e a l s o l u t i o n b e h a v i o u r . l ' h i s h a s been a s c r i b e d t o e l e c t r o n c h a r g e t r a n s f e r from L i t o Pb and t h e r e s u l t i n g tendency towards i o n i c bonding i n t h e m e l t n e a r t h e c o m p o s i t i o n Li4Pb. While t h i s c o m p o s i t i o n c o r r e s p o n d s t o t h e v a l e n c i e s o f L i and Pb i t s h o u l d b e n o t e d t h a t i n t h e s o l i d no i n t e r m e t a l l i c p h a s e s o f e x a c t l y t h i s s t o i c h i o m e t r y seem t o e x i s t . A c c o r d i n g t o Z a l k i n and Ramscy [ 3 2 ] ( s e e a l s o [ 9 ] ) t h e i n t e r - m e t a l l i c compounds w i t h Pb c o n c e n t r a t i o n s n e a r e s t

t o c = 20 a t % a r e L i Pb ( c = 1 8 . 5 a t % ) and 22 5

L i Pb ( c = 22.2 a t % ) . L i Pb a s s o c i a t e s i n t h e

7 2 7 2

m e l t have r e c e n t l y been assumed by P r e d e l and Oehme [ 3 0 ] t o e x p l a i n t h e i r c a l o r i c measurements, which were done a t v e r y f i n e c o n c e n t r a t i o n s i n t e r - v a l s . While i n most o t h e r e x p e r i m e n t a l r e s u l t s , p r e s e n t l y a v a i l a b l e , t h e s e c o n c e n t r a t i o n s a r e more o r l e s s u n d i s c e r n i b l e t h e d i s t i n c t i o n may be r e l e v a n t f o r c u r r e n t t h e o r s t i c a l a p p r o a c h e s ( s e e e .g. [32-341).

Our T-I d a t a can m o s t d i r e c t l y b e compared I

w i t h t h e r e s u l t s o f r e c e n t K n i g h t s h i f t measure- ments by van d e r t l a r e l e t a l . ( p r i v a t e comnunica- t i o n ) . The K v a l u e s , which had b e e n t a k e n n e a r t h e l i q u i d u s a t d i f f e r e n t t e m p e r a t u r e s , were e x t r a p o l a - t e d t o T = 1000K. For p u r e Li, where o n l y a v a l u e a t 473K was a v a i l a b l e , t h e same f r a c t i o n a l change o f K w i t h T a s found f o r ( T I ~ ) " 1 2 h a s been assumed Though t h e i s o t h e r m a l c-dependence o f K l o o k s v e r y s i m i l a r t o t h a t o f ( T I T ) - l f 2 ( F i g . 3 ) t h e e x p e r - i m e n t a l K o r r i n g a p r o d u c t T ~ T K ' t u r n s o u t t o b e n o t

c o n s t a n t . I n F i g . 4 t h e i n v e r s e K o r r i n g a p r o d u c t ,

- I 2

i . e . ( T I T ) n o r m a l i z e d t o K

,

i s shown ( l e f t - h a n d s c a l e ) . O b v i o u s l y t h i s n o r m a l i z e d r e l a x a t i o n r a t e i s s i g n i f i c a n t l y enhanced around c = 20 a t % Pb a s compared w i t h i t s v a l u e e . g . i n p u r e L i . A c c o r d i n g t o t h e a r g u m e n t s p r e s e n t e d a t t h e b e g i n n i n g o f s e c t i o n 3 q u a d r u p o l a r r e l a x a t i o n s h o u l d p l a y o n l y a minor r o l e .

F i g . 4. ( T I T ) - ' o f ' ~ i n o r m a l i z e d t o t h e s q u a r e o f t h e K n i g h t s h i f t K ( l e f t - h a n d s c a l e ) and Warren's enhancement f a c t o r qw f o r magnetic r e l a x a t i o n

( r i g h t - h a n d s c a l e ) v e r s u s c o n c e n t r a t i o n i n l i q u i d Li-Pb a t 1000 K .

An enhanced m a g n e t i c r e l a x a t i o n r a t e i s t o be e x p e c t e d i f t h e c o n d u c t i o n e l e c t r o n s a r e no l o n g e r n e a r l y f r e e b u t a r e s t r o n g l y s c a t t e r e d o r e n t e r l o c a l i z e d s t a t e s . W a r r e n [ 5 ] showed t h a t t h e enhan- cement q o f t h e e x p e r i m e n t a l r a t e o v e r t h e

W

K o r r i n g a r a t e g i v e n by ( I ) , i s r e l a t e d t o t h e c o r r e l a t i o n t i m e T o f t h e f l u c t u a t i n g h y p e r f i n e i n t e r a c t i o n and t o t h e d e n s i t y o f s t a t e s N(E F ) a t t h e Fermi e n e r g y by

T i s i n t e r p r e t e d a s t h e w a n ' r e s i d e n c e t i m e ' o f t h e e l e c t r o n s o n a n u c l e a r s i t e . For f r e e e l e c t r o n s w i t h Fermi v e l o c i t y vF we have T

%

a/VF % +% N(EF)

( a = i n t e r a t o m i c d i s t a n c e ) and h e n c e

nw

% 1 . When t h e mean f r e e p a t h o f t h e s c a t t e r e d e l e c t r o n s becomes a s s h o r t a s t h e d i s t a n c e a , c o n d u c t i o n p r o c e e d s v i a d i f f u s i o n and ^T w i l l b e i n c r e a s e d . A c c o r d i n g t o Warren [ 5 ] t h e c o n d u c t i v i t y

a

i n t h e d i f f u s i v e t r a n s p o r t regime i s r e l a t e d t o t h e

enhancement

nw

by

onw 2, ^% a.

.

( 5 )

0 i s a c o n s t a n t d e p e n d i n g on t h e i n t e r a t o m i c d i s - t z n c e and can be e s t i m a t e d t o be

oo %

3400 ~ - ' c m - l f o r Li-Pb a t c

2

20 a t % . Thus r e l a x a t i o n s h o u l d be enhanced (nw

2

I ) when o

4

3400 i2-lcm-l, i n rough agreement w i t h t h e NEE l i n i t a c c o r d i n g t o blot t [ 6 ] . T h i s i s what i s a c t u a l l y o b s e r v e d i f one compares t h e p r e s e n t r e s u l t s w i t h t h e above-mentioned c o n d u c t i v i t y measurements by Nguyen and Enderby

[261. I n F i g . 4 t h e r i g h t - h a n d s c a l e g i v e s

2

- I

a c c o r d i n g t o t h e d e f i n i t i o n ( 4 ) where ( T I )Korr i s c a l c u l a t e d from e q . ( I ) by i n s e r t i n g t h e experimen- t a l Knight s h i f t , i . e . qw = S o / ( ~ l ~ ~ L ) e x p . n u s 0

W

i n c l u d e s t h e c o r r e c t i o n f a c t o r K(a) [ I 9 1 f o r t h e e f f e c t of e l e c t r o n - e l e c t r o n i n t e r a c t i o n s : qw

%

K ( a )

3

0.62 f o r p u r e L i a t 1000K. From F i g . 4 we r e a d r o u g h l y t h e v a l u e

ow 2

1.6 f o r c % 20 a t % . T h i s v a l u e t o g e t h e r w i t h t h e minimum c o n d u c t i v i t y o f 2000 ~ - ' c m - ' a p p r o x i m a t e l y f u l f i l s e q . ( 5 ) and f i t s w e l l i n t o t h e s y s t e m a t i c s f o r l i q u i d m e t a l s and s e m i c o n d u c t o r s shown i n F i g . 1 1 of W a r r e n ' s p a p e r [ 5 1 .

A more d e t a i l e d a n a l y s i s , e.g. w i t h r e s p e c t t o t h e e l e c t r o n i c c o r r e l a t i o n t i m e T ~ , w i l l be p o s s i b l e when more a c c u r a t e d a t a around c = 20 a t % , and a l s o a t h i g h e r T , a r e combined w i t h v a l u e s f o r N(E F ) which may b e e s t i m a t e d from e x p e r i m e n t a l con- d u c t i v i t i e s u s i n g M o t t ' s t h e o r y [ 6 1 .

ACKNOWLEDGEMENT

We a r e g r a t e f u l t o H . Ruppersberg f o r numerous s t i m u l a t i n g d i s c u s s i o n s and g e n e r o u s s u p p o r t i n sample p r e p a r a t i o n and a n a l y s i s . Thanks f o r h e l p f u l d i s c u s s i o n s a r e a l s o due t o T.P. Das, R. Evans, D . Q u i t n a n n and W. S c h i r m a c h e r . We a r e o b l i g e d t o W. F r a u e n f e l d , G . S t a h l and N. Z i n s e r f o r e x p e r t t e c h n i c a l a s s i s t a n c e i n p r e p a r i n g most o f t h e s a m p l e s . We t h a n k C. van d e r Mare1 and W. van d e r Lugt f o r s e n d i n g u n p u b l i s h e d K n i g h t s h i f t d a t a . T h i s work i s s p o n s o r e d by t h e B u n d e s n i n i s t e r i u m f c r Forschung und T e c h n o l o g i e .

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