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DIFFUSION OF TRANSITION ADATOMS ON PERFECT AND STEPPED TRANSITION METAL
SURFACES FROM BINDING ENERGY CALCULATIONS
J. Jardin, M. Desjonquères, D. Spanjaard
To cite this version:
J. Jardin, M. Desjonquères, D. Spanjaard. DIFFUSION OF TRANSITION ADATOMS ON PER- FECT AND STEPPED TRANSITION METAL SURFACES FROM BINDING ENERGY CALCU- LATIONS. Journal de Physique Colloques, 1984, 45 (C9), pp.C9-9- C9-12. �10.1051/jphyscol:1984902�.
�jpa-00224378�
JOURNAL DE PHYSIQUE
Colloque C9, supplkment a u n012, Tome 45, ddcernbre 1984 page c 9 - 9
DIFFUSION OF TRANSITION ADATOMS ON PERFECT AND STEPPED TRANSITION METAL SURFACES FROM BINDING ENERGY CALCULATIONS
J . P . J a r d i n , M . C . ~ e s j o n q u ~ r e s * and D . ~ p a n j aard**
Laboratoire P.M. T.M. (CNRSI, Universite' Paris-Nord, 93430 ViZZetaneuse, France
*Centre d r E t u d e s NucZe'aires de Saclay, S e r v i c e de Physique d e s Atomes e t des S u r f a c e s , 91191 G i f - s u r - Y v e t t e , France
**Laboratoire de Physique d e s ~ o Z i d e s + , Universite' Paris-Sud, Centre drOrsay, 91405 Grsay, France
Resume - Nous c a l c u l o n s l e s l i g n e s de n i v e a u x de 1 ' e n e r g i e de l i a i s o n d ' u ~ w m e d e 1 a s e r i e de t r a n s i t i o n 5d s u r 1 a s u r f a c e avec marches [ m ( l l O ) x(O1 l ) ]
du tungstgne. Nous e n deduisons l e s chemins de d i f f u s i o n e t l e s 6 n e r g i e s d ' a c t i v a t i o n correspondantes e x t r a p o l e e s 8 0 K. Ces r e s u l t a t s s o n t compares 8 ceux obtenus s u r une s u r f a c e p a r f a i t e (110) e t s o n t e n assez bon a c c o r d avec l e s experiences de FIM.
A b s t r a c t - We c a l c u l a t e t h e b i n d i n g energy c o n t o u r maps f o r a s i n g l e adatom o f t h e 5d t r a n s i t i o n s e r i e s on a stepped C m ( l l O ) ~ ( 0 T l ) l W s u r f a c e f r o m w h i c h t h e d i f f u s i o n channels and c o r r e s p o n d i n g a c t i v a t i o n e n e r g i e s a r e deduced. These r e s u l t s a r e compared t o t h o s e o b t a i n e d f o r a p e r f e c t (110) s u r f a c e and a r e i n r a t h e r good agreement w i t h FIM experiments.
S u r f a c e d i f f u s i o n i s a s u b j e c t o f growing i n t e r e s t due t o i t s t e c h n o l o g i c a l a p p l i - c a t i o n s . A l t h o u g h one f i n d s i n t h e l i t e r a t u r e an i n c r e a s i n g number o f e x p e r i m e n t a l s t u d i e s , p a r t i c u l a r l y u s i n g F i e l d I o n Microscopy (FIM) , t h e t h e o r e t i c a l works a r e r a t h e r scarce. Most o f t h e s e works use e i t h e r p a i r p o t e n t i a l s d e r i v e d f r o m t h e b u l k p r o p e r t i e s o r t h e j e l l i u m model / I / . None o f t h e s e models i s w e l l s u i t e d t o t r a n s i - t i o n m e t a l s s i n c e i t i s w e l l known t h a t cohesive energy o f t r a n s i t i o n m e t a l s c a n n o t be w r i t t e n as a sum o f p a i r w i s e p o t e n t i a l s and,obviously,the j e l l i u m t h e o r y i s n o t adequate f o r t h e d valence e l e c t r o n s which, due t o t h e i r l o c a l i z a t i o n , a r e much b e t t e r d e s c r i b e d i n t h e t i g h t - b i n d i n g t h e o r y . Such a n approach has been developed by Desjonqueres and S p a n j a a r d /2/ t o s t u d y b i n d i n g and a c t i v a t i o n e n e r g i e s o f s i n g l e t r a n s i t i o n adatoms on f l a t t r a n s i t i o n m e t a l bcc s u r f a c e s .
We p r e s e n t h e r e some r e c e n t r e s u l t s o b t a i n e d f o r a d s o r p t i o n o f t r a n s i t i o n adatoms on a stepped [ m ( l l O ) x ( 0 1 1 ) I bcc t r a n s i t i o n m e t a l s u r f a c e which w i l l be compared w i t h p r e v i o u s r e s u l t s on f l a t s u r f a c e s .
We assume n e u t r a l a d s o r p t i o n and we s e p a r a t e t h e energy i n t o two c o n t r i b u t i o n s : a n a t t r a c t i v e band t e r m c a l c u l a t e d i n t h e t i g h t - b i n d i n g a p p r o x i m a t i o n and a phenomeno- l o g i c a l r e p u l s i v e term, which i s a p a i r p o t e n t i a l o f t h e Born-Mayer t y p e , t o ensure s t a b i l i t y . The band term, which comes f r o m t h e p e r t u r b a t i o n o f t h e s u b s t r a t e d-band and f r o m t h e broadening o f t h e d-adatom l e v e l when t h e bonds a r e formed, i s n o t p a i r w i s e , s i n c e f o r example t h e l a t t e r c o n t r i b u t i o n , which i s t h e l e a d i n g one, va- r i e s r o u g h l y as t h e square r o o t o f t h e c o o r d i n a t i o n number o f t h e adsorbate. T h i s band term i s d e r i v e d f r o m t h e l o c a l d e n s i t i e s o f s t a t e s w h i c h a r e o b t a i n e d f r o m t h e c o n t i n u e d f r a c t i o n t e c h n i q u e w i t h t h r e e e x a c t moments / 3 / .
The t i g h t b i n d i n g hopping i n t e g r a l s a r e drawn f r o m i n t e r p o l a t i o n scheme and t h e i r v a r i a t i o n w i t h d i s t a n c e i s assumed t o be e x p o n e n t i a l as suggested by d i r e c t c a l c u l a - t i o n s . The parameters o f t h e r e p u l s i v e p o t e n t i a l a r e f i t t e d t o g i v e a good v a l u e o f t h e cohesi.ve energy, i n t e r a t o m i c s p a c i n g and b u l k modulus o f t h e s u b s t r a t e . A l l
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984902
C9-10 JOURNAL DE PHYSIQUE
t h e s e parameters a r e assumed t o be c o n s t a n t a l o n g t h e d s e r i e s . The second s e t o f t i g h t - b i n d i n g parameters a r e t h e e f f e c t i v e a t o m i c l e v e l s w h i c h a r e determined s e l f - c o n s i s t e n t l y t o s a t i s f y t h e charge n e u t r a l i t y o f each atom o f t h e a d s o r p t i o n system.
The l e a d i n g parameter of t h i s model i s t h u s t h e number of d e l e c t r o n s o f t h e adsorbate and s u b s t r a t e .
I 1 - RESULTS
We s t u d y t h e a d s o r p t i o n on a p e r f e c t (110) and on a stepped [ m ( l l O ) x ( O ~ l ) ] b c c t r a n - s i t i o n m e t a l s u r f a c e shown i n f i g u r e 1. I n t h e case o f t h e p e r f e c t s u r f a c e t h e e q u i - l i b r i u m s i t e s and d i f f u s i o n channels a r e e a s i l y guessed from symmetry c o n s i d e r a t i o n s . The most s t a b l e s i t e i s an a l m o s t t e r n a r y s i t e T and t h e s a d d l e p o i n t f o r d i f f u - s i o n corresponds t o a b r i d g e between n e a r e s t n e ~ g h b o u r s (6 1 ) /2/.
The case of stepped surfaces i s more t e d i o u s . Due t o t h e i r l o w e r symmetry, we must d e r i v e t h e e q u i 1 ib r i u m s i t e s and d i f f u s i o n p a t h s f r o m b i n d i n g energy c o n t o u r maps.
A t y p i c a l example (W adatom/W s u b s t r a t e ) i s g i v e n i n f i g u r e 2. T h i s - f i g u r e shows t h e remarkable p o i n t s ( l o c a l minima and s a d d l e p o i n t s ) which a r e l a b e l l e d i n f i g u r e 1. The most s t a b l e a d s o r p t i o n s i t e 4 i s i n t h e ledge, t h i s was expected s i n c e i t corresponds t o t h e maximum c o o r d i n a t i o n ( t h r e e f i r s t and t h r e e n e x t n e a r e s t n e i g h b o u r s ) . A l t h o u g h TG has t h e same c o o r d i n a t i o n ( t h r e e f i r s t and one n e x t nearest n e i g h b o u r s ) as a t e r n a r y a d s o r p t i o n s i t e T on t h e f l a t s u r f a c e , i t s b i n d i n g energy i s i n c r e a s e d as a r e s u l t o f t h e m o d i f i c a t i o n o f t h e e f f e c t i v e l e v e l s o f t h e s u r r o u n - d i n g atoms due t o t h e v i c i n i t y o f t h e s t e p , a f e a t u r e which cannot be e x p l a i n e d i n a p a i r w i s e p o t e n t i a l t h e o r y . A s i m i l a r e f f e c t has been observed on t h e (211) p o l e o f a W F I M t i p by F i n k and E h r l i c h / 4 / . F o r t h e same r e a s o n t h e t e r n a r y s i t e s T i and T i , which would be e q u i v a l e n t on t h e f l a t s u r f a c e have n o t e x a c t l y t h e same b i n d i n g energy because o f t h e i r p o s i t i o n r e l a t i v e t o t h e s t e p .
The p o s s i b l e d i f f u s i o n channels a r e shown i n f i g u r e 1. The a c t i v a t i o n e n e r g i e s ( e x t r a - p o l a t e d a t 0 K ) a r e o b t a i n e d f r o m t h e b i n d i n g energy d i f f e r e n c e between t h e s a d d l e
F i g . 1 - Step g e o m e t r y , l a b e l l i n g o f s i t e s F i g . 2 -
and d i f f u s i o n channels.
B i n d i n g energy c o n t o u r maps f o r a W adatom on a ' y J [ m ( l l O ) x ( O T l ) l s u r f a c e
F i g . 3 - S u r f a c e d i f f u s i o n a c t i v a - t i o n e n e r g i e s f o r 5d adatoms on W [ m ( 1 1 0 ) ~ ( 0 1 1 ) ] s u b s t r a t e as a func- t l n o f t h e i r number o f d e l e c t r o n s . F u l l c i r c l e s a r e experimental d a t a .on W(110). F o r t h e l a b e l l i n g , see F i g . 1
p o i n t and t h e e q u i l i b r i u m s i t e . The r e s u l t s o b t a i n e d f o r t h e p e r f e c t s u r f a c e a r e i n r a t h e r good agreement w i t h t h e measurements o f B a s s e t t
( f i g . 3 ) / 5 / . We f i n d t h a t t h e presence o f t h e s t e p does n o t change s i g n i f i c a n t l y t h e a c t i v a - t i o n energy f o r d i f f u s i o n i n a d i r e c t i o n p a r a l - l e l t o t h e ledge, even f o r a n adatom d i f f u s i n g i n t h e l e d g e ( f i g . 3 ) . T h i s i s o b v i o u s l y n o t t h e case f o r d i f f u s i o n p e r p e n d i c u l a r t o t h e s t e p as e v i d e n c e d by t h e p r o f i l e s o f t h e poten- t i a l energy o f t h e adatom a l o n g t h i s d i r e c t i o n ( f i g . 4). An adatom on t h e upper t e r r a c e , d i f f u - s i n g towards t h e step, i s r e f l e c t e d by t h e o u t e r edge o f t h e s t e p due t o t h e o c c u r r e n c e o f an e x t r a b a r r i e r h e i g h t AEb w h i c h l i e s i n t h e range 0.2 - 0.5 eV. Experiments performed on a (110) W FIM t i p by B a s s e t t e t a1. /6/ and Wang and Tsong /7/. g i v e r e s u l t s i n t h i s range o f v a l u e An adatom on t h e l o w e r t e r r a c e w i l l be t r a p p e d by t h e s t e p s i n c e t h e l a s t d i f f u s i o n b a r r i e r B i L i s n o t i n c r e a s e d compared t o t h e e q u i v a l e n t one on t h e f l a t surface. F i n a l l y l e t us n o t i c e t h a t a l l t h e s e a c t i v a t i o n e n e r - g i e s v a r y r o u g h l y p a r a b o l i c a l l y w i t h t h e number o f d e l e c t r o n s o f t h e adsorbate. Consequently t h e e x t r a b a r r i e r h e i g h t decreases a t t h e end o f t h e s e r i e s w h i c h i s c o n s i s t e n t w i t h t h e weakness o f t h e b a r r i e r observed by B a s s e t t f o r P t and by B u t z and Wagner f o r Pd on a ( 1 1 0 ) W s u r f a c e /8/.
F i g . 4 - P r o f i l e o f t h e p o t e n t i a l energy o f an adatom d i f f u s i n g a c r o s s t h e s t e p s . F o r t h e l a b e l l i n g , see F i g . 1. aEb i s t h e e x t r a b a r r i e r h e i g h t . AEU i s t h e e x t r a b i n d i n g energy near t h e o u t e r edge.
L e t us remark t h a t t h e model can be a p p l i e d t o any a t o m i c c o n f i g u r a t i o n of t r a n s i t i o n m e t a l s u r f a c e s ( s t e p w i t h any o r i - e n t a t i o n , k i n k s , advacancies, e t c . . . )
JOURNAL DE PHYSIQUE
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