404 Surface Science 156 ( 1985) 404-409 North-Holland. Amsterdam

SPATIAL ATOMIC DISTRIBUTION IN SMALL BIMETALLIC CLUSTERS *

C.A. BALSEIRO

Centro Atbmico Bnriloche. S.C. Bariloche, Argentina

and

J.L. MORAN-Li)PEZ **

Institute ftir Festktirperforschung der Kernf#~.~chungsanlage Jiilich, D - 5170 Jiilich, Fed, Rep. of

Germany

Received 10 July 1984; accepted for publication 20 July 1984

Within the regular solution model the spatial distribution of atoms in cube-octahedral clusters

(55 atoms) is studied. All the sites located at the same distance from the center are considered

equivalent and the atoms distributed at random with a characteristic concentration x,( i = 1.2. 3.4).

For a system that orders at low temperatures, we calculate the equilibrium values at different

temperatures.

There is a large number of publications reporting that the best catalysts are obtained in the form of small particles. In particular, bimetallic clusters are used to improve the selectively for certain chemical reactions [l-3]; examples of those catalysts are RuCu, OsCu, PtRd, PtIr, etc., small particles.

In a small particle a large fraction of its atoms is exposed to chemical reactions. Therefore, knowledge of their spatial distribution is necessary to

understand its catalytic activity. Generally, it is assumed that the two kinds of atoms are distributed at random in the whole particle. However, this assump- tion could be valid only at high temperatures. At low temperatures it is

expected that a kind of ordering should occur. Here, we study within the regular solution model [4] the spatial distribution

of atoms in bimetallic cube-octahedral clusters with 55 atoms. As shown in fig.

* Work partially supported by Consejo National de Ciencia y Tecnologia, through the

Mexico-Argentina exchange program No. 140113 H21-003. ** On leave from Departamento de Fisica. Centro de investigation y Estudios Avanzados de1

IPN, Apdo. Postal 14-740, 07000 Mexico, DF, Mexico.

0039-6028/85/$03.30 @ Elsevier Science Publishers B.V. (North-~oiland Physics Publishing Division)

1, this number of atoms forms a perfect cube-octahedra in which the surface atoms are afi the second (6), third (24) and fourth (12) nearest neighbours of the central atom. The first nearest neighbours (12) are also shown in the figure and in the particle they lie below the surface.

We call the first, second, third and fourth shell all the sites corresponding to the first, second, third and fourth nearest neighbours respectively and we denote the number of nearest neighbours lying in she11 j to an atom in shell i by Zij. Those values are given in table 1.

We consider a particle with NA atoms of type A and 55 - NA atoms of type B. distributed in all the different shells. The concentration in shell i is given by

xj = e*,i&? 0)

where #A,i and Nj are the number of atoms A and the total number of sites in the i th shell, respectively.

Fig. 1. The first (solid circles), second (2). third (3) and fourth (4) nearest neighbours of the central atoms in a 5%atom cube-octahedra.

406 C.A. Balseiro. J. L. Morrin-Lhper / Spatial atomic distrihutron

By assuming now that the contributions to the energy are the short-range pairwise interactions UAA, U,, and U,,, the internal energy of the system can

be written

U= 12W[ X”X, + 2x; + 2X,X, + 4x,x, + 2x,x, + 2x: +x,x4 + 4x3+

+ +(A - l)( x0 + 12x, + 4x, + 10x, + 5x,)],

where

(2)

w = u,, + u,, - 2u,, . (3)

A = (Ca, - &)/‘I+‘. (4)

A particle with W > 0 will tend to develop ordered structures [4] at low temperatures and positive values of A mean a tendency [5] to segregate atoms A to the surface.

The configurational entropy is given by

N, !

szkF1n(q - N~,,)!N~,,!

Now, in order to get the spatial configuration at a given temperature we

minimize the free energy

F= U- TS, (6)

with respect to all concentrations with the constraint that the average con- centration

is kept fixed. The results for a particle with parameters W = 4 and A = 0.5 are shown in

figs. 2 and 3. In fig. 2 we show the equilibrium values of the number of A-atoms, hi,,, as a function of the total number of A-atoms in the cluster, NA. for different temperatures. The temperature is measured in units of k.

Table 1

Number of nearest neighbours lying in shell j to an atom in shell I. Z,,,: the last column (T) is the total number of nearest neighbours

i J=o j=l J=2 J=3 j=4 7

0 _ 12 0 0 0 12

1 1 4 2 4 1 12

2 0 4 0 4 0 8

3 0 2 1 2 2 I

4 0 1 0 4 0 5

C. A. Balseiro, J. L. Morirn- Lirpez / Spatial atomic distribution 407

At low temperatures (2’ = l), as one starts to substitute B-atoms by A-atoms in the cluster, they go to the first and third shell. But when one gets to NA = 11, the equilibrium configuration is obtained by moving the A-atoms to the second and fourth shell. Then, just after the two shells are full, additional substitutions drive the A-atoms to the first and third shell.

_.....- 3StiELL

- 1 SHELL -I- ZSHELL

--- 3SHELL

I I , I I I I 1 I Y - - 1SHELL 4'

20- -I-.- ZSHELL .-* ,

---- 3SHELL /+ . . . . . . &SHELL /+

15- TZL +

a .J’

Fig. 2. The number of atoms NA., in the different shells as a function of the total number of A-atoms NA and for three different temperatures. The parameters we used were W= 4 and

A = 0.5 in units of k.

408 C.A. Balseiro, J.L. Morirn-Lbpez / Spaiial atomic distribution

At higher temperatures (T = 2) the kind of transition observed at NA = 11 takes place at NA = 15 but it is not so sharp. Finally at T = 4 the occupation in

all shells is a smooth function of NA and practically no order is observed in the

whole range of NA. To illustrate the temperature dependence of the spatial arrangement we

show in fig. 3 a particle with NA = 15 and at the different temperatures considered. One clearly sees that at low temperatures (T = 1) the atoms are arranged in an ordered way, NA,z = 6, NA 4 = 9. As one increases the tempera- ture a kind of order-disorder transformation takes place and at T = 4 practi- cally all A-atoms are randomly distributed.

A similar model for surface segregation in small particles with a tendency to phase separation at low temperatures (W-c 0) was studied before [6]. However, in that model. all the atoms lying at the surface were assumed equivalent. As

N~=l5 T= 1

T= 2

T= 4

Fig. 3. Spatial distribution of A-atoms (black circles) in a cube-octahedra with NA = 15 and for three different temperatures.

C.A. Botseiro, J.L. Morhtipez / Spatial atomic distribution 409

we showed here, in a small cluster, as in the one we considered, it is important to distinguish the surface atoms that belong to the second, third and fourth shell since the coordination number is different (column T of table 1).

In conclusion, we have shown that the spatial distribution of atoms in bimetallic clusters suffer appreciable changes as a function of temperature and that the assumption generally made about a random distribution of atoms is valid only at high temperatures.

It is a pleasure to thank Professor K.H. Bennemann for helpful discussions.

References

[l] J.H. Sinfelt, J. Catalysis 29 (19873) 308.

[Z] J.H. Sinfelt, Platinum Metals Rev. 20 (1976) 114.

[3] J.H. Sinfelt, Rev. Mod. Phys. 51 (1979) 569.

[4] R.A. Swalin, Thermodynamics of Solids (Willey, New York, 1972).

[5] J.L. Morb-Lbpez and L.M. Falicov, Phys. Rev. B18 (1978) 2542.

(61 D. TomBnek, S. Mukherjee and K.H. Bennemann, Phys. Rev. B28 (1983) 665.