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TRAJECTORY TREATMENT OF THE FA (II)
-CENTER IN KCl : Li DECAY TIME IN THE
EXCITED STATE
R. Englman, A. Ranfagni, A. Agresti, D. Mugnai
To cite this version:
TRAJECTORY TREATMENT OF THE F ~ (
I I )
-CENTERI N
KC1:L i
DECAY T I M E
I N
THE EXCITED STATER. Englman, A. ~ a n f a ~ n i ' , A. ~ ~ r e s t i + and D . ~ u g n a i +
Soreq NucZear Research Center, Yavne, IsraeZ
' ~ s t i t u t o
d i Ricerca suZZe &de Elettromegnetiche del CNR, Firenze, ItaZy
A b s t r a c t
-
We s i m u l a t e t h e t e m p e r a t u r e dependence of t h e decay t i m e o f an--
i m p u r i t y i n i t s e x i c e t d s t a t e by o b t a i n i n g t h e c l a s s i c a l t r a j e c t o r i e s o f t h e i o n s i n t h e c r y s t a l . The F A ( I I l - c e n t e r
i n
K C 1 : L i B s t r e a t e d .Recent developments o f m o n i t o r i n g t e c h n i q u e s i n t h e r a n g e o f p i c o s e c o n d s have a l l o - wed measurements o f c o n f i g u r a t i o n a l r e l a x a t i o n t i m e s T R i n e x c i t e d S t a t e s o f i m p u r i - t i e s
i n
c r y s t a l s . By r e c o r d i n g t h e r i s e t i m e o f e m i s s i o n frorn t h e r e l a x e d e x c i t e d s t a t e , a d e c r e a s ei n
T R from a b o u t 1 5 ps t o 1-2 p s was o b s e r v e d f o r t h e F A ( I I ) c e 2 t e r i n KC1:Li upon r a i s i n g t h e t e m p e r a t u r e t o a b o u t 30°K /1/ and a b o u t t h e same d e c r e a s e was found more r e c e n t l y f o r t h e l ~ ~ ~ - s t a t e i n K1:Ag /2/. The a n a l y s e s of t h e d a t a , which were a b l e t o a c c o u n t f o r o n l y a s r n a l l f r a c t i o n of t h e e n e r g y d i s - p a t e d i n t h e c o n f i g u r a t i o n a l r e l a x a t i o n , ernployed a rnultiphonon r e l a x a t i o n f o r m u l a(E7. 3.36 i n / 3 / l f o r t h e t e m p e r a t u r e dependence o f T R . T h i s quantum m e c h a n i c a l e x p r e s s i o n g i v e s t h e r e s i d e n c e tirne -rr i n t h e i n i t i a l s t a t e b e f o r e t r a n s i t i o n t o a n e i g h b o r i n g l e v e l b e l o n g i n g t o a d i f f e r e n t s t a t e .
We have performed compuntation o f t h e c l a s s i c a l t r a j e c t o r i e s of t h e i o n s f o r t h e F A I I I ) c e n t e r f o l l o w i n g e x c i t a t i o n . The model f o r t h e c e n t e r i s shown i n F i g u r e 1.
where t h e h o r i z o n t a l a x i s r e p r e s e n t s n e i g h b o r - c o r e l a t e d jumps o f t h e vacancy between e q u i v a l e n t 100 t y p e p o s i t i o n s . We u s e a c r y s t a l - m o d e r e p r e s e n t a t i o n [ a m p l i t u d e Qq,,,
mode i n d e x s , wave number q l f o r t h e i o n i c d i s p l a c e r n e n t s , i n s t e a d of t h e more common i n d i v i d u a l atom d i s p l a c e m e n t s . We s o l v e a b o u t 104 e q u a t i o n s of motions f o r Qq,,
and o b t a i n t h e t i m e o f r e s i d e n c e r r a s w s l l a s decay ( ~ ' 1 and c o r r e l a t i o n ( T ~ f o r ~ ~ )
t h e decay of Qvac.
The c l a s s i c a l motions p r o c e e d a l o n g an a d i a b c t i c p o t e n t i a l e n e r g y s u r f a c e (APES-1 t h a t i s s t a b l e (namely, harmonicl f o r a l 1 d i s p l a c e m e n t s e x c e p t Qvac. I n F i g u r e 2 we show t h e r e l a t i m s h i p o f O u r c l a s s i c a l model w i t h t h e m u l t i p h o n o n - r e l a x a t i o n model i n /1/. T h e i r f o r m a l i s m i m p l i e s t u n n e l i n g from t h e i n i t i a l n o n - a d i a t a t i c V2 t o t h e s u r f a c e s VI o r Vg.
JOURNAL
DE
PHYSIQUECon1 igurations:
Vacancy Saddlepoint Vacancy
Qvac i n t h e 110 ( = X I ) d i r e c t i o n , i s (k:q,J:s)
where
1 K K2
Qv~c-F
1
1
Q k , j e k , j ( k / K 1 1 / 2 and e,,s=mF(uq,s)i qxl F ( u ) - ~ - ~ ~ / ~ o ,N K= 1 j =l
eq,s and F ( w l g i v e t h e mode s e l e c t i v e i n t h e c o m p o s i t i o n o f Qvac; WD i s t h e c i r c u - l a r Debye f r e q u e n c y . The i n i t i a l c o n d i t i o n s f o r t h e a m p l i t u d e s a t t e m p e r a t u r e T a r e where k B ~ " q , s = [ n q , s + 1 / 2 ) h ~ ~ , ~ a a r e random a n g l e s .
III
-
RESULTSThe a m p l i t u d e Qvac shows t h r e e c h a r a c t e r i s t i c b e h a v i o r s , dependine on t h e e n e r g y excess aE and t h e Debyefreauency v =wD/2.rr. F o r a p e r i o d i c m o t i o n , i n t h e l o w e r p o r t i o n , one a s s o c i a t e s t h e d e c a ~ ?ime w i t h t h e t i m e o f s t a y rr or r e ç i d e n c e t i m e n e a r t h e Qq,,=O, 100 p o s i t i o n .
Q u a n t i t a t i v e l y , t h i s appears as i n F i g u r e 4, where c u r v e s a r e shown f o r t h r e e va- l u e s o f t h e h i g h - f r e s u e n c v c u t - o f f p a r a m e t e r A i n F ( w ) and f o r s i m u l a t i o n s w i t h a number o f modes %
4
K3 3 1o4 ( K = 3 0 ) .v,
(lol*s-')
2 A E
F i g . 3
-
"Phase diagram" f o r t h e m o t i o n o f Qvac i n AE-vo p a r a m e t e r s p a c e , f = . ,JOURNAL
DE
PHYSIQUE
F i g . 4
-
The vacancy mode a m p l i t u d e r i s e s a f t e r a r e s i d e n c e t i m e o f c c a 2-5 Debye p e r i o d s and p e r f o r m s a d e c a j n g o s c i l l a t o r ? motion around t h e RES c o n f i g u r a t i o n .REFERENCES
/1/ W i e s e n f e l d , J.M., M o l l e n a u e r , L.F. a n d I p p e n , E . P . , P h y s . Rev. L e t t . ( 1 9 8 1 ) 1 6 6 8 .
/2/ N i k o l a u s , B. a n d S c h m i t t , K . , A p p l . P h y s . B
2
[ 1 9 8 5 1 ./ 3 / Englman, R., Non r a d i a t i v e Oecay of I o n s a n d M o l e c u l e s i n S o l i d s [ N o r t h - H o l l a n d , Amsterdam 1 9 7 9 1 .