SHORT RANGE ORDER AND QUADRUPOLAR NUCLEAR SPIN RELAXATION IN LIQUID ALLOYS

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SHORT RANGE ORDER AND QUADRUPOLAR NUCLEAR SPIN RELAXATION IN LIQUID ALLOYS

E. Weihreter, M. Hartrott, D. Quitmann, J. Rossbach, F. Willeke

To cite this version:

E. Weihreter, M. Hartrott, D. Quitmann, J. Rossbach, F. Willeke. SHORT RANGE ORDER AND QUADRUPOLAR NUCLEAR SPIN RELAXATION IN LIQUID ALLOYS. Journal de Physique Col- loques, 1980, 41 (C8), pp.C8-160-C8-162. �10.1051/jphyscol:1980841�. �jpa-00220347�

JOURNAL DE PHYSIQUE CoZloque C8, suppZ6ment au n08, Tome 41, aoCt 1980, page C8-160

SHORT RANGE ORDER AND QUADRUPOLAR NUCLEAR S P I N R E L A X A T I O N I N L I Q U I D ALLOYS E. weihreteri, M.V. Hartrott, D. Quitmann, J. Rossbach ++ and F. Willeke

I n s t i t u t fiir Atom- und Festkiirperphysik, Freie Universitat Berlin, R.F.A.

Abstract.- Measurements of the quadrupolar part of the nuclear spin relaxation rate, R , are repor- ted for the liquid metallic alloys In-Sn and Sn-Sb. The relaxation rate has been obserged as a func- tion of concentration and temperature. We used the 340 ys isomeric state 1 1 7 m ~ b in a TDPAD experi- ment. Inspection of the systematical trends in the data for R in In-X alloys suggests a correlation between R and the concentration fluctuations. The eaplanatio8 for the sensitivity of Rg is sought by discus%ng short range order in liquid alloys.

E x p e r i m e n t and R e s u l t s

We h a v e measured R 3 f o r a n u c l e a r i s o m e r i c s t a t e which i s p r o d u c e d and a l i g n e d by a n u c l e a r r e a c t i o n . The i s o m e r i c s t a t e de- c a y s by y - e m i s s i o n , t h e a n g u l a r d i s t r i b u - t i o n o f t h e Y-rays b e i n g d i r e c t l y c o n n e c t e d t o t h e d e g r e e o f a l i g n m e n t o f t h e s p i n s o f t h e i s o m e r i c s t a t e . The 340 p s i s o m e r

7 m ~ b was p r o d u c e d by 5 ~ n ( a , 2n) 1 1 7mSb o r 1 1 8 ~ n ( d 1 3 n ) 1 7 m ~ b . D e t a i l s o f t h e ex- p e r i m e n t were e s s e n t i a l l y a s i n /vHaH 7 9 / ; t h e d e u t e r o n beam e n e r g y was 34 P!eV.

The a l l o y s were m e l t e d from t h e e l e m e n t s (99.999 ^% e x c e p t f o r t h e 18sn, which was e n r i c h e d t o 96 % a n d had a c h e m i c a l p u r i t y o f 99.9 % ) i n g r a p h i t e c r u c i b l e s u n d e r p u r i f i e d A r a n d were c r u s h e d a n d r e m e l t e d t w i c e . C y l i n d r i c a l p r o b e s ( 6 mm d i a m e t e r , 1.6 t o 2 mm t h i c k n e s s ) w e r e h e a t e d i n a g r a p h i t e c r u c i b l e c o v e r e d by a n 8 Mm mica window u n d e r o n e a t m o s p h e r e o f p u r i f i e d Ar.

The d a t a were a n a l y z e d i n t h e way d e s c r i b e d i n / v H a H 7 9 / . A s t r o n g n e u t r o n background, p r e s e n t when we employed t h e I 8 s n ( d , 3n) r e a c t i o n , s y s t e m a t i c a l l y i n c r e a s e d t h e ex- p e r i m e n t a l R v a l u e s , and t h e c o r r e s p o n d i n g c o r r e c t i o n h a s b e e n a p p l L e d . I n t h e s y s t e m s u n d e r c o n s i d e r a t i o n h e r e , the q u a d r u p o i a r

c o n t r i b u t i o n R e x c e e d s t h e m a g n e t i c p a r t

Q

R M o f t h e t o t a l r e l a x a t i o n r a t e R=R +R 2 M' Using t h e a r g u m e n t s e x p l a i n e d i n /vHaH 79/

and d a t a from /CarB 7 7 / , i ? n c o u l d b e e s t i -

r l

mated w i t h s u f f i c i e n t a c c u r a c y f o r Sb i n I n Snc. (e.g. R ( 117

I -c !I S b I n o . Sno .5) =

- 1

! 1 3 0 + 4 0 ) s a t T = 9 7 3 K!. - P r o d u c i n g t h e p r o b e n u c l e u s 7 m ~ b from e i t h e r o f t h e a l l o y p a r t n e r s we measured a c o m p l e t e com- p o s i t i o n d e p e n d e n c e i n In-Sn, s e e f i g . 1 . A t e m p e r a t u r e d e p e n d e n c e a p p e a r s i n f i g . 2.

A f a v o r a b l e c a s e f o r a j o i n t e f f o r t o f NP:R a n d TDPAD ( l i k e In-Sb) i s Snl-cSbc; we p r e - s e n t i n f i g . 3 t h e d a t a f o r t h e S n - r i c h r e g i o n .

r i g . 1 R o f 1 1 7 m ~ b i n In-Sn l i q u i d a l l o y s .

12

~ o t s from I n ( X I 2 n ) , t r i a n g l e s from Sn ( d l 3n)

.

S q u a r e from /vHaH 79/.

+ Now at BESSY, Berlin

++ Now at RESY, Hamburg

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980841

atoms o f t y p e A produce a t t h e probe nuc- l e u s , and

F i g . 2 R Of

Q " 7 m ~ b i n I n o . 5 Sno-i

F i g . 3 RQ o f 1 1 7 m ~ b i n Sn-Sb l i q u i d a l l o y s

D i s c u s s i o n

The q u a d r u p o l a r n u c l e a r s p i n r e l a x a t i o n r a t e measures e s s e n t i a l l y t h e c h a r g e den- s i t y f l u c t u a t i o n s . The t h e o r y developed f o r l i q u i d m e t a l s i n /Sho 74/, /War 74/, p r e - d i c t s f o r a l l o y s :

( A new a n s a t z f o r l i q u i d m e t a l s i s p r e s e n t - ed i n /BosQ 8 0 / . ) The s c a t t e r i n g law f o r t h e c o r r e l a t i o n between c o n c e n t r a t i o n f l u c - t u a t i o n s , S c c ( q , w ) , h a s been i n t r o d u c e d t o - g e t h e r w i t h SNN(q,w) and S N C ( q , w ) , s e e /BhaT 70/. S s ( q , w ) r e f e r s t o t h e probe atom. VA(q) i s t h e F o u r i e r t r a n s f o r m o f t h e e f f e c t i v e f i e l d g r a d i e n t which n e i g h b o u r

For t h e q u a l i t a t i v e t r e a t m e n t below w e may n e g l e c t t h e c o n t r i b u t i o n s R and R -

~ N N aNc

-

The e l e c t r i c f i e l d g r a d i e n t f u n c t i o n V ( q ) A i s t a k e n t o be p r o p o r t i o n a l t o t h e i o n i c c h a r g e Z A , b e c a u s e a l l s h i e l d i n g e f f e c t s a r e assumed t o b e e f f e c t i v e l y l i n e a r . Any f u r t h e r changes i n t h e e l e c t r o n s t a t e s w i t h c h a n g i n g p a r t n e r element w i l l be n e g l e c t e d h e r e b e c a u s e a ) t h e r e i s a n , u n i v e r s a l c o r - r e l a t i o n /Rag 76/ between t h e e l e c t r i c f i e l d g r a d i e n t a t a g i v e n probe atom and t h e c a l c u l a t e d l a t t i c e sum; b ) on t h e o t h e r hand, l a r g e changes i n R a a r e found even

f o r e q u i v a l e n t a l l o y s (In-Cut Ag, Au;

In-Zn, Cd, Hg /vHaH 7 9 / ) . - These assump- t i o n s /vHaH 79/ were d e r i v e d from system- a t i c i n v e s t i g a t i o n s o f R i n In-X /vHaH 79/

.;I

and PL-X /iios:I OC/ l i q u i d a l l o y s , and t h e p r e s e n t d a t a c o n f i r m t o t h e t r e n d s o f t h e s e two a l l o y g r o u p s .

An e m p i r i c a l model f u n c t i o n f o r V h a s been

proposed by Schirmacher /Sch 76/

The p a r a m e t e r p i s r e l a t e d t o t h e i n t e r - atomic d i s t a n c e .

The aim o f t h e f o l l o w i n g q u a l i t a t i v e d i s - c u s s i o n i s t o d e m o n s t r a t e t h e c l o s e p a r a l - l e l i t y between t h e d e v i a t i o n o f t h e ob- s e r v e d v a l u e s o f R from a s i m p l e p r o p o r - t i o n a l i t y t o ( Z A - Z B ) 2 - c ( l - c ) and t h e Q

s t r e n g t h o f c o n c e n t r a t i o n f l u c t u a t i o n s c h a r a c t e r i s t i c f o r h e t e r o c o o r d i n a t i o n / l e i H 7 8 / .

C o n c e n t r a t i o n f l u c t u a t i o n s o f t h e h e t e r o - c o o r d i n a t i o n t y p e mean a p r e f e r e n t i a l AB c o o r d i n a t i o n o f n e a r e s t n e i g h b o u r s , i . e . a s u p e r s t r u c t u r e o f c o a r s e n i n g o r t h e s t r u c - t u r e o f t h e a l l o y around t h e probe atom.

A l l o y s w i t h h e t e r o c o o r d i n a t i o n have reduced c o n c e n t r a t i o n f l u c t u a t i o n s a t s m a l l q , b u t

c8-162 JOURNAL DE _PHYSIQUE

a t l a r g e r q , a peak ( c a l l e d prepeak i n s c a t t e r i n g e x p e r i m e n t s ) r e v e a l s i n c r e a s e d f1uctu:tions. T h i s c o r r e p o n d s t o t h e sum r u l e - dqq I s c c ( q ) - c ( I - c ) 2 1 ⁼ 0 . I t a p p e a r s r e a s o n a b l e t o assume t h a t t h e peak of S c c ( q ) . above i t s a v e r a g e c ( 1 - c ) a t some f i n i t e q w i l l be t h e l a r g e r , t h e s t r o n g e r t h e r e d u c t i o n a t q = 0 , i . e . t h e s m a l l e r

S c c ( 0 ) . Plodel c a l c u l a t i o n s show t h a t t h e f i r s t s t r o n g peak o f V ( q ) 2 i s a t s i m i l a r

C

q - v a l u e s a s t h e t y p i c a l p o s i t i o n o f t h e f i r s t peak o f S c c ( q ) . T h i s argument p r e - d i c t s t h a t S c c ( 0 ) and R a n t i - c o r r e l a t e i n a d d i t i o n t o t h e p r o p o r t i o n a l i t y a

R,o(ZA-2,) 2 . iVe t e s t i n f i g . 4 t h e s i m p l e a n s a t z R cxl/Scc(0) f o r t h e a n t i c o r r e l a t i o n

a ₂

by p l o t t i n g R ₃ a g a i n s t ( Z A - Z B ) / S c c ( 0 ) .

S c c ( 0 ) was o b t a i n e d from thermodynamic d a t a f o r AH /Hul 65/ by u s i n g t h e conformal s o l u t i o n model AH=NW-c(1-C) ; S c c ( 0 ) = c ( 1 - c ) / L l - 2 ~ c ( 1 - c ) / k B ~ ] . ( F o r t h e p l o t i n f i q . 4 R and S (0) a r e t a k e n a t Tpl).'

2 CC

T h i s s t r u c t u r a l e f f e c t may w e l l be enhanced by a c o n c o n i t a n t dynamic e f f e c t o c c u r r i n g e . g . v i a t h e de Gennes narrowing o f

S c c ( q r u ) ; s e e sol^ ^{8 0 / .}

must a w a i t i t s c o r r o b o r a t i o n i n o t h e r a l l o y - groups a s w e l l a s i t s t h e o r e t i c a l formula- t i o n . S e v e r a l e x t e n s i o n s o f f e r t h e m s e l v e s f o r f u r t h e r s t u d y : t h e s e p l a n a t i o n o f t h e enhancement o f RQ w i l l i n i t s e l f r e q u i r e a m i c r o s c o p i c model f o r t h e s p a t i a l a r r a n g e - ment o f c h a r g e s a s w e l l a s f o r t h e i r dyna- m i c s , i n t h e l i q u i d phase of b e f o r e c o o r d i n - a t i n g a l l o y s ( e . g

.

.

.

Acknowledgements

ide a r e o b l i g e d t o Kernforschungszentrum K a r l s r u h e f o r machine t i m e , and t o Deutsche Forschungsgemeinschaft ( S f b 161) f o r f i n a n - c i a l s u p p o r t .

50 1 R e f e r e n c e s

F i g . 4 The c o r r e l a t i o n o f R o f

3 1 7 m ~ b t o S o ( 0 ) from thermodynamic d a t a i n Ino.5Xo.5 a l l o y s . I n t h e c a s e o f X=Zn, Rg, Cu and A s t h e thermodynamic d a t a a r e u n c e r t a i n .

We c o n s i d e r khe o b v i o u s c o r r e l a t i o n i n f i g . 4 a s a s t r o n g s u p p o r t f o r t h e importance which c o n c e n t r a t i o n f l u c t u a t i o n s have f o r RQ. The proposed e x p l a n a t i o n o f t h e enhance- ment o f R i n h e t e r o c o o r d i n a t e d a l l o y s

Q

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