THERMAL DISORDER OF SURFACE ATOMS STUDIED BY SURFACE EXAFS

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THERMAL DISORDER OF SURFACE ATOMS STUDIED BY SURFACE EXAFS

D. Chandesris

To cite this version:

D. Chandesris. THERMAL DISORDER OF SURFACE ATOMS STUDIED BY SURFACE EXAFS.

Journal de Physique Colloques, 1986, 47 (C8), pp.C8-479-C8-486. �10.1051/jphyscol:1986890�. �jpa- 00226221�

THERMAL DISORDER OF SURFACE ATOMS STUDIED BY SURFACE EXAFS

D. CHANDESRIS

LURE (Laboratoire C N R S , C E A , M E N ) , Universite de Paris-Sud, F-91405 Orsay Cedex, France

RESUME

Nous a v o n s B t u d i e l l a n i s o t r o p i e du f a c t e u r Debye-Waller d e s u r f a c e q u i r e g i t l ' a m o r t i s s e m e n t d e s o s c i l l a t i o n s EXAFS. Pour c e l h , n o u s a v o n s mesurh l ' a b s o r p t i o n a u d e l h du s e u i l K du c o b a l t p o u r une monocouche d e C o b a l t a d s o r b e e s u r l a f a c e ( 1 1 1 ) du c u i v r e . Le f a c t e u r Debye-Waller est d e d u i t d e l a dependance e n t e m p e r a t u r e d e l l a m o r t i s s e m e n t du s i g n a l EXAFS. L ' u t i l i s a t i o n du rayonnement s y n c h r o t r o n , q u i e s t l i n g a i r e m e n t p o l a r i s 6 , a p e r m i s d e & p a r e r l e s i g n a l d 6 3 une l i a i s o n e n t r e deux a t o m e s d e s u r f a c e d e c e l u i d 6 3 une l i a i s o n e n t r e un atome d e s u r f a c e e t un a t o m e d e l a c o u c h e i n f e r i e u r e . On a pu a i n s i d h t e r m i n e r l ' a n i s o t r o p i e d e v i b r a t i o n d e s a t o m e s d e s u r f a c e . Ces r 6 s u l t a t s e x p e r i m e n t a u x o n t 6 t h compares a u x d g p l a c e m e n t s c a r r g s moyens r e l a t i f s d e s a t o m e s d e s u r f a c e c a l c u l e s d a n s l l a p p r o x i m a t i o n harmonique. Le bon a c c o r d e n t r e l e s r e s u l t a t s e x p e r i m e n t a u x e t l e s c a l c u l s m o n t r e n t l a c a p a c i t e d e l7EXAFS h f o u r n i r une i n f o r m a t i o n q u a n t i t a t i v e s u r l ' a m p l i t u d e d e s v i b r a t i o n s t h e r m i q u e s d e s a t o m e s d e s u r f a c e .

ABSTRACT

We h a v e s t u d i e d t h e a n i s o t r o p y o f t h e s u r f a c e Debye-Waller f a c t o r i n v o l v e d i n a s u r f a c e e x t e n d e d X-ray a b s o r p t i o n f i n e s t r u c t u r e (SEXAFS) e x p e r i m e n t . It was p e r f o r m e d a t t h e CoK e d g e o n a monolayer o f c o b a l t d e p o s i t e d o n t h e ( 1 11 ) f a c e O f

c o p p e r . E x p e r i m e n t a l l y , t h e Debye-Waller f a c t o r is deduced f r o m t h e t e m p e r a t u r e dependence o f t h e damping o f t h e EXAFS o s c i l l a t i o n s . The u s e o f p o l a r i z e d s y n c h r o t r o n r a d i a t i o n a l l o w s t o d i s t i n g u i s h between bonds i n v o l v i n g two s u r f a c e atoms o r o n e s u r f a c e atom o n l y and t h e n d e t e r m i n e t h e a n i s o t r o p y o f t h e s u r f a c e atom v i b r a t i o n s . These e x p e r i m e n t a l r e s u l t s h a v e been compared t o t h e mean s q u a r e r e l a t i v e d i s p l a c e m e n t s o f s u r f a c e a t o m s c a l c u l a t e d i n t h e harmonic a p p r o x i m a t i o n . The a g r e e m e n t between t h e o r e t i c a l a n d e x p e r i m e n t a l r e s u l t s is good a n d shows t h e a b i l i t y o f EXAFS a s a v a l u a b l e t o o l f o r t h e s t u d y o f t h e a m p l i t u d e o f s u r f a c e v i b r a t i o n s .

I n t h e h a r m o n i c a p p r o x i m a t i o n , t h e Debye-Waller f a c t o r which g o v e r n s t h e t e m p e r a t u r e dependence o f t h e damping o f o s c i l l a t i o n s i n ( S . ) EXAFS i s g l v e n by -2k202 wkere k is t h e p h o t o e l e c t r o n wave number a n d a ? t h e mean s q u a r e r e l a t i v e

e J J

d i s p l a c e m e n t (MSRD) a l o n g t h e b o n d i n g d i r e c t i o n ;. between t h e c e n t r a l atom 0 and

i t s n e i g h b o u r j : J '

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986890

JOURNAL DE PHYSIQUE

where T is t h e absolut: t e m p e r a t u r e and

=

0 J

0 ( j ) ( l g 2 ) .

T h i s f a c t o r h a s been s t u d i e d f o r bulk m e t a l both e ~ p e r i m e n t a l l y ( " ~ ) and t h e ~ r e t i c a l l y ( ~ " ) . These s t u d i e s have p u t forward f i r s t t h e importance o f t a k i n g i n t o account t h e c o r r e l a t i o n between t h e motions o f atoms 0 and j , t h e n t h e p o s s i b l e a n i s o t r o p y o f a ? i n s o l i d s , such a s Zn, i n which a l l bonds a r e n o t e q u i v a l e n t . Such a n a n i s o t r o p y is obviously a l s o expected when t h e c e n t r a l atom J 0 is a s u r f a c e atom.

It h a s been observed i n t h e c a s e o f a monolayer o f c o b a l t on t h e (111) f a c e o f copper. even though t h i s e f f e c t is a l r e a d y p r e s e n t i n t h e c a l c u l a t i o n f o r c l e a n su~~a","e~"), t h e p r e s e n c e o f a n adsorbed monolayer, with a d i f f e r e n t X-ray

( 6 ) a b s o r p t i o n t h r e s h o l d , is r e q u i r e d f o r t h e SEXAFS probe

.

The aim o f t h e experiment was t o compare t h e mean s q u a r e r e l a t i v e d i s p l a c e m e n t s o f t h e s u r f a c e atoms i n d i r e c t i o n s p a r a l l e l and p e r p e n d i c u l a r t o t h e s u r f a c e . One e x p e c t s v i b r a t i o n s p e r p e n d i c u l a r t o t h e s u r f a c e t o have a l a r g e r a m p l i t u d e than t h e p a r a l l e l o n e s s i n c e e v e r y s u r f a c e atom h a s l o s t h a l f h i s bondings p e r p e n d i c u l a r t o t h e s u r f a c e . We w i l l d e m o n s t r a t e t h a t SEXAFS w i t h p o l a r i z e d l i g h t g i v e s c l e a r i n f o r m a t i o n on b o t h MSRD. According t o E i s e n b e r g e r a n d Brown(7), t h e e x p r e s s i o n o f t h e EXAFS m o d u l a t i o n s f o r a n atom imbedded i n a medium with a p a i r d i s t r i b u t i o n g ( r ) is :

where f ( k , + ) is t h e b a c k s c a t t e r i n g a m p l i t u d e f u n c t i o n , k , t h e p h o t o e l e c t r o n wave number, a ( k ) , t h e t o t a l phase s h i f t and L , t h e e l e c t r o n mean f r e e path. When t h e d i s t r i b u t i o n f u n c t i o n is a p u r e Gaussian and f o r a d i s c r e t e l a t t i c e , t h e i n t e g r a l i n eq. 2 becomes :

2 2

N. - 2 k o . - 2 ; . /L

e J s i n ( 2 k r . + a ( k ) )

J r , ^J

t h

where

r .

J t h

c o r r e s p o n d i n g MSRD ( s e e eq. 1 ) and N . t h e number o f t h e j- neighbours. ^j J

I t is customary t o u s e t h i s formula i n t h e i n t e r p r e t a t i o n o f t h e EXAFS s p e c t r a t o determine t h e t e m p e r a t u r e dependence of t h e Debye-Waller f a c t o r o . i n t h e c a s e o f i s o t r o p i c systems" )

.

( 9 a K i s o t r o p y ) , on P t , 1 r ( * ) ( t h e r m a l d i s o r d e d ) and on t h e N i (100) f a c e

.

A p r o p e r t y o f s y n c h r o t r o n r a d i a t i o n v e r y v a l u a b l e f o r s u r f a c e EXAFS is its p o l a r i z a t i o n . For l i g h t l i n e a r l y p o l a r i z e d and f o r K o r L , edge, t h e N . term of

J

N! = 3 1 cos2 a

J i = l i

where cc is t h e angle between t h e e l e c t r i c f i e l d vector 2 of t h e X-rays and t h e v e c t o r i r i from t h e c e n t r a l atom t o t h e i t h atom of t h e c o o r d i n a t i o n sphere j. Then i n s u r f a c e EXAFS, by changing the a n g l e between t h e s u r f a c e and t h e p o l a r i z a t i o n of t h e l i g h t , it w i l l be p o s s i b l e t o be s e n s i t i v e t o bondings p a r a l l e l t o t h e s u r f a c e plane ( i n normal incidence) o r t o bondings perpendicular t o t h e s u r f a c e ( i n grazing incidence) and t o measure t h e corresponding MSRD of t h e atoms. Therefore, d e s p i t e of t h e system anisotropy, it is j u s t i f i e d t o use formula ( 3 ) f o r each p o l a r i z a t i o n . Moreover, when we a r e working a t r e l a t i v e l y low temperatures, we can assume only s m a l l d e v i a t i o n s from t h e gaussian d i s t r i b u t i o n . Thus, we determine t h e v a r i a t i o n of t h e Debye-Waller f a c t o r between two temperatures by t h e r a t i o method. For each p o l a r i z a t i o n

s i n c e a l l t h e o t h e r f a c t o r s i n eq. 3 a r e s t r i c t l y i d e n t i c a l a t To and T I . The power of t h i s method is due t o t h e s i m p l i c i t y o f formula ( 4 ) . We do not need any b a c k s c a t t e r i n g amplitudes and phase s h i f t s determined on a model compound with t h e well known quest ion of t r a n s f e r a b i l i t y o f amplitudes and phase s h i f t s . Furthermore, t h e p o s s i b l e presence o f some s t a t i c d i s o r d e r a t t h e s u r f a c e could damp t h e EXAFS o s c i l l a t i o n s and lead t o a wrong determination o f t h e Debye-Waller f a c t o r . This e m p i r i c a l procedure e l i m i n a t e s t h i s e f f e c t s i n c e t h e s t a t i c d i s o r d e r is maintained when t h e sample is cooled. (Another kind of r a t i o method h a s already been used i n s u r f a c e EXAFS t o determine s i t e s by comparing amplitudes measured i n d r f f e r e n t p o l a r i z a t i o n c o n d i t i o n s

The experimental study was done f o r one mcinolayer of c o b a l t adsorbed on t h e 11) face o f c o p p e r ( 1 2 ) . Why have we chosen t h i s system ? The f i r s t reason is t h a t is a w e l l known system : s t u d i e s by LEED and Auger spectroscopy 3, have shown t h a t c o b a l t grows l a e r by l a y e r a t room temperature. ( I n a previous p a r t of t h i s SEXAFS i n v e s t i g a t i o n '12) we have confirmed t h e two dimensional c h a r a c t e r of t h e monolayer o f c o b a l t ) . The second reason was t o choose metals with Debye temperatures j u s t above room temperature. I n t h a t case t h e thermal damping o f EXAFS o s c i l l a t i o n s is a p p r e c i a b l e a t room temperature but is is n e v e r t h e l e s s reasonable t o use t h e harmonic approximation up t o t h i s temperature. The t h i r d reason i s t h a t t h e bulk e l a s t i c p r o p e r t i e s of t h e s e metals a r e w e l l known. A t l e a s t , t h e (111) f a c e o f a face centered cubic metal is a dense f a c e and then, t h e r a t i o between t h e EXAFS s i g n a l due t o t h e adsorbate-adsorbate d i s t a n c e and t h e a d s o r b a t e s u b s t r a t e d i s t a n c e is 911.5 when the p o l a r i z a t i o n of t h e l i g h t is p a r a l l e l t o t h e s u r f a c e and about 1/9 when i t is a t 7 5 O from t h e s u r f a c e . Thus i t i s a system i n which t h e two c o n t r i b u t i o n s a r e well separated.

The experimental s p e c t r a obtained i n normal incidence above t h e K edge of c o b a l t a t both 77K and 300K a r e shown i n Fig. l a . The d a t a a c q u i s i t i o n time was about one hour f o r each EXAFS spectrum extending up t o 600 eV above t h e edge. The r e l e v a n t s t e p s of t h e EXAFS a n a l y s i s a r e displayed i n Fig. lb-c-d : t h e EXAFS o s c i l l a t i o n s f o r

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38-I t o 1 2 . 5 8-I ( F i g . l b ) , t h e F o u r i e r transform ( F i g . I c ) corresponding t o t h e window l i m i t e d by t h e arrows i n Fig. l b which e x h i b i t s t h e peaks o f t h e f i r s t ,

second, t h i r d and f o u r t h n e a r e s t neighbours and, f i n a l l y (Fig. 1 d ) , t h e i n v e r s e F o u r i e r t r a n s f o r m of t h e f i r s t neighbours peak. The i n f l u e n c e of t h e t e m p e r a t u r e on t h e damping of o s c i l l a t i o n s is c l e a r l y put forward by t h e decrease of t h e i r amplitude f o r l a r g e v a l u e s of k.

transform 01

...

Photon energy 7700 7900 8100 hv(eV)

Wave number

I

Figure 1 : ( a ) Experimental a b s o r p t i o n s p e c t r a of a monolayer of Co on Cu (1 11) a t t h e K edge of c o b a l t a t both 77 and 300 K. The p o l a r i z a t i o n of t h e l i g h t is p a r a l l e l t o t h e s u r f a c e . ( b ) EXAFS modulation [k x ^{( k ) ]} normalized t o t h e h e i g h t of t h e edge jump. The arrows i n d i c a t e t h e limits of t h e c o s i n e window used f o r t h e Fourier transform. ( c ) F o u r i e r t r a n s f o r m s of t h e s p e c t r a . The peaks corresponding t o t h e f i r s t , second, t h i r d , and f o u r t h - n e a r e s t neighbors ( n n ) c l e a r l y appear. ( d ) I n v e r s e F o u r i e r transform of t h e f i r s t - n e i g h b o r peak. ( e ) Logarithm of t h e r a t i o of t h e amplitudes a t 77 and 300 K a s a f u n c t i o n of k2 f o r t h e f i r s t s h e l l o f neighbors.

P o i n t s a r e t h e experimental d a t a and t h e continuous l i n e is t h e l i n e a r r e g r e s s i o n corresponding t o t h e s e d a t a .

I n Fig. l e we have r e p r e s e n t e d Log x ( T (T = = 77 100 K) K, a s a f u n c t i o n of k2 f o r t h e p o l a r i z a t i o n of t h e l i g h t p a r - a l l e l t o t h e s u r f a c e . The l i n e a r i t y is well confirmed i n t h e range 10 t o 100 A - ~ of k2 and j u s t i f i e s t h e use of formula ( 3 ) . t h e s l o p e of t h e l i n e g i v e s t h e v a r i a t i o n of t h e Debye-Waller f a c t o r p a r a l l e l t o t h e s u r f a c e 2

: Ao / / between 77 K and 300 K.

I n f i g . 2 , t h e r e s u l t s o b t a i n e d f o r t h e monolayer of c o b a l t adsorbed on t h e ( i l l ) f a c e of copper i n d i r e c t i o n s p a r a l l e l and p e r p e n d i c u l a r t o t h e s u r f a c e ( A a 2 and AoL 2 ) a r e compared t o t h o s e o b t a i n e d f o r bulk c o b a l t and copper (ha2 and A,, 2 / /

Cu ) i n t h e same experimental c o n d i t i o n s . Note t h a t bulk v a l u e s of do2 ':re i n good

( 1 4 ) agreement with p r e v i o u s ones measured in c l a s s i c a l EXAFS

.

K a s a f u n c t i o n of k 2 f o r t h e f i r s t s h e l l o f neighbours ( l i n e a r r e g r e s s i o n o f t h e experimental d a t a ) . - ^bulk c o b a l t and copper,

-.-.-

p a r a l l e l A s expec

I t appears a s i g n i f i c a n t anisotropy i n the Debye-Waller f a c t o r s normal and t o t h e s u r f a c e : A O ~ _{/ /} = 3.9 + ^{0.3 x 10} -3fi-2 and Ao2 = 4.9 + ^{0.5 x 1} o - ~ A * . t e d , t h e mean square r e l a t i v e displacement of t h e s u r f a c e c o b a l t atoms I

- 3 2 p a r a l l e l t o t h e s u r f a c e is c l o s e t h e c o b a l t bulk one = 3.8

+

-

a r e summarized i n t a b l e 1 . I

Note t h a t Ao corresponds t o a Co-Cu bond while A D / / corresponds t o a Co-CO bond. Since the Co f o r c e c o n s t a n t s a r e l a r g e r than t h e Cu ones, one can wonder i f t h e

I

observed a n i s o t r o p y is a s u r f a c e e f f e c t o r a simple bonding e f f e c t . I t is c l e a r t h a t h y p o t h e t i c a l Co-Cu bulk would lead t o Ao (Co) < Ao (CoCu) < Ao (Cu) and not (Cu) < d o (Co/Cu (S-B)) a s i t is t h e case. Therefore, t h i s e f f e c t is c l e a r l y due t o t h e presence of t h e s u r f a c e and can be understood a s follows. The MSRD of t h e atoms is d i r e c t l y r e l a t e d t o t h e phonon d e n s i t y of s t a t e s . I n f a c t whereas t h e phonon d e n s i t y of s t a t e s f o r a bond p a r a l l e l t o t h e s u r f a c e is r a t h e r s i m i l a r t o t h e bulk one, it is perturbed f o r bonds involving s u r f a c e and bulk atoms. I t is due t o t h e

C8-484 JOURNAL DE PHYSIQUE

e x i s t e n c e o f s u r f a c e phonon modes l e a d i n g t o a n i n c r e a s e o f t h e weight of t h e low frequency modes. T h i s o b v i o u s l y enhances t h e v a l u e of a f o r a s u r f a c e - b u l k p a i r .

The p r e s e n t d a t a g i v e i n a theory independent f a s h i o n t h e t e m p e r a t u r e dependent v a r i a t i o n s o f t h e a m p l i t u d e s o f t h e dynamical r e l a t i v e d i s p l a c e m e n t s , b o t h p a r a l l e l and p e r p e n d i c u l a r t o t h e s u r f a c e , around t h e atomic p o s i t i o n s o f t h e u n r e c o n s t r u c t e d ( I XI ) Co/Cu (1 11 ) s u r f a c e . T h i s k i n d o f r e s u l t s is complementary t o t h a t o b t a i n e d by h i g h r e s o l u t i o n e l e c t r o n e n e r g y l o s s s p e c t r o s c o p y which d e t e r m i n e s t h e s u r f a c e phonon d i s p e r s i o n c u r v e s . The b e s t r e l a t e d r e s u l t s c a n b e found i n t h e e v a l u a t i o n from LEED o f mean s q u a r e d i s p l a c e m e n t s o f s u r f a c e atoms l a r g e r t h a n t h e bulk o n e s ( 1 5 ) . Note t h a t t h i s d i f f r a c t i o n t e c h n i q u e a l l o w s a n e s t i m a t i o n o f a b s o l u t e

2 2

mean s q u a r e d i s p l a c e m e n t s <u > and t h e n t h e a n i s o t r o p y r a t i o s ( u > ^/ <u2 > o f LEED

2 2 I / /

and ol / a / / o f SEXAFS c a n n o t be simply r e l a t e d : Beni and Platzman ( 2 ) have shown t h a t che d i s p l a c e m e n t c o r r e l a t i o n f u n c t i o n which must b e c o n s i d e r e d i n EXAFS is o f t h e same o r d e r o f magnitude t h a n t h e mean s q u a r e d i s p l a c e m e n t o f atoms.

F i g u r e 3 : Local d e n s i t i e s o f modes on t h e f i r s t t h r e e l a y e r s (- s u r f a c e , - - - f i r s t u n d e r l a y e r ,

...

S u r f a c e p r o j e c t e d d e n s i t i e s o f 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 l o n g f i r s t n e a r e s t n e i g h b o u r s bonds i n t h e s u r f a c e ( c ) and between t h e s u r f a c e and t h e f i r s t u n d e r l a y e r ( d ) compared t o bulk one (dashed c u r v e ) .

I n o r d e r t o i l l u s t r a t e t h e o r i g i n o f t h e a n i s o t r o p y o f t h e s u r f a c e Debye-Waller f a c t o r , we have reproduced i n f i g u r e 3 t h e l o c a l phonon d e n s i t y o f modes f o r m o t i o n s p e r p e n d i c u l a r ( a ) and p a r a l l e l ( b ) t o t h e s u r f a c e . T h i s c a l c u l a t i o n ( 1 6 ) i s done i n t h e harmonic approximation c o n s i d e r i n g c e n t r a l and a n g u l a r f o r c e s between f i r s t and second n e a r e s t neighbours. I t is c l e a r t h a t f o r motions p a r a l l e l t o t h e s u r f a c e t h e d e n s i t y o f modes f o r t h e s u r f a c e l a y e r is v e r y s i m i l a r t o t h a t one o f t h e

d e n s i t y o f modes c o n t r i b u t i n g t h e r e l a t i v e v i b r a t i o n a l motion n ( w ) by t h e r e l a t i o n :

The values o f n ( w ) f o r a s u r f a c e - s u r f a c e bonding o r a surface-bulk bonding is represented i n f i g u r e 3 (c-d) where we can c l e a r l y s e e the e f f e c t of t h e s u r f a c e v i b r a t i o n mode on t h e surface-bulk "two s i t e s " d e n s i t y of modes.

The same c a l c u l a t i o n h a s been done f o r the experimentally s t u d i e d system : one monolayer of c o b a l t adsorbed on t h e (111) f a c e of copper. The only input parameters i n t h e c a l c u l a t i o n a r e t h e e l a s t i c c o n s t a n t s f o r Co-Co (Cu-Cu) bonds ;

the Co (Cu) bulk f o r c e c o n s t a n t s (determined from experimental e l a s t i c c o n s t a n t s ) a r e used and f o r Co-Cu bond i t is t h e i r geometrical average.

2 2 2

The c a l c u l a t e d h a . = o . (300 K) - o . (77K) values s u c c e s s f u l l y compare with

J J J

the experimental d a t a (Table 1 and f i g u r e 4 ) . This r e s u l t enhances t h e confidence i n such c a l c u l a t i o n s t o d e s c r i b e c l e a n s u r f a c e s .

Figure 4 : T h e o r e t i c a l (open c i r c l e s ) and experimental ( f i l l e d c i r c l e s ) values of h a 2 = 0 2 (300 K) - ^{u 2} (77 K) f o r t h e d i f f e r e n t systems.

I n conclusion, we think we have shown t h e power of s u r f a c e EXAFS t o o b t a i n q u a n t i t a t i v e information about t h e l o c a l modes o f v i b r a t i o n a t t h e surface. The next s t e p w i l l be t o make t h e same kind of study on c l e a n s u r f a c e s . We have a l s o shown t h a t s u r f a c e v i b r a t i o n s can be a n i s o t r o p i c and some c a r e must be taken i n t h e i n t e r p r e t a t i o n of polarization-dependent amplitude r a t i o s and low-temperature d a t a a r e more a d v i s a b l e even t o determine geometrical parameters.

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