Surface diffusion of dimers: I repulsive interactions

surface science Surface Science 391 (1997) 267 277

ELSEVIER

Surface diffusion of dimers: I repulsive interactions A.J. Ramirez-Pastor, M. Nazzarro, J.L. Riccardo, V. Pereyra * Departamento de Fisica and ('entro Latinoamericano de Estudios llya Prigogine. Unit'ersidad Nacional de San Luis, CONICET, Chacabuco 917, 5700 San Luis, Argentina Received 31 December 1996; accepted for publication 18 June 1997

Abstract

We analyze the diffusion process of rigid homonuclear dimers (AA) adsorbed on a simple cubic (sc(100)) surface. The coverage dependence of the collective diffusion coefficient is obtained by means of Monte Carlo simulations in the framework of the Kubo Green formalism. Different microscopic diffusion mechanisms are introduced and their influence in the collective motion have been investigated. Repulsive adsorbate adsorbate interaction, JAA,is considered in order to analyze the influence of such parameter on the diffusion process. The behavior of the diffusion coefficient in the critical region is studied, where several ordered adsorbate structures appear depending on the values of JAA. ~ 1997 Elsevier Science B.V. Keywords: Computer simulations; Surface diffusion; Surface phase transitions

I. Introduction

The diffusion of adsorbed molecules on solid surfaces plays an important role in many surfaces processes, involving heterogeneous catalysis, adsorption, desorption, oxidation, lubrication, coating, melting, roughening, crystal and film growth, etc. Therefore, increasing interest and efforts have been devoted to developing and understanding the mechanisms of surface diffusion [123]. Experimentally, a number of techniques for studying surface diffusion have been developed during the last decades, e.g. the fluctuation method based on field electron microscopy (FEM) or scanning tunneling microscopy (STM) together with field ion microscopy (FIM). However, the data that are currently available for molecules do * Corresponding author. Fax: (+ 54) 652 30224; e-mail: [email protected] 0039-6028/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0039-6028 (97) 00496-2

not possess sufficient resolution to allow the elucidation of diffusion mechanisms. In many cases, the evaluation and interpretation of such data has been rather complicated. Computer simulations through Monte Carlo (MC) [4,5,7,8, 16] and molecular dynamics (MD) [24 29] offer a powerful way to probe such microscopic mechanisms and to analyze and interpret surface diffusion data. Monte Carlo simulation has been used mostly by employing of the lattice gas model for the adsorbed monolayer. Most of these studies are devoted to the analysis of tracer and collective surface diffusion on homogeneous surfaces [2 9], where the influence of the adsorbate adsorbate interactions and phase transitions has been deeply analyzed. These studies have shed much light on the equivalence between different methods of computationally determining collective diffusion constants (e.g. Kubo-Green formalism and density fluctuation method [7,8]). Surface

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diffusion on heterogeneous substrates has been also studied in the framework of the lattice gas model [11-15,30-32]. Molecular dynamics has proved to be effective at high temperatures relative to the diffusion activation barrier; however, at sufficiently low temperatures, the time between diffusive hops increases greatly, making MD simulations no longer practical {33]. Significant experimental contributions to the understanding of local diffusion modes of simple adatoms and diatomic clusters are those of Gomer [ 1], Basset [ 17, 22] and Tsong et al. [20, 21 ], who have reported distinct migration steps for metallic dimers on transition metal surfaces [Pt z W ( I I 0 ) , W2-W(ll0)], such as dimer rotation, stable dimer displacements and sequential dissociation recombination displacements. The observation of the motion of adatoms and clusters provides much information about the particle substrate and interparticle interactions, which turn to be of essential interest in surface adsorption, film growth and surface reactions. Static minimum-potential-energy calculations have been used to elucidate the intrinsic mechanism of the microscopic movement of the molecules, as shown in a recent paper [34], where the diffusion mechanisms of a rigid homonuclear dimer (AA) adsorbed on fcc(100) (face centered cubic) crystal surfaces have been discussed. The various modes of dimer motion on fcc(100) are analyzed, and in comparison with monoatomic diffusion, the authors have found several complicated diffusion mechanisms in this simple system. The characteristics of the dimer motion have also been observed in sc(100) surfaces [35]. It is worth mentioning that prior theoretical studies [36] have dealt with multistate diffusion of particles and dimers within the framework of stochastic theory. Most of the above works have a common feature; namely, only diffusion at extremely low surface concentration of adsorbates has been addressed. Collective surface diffusion of polyatomic clusters has received much less attention, so the lack of systematic experimental research in this area makes the testing of model predictions particularly difficult. Among the few papers concerned with detailed information of dimer diffusion at finite coverage are Refs [37 40] (particularly relevant to the pre-

sent study are the systems CO N i ( l l l ) and C O - N i ( l l 5 ) in Ref. [40]). Although interesting studies have been devoted to the motion of strongly bounded diatomic molecules, the consequence of elementary jump mechanisms and molecular interactions on the collective diffusion of dimers is still poorly understood. In this paper, we present a study of the collective motion of dimers on homogeneous monolayer surfaces. Diffusion of homonuclear dimers (AA) adsorbed on sc(100) surfaces has been studied in the framework of the Kubo Green theory. Several coefficients, like the collective D, jump Dj and tracer D* diffusion coefficients are calculated as a function of the surface coverage 0 and temperature T. Different mechanisms of dimer motion are introduced and the consequences on the collective diffusion are analyzed. In particular, for the noninteracting case, the effect of the microscopic mechanism of motion on the collective diffusion coefficient D as a function of the surface coverage 0 clearly differentiates from the other contributions. In the present work, the adsorbate-adsorbate interactions, JAA, are taken to be repulsive; different ordered structures are obtained due to the character of the interactions. The model system's predictions are expected to be a qualitative guide to the behavior of chemisorbed diatomic species in which diffusion proceeds as thermally activated jumps. The paper is organized as follows: in Section 2, a description of the lattice gas model, which represents the adsorbed dimer configuration, and the corresponding Hamiltonian are given, as well as the description of the elemental motion mechanisms and their implementation in the Monte Carlo simulation. In Section 3, the surface diffusion coefficients are determined. The noninteracting case and the repulsive case are described and discussed in Section 4. Finally, in Section 5, we make our final remarks and conclusions are drawn.

2. Model and diffusion mechanisms

The homonuclear (AA) diatomic molecule adsorbed on an sc(100) surface is modeled as two

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A.J. Ramirez-Pastor el al. Sur/ace Science 391 (1997) 267 277

interaction centers at a fixed separation, which is equal to the lattice constant a. We have not considered here the high-frequency stretching motion along the molecular bond. The dimer bond length remains constant throughout the treatment. The sc(100) surface is represented as an array of N o = L x L adsorptive sites which correspond to the four-fold coordinated ones, where L is the linear size of the array. In order to describe the system of N dimers adsorbed on No sites at a given temperature T, let us introduce the spin variable si which can take the following values si=O if the corresponding site is empty and si= 1 if the site is occupied by "A" atom, respectively. Under this consideration, the Hamiltonian of the system is given by H=JAA

2

Sisj--NJAA

(1)

(i,j) ,i

where JAA is the nearest-neighbor interaction constant which is assumed to be repulsive (positive) and (i,j)" represents pairs of N N sites. In this way, we have calculated the total interaction energy for all the possible pairs of atoms (bonds), including those corresponding to the dimer, then we subtract the interactions' corresponding N dimers. As the surface is assumed to be homogeneous, the interaction energy between the adsorbed dimer and the atoms of the substrate is neglected for the sake of simplicity. It should be pointed out that any dissociation followed by a rebonding effect and exchange process which may occur in some systems [41] are not considered in our study. The basic step of surface diffusion is the jump of the adsorbed dimer to some of the empty nearest-neighbor sites. We introduce, in this work, two possible mechanisms for such transition. In the first mode, the dimer attempts to move one lattice unit parallel to its bond. The motion of a single molecule will be a one-dimensional translation [Mode I, see Fig. l(a)]. In the second mode, the dimer attempt is a 90 ° rotation, where one of its components remains in its position. This elemental motion mechanism enables the dimer to change its direction during diffusion on the surface [Mode II, see Fig. l(b)]. A third mode we also use in this paper is the combination of the two modes described above (Mode III).

Diffusional Mechanisms 0

0

0

0

0

0

:i) °°ooo° o°° o° 0

0

0

0

0

0

0

0

0

(a) o

o

o

o~oi

o

f

o o

o

o o

o

I"--II f

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

O

O

0

0

0

0

f

0

0

,o-5 H

f

o

o

0

0

O

O

O

0

0

O

0

0

0

(b) Fig. 1. Microscopic motion mechanisms, i and f denote the initial and final state respectively: (a) Mode I, quasi one-dimensional displacement in vertical direction; (b) Mode I1, 9 0 rotation.

Although in some real systems such as Pt 2 and Pt3 W(110) [22] and W 2 - W ( 1 1 0 ) [21], the rate of mode II is significantly larger than that observed for mode I at the zero coverage limit; both have been separately checked in this work in order to distinguish their statistical (say, configurational) weight at finite coverage.

A.J. Ramirez-Pastor et al. / Suu'ace Science 391 (1997) 267 277

270

Under this consideration, the activation energy for a jump of a dimer adsorbed on a pair of site j , j ' to the site l, l' is AE. The associated jump probability Pj is then given by

Pj

=

K

.

if ordered lattice gas phases are formed at low temperatures, substantially longer equilibration cycles are often required ( ~ 106 MCS). All calculations are performed in a Parix parallel computer with eight nodes.

(2)

Here h" is a normalization factor which essentially determines the time in which an adsorbed dimer is allowed to attempt a jump. In order to perform a jump, the well-known inequality ~
3. Determination of surface diffusion coefficients

The tracer diffusion coefficient D* is determined from measurements of the mean square displacement of N=ONo tagged adsorbed dimers, ArM) according to [1,3]: D* = lim t~oc

t

([Ari(t)]2)

(3)

,

i=1

where t is the time and the Ari values are expressed in units of the lattice constant. Here, q(t) is taken as the coordinates of the center of mass of a given dimer. The chemical diffusion coefficient, D, is determined by using of the K u b o - G r e e n formalism [2]:

D

(@/k.T]

= \~/Dj

=[((c]N)2)I

L (N)

1

De,

(4)

where ~ is the chemical potential; 0 is the coverage; 2n is the normalized mean-square fluctuation: and De is the jump diffusion coefficient given by [1] Dj = lim -,~o~ 4t N

i=1

Ari

.

(5)

The procedure for simulating the diffusion process, in the framework of Kubo Green formalism, consists of two well-defined steps. First, the calculation of the thermodynamic factor [first factor in Eq. (4)] is carried out in either one of its two equivalent forms (@/i~ In O)t=kRT[((ijN)2)/ ( N ) ] -1 by simulating the adsorption equilibrium in the grand canonical ensemble; second, the calculation of the jump diffusion coefficient, De, is carried out by using Eq. (5), which is performed in the canonical ensemble. In the same procedure, D* and V are calculated as well. All results for D, D e and D* are given in units of D(0), Dj(0) and D*(0) - the chemical, jump and tracer diffusion coefficients for one single adparticle, respectively.

A.J. Ramirez-Pastor et al.

4. Results

Joe O0

4.1. Isotherms and mean-square.)quctuations Fig. 2 shows typical dimer isotherms, obtained in the grand canonical ensemble, for various temperatures (the method used to calculate them is well discussed in Ref. [42]). There is no evidence of discontinuity for all the curves in Fig. 2, i.e. of first-order transition at any temperature investigated. However, at low temperatures, we can see the typical steps which correspond to some ordered-phase structures. In fact, we have shown in Fig. 3(a and b) a snapshot of configurations corresponding to the steps 0=0.5 and 0=0.66 for the lowest temperature in Fig. 2. At 0=0.5, a welldefined array of dimers, resembling a c2 x 2 phase, is found. The ordered structure is due to the repulsive interactions between the adsorbed dimers. The equilibration of the adsorbed system at this temperature required a large number of MCS (1.5 x 106 MCS). As the chemical potential/* increases, the incoming dimers are adsorbed forming, at 0=0.66, domains of zig-zag one-dimer-width strips at + 4 5 from the lattice symmetry axes, separated from each other by single-site empty channels. The periodicity of the zig-zag varies from 1 to L. The largest value corresponds to diagonal strips throughout the lattice. The internal energy per 1.0

n

• ~' ' -

0.8

(1.6

0 0.4

- - - - ' h A I A A L ~ A ~ ' I & & ~1 I

,/

/ I ~ m1 l I I1l I I I

./ L

y/

•

0.2

0.0 - ~ . -1

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Sur/ctce Science 391 (1997) 267 277

0

00

eo OO

00

O0 Og

O0 OO

O0 BO!

O0

OO

00

O0

OO

O0

00 O0

O0 OO

00 00

O0 OO

00

O0

OO

OO

O0

O0

O0

O0

00

(a) O~ O0 00 OO OO OO 00 00 • OO iO0 00 • 00 00 O0 O0 OO 00 0~ 00 • 00 O0 00 • 00 00 O0 O0 00 BO OO 0~ • BO 00 ~ OO • O0 OO OO OO @@ BO @0 @@ • 00 00 00 •

I

Fig. 2. Simulated adsorption isotherms for different ratios between temperature and repulsive nearest neighbor interaction [77JAA=~£ (circles), T/J~A=0.5 (triangles) and T/JAA--0.2 (squares)] (kB has been arbitrarily chosen for simplicity).

(b) Fig. 3. Snapshot of: (a) the c2 x 2-ordered phase at 0=0.5; (b) the ordered phase (zig-zag strips) at 0=0.66.

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A.J. Ramirez-Pastor et al. / SutJace Science 391 (1997) 267 277

dimer,

corresponding

to

such

structures,

is

E = JAA.

Since the symmetry particle-vacancy, valid for monoatomic species, is broken for dimers, the ordered phases are not symmetric around 0=0.5 (so are the isotherms and phase diagram). This effect is also observed in the calculation of the entropy as a function of coverage where a deep minimum appears for the different ordered structures for 0>0.5 [43]. The thermodynamic factor, which is the inverse of the mean-square fluctuations, is shown in Fig. 4 as a function of coverage and for different temperatures. The microscopic motion mechanism does not affect the mean square fluctuations. The thermodynamic factor, [<((JN)2>/'] 1 increases for all coverage as the temperature decreases and is sharply peaked at 0=0.5 and rather roundly peaked at 0=0.66. The well-pronounced maximum corresponding to half coverage is due to the formation of a c2 x 2-ordered structure, as in the monoatomic case [7]. The local maximum at 0 =0.66 is less pronounced than the one at 0=0.5. The reason for this effect is the coexistence of several ordered structures with the same internal energy per dimer. In other words, the c2 x 2 phase has only two possible structures, according to the orientation (horizontal and vertical ), with the same energy, while the zig-zag phase has many different degenerate structures with the I0'

'~

~

i0 ~

i\.

-,,1''%-

.i

I0 i

v I0 °

0.0

o2

04

0!6

0!8

,0

0 Fig. 4. Thermodynamic factor (inverse of mean-square fluctuations) as a function of coverage for different temperatures [T,/JAA--3C (circles), T/JAA=0.5 (triangles) and T/JAA--0.2 (squares)].

same energy, corresponding to all the possible arrangements of the diagonal rows (columns). Accordingly, the mobility of the adsorbed phase for 0=0.66 enhances with respect to that at 0=0.5 as seen in Fig. 6(a and b).

4.2. Tracer and jump d(fJusion coejflcients The calculations of the different diffusion coefficients and the vacancy factor Vare performed in the canonical ensemble as well. The tracer and jump diffusion coefficients are very sensitive to the microscopic motion mechanism. In Fig. 5(a and b), we can observe the behavior of D*/D*(O) and Dj/Dj(O) versus coverage for the noninteracting case (T/JAA = ~ ) , obtained by using the diffusion modes introduced above. Fig. 5(a) shows D* obtained from the one-dimensional translation mode (mode I), the rotation mode (mode II) and the combined mode (mode III). The reason for the differences is the increasing number of possible sites which can be chosen in a single jump attempt, t/, with the motion mode (~ = 2, 4 or 6 by using mode I, II or Ili, respectively). As the vacancy factor increases with r/for a given coverage, so do the mobility and diffusion coefficients D*, Dj and D. The differences are less marked for Dj since it characterizes the motion of the center of mass of the system such that contributions from different dimers are more likely to cancel out. The qualitative as well as the quantitative behavior of diffusion coefficients for mode III (which has been used for the analysis in Sections4.3 and 5) is essentially driven by the contribution of mode II. Furthermore, the latter turns out to be relevant in the few experimental systems in which surface migration of strongly dimers has been addressed [21,22,44 46]. The temperature dependence of tracer and jump diffusion coefficients is analyzed by using of mode III. Its behavior is quite similar to the mean-square fluctuations. In Fig. 6(a and b), we have plotted D*/D*(O) and Dj/Dj(O) versus 0 for different temperatures. As T decreases, the ordered structures appear due to the repulsive interactions and the motion of the adsorbed dimer occur with more difficulty. In fact, at 0=0.5, both diffusion coefficients D* and Dj are strongly suppressed in the

273

A.J. Ramirez-Pastor et al. Surlhce Science 391 (1997) 267 277 i

1.0 0.8

,

i

.

I~-'l~'~-o

u

•

i

,

i

10°

,

(a) ~-~

10 -t

0.6 10_2

0.4 0.2

;

10-3

~=

(a

0.0 1.0 .--.

I

~

I

I

,

I

,

,

I

I0 o ~ _ ~ &

,

I

,

I

t

•

(b)

0.8

~" 0.6

lO-t

a-

0.4

10-' 0.2

(b)

0.0 ,

I

,

I

2.5 ~"

r~

t

(c)

2.0

I

,

I

10-3

,

'

I

'

I

'

I

'

I

,

~o~°~

1.5

10°

•

1.0

0'50.0

0'.2

014

0'.6

018

1.0

0

0.0

0:2

014

016

018

1.0

0

Fig. 5. (a) Tracer diffusion coefficient as a function of coverage for the noninteracting case calculated by using of the different elemental motion modes (down triangles, Mode 1; diamonds, Mode II: circles, Mode IIl ): (b) same as (a) for the jump diffusion coefficient; and (c) same as (a) for the collective diffusion coefficient.

Fig. 6. (a) Tracer diffusion coefficient versus coverage for repulsive nearest-neighbor interactions and for different temperatures [T,'JAa-~ (circles), T/JAA=0.5 (triangles) and T:JaA=0.2 (squares)]; (b) the same for the jump diffusion coefficient: and (c) the same for the collective diffusion coefficient.

presence o f a c2 x 2 structure; this effect also a p p e a r s in m o n o a t o m i c diffusion. The second mini m u m at 0 = 0 . 6 6 can be r a t i o n a l i z e d in terms o f the zig-zag ( s t r i p - o r d e r e d ) phase discussed in Section 4.1. This structure is less stable t h a n the c2 x 2 - o r d e r e d phase due to the fact the fluctuations between different zig-zag strips with the same internal energy per d i m e r are higher than in the c2 x 2 phase. In o r d e r to emphasize this fact, in Fig. 7 we have shown the v a c a n c y factor V as a function o f coverage and for different temperatures. It is interesting to note that the v a c a n c y

factor is very sensitive to the c2 x 2 order, but not to the zig-zag row o r d e r present at 0 = 0 . 6 6 [as shown in Fig. 3 ( b ) , two o u t o f three sites are occupied in this phase]. 4.3. Collective diffitsion coefficient In Fig. 5(c), we have shown the collective diffusion coefficient for the n o n i n t e r a c t i v e case T/JAA = OO as a function o f 0 a n d by using the different m o t i o n modes. The effect o f the elementary m o d e I on D(O)/D(O) is quite significant with

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A.J. Ramirez-Pastor el al. /' smjace Science 391 (1997) 267 277

,0~._~_'~&v_._.-._.=

V

'

0.4

0.2

%0

0L~

I

0~

I

0

0~

01~

10

Fig. 7. The vacancy factor l/ as a function of coverage and for different temperatures [T/JAA= z (circles). Z.'J~,~=0 5 (triangles) and T/J~,,=0.2 (squares)].

respect to mode II. However, in the combined mode III, the main contribution comes from elementary rotations (mode Il) as stated before [see Fig. 5(a and b)]. The collective diffusion coefficient obtained by the use of modes II and III (for noninteracting dimers) increases monotonically with 0 [Fig. 5(c)]. Since [ ( ( ( ~ N ) 2 ) / ( N ) ] -1 is identical for the three cases, the differences are due to the jump diffusion coefficient Dj(0). In Fig. 6(c), we can see the collective diffusion coefficient calculated by the use of motion mode III for repulsive interaction between nearest-neighbor dimers and for three different temperatures, T,/JAA=OC (Langmuir case), T,/JAA~-0.5 and T/JaA = 0.2. For finite temperature T./JAA= 0.5, the collective diffusion coefficient increases with coverage and presents a maximum at 0=0.5. This result is similar to the monoatomic case where diffusion increases due to the repulsive interactions. For lower temperatures, the collective diffusion coefficient increases with 0 and shows a local maximum at 0~0.3. Due to the formation of the c2 × 2-ordered phase, the mobility decreases to a sharp minimum at 0=0.5. At half coverage, a finite discontinuity in D(O) seems to appear. The breaking of the ordered structure increases the number of unstable configurations and, consequently, the mobility of the adsorbed particles. For this reason, the diffusion coefficient jumps from the deep minimum to a local maximum. However, whether this behavior displays a discon-

tinuity or a rapid variation of D(O) still remains unclear. The thermodynamic factor is continuous function of 0, and Dj [Fig. 6(b)] shows a very high variation for 0--+0.5 +. As the coverage increases, the formation of the zig-zag-ordered structure suppresses the mobility of the particles and, accordingly, the diffusion coefficient presents a new local minimum at 0 = 0.66. Finally, at high coverage, 0>0.66, the diffusion coefficient increases due to the fast increase of the mean-square fluctuations as a function of 0, but it decreases again for 0 ~ 1 to reach the limit D(1)/D(O). Even though the asymptotic limit D(1)/D(O) depends on the elementary diffusion mode [as shown in Fig. 5(c)], for a given mode, it is expected to be independent of the temperature, as shown in Fig. 6(c). In addition, it is worth to mentioning that the asymptotic limit of D(O)/D(O) can hardly be ascertained from MC simulations since it results from two factors, one of which (the thermodynamic factor) goes to infinity, whereas the other (Dj) tends to zero as 0 ~ 1 (computationally, it would require following up the displacement of the centers of mass of the dimers in a lattice with only two vacant sites). Nevertheless, neither symmetry around 0 = 0 . 5 for D(O) nor D ( I ) / D ( 0 ) = 1 would be expected, in general, provided that the particle-hole symmetry, valid for monomers, does not hold for dimers. It has been formally stated that D(1)/D(O) for monomers in one dimension with interaction between nearest neighbors equals /V1/W 2 [47], w 1 (1!'2) being the transition probability for an elementary jump of a particle having one (all) nearest-neighbor empty site at the initial and final state. It is straightforward that D(1)/D(O) will ultimately depend on the rules defining the transition probabilities. In general, if only the initial state counts for determining the jump activation energy, then wlCw2 and D(1)/D(O)¢=I. Conversely, if the energy difference between the final and initial state defines the diffusion barriers then w~=w2 and D(1)/D(O)=I. However, for interacting monomers in two dimensions, no analytical solution for this limit is available [47]. The authors are not aware of any approximate solution for the chemical diffusion constant of interacting dimers at high coverage.

A.J. Ramirez-Pastor et al. / Sur/ace Science 391 (1997) 267 277

Now we briefy discuss qualitative similarities of our simulation system and experimental studies of CO-Ni(111 ) from Ref. [40]. Surface diffusion of CO on N i ( l l l ) was first addressed in Ref. [37] and more recently in Ref. [40]. A thorough investigation of field-emission current correlation functions lead to a coverage independent activation energy E d = 6 . 8 k c a l and a prefactor Do which varied over a order of magnitude with 0 (as shown in Fig. 8). In as much as the collective diffusion constant D was given in Ref. [40] as - Ed

all features of the coverage dependence of D are those of Do. Thus the comparison between Do 10-2 4,,,,,a o ,,,,,,~

(a)

.d

10-3 10"2

q

I

~

I

• ~

I

~

[

[]

10 -3 0 (I

i

i'i

02

i

I

04

0!6

[]

i

I

08

shown in Fig. 8(b) and D(O)/D(O) (in arbitrary units) in Fig. 6(c) [also shown in Fig. 8(a)] becomes meaningful. The qualitative agreement between the results shown in Fig. 8(a and b) is remarkably good. Despite the position of the local extrema, the simulated and experimental diffusion coefficients are a monotonically increasing function of 0 at low coverage, they reach a broad maximum followed by two sharp minima (separated by a sharp maximum) at medium coverages and tend to decrease for 0~1 (we should bear in mind that our simulations were carried out on a square lattice whilst three-fold sites in Ni( 111 ) lie on a triangular lattice). Since CO Ni( 111 ) strongly resembles the surface migration of dimers, one may feel tempted to suggest dimer-like elementary jump mechanisms for this system. The way CO migrates on Ni( 111 ) is still unclear [40]. However, CO adsorbs via the C end hence monomer-like migration with repulsive interactions could be expected. Ultimately, there may be other reasons for the two minima in Fig. 8 (b) such as the developing of different adsorption sites for CO as coverage increases, interactions to neighbors other than nearest ones, etc. Hence, even though D seems to resemble some features of the simulations carried out here, further experimental evidence would be necessary to draw definitive conclusions.

5. Final r e m a r k s and c o n c l u s i o n s

i

E

275

i

0

0 Fig. 8. Comparison between D(O)/D(O) for strongly interacting dimers (T/'JAA=0.2) and Do~cD for C O - N i ( I l l ) : (a) simulation results in arbitrary units [also shown in Fig. 7(c)]: (b) experimental data from Re['. [40].

In this paper, we studied the collective diffusion coefficient D(O) for homonuclear dimers (AA) adsorbed on homogeneous substrates. We considered, in particular, the case of repulsive interactions between adparticles. In order to study the diffusion process, we introduced different microscopic motion mechanisms for the displacement of dimers on the surfaces. The collective, as well as the tracer and jump diffusion coefficients, present considerable differences depending on the elemental motion mechanism. Such differences are more clearly observed for noninteracting dimers (Langmuir gas). The repulsive case presents an interesting behavior at low temperatures (T/'JAA<0.5); in fact, the repulsive interactions induce two well-defined and ordered structures in

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A.J. Ramirez-Pastor et al. / SmJace Science 391 (1997) 267 277

the adsorbed phase. At 0=0.5, the ordered phase corresponds to a c2 x 2 structure, while at 0 = 0.66, a zig-zag stripped and ordered phase is the most stable structure. The existence of the ordered phases has appreciable effects on the adsorption isotherm, where they correspond to steps in the coverage as functions of the chemical potential. As a consequence, the mean-square fluctuations present two well-defined minima at the corresponding coverages. The tracer and jump diffusion coefficients also present two minima at 0 =0.5 and 0.66. This effect is due to the mobility being strongly suppressed in the presence of a highly correlated ordered phase. The collective diffusion coefficient is the product of the thermodynamic factor and the jump diffusion coefficient, which display opposite behaviors. Consequently, at 0 = 0.5, the effect of both factors produces a rapid variation which is very different of the monoatomic diffusion process. At 0=0.66, the minimum in the collective diffusion coefficient is produced by the ordered zig-zag phase. A qualitative comparison was carried out between the simulated system and CO-Ni( 111 ), which seems to display some characteristics of dimer diffusion with repulsive interactions on regular surfaces.

Acknowledgements This work is partially supported by the CONICET (Argentina) and Fundaci6n Antorchas (Argentina). The European Economic Community, Project ITDC-240, is greatly acknowledged for the provision of valuable equipment. The authors would like to acknowledge stimulating discussions with G. Zgrablich, C. Uebing, F. Bulnes and F. Nieto.

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