HIGH RESOLUTION SPONTANEOUS RAMAN INVESTIGATION OF THE RELAXATION OF TWO-PHONON BOUND STATES IN SOLID CO2

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HIGH RESOLUTION SPONTANEOUS RAMAN

INVESTIGATION OF THE RELAXATION OF

TWO-PHONON BOUND STATES IN SOLID CO2

P. Ranson, R. Ouillon, S. Califano

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C7, suppl6ment au nOIO, Tome

46,

o c t o b r e 1985 _{page C7-311}

HIGH RESOLUTION SPONTANEOUS

RAMAN

INVESTIGATION OF THE RELAXATION OF TWO-PHONON BOUND STATES IN SOLID C 0 2

P. Ranson, R. O u i l l o n and S. c a l i f a n o '

Dgpartement de Recherches Physiques, L.A. 71, Universitd P. e t M. Curie, T.22,

$

pZace Jussieu, 75230 Paris Cedex 05, France

Laboratorio d i Spettroscopia MoZecoZare, Universita' d i Firenze, v i a G. Capponi 9, 50121 Firenze, I t a l y

R&sum&

-

Le d o u b l e t d e Fermi du c r i s t a l de C02 e s t 6tudi.E dans l a gamme de t e m p d r a t u r e 1.6

-

130 K p a r s p e c t r o m d t r i e Raman

P

h a u t e r d s o l u t i o n . Le ddpha- s a g e d e s deux composantes d e s y m d t r i e Ag e t Fg de chaque bande d u d o u b l e t e s t i n t e r p r d t d au moyen de p r o c e s s u s de r e l a x a t i o n anharmoniques

P

q u a t r e phonons

.

A b s t r a c t

-

High r e s o l u t i o n Raman s p e c t r a of t h e Fermi d i a d i n c r y s t a l l i n e C02 were performed i n t h e t e m p e r a t u r e r a n g e 1.6

-

130 K . The d e p h a s i n g o f b o t h Ag and Fg components o f t h e 51+ and

a-

h y b r i d l e v e l s i s i n t e r p r e t e d i n terms of four-phonon anharmonic p r o c e s s e s .

I

-

INTRODUCTION

Two main s p e c t r o s c o p i c t e c h n i q u e s have been e x t e n s i v e l y used i n r e c e n t y e a r s t o s t u d y t h e r e l a x a t i o n of e l e m e n t a r y v i b r a t i o n a l e x c i t a t i o n s i n m o l e c u l a r c r y s t a l s : picosecond CARS (Coherent Anti-Stokes Raman S c a t t e r i n g ) i n t h e time domain and s p o n t a - neous Raman s c a t t e r i n g i n t h e f r e q u e n c y domain.

I n r e c e n t p a p e r s (1) we have shown t h a t h i g h r e s o l u t i o n spontaneous Raman s c a t t e r i n g i s a v e r y c o n v e n i e n t t o o l f o r t h e s t u d y o f t h e r e l a x a t i o n of l o n g l i v i n g phonons up t o a b o u t 2 n s .

I n p a r t i c u l a r , h i g h r e s o l u t i o n Raman s p e c t r o s c o p y i s b e s t a d a p t e d t o s t u d y s e p a r a t e l y t h e r e l a x a t i o n o f v e r y c l o s e l y i n g Raman bands such a s t h o s e a r i s i n g from weak f a c t o r group s p l i t t i n g s of i n t e r n a l modes i n m o l e c u l a r c r y s t a l s . A s a n example we r e p o r t h e r e on t h e r e l a x a t i o n of t h e f a c t o r group components of b o t h t h e

Q-

and

a+

p a r t n e r s o f t h e Fermi d i a d wl : 2w2 i n s o l i d C02 i n t h e t e m p e r a t u r e range 1.6

-

130 K . These new d a t a improve p r e v i o u s r e s u l t s o b t a i n e d by means o f picosecond CARS ( 2 ) where o n l y Ag modes were i n v e s t i g a t e d .

I1

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THE w1 : 2w2 HYBRID BOUND STATES I N SOLID C02

The Raman Fermi d i a d i n C02 a r i s e s from t h e anharmonic i n t r a m o l e c u l a r c o u p l i n g between t h e fundamental

wl

(symmetric s t r e t c h i n g ) and t h e o v e r t o n e 2w ( b e n d i n g ) ( 3 ) . I n t h e c r y s t a l , owing t o i n t e r m o l e c u l a r c o u p l i n g t h e Raman spectrum % i s p l a y s two h y b r i d bound s t a t e s w i t h f r e q u e n c y

51-

= 1276 cm-' and 51+ = 1384 cm-' on b o t h s i d e s of a b r o a d , a l m o s t s t r u c t u r e l e s s two-phonon continuum e x t e n d i n g from 1300 t o 1350 cm-' ( 4 ) .

Two f a c t o r group components, one Ag and one Fg, a r e p r e d i c t e d i n t h e c r y s t a l f o r e a c h of t h e s e bound s t a t e s owing t o t h e o c c u r r e n c e of f o u r molecules i n a c u b i c u n i t c e l l . Using o u r tandem Fabry-Perot p l u s s p e c t r o m e t e r i n s t r u m e n t ( 1 ) w i t h a l i m i t i n g

r e s o l u t i o n of 0.004 cm-' we succeeded i n r e s o l v i n g ~ c o m p l e t e l y , f o r t h e f i r s t time, t h e s e f a c t o r group components and i n measuring t h e i r band p r o f i l e and f r e q u e n c y w i t h h i g h a c c u r a c y ( 6 ) . I n t h e p r e s e n t p a p e r we d i s c u s s t h e e v o l u t i o n w i t h t e m p e r a t u r e of

t h e s e band p r o f i l e s i n t h e range 6

-

130 K .

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C7-312 J O U R N A L D E PHYSIQUE

E x t e r n a l modes

4

Schematic drawing of t h e e n e r g y l e v e l s of c r y s t a l l i n e CO (w < 1500 em-')

2

111

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EXPERIMENTAL RESULTS

The e x p e r i m e n t a l set-up was d e s c r i b e d i n r e f . 1. E x p e r i m e n t a l bandwidths a r e p l o t t e d a s a f u n c t i o n of t e m p e r a t u r e f o r t h e f o u r bands s t u d i e d (two components o f 52- and two of 52,) i n f i g . I and f i g . 11. F o r t h e 52+ b a n d s , measurements were l i m i t e d t o t h e t e m p e r a t u r e range 6

- 80 K s i n c e , a t h i g h e r t e m p e r a t u r e s , t h e s e bands a r e t o b r o a d

t o b e a n a l y z e d under h i g h r e s o l u t i o n . The measured bandwidths y remain p r a c t i c a l l y c o n s t a n t up t o 10 K and b e g i n t o b r o a d e n o n l y above t h i s t e m p e r a t u r e . A c t u a l l y t h e two components of t h e 52+ bound s t a t e broaden i n a s i m i l a r way whereas t h e two components of t h e 52- bound s t a t e f o l l o w two d i f f e r e n t r e g i m e s , t h e Ag b e i n g narrower a t 1.6 K and l a r g e r a t h i g h e r t e m p e r a t u r e t h a n t h e Fg component.

The components of t h e 52, s t a t e show a p e r f e c t l o r e n t z i a n shape o v e r t h e e n t i r e t e m p e r a t u r e range s t u d i e d . A t v e r y low t e m p e r a t u r e t h e two components of t h e 51- bound s t a t e a r e n a r r o w e r t h a n t h e i n s t r u m e n t a l s l i t f u n c t i o n (0.004 em-') and t h u s t h e i r band p r o f i l e c a n b e c o r r e c t l y d e t e r m i n e d o n l y above 20 K. A t v e r y low tempera- t u r e t h e Fg component h a s a s l i g h t asymmetry w i t h a t a i l e x t e n d i n g on t h e low f r e q u e n c y s i d e . A s t h e t e m p e r a t u r e i n c r e a s e s t h i s t a i l g r a d u a l l y d i s a p p e a r s and t h e band t e n d s t o be l o r e n t z i a n . The s p l i t t i n g between t h e 52, and

Q-

l e v e l s i s i n s t e a d p r a c t i c a l l y i n s e n s i t i v e t o t h e t e m p e r a t u r e v a r i a t i o n i n t h e range s t u d i e d , c l e a r l y i n d i c a t i n g t h a t t h e i n t r a m o l e c u l a r t h i r d o r d e r anharmonic c o u p l i n g term K122 ( 3 ) ,

r e s p o n s i b l e of t h e Fermi r e s o n a n c e , i s c o n s t a n t . IV

-

DISCUSSION

Although a complete t h e o r y d e s c r i b i n g t h e r e l a x a t i o n of h y b r i d v i b r o n bound s t a t e s i s s t i l l l a c k i n g , a c o n v e n i e n t a n a l y s i s o f t h e e x p e r i m e n t a l r e s u l t s can b e made

f o l l o w i n g t h e t h e o r e t i c a l approach used i n o u r p r e v i o u s work t o i n t e r p r e t t h e low t e m p e r a t u r e bandwidths ( 1 ) .

As d i s c u s s e d i n r e f . 7 t h e r e l a x a t i o n of t h e v i b r o n bound s t a t e s 52+ and 52- c a n be c o n v e n i e n t l y a n a l y z e d i n terms of d e p o p u l a t i o n and d e p h a s i n g p r o c e s s e s . S t r a i n i n h o m o g e n e i t i e s and e n e r g y t r a p p i n g by i s o t o p i c i m p u r i t i e s c a n a l s o c o n t r i b u t e t o t h e t o t a l w i d t h s .

A t v e r y low t e m p e r a t u r e s p u r e d e p h a s i n g p r o c e s s e s , due t o t h e anharmonic c o u p l i n g w i t h t h e t h e r m a l b a t h , c a n be n e g l e c t e d owing t o t h e low number o f e x c i t e d t h e r m a l phonons. The e x t r e m e l y low width o f t h e 52- components shows t h a t t h e e f f e c t of i m p u r i t i e s i s a l s o s m a l l and c a n n o t exceed t h e r e s i d u a l bandwidths which a r e lower t h a n 0.004 cm-'

.

The r e l a x a t i o n i s t h u s l a r g e l y dominated by d e p o p u l a t i o n decay p r o c e s s e s .

S i n c e t h e two

Q+

components l i e above t h e two-phonon continuum, four-phonon decay p r o c e s s e s o f t h e t y p e

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according t o e q . 4 of r e f e r e n c e 8, a simple law of t h e type :

where: i s t h e occupation number of t h e l a t t i c e phonon w c r e a t e d i n t h e p r o c e s s .

P P

The S2- s t a t e s occur i n s t e a d below the two-phonon c o n t i n u r n and t h e r e f o r e no down- conversion processes a r e p o s s i b l e . The very narrow low temperature width i s t h u s c o n t r o l l e d only by t h e decay i n t o l o c a l i z e d i m p u r i t y l e v e l s o r by pure dephasing mechanisms. As t h e temperature i n c r e a s e s , up-conversion p r o c e s s e s i n v o l v i n g t h e f u s i o n with a l a t t i c e phonon u p , t o decay i n t o the two-phonon continuum became p o s s i b l e . A process of t h i s type can be r e p r e s e n t e d a s

where t h e momentum c o n s e r v a t i o n K

+

K ₊

_E2

₌_{0 h o l d s as b e f o r e . From e q . 4 of}

r\, %'

r e f e r e n c e 8 t h i s process obeys t h e simple r e l a t i o n :

where BU i s an average coupling c o e f f i c i e n t assumed t o be c o n s t a n t i n t h e

6

space. Using e q s . (2) and (4) and assuming t h a t only one down-process i s e f f e c t i v e f o r the thermal e v o l u t i o n of

y

_R,

and t h a t only one up-process i s e f f e c t i v e f o r y _52- we have

7

obtained t h e r e s u l t s c o l l e c t e d i n t a b l e I and show by t h e continuous curves o f f i g s . I and 11.

TABLE

I

V i bron component Frequency (cm-') y(cm-') B u ( c V 1 ) w ,(cm-')

P

T = 6 K T = 9 0 K T - t O

A s t r i k i n g p o i n t of our d a t a i s t h e h i g h e r e f f i c i e n c y of dephasing process i n each

52- o r

R+

band f o r t h e Ag mode t h a n f o r t h e corresponding Fg one. This r e s u l t i n d i c a t e s c l e a r l y t h e i n f l u e n c e of mode symmetry i n v i b r a t i o n a l r e l a x a t i o n .

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C7-314 JOURNAL

DE

PHYSIQUE

TEMPERATURE DEPENDENCE OF THE LINEWIDTH FOR THE TWO COMPONENTS OF THE 0- (FIG. 1) a n d Q+ (FIG. 1 1 ) BOUND STATES.

C r o s s e s a n d c i r c l e s : o u r d a t a f o r Ag and Fg r e s p e c t i v e l y T r i a n g l e s : p i c o s e c o n d CARS d a t a b y G a l e ( 2 ) S o l i d l i n e : c a l c u l a t e d c u r v e s f r o m e q u a t i o n 4 f o r

a-

a n d f r o m e q u a t i o n 2 f o r

a+

F i g . I F i g . I1 a25 A (120-

-

E

LJ 0 50 100 TEMPERATURE ( K 1 REFERENCES TEMPERATURE ( K 1

1- R. OUILLON, P. RANSON and S . CALIFANO, Chem. P h y s . 91 (1984) 119

- P. RANSON, R. OUILLON, B. HALAC a n d S . CALIFANO, J. d e Chimie P h y s i q u e 82,

n o 213 (1985) 169

2- G.M. GALE, P . GUYOT-SIONNEST,

W.Q.

ZHENG a n d C. FLYTZANIS, P h y s . Rev. L e t t e r s , 5 4 (1985) 8 2 3

- G.M. GALE, J. d e Chimie Physique, 8 2 , n o 2 1 3 ( 1 9 8 5 ) 3- F . BOGANI a n d P.R. SALVI, J. Chem. P h y s . , 81 (1984) 4991 4- A. ANDERSON a n d T.S. SUN, Chem. P h y s . L e t t e r s , 8 (1971) 5 3 7

5- J.C. DECIUS a n d R.M. HEXTER, M o l e c u l a r V i b r a t i o n s i n C r y s t a l s , McGraw H i l l (1977) 6- R. OUILLON, P. RANSON a n d S . CALIFANO, J . Chem. P h y s . (1985) i n p r e s s

7- A. LAUBEREAU a n d W. KAISER, Rev. Mod. P h y s . 5 0 (1978) 6 0 7 8- L. HESS a n d P. PRASAD, J . Chem. P h y s . 72 (1980) 9 7 3