FIELD ADSORPTION AND EVAPORATION

HAL Id: jpa-00225890

https://hal.archives-ouvertes.fr/jpa-00225890

Submitted on 1 Jan 1986

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

FIELD ADSORPTION AND EVAPORATION

H. Kreuzer, K. Nath

To cite this version:

H. Kreuzer, K. Nath. FIELD ADSORPTION AND EVAPORATION. Journal de Physique Colloques, 1986, 47 (C7), pp.C7-3-C7-6. �10.1051/jphyscol:1986701�. �jpa-00225890�

JOURNAL DE PHYSIQUE

Colloque C7, supplement au n o 11, Tome 47, Novembre 1986

FIELD ADSORPTION AND EVAPORATION

H.J. KREUZER and K. NATH

Department of Physics, Dalhousie University, Halifax, N. S. B3H3J5, Canada

Abstract - A microscopic tight-binding cluster model is used to calculate the tield-induced adsorption of He on tungsten. Likewise field evaporation of tunqsten ions is comted as a function of electric field strength. The impor- tance of local field effects - here taken from self-consistent jellium calcu- lations

-

Adsomtion of qases on metals is stronqly enhanced in lame electric fields of the order of several volts per Angstrom. Theoretical understanding of field-induced adsorption has been sought within the framework of phenomenological models of which the very first one by Tsong and Miiller /1/ still seems the most popular. It assumes:

(i) the metal-gas system can be modeled by a gas atom-metal atom dimer, i.e. the metal bulk properties are of lesser importance;

(ii) the electric field is constant over the dimer, in contrast to standard electrostatics according to which the electric field d m = to zero at the image olane just outside the metal:

(iii) the binding comes about through the interaction of the induced dipoles on the two atoms of the dimer. The field-induced binding energy is then given

Here a and a are the polarizabilities of the surface metal atom and the adsorbed atom, MresDec#%vely, and d is their separation. Recent calculations within the jellium model of a metal give evidence how the electric field decays into the metal and haw this decay depends on the field strength far from the metal, and on the electron density in the conduction band (see Ejg. 1 for pxamples)

.

p.

We note that in zero field, the minimum of the physisorption potential of He on most metals is more than 3.5 fi from the topnost lattice plane. Moreover, there is no reason to believe that d stays constant as the electric field pushes the surface electrons into the metal decreasing d appreciably to the point, where dipole inter- actions are insufficient and electronic effects come into play, eventually leading to chemisorption. We have developed a microscopic theory of field adsorption and evaporation that follows up on these ideas /3/.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986701

C7-4 JOURNAL DE PHYSIQUE

The theory is based on t h e ASED-MO (atom superposition and e l e c t r o n d e l o c a l i z a t i o n molecular o r b i t a l ) c l u s t e r model. One assumes t h a t t h e s i n g l e e l e c t r o n Droperties

(energy l e v e l s and wavefunctions) of t h e i s o l a t e d atoms a r e k n m . Bringing N metal atoms together t o form a metal c l u s t e r one c a l c u l a t e s its p o t e n t i a l energy a s t h e sum of Coulomb energies between t h e unperturbed atoms plus a contribution from mutual e l e c t r o n overlap ( t i g h t binding Hiickel t-). The apulied electric f i e l d , a s taken from s e l f c o n s i s t e n t jellium c a l c u l a t i o n s /4/, is taken f u l l y i n t o account i n t h e Hamiltonian of t h e metal c l u s t e r plus-qas-atom. It leads t o p o s i t i o n dependent s h i f t s i n t h e e l e c t r o n l e v e l s of t h e various atoms of t h e c l u s t e r and a d d i t i o n a l off-diagonal matrix elements t h a t can be analyzed a s contributinq t o ~ o l a r i z a t i o n , hyperpolarization, gradient corrections, etc. /5/.

2. FIELD ADSORPTION

I n Fig. 1 w e show t h e p o t e n t i a l energy curves f o r H e i n f r o n t of a c l u s t e r of 4 t o 14 atoms representing W(111) surfaces i n an asymptotic f i e l d F = 3 ~ / 8 . Also shown is t h e f i e l d p o t e n t i a l VF( z ) and t h e f i e l d F ( z ) = 4 V ( z ) /dz f o r a metal with Wigner- S e i t z r a d i u s r = 3. Curves ( a ) t o (c) a r e approximarions i n which only l o c a l energy s h i f t s ( a ) plG l i n e a r p o l a r i z a t i o n of H e (b) p l u s l i n e a r p o l a r i z a t i o n of W (c) _{a r e} successively added. Curve ( d ) takes a l l f i e l d e f f e c t s i n t o consideration. ^To summa- r i z e the r e s u l t s as a function o f asymptotic f i e l d s t r e n g t h we give i n Fig. 2 t h e p o s i t i o n of t h e binding minimum z in, t h e a c t i v a t i o n energy Q ( d i f f e r e n c e between m i n i m u m and top of t h e a c t i v a t i o n krrier) and t h e charge t r a n s f e r A q a t t h e binding minimum. To demonstrate how important t h e l o c a l electric f i e l d is f o r f i e l d adsorp- t i o n w e give t h e same d a t a i n Fiq. 3 f o r a metal with r = 1.5, a value rtmre accep- t a b l e f o r tungsten (one has t o be aware of some d i f f i c u 5 t i e s t o a s s o c i a t e a jellium model of s-electrons with a t r a n s i t i o n metal). W e note:

(i) a d r a s t i c inward motion of t h e adsorption site f o r f i e l d s l a r g e r than about 3 v/a;

(ii) a concurrent increase i n binding energy from about 1 0 m e V i n F=O t o a few hundred meV;

(iii) an appreciable charge t r a n s f e r t o t h e metal. These trends can be character- ized as a t r a n s i t i o n from physisorption i n zero f i e l d (with van d e r Waals a t t r a c t i o n ) t o chemisorption i n stronq f i e l d s due t o e l e c t r o n i c bond formation

Fig. 1 - P o t e n t i a l energy curves 2.0

f o r t h e He/W(111) system. The electric f i e l d F and electric w- t e n t i a l V a r e taken from jellium ^,.5 c a l c u l a t i o n s F /4/. The tunqsten

c l u s t e r has 1 4 atoms. Curves ( a ) includes only l o c a l s i n g l e e l e c t r o n energy s h i f t s ; ( b ) inlcudes polari- zation of He; (c) a l s o of W and ( d l '"

inlcudes a l l f i e l d e f f e c t s .

F

-

3

0.5

0

2 6

Fig. 2 - Adsorption p o s i t i o n Z a c t i v a t i o n energy Q f o r desorption, and Ahpie t r a n s f e r

as a function of asymptotic f i e l d strength.

The l o c a l f i e l d v a r i a t i o n is taken from jel- liium c a l c u l a t i o n s /4/ with rs = 3 .

3. FIELD EVAPORATION

Fig. 3 - Same as Fig. 2 but f o r rs = 1.5.

F i e l d evaporation can only t a k e place i f t h e electric f i e l d penetrates i n t o t h e metal. Taking t h e l o c a l f i e l d v a r i a t i o n s again from t h e s e l f c o n s i s t e n t jellium c a l c u l a t i o n s /4/, w e show i n Fig. 4 t h a t t h e a c t i v a t i o n b a r r i e r disappears f o r rS = 3 i n a f i e l d of 4 ~ / 8 and f o r r = 1.5 a t 8 ~ / 8 . The f a c t t h a t t h e zero f i e l d binding energy is only 6.8 e V per 'atom r a t h e r than 8.2 e V as suggested by t h e cohesive energy of tungsten is not s u r p r i s i n g as Hiickel-type c a l c u l a t i o n s t y p i c a l l y a r e not b e t t e r than 20 - 50 %, anyway. Hawever, t h e trend of a c t i v a t i o n energy as a function of f i e l d s t r e n g t h a s depicted i n Fig. 4 is t r u t h o r t h y . Higher e l e c t r o n d e n s i t i e s (lower r ) reduce f i e l d penetration and t h u s r e q u i r e l a r g e r evaporation f i e l d strengths.

To allow a comparison of our He-tungsten r e s u l t s with experimental d a t a , we suggest t o (i) c h a r a c t e r i z e tungsten with r = 1.5 and ( i i ) t o s c a l e t h e electric f i e l d such t h a t our evaporation f i e l d o f 8 v/gSis set equal t o t h e experimental value of 5.6 ~ / g . The a c t i v a t i o n energy (curve ( d ) from Fig. 3 ) can then be compared with d a t a by Ernst e t a l . (Fig. 1 and 2 i n t h e following contribution of t h i s volume by Ernst et a l l .

4. CONCLUSIONS

W e have discussed a microscopic theory of f i e l d adsorption and evaporation. F i r s t r e s u l t s a r e very encouraging. They shaw, i n p a r t i c u l a r , t h a t f i e l d adsorption must be understood a. a t r a n s i t i o n from physisorption t o chemisorption. There is much

JOURNAL DE PHYSIQUE

Fig. 4 - The a c t i v a t i o n energy f o r f i e l d evaporation f o r W from a W c l u s t e r .

l e f t t o improve t h e c l u s t e r model, i n p a r t i c u l a r , t o make it self-consistent with t h e f i e l d calculated f o r a s p e c i f i c adsorption site r a t h e r than a f l a t jellium surface.

The author acknowledges a fellowship of t h e Max-Planck-Gesellschaft, which allowed d e t a i l e d discussions during a v i s i t t o t h e Fritz-Haber-Institut.

REFERENCES

/1/ Tsong, T.T., and Miiller, E.W., Phys. Rev. Lett. 25 ⁽ 1970) 91 1 ; J. Chem. Phys.

-

/2/ Wang, S.C., and Tsong, T.T., Phys. Rev. B 2 (1 982) 6470.

/3/ Tomanek, D., Kreuzer, H.J., and Block, J.H., Surf-Sci. 157 (1985) L 315:

Nath, K., Kreuzer, H.J., and Anderson, A.B., Surf. ~ c i

.%

-

/5/ Nath, K., and Kreuzer, H.J., Surf. S c i . ( i n p r e s s ) .