Simple model for an adsorbate-induced surface phase transition

Surface Science 164 (1985) L807-L810 North-Holland, Amsterdam

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S U R F A C E S C I E N C E LETTERS S I M P L E M O D E L FOR AN A D S O R B A T E - I N D U C E D S U R F A C E P H A S E TRANSITION V.P. Z H D A N O V Institute of Catalysis, Novosibirsk 630090, USSR Received 17 April 1985; accepted for publication 8 July 1985

A qualitative model is proposed for the description of an adsorbate-induced surface reconstruction in terms of the theory of first-order phase transitions.

Adsorbate-induced phase transitions of the metal surface have been observed for several systems. In particular, Norton et al. [1,2] have reported results of an extensive study of the (5 × 20) to (1 x 1) phase transition that occurs when a clean Pt(100) surface is exposed to hydrogen, CO or NO. The authors suggest that this phase transition can be regarded as a first-order phase transition. In this Letter we present a simple qualitative model for such reconstruction. An alternative model, describing an induced reconstruction as a second-order phase transition, is analysed in refs. [3]. A real surface reconstruction induced by adsorption is a very complex phenomenon. To simplify our consideration, we use the following assumptions. Any surface atom is located in the positions I or II (fig. 1). For a clean surface, position 1 is stable and position II is metastable. Adsorbed particles are described in the framework of a lattice-gas model. Interaction between surface atoms and adsorbed particles leads to stabilization of the metastable phase (fig. 1). In the mean-field approximation, the total free energy of the system can easily be obtained as F = F.d,j + F~ + F i , . ,

E d J N , = - E , O + zc02/2 + T[O In 0 + ( 1 - 0) ln(1 - 0)], F s / N ~= aEK + T[K an K + ( 1 - x) ln(a - K)], ~ ° t / N~ = - zaOK, where Fad and 'FS is the free energy of adsorbed particles and surface atoms, Fint is the interaction energy (this energy stabilizes the metastable phase), Ns is the number of surface atoms, 0 is the adsorbate coverage, E a is the adsorption 0039-6028/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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lCP. Zhdanov / A dsorbate-induced surface phase transition -I

u(q)

I

I

I

I

0.2

0.4

0.6

0.8

+

a. -2

kJ

-3 q

0

e

Fig. 1. H y p o t h e t i c a l p o t e n t i a l energy for d i s p l a c e m e n t of a surface atom. The solid line is the p o t e n t i a l curve for a clean surface, the d a s h e d line that for an a d s o r b a t e - c o v e r e d surface, q is a c o o r d i n a t e of displacement. Fig. 2. P a r a m e t e r (/~ + E a ) / T as a function of coverage. The solid line c o r r e s p o n d s to the curve d e t e r m i n e d from eq. (3) for zc~ = 7 k c a l / m o l , zc = 5 k c a l / m o l and A E = 3 k c a l / m o l (these values are also used in figs. 3 and 4), T = 450 K. The d a s h e d line shows the value of the chemical p o t e n t i a l in the t w o - p h a s e region.

energy, z is the number of the nearest neighbour sites, c is the energy of the lateral interaction of adsorbed particles, zlE is the energy difference between positions II and I at a clean surface, • is the coverage of surface atoms located in position II, c~ is the interaction energy parameter. The chemical potential of adsorbed particles is defined as

t~= S F / S N = - E a + z~O + T ln[ O / ( 1 - O )] - za~, (1) where N = N,O is the number of adsorbed particles. In the case of thermodynamical equilibrium, we have OF/OK = 0, or A E + T ln[K/(1 - ~)] -zc~O=O. (2) Using eqs. (1) and (2), we derive

{ tt + E, ~ exp~-)

O 1-O

( z~O exp

T

z~ T{l+exp[(AE-ze~O)/T]}

) "

(3)

This equation defines a phase diagram of the system. At temperatures below the critical temperature, T < T~, the right-hand part of eq. (3) is a non-monotonous function of coverage (fig. 2). Thus, the phase separation occurs at T < T~. The real value of the chemical potential in the two-phase region (the dashed line in fig. 2) is defined by the famous rule: the shaded areas in fig. 2 must be equal to each other. An example of the phase diagram of the adsorbed layer is presented in fig. 3.

V.P. Zhdanov / Adsorbate-induced surface phase transition I

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! I I ! I

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0.4- --

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0

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1

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0,2

0,4

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Fig. 3. Phase diagram of the adsorbed layer. A is a one-phaseregion, B is a two-phase region. Fig. 4. Adsorption isotherm at T = 450 K. Hysteresis is indicated by dashed lines.

Eq. (3) can also be used to construct isotherms or isobars of adsorption. For example, in the case of monomolecular adsorption, the chemical potential of adsorbed particles is equal to the chemical potential of particles in the gas phase. The chemical potential for the gas phase is /~ = T In(Ug/Zg),

(4)

where Ng is the concentration of particles and Zg is the partition function. Eqs. (3) and (4) define isotherms and isobars of adsorption. An example of an adsorption isotherm is presented in fig. 4. The nucleation mechanism which occurs during adsorption (or desorption) and phase transition can cause a hysteresis in the adsorption-desorption or adsorption-reaction-desorption equilibria. Apparently, such hysteresis is observed in the cases of CO adsorption [2] and hydrogen oxidation [4] on a Pt (100) surface. Unfortunately, at the present time, it is not certain whether the hysteresis observed in some systems [2,4] is simply related to nucleation and growth phenomena. The author expresses his thanks to Dr. V.A. Sobjanin for useful discussions.

References [1] P.R. Norton, J.A. Davies, D.K. Creber, C.W. Sitter and T.E. Jackman, Surface Sci. 108 (1981) 205. [2] R.J. Behm, P.A. Thiel, P.R. Norton and G. Ertl, J. Chem. Phys. 78 (1983) 7437.

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V.P. Zhdanov / Adsorbate-induced surface phase transition

[3] K.H. Lau and S.C. Ying, Phys. Rev. Letters 44 (1980) 1222; T. Inaoka and A. Yoshimori, Surface Sci. 115 (1982) 301; S.C. Ying and L.D. Roelofs, Surface Sci. 125 (1983) 218; 147 (1984) 203. [4] V.A. Sobjanin, G.K. Boreskov and A.R. Cholach, Dokl. Akad. Nauk SSSR 278 (1984) 1422; 279 (1984) 1410.