NUCLEAR SPIN-LATTICE RELAXATION IN A LITHIUM-SILICATE GLASS

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NUCLEAR SPIN-LATTICE RELAXATION IN A LITHIUM-SILICATE GLASS

P. Heitjans, B. Bader, K. Dörr, H. Stöckman, G. Kiese, H. Ackermann, P.

Freiländer, W. Müller-Warmuth

To cite this version:

P. Heitjans, B. Bader, K. Dörr, H. Stöckman, G. Kiese, et al.. NUCLEAR SPIN-LATTICE RELAX-

ATION IN A LITHIUM-SILICATE GLASS. Journal de Physique Colloques, 1982, 43 (C9), pp.C9-

143-C9-147. �10.1051/jphyscol:1982927�. �jpa-00222456�

JOURNAL

PHYSIQUE

CoZloque

suppZQment au n022, Tome

dDcembre 1982 page

NUCLEAR S P I N - L A T T I C E RELAXATION I N A L I T H I U M - S I L I C A T E GLASS P. H e i t j a n s ,

Bader,

D E r r ,

StGckmann,

K i e s e ,

Ackermann,

F r e i l a n d e r

~ Z l l e r - w a r m u t h x

Fachbereieh Physik, Universitdt Marburg, W . Germany, and I n s t i t u t Laue-Langevin, GrenobZe, France

" I n s t i t u t fiir PhysikaZische Chemie, Universitdt Miinster,

Resume.-La v i t e s s e de r e l a x a t i o n s p i n - r e s e a u T;' d u 8 L i dans l e v e r r e de s i l i c a t e (SiO ) ( L i 2 0 ) 0 a e t e mesuree dans 1 ' i n t e r v a l l e de t e m p e r a t u r e

6K .< T c 3 4 0 ~ ~ e ? ~ ~ $ o u r u n I e r v a l l e de champ magnetique 1 4 mT

B

830 mT

u t i l i s a n t l a d e c r o i s s a n c e B a s s y m e t r i q u e des noyaux 8 ~ i p o l a r i s e s . La p o l a - r i s a t i o n a m o n t r e une d e c r o i s s a n c e non-expo e n t i e l l e . On a t r o u v 6 gue T i 1 depend a p p r o x i m a t i v e m e n t l i n e a i r e n e n t de B-F e t T p o u r T

170K . ^Les

r P s u l t a t s p e u v e n t & t r e e x p l i q u e s a l ' a i d e d ' u n modPle phPnom6nologique.

Abstract.- 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; ' o f 8 ~ i i n t h e s i l i c a t e g l a s s ( S i 0 2 ) 0 . 6 7 ( L i 2 0 ) ~ . 3 3 has been measured o v e r t h e t e m p e r a t u r e range

6K < T < 340K and t h e magnetic f i e l d range 1 4 mT <

< 830 mT u s i n g t h e

asymmetric @-decay r a d i a t i o n o f p o l a r i z e d 8 ~ n u c l e i . The p o l a r i z a t i o n i showed n o n - e x p o n e n t i a l decay. T ~ - 1 was f o u n d t o depend a p p r o x i m a t e l y l i n e a r l y on B'I and T f o r T < 170K. The r e s u l t s can be e x p l a i n e d w i t h i n t h e frame o f a phenomenological model.

1. I n t r o d u c t i o n . - N b 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 (SLR) i n g l a s s e s d i f f e r s c o n s i d e r - a b l y f r o m t h a t i n t h e i r c r y s t a l l i n e c o u n t e r p a r t s . I n cases where c o m p a r a t i v e measure- ments have been p e r f o r m e d (see /1,2/ and r e f e r e n c e s t h e r e i n ) t h e r e l a x a t i o n r a t e ~ 7 1 i n t h e amorphous s t a t e exceeds t h a t i n t h e c r y s t a l l i n e s t a t e b y a t l e a s t one o r d e r o f magnitude. Furthermore, a t t e m p e r a t u r e s T below, say, 150K t h e T dependence o f T;'

i s t y p i c a l l y much weaker t h a n i n p u r e i n s u l a t i n g c r y s t a l s where, f o r n u c l e i w i t h s p i n I

1 / 2

i s d e t e r m i n e d b y q u a d r u p o l a r c o u p l i n g v i a t h e two-phonon Raman p r o c e s s / 3 / . On t h e o t h e r hand, b o t h i n amorphous and c r y s t a l l i n e i n s u l a t o r s T ~ I was r e p o r t e d t o be p r a c t i c a l l y independent o f t h e magnetic f i e l d

i n t h e low-T r e g i o n . As an excep- t i o n , a s i g n i f i c a n t B dependence of TT' was f o u n d f o r I1El i n v i t r e o u s N a ~ B 4 0 7 b u t was n o t c o n s i d e r e d f u r t h e r by t h e a u t h o r s /I/. The r e l a x a t i o n d a t a i n g l a s s e s a t low T have m o s t l y been i n t e r p r e t e d /1,4,5/ w i t h i n t h e frame o f t h e t u n n e l i n g model i n v o l - v i n g t w o - l e v e l systems /6,7/ w h i c h i s a b l e t o e x p l a i n many o f t h e anomalous t h e r m a l and a c o u s t i c p r o p e r t i e s o f g l a s s e s . These and o t h e r r e l a x a t i o n mechanisms p r o p o s e d i n t h e Last y e a r s /8,9/ a r e a l l based on q u a d r u p o l a r c o u p l i n g .

I n t h e p r e s e n t paper an i n v e s t i g a t i o n o f t h e T and B dependence o f TT? i n a l i t h i u m - s i l i c a t e g l a s s i s r e p o r t e d w i t h emphasis on t h e Low-T r e g i o n . SLR i n l i t h i u m - s i l i c a t e g l a s s e s was s t u d i e d p r e v i o u s l y i n a b r o a d range around room t e m p e r a t u r e and a t one B v a l u e b y n u c l e a r magnetic resonance (NMR) on 7 ~ i / l o / . We have p e r f o r m e d analogous measurements on t h e R - a c t i v e n u c l i d e 8 ~ i u s i n g a @ - r a d i a t i o n d e t e c t i o n t e c h n i q u e which e a s i l y a l l o w s wide range v a r i a t i o n o f b o t h T and 6.

2. E x p e r i m e n t a l . - The e x p e r i m e n t s were c a r r i e d o u t a t t h e H i g h F l u x R e a c t o r Grenoble

u s i n g t h e In-Beam tdMR S p e c t r o m e t e r S6. The g l a s s ( S i 0 2 ) ~ . 6 7 ( L i 2 0 ) 0

t o p i c a l l y p u r e 7 ~ i , which had been p r e p a r e d b y S c h o t t (Rainz), was i r r a d i a t e d w i t h

p o l a r i z e d t h e r m a l n e u t r o n s . By ne t r o n c a p t u r e p o l a r i z e d 6 - a c t i v e 8 ~ i ( T i 1 2 = 0.8s) were produced. The k! LI p o l a r i z a t i o n P was m o n i t o r e d v i a t h e asymmetry n u c l e i

o f t h e @ - r a d i a t i o n d i s t r i b u t i o n w i t h r e s p e c t t o 6. The SLR r a t e TTI o f 8 ~ i was

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982927

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measured w i t h o u t a p p l i c a t i o n o f a 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 b y r e c o r d i n g t h e t r a n s i e n t p o l a r i z a t i o n P ( t ) a f t e r a n e u t r o n a c t i v a t i o n p u l s e .

As t h e p o l a r i z a t i o n o f t h e p r o b e n u c l e i stems f r o m t h e n u c l e a r r e a c t i o n , i t i s i n d e - pendent o f any Boltzmann f a c t o r . Thus measurements can be done a l s o i n v e r y low f i e l d s w i t h o u t Loss o f s e n s i t i v i t y and B may be v a r i e d o v e r two o r d e r s o f magnitude.

A n o t h e r r e l e v a n t f e a t u r e i s t h e extreme d i l u t i o n o f t h e n e u t r o n - a c t i v a t e d p r o b e n u c l e i ( t y p i c a l r e l a t i v e c o n c e n t r a t i o n : 10-17). A S a consequence 8 ~ i i s s u b j e c t t o h e t e r o - n u c l e a r i n t e r a c t i o n o n l y and s p i n - d i f f u s i o n i s i n h i b i t e d ( f o r d e t a i l s see / ? I / ) .

3. Measurements.- The p r e s e n t SLR measurements were done i n t h e range T = 6...340K and B = 14...830 mT, r e s p e c t i v e l y . G e n e r a l l y , t h e 8 ~ i p o l a r i z a t i o n as a f u n c t i o n o f t i m e

was f o u n d t o d e v i a t e s i g n i f i c a n t l y from a s i m p l e e x p o n e n t i a l . On t h e o t h e r hand, t h e f u n c t i o n

P ( t ) = P, e x p (-ml) ⁽¹

p r o v e d t o f i t t h e d a t a q u i t e w e l l (see F i v a l u e s o b t a i n e d i n t h i s way a r e t a k e n as f i c a t i o n f o r eq. (1) i s g i v e n below.

g. 1 f o r an example). I n t h e f o l l o w i n g TI t h e s p i n - l a t t i c e r e l a x a t i o n times. A j u s t i -

F i g . 1: R e l a t i v e p o l a r i z a t i o n !/Po (on F i g . 2: Temperature dependence o f t h e l o g a r i t h m i c s c a l e ) o f O L i i n 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 i 0 2 ) o m 6 7 ( L i 2 0 ) o , 3 3 g l a s s ~ 7 1 o f 8 ~ i i n (Si02)0.67(Li20)0,33 v e r s u s square r o o t o f t i m e

f o r v a r i o u s m a g n e t i c f i e l d s B.

(T = 8K, B = 30 mT; f i t acc.

eq. ( I ) : TI = 13.3(1.3)s)

F i g . 2 shows t h e o v e r a l l b e h a v i o u r o f T T ~ v e r s u s 1 / T f o r some B v a l u e s . The s t r o n g i n c r e a s e o f ~7~ w i t h T i n t h e h i g h t e m p e r a t u r e range T > 170K can be a s c r i b e d t o t h e q u a d r u p o l a r c o u p l i n g o f 8 ~ i t o f l u c t u a t i n g e l e c t r i c f i e l d g r a d i e n t s produced b y c l a s s i c a l d i f f u s i o n o f t h e a l k a l i i o n s . T h i s p r o c e s s has been s t u d i e d i n some d e t a i l w i t h 7 ~ a t one f i x e d B v a l u e i - ~ ~ ~ / l o / .

I n t h e low t e m p e r a t u r e range 6 s T/K < 170, T ~ I depends about l i n e a r l y on T (see F i g . 3) i n accordance w i t h measurements i n o t h e r g l a s s e s where T ~ I - ^{TI'Y w i t h}

( y ( & 1 has been o b s e r v e d /I/. The s u r p r i s i n g r e s u l t , however, i s t h e d i s t i n c t f i e l d

dependence o f T ~ I . I n s p e c t i o n o f F i g . 4 shows t h a t TT' - B - I i s a p p r o x i m a t e l y v a l i d

i n t h e whole low-T regime. As o u r e x p e r i m e n t a l method i n v o l v e s a n u c l e a r r e a c t i o n ,

r a d i a t i o n d e f e c t s cannot be e x c l u d e d w h i c h m i g h t i n f l u e n c e t h e B dependence. Very

r e c e n t 7 ~ i - ~ ~ 4 ~ measurements , however, p e r f o r m e d a t t w o B v a l u e s e x h i b i t a

de-

pendence s i m i l a r t o t h a t o b s e r v e d f o r 8 ~ i (K. Meise-Gresch, p r i v a t e communication).

4 . Discussion.- I n t h e f o l l o w i n g we p r e s e n t a c r u d e model i n o r d e r t o e x p l a i n t h e t h r e e main r e s u l t s cf t h e p r e s e n t work w h i c h can be summarized b y t h e a p p r o x i m a t e r e l a t i o n s (i) P - ^{e x p}

ml)

(ii) T ~ I - T (iii) T ~ I - ^B-I.

f i g . 3: Low-temperature T; ' d a t a o f F i g . 4: F i e l d dependence o f r e l a x a t i o n 8 ~ i i n (Si02)0m67(Li20)0,33 t i m e TI o f $I-i i n

v e r s u s r e c i p r o c a l t e m p e r a t u r e ( S i 0 2 ) 0 m 6 7 ( L i 2 0 ) 0 33 f o r v a r i o u s f o r v a r i o u s 6 v a l u e s . The L i n e s t e m p e r a t u r e s i n t 6 e low-T regime.

r e p r e s e n t a f i t based on eq. The l i n e s r e p r e s e n t f i t s acc. t o

(12). TI - 66 y i e l d i n g a l .

We assume t h a t r e l a x a t i o n i s caused b y t h e c o u p l i n g o f

L i t o some n e a r b y d e f e c t whose f l u c t u a t i o n s a r e c h a r a c t e r i z e d b y t h e c o r r e l a t i o n t i m e

F o l l o w i n g common u s e we t e n t a t i v e l y t h i n k o f q u a d r u p o l a r r e l a x a t i o n i n d u c e d b y t h e f l i p s o f a n e a r b y two-

L e v e l system (TLS). I n a rough a p p r o x i m a t i o n t h e r e l a x a t i o n r a t e may be d e s c r i b e d b y

where r i s t h e d i s t a n c e t o t h e n e a r e s t TLS,

s p i n s i n t h e f i e l d 6, and A d e n o t e s t h e c o u p l i n g s t r e n g t h . For

we assume an A r r h e n i u s - t y p e b e h a v i o u r

T

= -ro exp(E/kT). (3)

T h i s dependence i s e.g. e x p e c t e d /12/ if t r a n s i t i o n s between t h e t w o l e v e l s a r e due t o a m u l t i - p h o n o n p r o c e s s i n v o l v i n g an i n t e r m e d i a t e s t a t e . T h i s m i g h t be t h e case a t t h e t e m p e r a t u r e s a p p l i e d i n t h i s study.

A c c o r d i n g t o eqs. (2) a d (3) t h e r e l a x a t i o n r a t e depends on b o t h d i s t a n c e and e n e r - gy o f t h e TLS. I f each 8 L i i n t e r a c t s w i t h a d i f f e r e n t TLS t h e o b s e r v e d t o t a l p o l a r i - z a t i o n w i l l be a s u p e r p o s i t i o n o f e x p o n e n t i a l s each h a v i n g i t s own decay c o n s t a n t A(r,E), i - e .

P ( t ) = Po ii e-X(rpE)'t g ( r ) f ( E ) d r d~ ( 4 ) where g ( r ) and f ( E ) d e n o t e space and e n e r g y d i s t r i b u t i o n f u n c t i o n , r e s p e c t i v e l y , o f t h e TLS.

For f ( E ) we p u t / I /

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where Emax i s o f t h e o r d e r o f 0.1 eV / 7 / . g ( r ) i s g i v e n b y

4 n 3 2

g ( r ) d r = exp

n r 1 ' 4 1 ~ n r d r 3

where n i s t h e number o f TLS p e r volume. 4 T r d r i s t h e p r o b a b i l i t y t o f i n d a TLS 2 w i t h i n t h e range f r o m r t o r + dr, whereas e x p ( - 9 n r 3 ) i s t h e p r o b a b i l i t y t o f i n d n o TLS a t d i s t a n c e s s m a l l e r t h a n r. Eq, (6) i s based on t h e assumption t h a t o n l y t h e

- n e a r e s t TLS c o n t r i b u t e s t o r e l a x a t i o n because of t h e r-6 dependence o f A.

I n t h e e v a l u a t i o n of t h e i n t e g r a l s i n ( 4 ) t w o a p p r o x i m a t i o n s a r e made.

F i r s t , t h e e x p o n e n t i a l i n (4) i s r e p l a c e d by a s t e p f u n c t i o n

Now t h e r - i n t e g r a t i o n can be performed y i e l d i n g E

~ ( t )

= jmax exp

f i t ) d ~

Emax o

w i t h

ACE)

=

3 I+(UT(E))~ '

Second, t h e inhomogeneous a v e r a g i n g o v e r E i n (8) i s a p p r o x i m a t e d b y a homogeneous averaging, i .e.

where

Eq. (10) i s i d e n t i c a l w i t h t h e p h e n o m e n o l o g i c a l r e l a t i o n (1) f o u n d t o r e p r e s e n t t h e e x p e r i m e n t a l P ( t ) - c u r v e s q u i t e w e l l .

The above a p p r o x i m a t i o n s a r e a d m i t t e d l y r a t h e r crude. A more d e t a i l e d approach u s i n g a s t a t i s t i c a l model /13/ i s i n p r o g r e s s .

a l s o y i e l d s eq. (10).

From eqs. (111, (9) and (2) we r e a d i l y o b t a i n T;

' = (AT- 3 n)2.Am - _Emax ^{k T} - I - ( a r c t a n ( w o e Emax/kT ) - a r c t a n

. ⁽¹²⁾

I n t h e case w ~ ~ . e x p (Emax/kT)>> I,uT,<< 1 eq. (12) y i e l d s

Eq. (13) r e f l e c t s t h e l i n e a r dependence o f T-I on T and B-I b e i n g o b s e r v e d e x p e r i -

m e n t a l l y . 1

The l i n e s drawn i n F i g . 3 r e p r e s e n t a f i t t o t h e d a t a u s i n g eq. (12). The agreement i s r a t h e r good c o n s i d e r i n g t h e crude a p p r o x i m a t i o n s a p p l i e d i n d e r i v i n g eq. (12).

I n t h e f i t Emax/k c o u l d be v a r i e d o v e r a wide range (800...2000K) w i t h o u t i n f l u e n - c i n g t h e q u a l i t y o f t h e f i t s i g n i f i c a n t l y . F i x i n g Emax/k = 1500 K t h e f i t y i e l d e d

4 n 2 -los

(7) A = 9.8 s" and ro = 1.5-10 .

I n p r i n c i p l e i t i s p o s s i b l e t o e s t i m a t e t h e c o n c e n t r a t i o n n f r o m t h i s r e s u l t if some assumption f o r t h e c o u p l i n g s t r e n g t h A i s made. This, however, s h a l l n o t be t r i e d h e r e i n v i e w o f t h e h y p o t h e t i c a l c h a r a c t e r o f t h e r e l a x i n g c e n t r e .

I n t h i s c o n t e x t we draw a t t e n t i o n t o t h e f o l l o w i n g f a c t . The e q u a t i o n s ( 2 ) and (3)

b e i n g t h e s t a r t i n g p o i n t i n t h e d e r i v a t i o n o f (12) a r e a p p r o p r i a t e a l s o i n t h e case

o f n u c l e a r r e l a x a t i o n by a nearby paramagnetic d e f e c t whose c o r r e l a t i o n t i m e i s governed by an Orbach process. Besides,

has been shown /14/ that, i n t h e absence o f s p i n d i f f u s i o n , r e l a x a t i o n v i a paramagnetic c e n t r e s i s d e s c r i b e d by eq. (I).

Since t h e p r e f a c t o r A c o n t a i n s t h e n u c l e a r d i p o l e moment o r t h e quadrupole moment, r e s p e c t i v e l y , a comparison o f t h e r e l a x a t i o n r a t e s o f t h e i s o t o p e s 7 ~ i and 8 ~ i should g i v e i n f o r m a t i o n on t h e t y p e o f i n t e r a c t i o n . T h i s comparison i s n o t t r i v i a l and w i l l be done i n f u t u r e work.

Acknowledgement.- We are g r a t e f u l t o D r . K a r i n Meise-Gresch f o r communicating un- p u b l i s h e d (Li-NMR data and f o r h e l p f u l discussions. T h i s work i s sponsored by t h e Gundesministerium f u r Forschung und Technologic.

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