DYNAMICAL PROPERTIES OF Au METAL AND CLUSTERS FROM EXAFS

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DYNAMICAL PROPERTIES OF Au METAL AND CLUSTERS FROM EXAFS

A. Balerna, S. Mobilio

To cite this version:

A. Balerna, S. Mobilio. DYNAMICAL PROPERTIES OF Au METAL AND CLUS- TERS FROM EXAFS. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-1009-C8-1014.

�10.1051/jphyscol:19868194�. �jpa-00226101�

JOURNAL DE PHYSIQUE

Colloque C8, suppl6ment au n o 12, Tome 47, d6cembre 1986

DYNAMICAL PROPERTIES OF Au METAL AND CLUSTERS FROM EXAFS

A. BALERNA and S. MOBILIO

INFN, Laboratori Nazionali di Frascati, c p . 13, I-00044 Frascati, Italy

ABSTRACT

The L, edge of Au b u l k h a s been s t u d i e d by X-ray a b s o r p t i o n Spectroscopy i n t h e t e m p e r a t u r e range 16-300 K . An e f f e c t i v e Debye t e m p e r a t u r e o f 165 K h a s been e v a l u a t e d from t h e s p e c t r a , i n good agreement w i t h h e a t c a p a c i t y measurements. The b e h a v i o r s of t h e E x a f s Debye Waller f a c t o r s have been c a l c u l a t e d a l s o f o r Au c l u s t e r s by u s i n g a f r e e bounded s p h e r e d e n s i t y of s t a t e . An e x c e l l e n t agreement h a s been found w i t h e x p e r i m e n t a l d a t a p r e v i o u s l y r e p o r t e d . T h i s confirm t h a t t h e dynamical p r o p e r t i e s of Au c l u s t e r s a r e w e l l d e s c r i b e d by a l i q u i d d r o p model i n agreement w i t h h e a t c a p a c i t y measurements

.

INTRODUCTION

I n p r e v i o u s p a p e r s ( r e f . 1-2) w e r e p o r t e d a complete s t r u c t u r a l c h a r a c t e r i z a t i o n of vacuum e v a p o r a t e d g o l d c l u s t e r s s u p p o r t e d on mylar, u s i n g Exafs. I n t h e d i a m e t e r r a n g e e x p l o r e d (11-60 A ) a c o n t r a c t i o n i n n e a r e s t neighbor (nn) and n e x t n e a r e s t neighbor d i s t a n c e s were found, i n agreement w i t h a s i m p l e macroscopic l i q u i d d r o p model. I n s u c h a model c l u s t e r s a r e imagined a s homogeneous s p h e r e on which s u r f a c e stress a c t s , t h u s s h o r t e n i n g t h e l a t t i c e parameter w i t h r e s p e c t t o t h e b u l k one.

No e v i d e n c e of s t r u c t u r a l t r a n s i t i o n from f c c t o i c o s a h e d r i c s t r u c t u r e was found e i t h e r from Exafs o r from Xanes, i n c o n t r a s t w i t h t h e o r e t i c a l c a l c u l a t i o n s ( r e f . 3 )

Moreover a n i n c r e a s e i n b o t h t h e s t a t i c and dynamic Debye Waller f a c t o r s was measured w i t h d e c r e a s i n g c l u s t e r d i a m e t e r . The s t a t i c d i s o r d e r i n c r e a s e i s due t o t h e f a c t t h a t c l u s t e r s grow i n a s l i g h t l y d i s t o r t e d f c c s t r u c t u r e : i n d e e d f i r s t neighbor d i s t a n c e s between atoms on t h e c l u s t e r s u r f a c e a r e e x p e c t e d t o b e d i f f e r e n t from t h a t of atoms i n s i d e t h e volume.

The i n c r e a s e of t h e dynamic Debye Waller f a c t o r i s due t o t h e s o f t e n i n g of t h e l a t t i c e v i b r a t i o n s induced by t h e h i g h number of s u r f a c e atoms ( r e f 4 ) . S u r f a c e atoms i n d e e d have a n h i g h e r m o b i l i t y t h a n t h e volume o n e s , s o a n Exafs measurements which a v e r a g e s t h e behavior of e a c h atom i n t h e sample must detect a n h i g h e r mean atomic m o b i l i t y .

The change of t h e c l u s t e r phonon spectrum c a n b e described i n terms of a s i z e dependent Debye t e m p e r a t u r e (TD o r % * h i g h e r m o b i l i t y r e s u l t i n g i n a lower TD ( r e f 5 ) . By u s i n g t h e w e l l known Beni and PlatZman a s y m p t o t i c e x p r e s s i o n :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868194

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where t h e two term r e f e r s t o volume and s u r f a c e mode r e s p e c t i v e l y . The l i n e term mode (2/3n)R can be neglected. The allowed s t a t e s i n t h e c l u s t e r are only t h o s e whose wavevector i s g r e a t e r t h a n qmii-n /D, s i n c e a c l a s s i c a l e l a s t i c standing wave must s e e boundaries s e p a r a t e d by a t l e a s t h a l f a wavelength. The high k c u t o f f qmax i s as u s u a l l y given by t h e normalization condition:

( t h e 0.65 f a c t o r comes from t h e behavior of t h e c o r r e l a t i o n f a c t o r which f o r T/TD > , 1 reaches t h e contant value of 0.351, we determined i n r e f 1 experimentally t h e c l u s t e r s TD ( s t a r s i n f i g . 1).

A s i z e e f f e c t i n t h e Debye temperature can be observed as i n many o t h e r p h y s i c a l parameter of

and can be used t o extimate t h e c l u s t e r Debye temperatures, from : TD=hv/X (continous l i n e i n f i g 1 ) .

The numerical mismatch between theory and experiment must be c a r e f u l l y i n v e s t i g a t e d . I n p a r t i c u l a r f o r t h e experimental d a t a , it must be observed t h a t t h e Debye temperature i s not a w e l l d e f i n e d p h y s i c a l parameter of a system, s i n c e i t i s from experimental d a t a deduced i n t h e h y p o t e s i s of a l i n e a r d i s p e r s i o n r e l a t i o n . Each phonon dependent physical q u a n t i t y l i k e t h e h e a t c a p a c i t y , Gruneisen c o n s t a n t , thermal expansion c o e f f i c i e n t e t c . can be used t o measure TD. But each measurement g i v e an e f f e c t i v e Debye temperature. Indeed each p h y s i c a l q u a n t i t y depend on t h e t r u e DOS properly weighted on t h e B r i l l o u i n zone. A s a consequence any d e v i a t i o n of t h e t r u e DOS from t h e Debye l i n e a r one can r e s u l t i n a d i f f e r e n t e f f e c t on TD.

small p a r t i c l e s ( r e f 6 ) .

The macroscopic l i q u i d drop model has been used t o e x p l a i n such s i z e e f f e c t i n low temperature s p e c i f i c h e a t , i n t h e Moessbauer r e c o i l f r e e f a c t o r , i n t h e lowering of t h e

m 0,94 melting temperature, i n t h e

i n c r e a s i n g of t h e mean square

s

atomic s t u d i e s t h e displacement. c l u s t e r phonon 1 n modes such 3 60.90- a r e assumed t o be given by t h e

e i g e n s t a t e s of t h e wave equation

(v'

The eigenvalue k a r e given by:

0'98:fl ^*

* -

4

1 I 1

2 0 4 0 6 0 80

I = a , , , ~ - ' (2)

o 61

where R i s t h e r a d i u s of t h e sphere

Fig.

d e r i v a t i v e of t h e 1-th s p h e r i c a l Bessel f u n c t i o n . The degeneracy of k i s (21+1).

It has been shown t h a t i n t h e l i m i t of l a r g e k t h e t r u e DOS given by t h e r o o t s of eq. 2 , can be w e l l approximated by:

So the comparison shown in fig. 1 will be meaningfull only if the Debye temperatures measured from Exafs, which weights principally the high k value of the Brillouin zone, are in good agreement with the TD value given by the normalitation condition.

EXPERIMENTAL AND DATA ANALYSIS

TO check this point, at least for bulk Au, we recorded L3 absorption spectra on gold metal in the temperature range 16-300 K at the Frascati SR facility, using the bending magnet beam line. The X-ray absorption spectra were analyzed using a standard procedure to extract Exafs modulation and then Fourier transformed (fig. 2 and fig. 3)

(ref 7 ) . The nn peak was inverse Fourier trasformed in the R range indicated by arrows in fig. 3 and Debye Waller factors obtained from the usual plot

lnCA,(k) /A,(k) 1 versus k2

Asand A,beeing the amplitude of the inverse FT of the sample and of the reference compounds respectively.

Bulk

1

Fig.

Fig.

The T=16 K measurement was used as reference. No significant asymmetry effect has been detected in the temperature range investigated, in agreement with Sandstrom et al., who recently showed on Pt that such asymmetry effects become important at temperature higher than 2*TD.

C8-1012 JOURNAL DE _PHYSIQUE

RESULTS AND DISCUSSION

Fig. 4 shows t h e e x p e r i m e n t a l , 7.5- AU B U I ~

DW f a c t o r s t o g h e t h e r w i t h t h e

e 3

t h e o r e t i c a l ones e v a l u a t e d i n b t h e c o r r e l a t e d Debye model f o r

f

It c a n be n o t e d t h a t a good

F

agreement i s found f o r TD=165 ,, K i n e x c e l l e n t agreement w i t h

b

t h e n o r m a l i t a t i o n c o n d i t i o n . So t h e comparison shown i n

f i g . 1 i s m e a n i n g f u l l . The O

Oo loo T (K) ^{20 0 300} o r i g i n of t h e mismatch c a n be

i n t h e method u s e d t o e v a l u a t e

t h e c l u s t e r s TD from t h e

Fig. 4

e x p e r i m e n t a l d a t a . I n f a c t i t

was assumed s t i l l v a l i d f o r c l u s t e r s t h e c o r r e l a t e d Debye model formula, a11 t h e e f f e c t s of t h e s u r f a c e modes b e e i n g i n c o r p o r a t e d i n a change of t h e Debye t e m p e r a t u r e . It i s not s u r p r i s i n g t h a t a t Small c l u s t e r d i a m e t e r , when t h e s u r f a c e mode c o n t r i b u t i o n become of t h e same o r d e r of magnitude a s t h e volume modes, t h e u s u a l c o r r e l a t e d Debye model formula must b e m o d i f i e d , s i n c e a s shown i n e q . 1 t h e phonon DOS depends on k f o r t h e s u r f a c e mode, w h i l e on k2 f o r t h e volume ones. For t h i s r e a s o n i n t h e s p e c i f i c h e a t measurements, f o r example a n a d d i t i o n a l 'Z2behavior i s found i n t h e c l u s t e r s b e s i d e s t h e u s u a l T~ t e r m (ref. 8)

To i n c l u d e t h e s u r f a c e mode c o n t r i b u t i o n i n t h e Debye c o r r e l a t e d model we used t h e i n t e g r a l e x p r e s s i o n :

PR(w) i s t h e n o r m a l i z e d p r o j e c t e d d e n s i t y of modes c o n t r i b u t i n g t o r e l a t i v e v i b r a t i o n a l motion a s s o c i a t e d t o t h e t o t a l DOS g i v e n by e q .

1.

We g e t (ref 9 ) : 2 v v 2

ajf( T ) = 2[(0,,,)~

-

I

+21(05,,)~-(~&,)~1 , w i t h :

The V,S,U,C indices mean volume,surface,uncorrelated and correlated respectively, N is the number of atoms per unit volume and Cl is k,R, As shown in fig 'XD 5 the surface contribution to the total DW factor is not negligeable, reaching the value of 25% of the total DW factor for the 15 A cluster, thus showing that as previously guessed it is not possible to use the bulk asymptotic formula 1 to calculate the clusters values and their Debye tesperatures.

Fig. 5 Fig.

On the other hand fig. 6 shows an excellent agreement between the theoretical behavior and the experimental data. This demonstrates that the dynamical properties of gold clusters are well described by the free bounded sphere density of states, which can be used to calculate also the clusters Debye temperature (solid line in fig. 1).

CONCLUSIONS

The main conclusion of all our Exafs work on Au gold clusters is that the macroscopic continuum liquid drop model, in absence of a structural transition, is able to explain both structural and dynamical properties provided the surface is taken into account, as origin of surface stress and of surface phonon modes. Such behavior is expected to be true for all clusters non interacting with the substrate as for example the noble metal clusters isolated in rare gas matrix.

Moreover even if many times it has been suggested that the temperature dependence studies of Exafs spectra are a powerfull tool to investigate the dynamical properties of systems, up to now few cases have been investigated in detail.

We have here demonstrated the sensitivity of such studies to detect changes in the phonon spectrum and hence their ability to test specific force constance models.

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REFERENCES

1. A.Balerna, E.Bernieri, P.Picozzi, A.Reale, S.Santucci, E.Burattini, S.Mobilio

-

2. A.Balerna, E.Bernieri, P.Picozzi, A.Reale, S.Santucci, E.Burattini, S.Mobilio

-

3. M.B.Gordon, F.Cyrot-Lackmann and M.C.Desjonqueres

-

80, 159 (1980)

4. D.P.Jackson

-

5. P.R.Chouchman and F.E.Karasz

-

6. I.D.Morokhov, V.I.Petinov, L.I.Trusov and V.F. Petrunin

-

Phys. Usp. 24, 295 (1981)

7. A.Balerna and S. Mobilio

-

8. S.Mobilio, F.Comin and L.Incoccia, Lab. Naz. di Frascati, Int.

Rep. 82/19NT (1982)

ACKNOWLEDGEMENT

We are gratefull to Prof. 1.Davoli and S.Stizza for prividing us the cryostat for low temperature measurements.

Fruitfull discussion with Prof. P.Picozzi and S. Santucci are kindly aknowledged.

Technical help from L. Moretto is also aknowledged.