RAMAN SCATTERING INDUCED BY DIELECTRIC-METALLIC COLLOID INTERFACES

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RAMAN SCATTERING INDUCED BY

DIELECTRIC-METALLIC COLLOID INTERFACES

J.-P. Buisson, E. Rzepka, L. Taurel

To cite this version:

J.-P. Buisson, E. Rzepka, L. Taurel. RAMAN SCATTERING INDUCED BY DIELECTRIC-

METALLIC COLLOID INTERFACES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-69-

C5-73. �10.1051/jphyscol:1984509�. �jpa-00224127�

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RAMAN SCATTERING INDUCED BY DIELECTRIC-METALLIC COLLOID INTERFACES

J.-P. B u i s s o n , E. Rzepka and L . Taurel

+

Laboratoire de Physique CristaZZine

,

B&t. 490, Uniuersite' de paris-Sud, 9 1405 Orsay Cedes, France

ResurnB - Nous m o n t r o n s q u e l ' e l a r g i s s e m e n t d e l a r a i e Rayleigh o b s e r v e s u r l e s s p e c t r e s d e diffusion R a m a n induits p a r d e s c o l l o i d e s m e t a l l i q u e s d a n s un d i e l e c t r i q u e , p e u t 6 t r e d Q au c a r a c t e r e plan d e I ' i n t e r f a c e colloide-cristal h a t e . La t r k s f a i b l e durBe d e vie d e s B t a t s Blectroniques e x c i t e s d e s colloi'des mBtalliques p e u t expliquer la t r 6 s f a i b l e i n t e n - s i t e d e la diffusion R a m a n multi-phonons. Les deux m o d e s localisBs B I ' i n t e r f a c e (111) colloi'de d e potassium-KI, calculBs a I'aide d'un modble e l e m e n t a i r e , s i t u e s B 8 3 cm-1 e t B 1 1 8 e m - ? , s o n t e n bon a c c o r d a v e c l e s r e s u l t a t s expBrirnentaux (84 crn-1 e t 1 2 0 cm-I).

A b s t r a c t - W e show t h a t t h e broadening of t h e Rayleigh line o b s e r v e d on t h e R a m a n s c a t t e r i n g s p e c t r a induced by m e t a l l i c colloi'ds in d i e l e c t r i c c a n c o m e f r o m t h e plane c h a r a c t e r of t h e colloi'd-matrix i n t e r f a c e . The very s h o r t l i f e t i m e of m e t a l l i c colloi'd e x c i t e d e l e c t r o n i c s t a t e s c a n e x p l a i n t h e v e r y w e a k i n t e n s i t i e s of t h e multiphonon Rarnan s c a t t e r i n g . Using a sirnple model, we h a v e c a l c u l a t e d t w o l o c a l i z e d m o d e s a t t h e (111) p o t a s s i u m colloi'ds-KI i n t e r f a c e , p e a k e d a t 8 3 cm-1 a n d 1 1 8 c m - I in good a g r e e m e n t w i t h t h e e x p e r i m e n t a l r e s u l t s (84 cm-1 and 1 2 0 cm-I).

T h e f i r s t - o r d e r R a m a n s c a t t e r i n g s p e c t r a induced by m e t a l l i c colloi'ds (Na, Ag) in d i e l e c t r i c s (NaI, NaCI, NaBr) h a v e a l r e a d y been d e s c r i b e d previously / I / . The m a i n r e s u l t s of this s t u d y a r e r e c a l l e d :

i) T h e very s t r o n g i n t e n s i t y of s c a t t e r i n g when t h e e x c i t i n g l a s e r line is in r e s o n a n c e w i t h t h e a b s o r p t i o n bands of t h e s u r f a c e plasrnons shows t h a t t h e l a t t e r a r e involved in t h e s c a t t e r i n g process.

ii) When t h e colloi'd m e t a l is t h e s a m e a s t h e h o s t c r y s t a l m e t a l , t h e o b s e r v e d m o d e s h a v e l o w e r f r e q u e n c i e s t h a n t h e phonon c u t - o f f v a l u e ( w g ) in t h e p u r e c r y s t a l . On t h e c o n t r a r y , s i l v e r colloi'ds in Nal, NaBr a n d N a C l i n d u c e l o c a l i z e d m o d e s a t higher f r e q u e n c i e s t h a n

wL.

iii) T h e a b o v e r e s u l t s s h o w t h a t t h e R a m a n s c a t t e r i n g o c c u r s a t t h e dielectric-colloi'd i n t e r f a c e .

However, t w o e f f e c t s s t i l l r e q u i r e i n t e r p r e t a t i o n :

i) T h e broadening of t h e Rayleigh line a s a f u n c t i o n of t h e t e m p e r a t u r e .

ii) T h e a b s e n c e of overtones. This i m p o r t a n t r e s u l t is t o be c o m p a r e d with t h e e n h a n c e d Rarnan s c a t t e r i n g of m o l e c u l e s a d s o r b e d on r n e t a l l i c s u r f a c e s (SERS)

121.

R e c e n t l y i t has b e e n o b s e r v e d a two-phonon R s r n a n s c a t t e r i n g of m o l e c u l e s ( 0 2 a n d C O ) adsorbed on a P t (1 11) s u r f a c e /3/, but t h e i n t e n s i t y i s m u c h w e a k e r t h a n t h a t of one-phonon lines.

T h e a i m of t h i s p a p e r i s t o show w i t h t h e help of a n e x a m p l e - t h e p o t a s s i u m colloi'ds in KI - w h a t m i g h t be t h e origin of t h e s e e f f e c t s a n d which p a r a m e t e r s a r e involved.

In o r d e r t o c a l c u l a t e t h e f r e q u e n c i e s of l o c a l i z e d m o d e s a t t h e colloi'd-dielectric i n t e r f a c e a s i m p l e t h e o r y applied t o t h e c a s e of p o t a s s i u m colloi'ds in K I w a s used.

EXPERIMENTAL RESULTS

R a m a n s c a t t e r i n g by p o t a s s i u m colloi'ds in KI o b t a i n e d by a g g r e g a t i o n of F c e n t e r s /4/

h a v e been studied. Thus in t h e s a m e s a m p l e , F c e n t e r s a n d colloi'ds a r e p r e s e n t simulta- neously. So, t h e o p t i c a l a b s o r p t i o n s p e c t r u m c o n t a i n s t h e F band due t o F c e n t e r s a n d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984509

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C5-70 JOURNAL

DE

PHYSIQUE

Fig. 1 - E x p e r i m e n t a l a b s o r p t i o n a n d R a m a n spectra o f K I c o n t a i n i n g F centers and K colloi'ds.

(a) absorption s p e c t r u m a t 78 K.

(b) R a m a n s p e c t r u m a t T = 10 k ;

XL

= 676.4 nm.

(c) R a m a n s p e c t r u m a t T = 1 0 K ;

X L =

752.5 nm.

(d) Raman spectrum a t T = 78 K ;

XL=

752.5 nm.

t h e C1 and C 2 bands due t o colloi'ds ( f i g . l a ) . T h e colloi'ds do n o t have t h e b o d y - c e n t e r e d c u b i c s t r u c t u r e o f t h e a l k a l i m e t a l b u t r e t a i n t h e 1 f a c e - c e n t e r e d c u b i c s t r u c t u r e of t h e o r i g i n a l c a t i o n s i t e s 151.

F u r t h e r m o r e i t was shown t h a t t h e r e l a x a t i o n o f t h e a t o m s i n t h e colloi'd f r o m t h e i r original position i n t h e h o s t l a t t i c e i s w e a k 151.

T h e o b s e r v e d R a m a n s p e c t r a i n s u c h a s a m p l e depends h e a v i l y on t h e l a s e r l i n e wavelength used. F i - g u r e s I b a n d I c s h o w t h e spectra o b t a i n e d w i t h t w o K r y p t o n l a s e r

n 5 0 loo 150 200

o

⁵⁰ ^loo 1% l i n e s : one a t 676.4 n m i n resonance

w

lcm-'

-

i n t h e F band and t h e o t h e r a t 752.5nm i n resonance i n t h e C l band. The spectrum i n fig. I b i s c h a r a c t e r i s t i c o f t h e F centers i n K I 161, and differs basically f r o m t h a t i n fig. I c which can be a t t r i b u t e d t o the colloi'd- m a t r i x interface, except the l i n e a t 96.5 c m - ' s t i l l due t o t h e F centers. The reason f o r t h i s a t t r i b u t i o n i s t h a t one can observe a pronounced resonance e f f e c t when t h e laser l i n e f a l l s i n t h e C1 and C 2 absorption bands themselves a t t r i b u t e d t o surface plasmons /I/.

Thus, t h e study o f potassium colloi'ds i n K I allows us t o compare R a m a n s c a t t e r i n g by a p o i n t d e f e c t (the F center) and R a m a n s c a t t e r i n g b y an i n t e r f a c e ( m e t a l l i c colloi'd-insulating c r y s t a l l i n e m a t r i x ) .

We have i n this way brought t o l i g h t t w o m a i n differences :

i) The background i s almost zero a t t h e base o f t h e Rayleigh l i n e on t h e F c e n t e r s p e c t r u m (fig. I b ) w h i l e i t is intense on the colloi'd s p e c t r u m (fig. I c ) and increases strongly w i t h t h e t e m p e r a t u r e (fig. I d ) as does t h e w i d t h o f t h e R a y l e i g h line.

i i ) The phonon c u t - o f f value w~ i n pure K I is shown on t h e spectra. I n fig. I c t h e Raman s c a t t e r i n g c a n c e l s above t h i s frequency (only a weak background remains) so t h a t one c a n deduce t h a t the lines observed on t h i s spectrum correspond t o a one-phonon scattering. O n t h e contrary, i n fig. I b t h e s p e c t r u m spreads o u t f a r above wR w i t h a non-negligible intensity.

It has been shown /7/ / 8 / t h a t t h e lines observed i n t h i s range are due t o a multi-phonon scattering.

I N T E R P R E T A T I O N

The i n t e r p r e t a t i o n o f these results requires a t h e o r e t i c a l m o d e l i n order t o compare R a m a n s c a t t e r i n g o f F centers t o t h a t o f colloi'ds. The t h e o r y o f Raman s c a t t e r i n g b y F centers has b e e n e x t e n s i v e l y developed /9/ and we m e r e l y r e c a l l the r e l e v a n t results. To t r e a t a colloi'd we consider t h a t i t c o n s t i t u t e s a two-dimensional d e f e c t f o l l o w i n g crystallographic planes, t h a t i s t o say, i n f i n i t e i n t w o directions and having a c e r t a i n thickness i n t h e d i r e c t i o n perpendicular t o t h e plane so defined. As shown by e x p e r i m e n t a l results, we suppose t h a t R a m a n s c a t t e r i n g processes occur i n the neighbourhood o f colloi'd-host c r y s t a l interface.

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A . - BACKGROUND AND BROADENING OF RAYLEIGH LINE

For a point defect the differential Stokes Raman scattering cross section relative to vibrations of r type is proportional to / 8 / :

(r)

where B _ t(E|_) depends on the wavelength of the incident energy E(_ and polarization directions of the incident light n and of the scattered light n1. The Cjlr) coefficients represent the coupling of the point defect with the neighbouring ions. The quantities pr s( r , u ) are the perturbed normalized projected densities of one-phonon states, and n(cu) = (exp(fi to/kgT)- 1)is the Bnse factor.

Fig. 2 — H i s t o g r a m of the unper- t u r b e d p r o j e c t e d densities of one- phonon states.

(a) projection on the T|vibrations of the first ionic shell surrounding the F center in K I .

(b) p r o j e c t i o n on the transverse v i b r a t i o n s of the c a t i o n i c (111) plane in K I at Kit - 0.

Fig. 3 — C a l c u l a t e d unperturbed f i r s t - o r d e r Stokes Raman spectra.

( ) : T= 10K ,• ( - - - ) : T = 78 k ; ( ) : T = 293 k.

(a) for a point defect.

(b) for a plane defect.

In the case of a two-dimensional d e f e c t , the translation symmetry is destroyed in the direction perpendicular to the interface, but remains in the other two. The wave vector in the defect plane k// remains a good quantum number and during a Raman scattering process the light can only interact with phonons at k// - 0. For these defects, in equation (1), we must replace the perturbed projected state densities pr s( r , w) by those of the interface related to k//= 0,i.e.: prs(k//=0,r,w).

The perturbed projected state densities of the interface are^ calculated from the perturbation and densities of unperturbed projected state densities : p °s( k / / = 0 (T, u), /10/ and at low f r e - quencies they behave similarly to the latter. We show (fig. 2b) the unperturbed state^density at k / / = 0 of transverse phonons projected on the cations ofan(111) interface in KI:pc'J,(k//=0,T,aj).

Note that (fig. 2b), when the frequency goes to zero, the projected state densities tend to a non-zero constant, which gives :

Therefore, following (2), —^—^ pc°c ( k / / = 0,T, w) tends to an infinite value when ui goes to zero (fig. 3b), producing a background at low frequencies as well as a broadening of the

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C5-72 JOURNAL DE PHYSIQUE

R a y l e i g h line. These e f f e c t s , f r o m t h e t e r m n(w), depend h e a v i l y on t e m p e r a t u r e (fig. 3b). I n t h i s f i g u r e we have n o r m a l i z e d t h e t h r e e curves so t h a t t h e o p t i c l i n e a t 100 c m - 1 has t h e same intensity. These results a r e consistent w i t h t h e e x p e r i m e n t (figs. I c and Id). I n figs. 2a and 3a w e show, f o r comparison t h e calculations f o r t h e F c e n t e r i n KI.

B. - TWO- PHONON R A M A N SCATTERING

It has been shown i n t h e case o f F centers t h a t multiphonon Raman s c a t t e r i n g is s t r o n g /7,8/. It depends on t h e wavelength o f t h e e x c i t i n g l i g h t and has i t s highest value when t h e laser l ~ n e is tuned i n t h e F band m a x i m u m 181. B y a c a l c u l a t i o n s l m i l a r t o t h a t o f ref. 8, i n w h ~ c h t h e spin-orbit coupling i s neglected, t h e t o t a l R a m a n cross section by m i d e n t i c a l phonons "in o f

T ;

s y m m e t r y i s g i v e n b y /?I/ :

where

and

2 = {EL

-

EF - i

Y/~}

1

E i s t h e energy o f t h e F band maximum, EL t h e energy o f t h e incident l i g h t and Y i s t h e inverse o f t h e l i f e t i m e o f the e x c i t e d e l e c t r o n i c l e v e l which gives r i s e t o t h e F F band. B 2 is t h e c o n t r i b u t i o n o f t h e

I? ;

modes t o t h e secondmoment o f t h e F band. The f a c t o r (oi(r;)/d(r,,+) ) represents t h e r e l a t i v e s c a t t e r i n g cross section f o r m o d e "i". F r o m ( 3 ) a n d (4) t h e r a t i o o f t h e i n t e n - s i t y li(') of t h e Raman s c a t t e r i n g by t w o phononsl'i" over t h e i n t e n s i t y I{') o f the R a m a n s c a t t e r i n g by one phonon "i" is obtained. A t t h e resonance (EL = EF) this r a t i o i s shown i n fig. 4.

I n t h e case o f F centers, since t h e l i f e t i m e o f t h e f i r s t e x c i t e d s t a t e is about 1 0 - ~ - 1 0 - ~ s 1121 and t h e c o e f f i c i e n t 6 1 is o f t h e order o f several hundred crril ( N a I : 625 c m - I ; K I : 366 c m - I ) 181, t h e r a t i o y/B1 i s l o w e r t h a n 10-7 w h i c h corresponds t o a v i r t u a l l y z e r o value (fig. 4).

I n t h i s case we have :

R e l a t i o n (5) shows t h a t i f the s c a t t e r i n g system contains an intense resonant mode R, t h e r a t i o (oR(rl+)/ o ( T i ) ) is large f o r this mode. Then t h e second order R a m a n spectrum i s intense compared t o t h e f i r s t order spectrum and is structured. This i s t h e case o f F c e n t e r s i n N a B r 1131, K I 171 a n d N a l 181. O n t h e contrary, i n t h e absence o f an intense resonant mode, t h e second order R a m a n spectrum is w e a k a n d g i v e s r i s e t o a m o r e or less s t r u c t u r e d background. This occurs f o r F centers i n N a C l /14/, K C 1 1131 and R b C l /15/.

I n t h e case o f R a m a n s c a t t e r i n g b y potassium colloi'ds i n KI, the B1 p a r a m e t e r can be supposed t o have t h e same order o f magnitude as f o r F centers i n KI. O n t h e contrary, t h e l i f e t i m e s o f t h e e x c i t e d states, because o f t h e i r coupling w i t h t h e m e t a l l i c colloi'd e l e c t r o n i c states, can reasonably be supposed t o be much weaker. The l i f e t i m e s o f e x c i t e d e l e c t r o n i c levels f o r molecules adsorbed on a s i l v e r surface have been d e t e r m i n e d 1161.

The obtained values are f r o m t o I O - ~ ~ S , g i v i n g rise t o a damping f a c t o r o f t h e order f r o m 50 t o 5000 c m - I . When y is about 5000 c m - 1 , y / B 1 i s o f t h e order o f 10. Thus, fig. 4 shows t h a t t h e r a t i o o f t h e second-over t h e f i r s t - o r d e r is, a t t h e m a x i m u m resonance, about 0.06 and t h i s w i t h o u t t a k i n g i n t o account t h e oi(~;)/a(r;) factor. F r o m fig. I c , t h i s r a t i o is weak whatever t h e considered phonon, r e s u l t i n g I n a very weak second-order R a m a n spectrum.

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the damping factor.

( ~ ~ ( r ; ) / ~ ( r ; ) = I).

C.- C A L C U L A T I O N OF LOCALIZED MODE FRE-

\ I

^QUENCIES

We have t r i e d t o account f o r frequencies o f the strong 84 and 120 cm-lmodes. A calculation based o n a softening o f interionic force constantswas done i n the case o f an (111) interface, when anions are replaced by vacancies so as t o consti-

10

'

'u

¹⁰^' ^loC ^10' ^10' ^{t u t e}^ning^between^the^{o f the}^colloi'd.f i r s t longitudinal neighbours It was shown interionic induces that force t w o a 40% localized constant softe-

X/B, vibrational modes a t the interface : one a t

83 c m - I i n the interface plane and the other a t 118 cm-1 perpendicular t o the interface, i n agreement w i t h experimental results.

DISCUSSION

The theory of two-phonon Raman scattering developed i n this paper, i s valid f o r un point defect, but cannot be applied i n the case o f colloids. However, it does allow us t o determine the influence of some parameters on f i r s t

-

and second - order Raman scattering by colloi'ds. Moreover i t is not sure that the colloi'ds are large enough t o be treated as two- dimensional defect /5/. It has been shown i n the case o f silver colloi'ds i n NaI /I/, t h a t the size o f the colloi'ds modifies t o a slight extent the Raman spectra, i n particular the broadening of the Rayleigh line. This presumably shows, that other e f f e c t could also be a t t h e o r i g i n o f this broadening. For example, i t has been suggested / ? 7 / that i t comes from single- particle excitation of the electron gas o f the quasi m e t a l l i c particles.

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