Surface segregation in small supported particles

Apphed Surface Science 64 (1993) 9-20 North-Holland

surface science

Surface segregation in small supported particles O n n o L.J. G i j z e m a n Debye Instttute, Surface Sctence Dwtston, Unwerstty of Utrecht, Padualaan 8, 3584 CH Utrecht, The Netherlands

Received 4 November 1991, accepted for publication 8 September 1992

Surface segregation m small alloy particles on a support is investigated by means of Monte Carlo simulations as a function of the particle size. The results are compared with those in semi-mfimte systems in the same approximation Large differences in segregation behaviour are found, due to the limited supply of atoms for segregation and due to the effect of preferential adsorption of one component at the particle/support interface. The occurrence of certain ensembles of atoms on the surface which can be the sites for catalytic activityof the particles has also been studied and shows an unexpected particle size dependence. Again the bond strength between either component and the support may modify the observed trends

1. Introduction The surface composition of alloys has been the subject of a large n u m b e r of theoretical studies over the past decades [1-20]. These investigations have focussed on both the surface composition of the outermost layer(s) [1-7] and the thermodynamic aspects of phase transitions and phase separation [8-20] in the surface. The simplest theoretical approach to the problem of surface segregation is that of the " b r o k e n bond" model, in which only interactions between nearest neighbours (and sometimes next-nearest neighbours) are taken into account. These models can be developed along two lines. One is to find an (approximate) analytical expression for the free energy of the system and to determine which composition of the outermost layers minimizes this free energy [1-3]. A second approach uses Monte Carlo techniques, in which the system is allowed to equilibrate at a given temperature and the various quantities like surface composition and surface order parameters can be obtained by taking suitable averages [21-24]. Both approaches can in principle be applied to small alloy particles [26-31], provided that one assumes an a priori shape of the particle. The cubo-octahedron is a popular choice in this re-

spect [26,27,31]. In practice, however, small particles are always used while anchored to a (supposedly chemically inert) support. Thus for such a particle one should not only consider the process of segregation to the surface, but also the process of segregation to the p a r t i c l e / s u p p o r t interface. Apart from this, the constraint of mass balance must be taken into account. For semi-infinite systems the bulk provides an unlimited supply of atoms, whereas for small particles the number of atoms and thus the supply is finite and sometimes very small. A typical hemispherical particle of diameter 10 to 50 .A contains only some 35 to 3500 atoms. A somewhat different problem also arises in the context of small particles. This is the simple question what should be considered as the surface of a particle. Whereas the surface area of a catalyst can be determined by e.g. BET adsorption isotherms or selective chemisorption, these numbers do not give direct information on the number of surface atoms. For low-index singlecrystal planes the number of surface atoms is usually taken to be the number of atoms in the topmost layer, although in many cases the second a n d / o r third layer are visible in hard-sphere models. This procedure is also ambiguous for stepped surfaces, where strictly speaking the

0169-4332/93/$06 00 © 1993 - Elsevier Science Pubhshers B.V. All rights reserved

10

O.L.J Gqzeman / Surface segregatton m small supported partwles

number of atoms in the outermost layer would be ridiculously low, due to the large unit cell of the surface plane. A similar situation prevails in small particles, if one considers only those atoms furthest from the centre to be surface atoms. In the present paper we will consider the surface composition of small supported particles as a function of their size. This aspect of surface segregation is of course not present in semi-infinite systems or films of a reasonable (10 or more layers) thickness. It is not immediately obvious whether for small particles of a fixed composition segregation is unaffected by their size as is the case for semi-infinite systems. In fact, the data reported by Groomes and Wynblatt [31] on the surface composition of rather large (150-500 .~,) N i - P d particles show the extent of surface segregation to be strongly size-dependent. As a new element in the study of segregation in small particles we will consider the effect of segregation to the m e t a l / s u p p o r t interface on the surface composition. The calculations will be done in the most simple way conceivable, namely by using Monte Carlo simulations for the equilibrium composition and distribution of atoms in the particle, using only nearest neighbour-interactions. This procedure does give information on clustering and ordering, a question that cannot be answered by mean-field techniques and has not been addressed before. The chemical properties of any catalyst are, however, largely dependent not only on the overall surface composition of the catalyst, but also on the distribution of the various components in the surface. We will therefore study the occurrence of certain ensembles of atoms in the surface, such as the probability that two neighbouring surface atoms have the same or a different chemical nature. Again, this probability may be expected to depend upon the particle size. We will consider two examples, modelled to represent the C u - N i system (which shows phase separation below a critical temperature) and A g Pd (which forms ordered structures). The particle shape that will be considered is that of a spherical cap (see fig. la). A particular case of this geometry is that of a hemispherical particle with variable radius R. This will keep the surface-to-interface ratio constant. Thus, any ef-

a

b

c

R Fig. 1 The three shapes of parttcles considered in this work. Each is described as a spherical cap with either a constant surface-to-interface ratio (a), a constant interface area (b) or a constant surface area (c).

fects of an increase in particle size obtained by this procedure will not be caused by an enhanced or diminished segregation to the interface, due to its change in size, but rather by the chemical processes which determine the equilibrium distribution of atoms within the particle. Alternatively, we will consider particles in the form of a spherical cap with a fixed interface radius. Changing the "height" of such a particle will simultaneously increase the number of atoms and the surface area of the particle (fig. lb). A third possible geometry is a spherical cap with a constant surface area, but variable interface area (fig. lc). The calculational procedure is outlined in the next section and the results will be discussed in the final section of this paper. It is not our aim here to compare our results in detail with any experiment. In fact, apart from the experiments reported by Groomes and Wynblatt [31] we are not aware of any systematic study of alloy particle size effects on catalytic reactions. Their experiments were done, however, with particles with much larger dimensions than often used in catalytic reactions and cannot be handled effectively by Monte Carlo techniques due to the large number of constituting atoms. Furthermore, despite the fact that a Mont Carlo calculation does give "exact" results, these results are only quantitatively applicable if the underlying assumptions about the magnitude of the interatomic potentials are correct. Rather we want to show m this paper which qualitative effects can be anticipated from even the simplest treatment of surface segregation in small particles, as compared to semi-infinite systems, using a method that is known to give at least the right trend in most cases.

O.L.J. G,jzeman / Surface segregatton in small supported parncles

2. Calculational procedures As mentioned in the introduction the first choice to be made in the computations is the shape of the alloy particle. We have taken the shape to be that of a spherical cap of radius R consisting of atoms forming a face-centred cubic lattice. The bottom plane is taken to be a (111) plane. In constructing the particle an infinite half-space of an fcc lattice is considered with a (111) outer plane. A central site is selected and all sites having their centre within a given radius R of this central site are considered to be part of the particle and may be occupied by either component A or B (e.g. copper or nickel). In the calculation the pairwise interactions between A, B and the support S enter. They are denoted HAg, H s a , HAB, HAS and Has. This procedure is outlined in fig. 2, which shows a two-dimensional analogue for the case of a hemispherical particle. All atoms with their centre within the semi-circle are considered to be part of the alloy particle and the various interaction energies are indicated by lines between atoms. Each A atom will have z A neighbours, z A being 12 for a bulk atom and less for a surface atom. We define a surface atom as an atom that has less than 12 neighbours (either A, B or support (S) atoms). This immediately implies that not

11

only the atoms on the outer hemispherical surface are counted as surface atoms, but also those atoms somewhat removed from this surface. The justification for this is the fact that adsorption could take place on an empty fcc site which will create a nearest-neighbour bond with the atom considered. In principle, this atom can participate in bonding with adsorbates and thus should be counted as a surface atom. For any A or B atom we have the relations: z A = nAA + nAB + hAS,

(1)

Z B =nBB + nBA +nas,

(2)

where z A and z a are the number of nearest neighbours for an atom A or B and nAj and nBl the number of neighbours of type j for atom A and B, respectively. A Monte Carlo move consists of interchanging two randomly chosen A and B atoms. The energy change associated with this move is in the nearest-neighbour approximation: A E = ( n s a --nAB + 6)212 + ( z . - ZA) ( H A A / 2 -- H B B / 2 -- 0 ) + (riBS -- nAS) ( O + HAS -- Has (3)

--HAA/2 + H B B / 2 ) ,

where 6 = 1 if A and B are nearest neighbours and zero otherwise. Here we have introduced the regular solution parameter O defined by: (4)

0 = HAB - (HAA + H B a ) / 2 .

Thus the only independent parameters are /2, H A g - Haa and H A S - HBS. It should be noted that even if one takes HAS = Has, i.e. both types of atoms bind equally strongly to the support, the support effect is still present due to the fact that surface atoms need not have 9 nearest neighbours. The interchange of a bulk A atom with an interface B atom yields in this case: /rE 1 = (naB --nAn + 6 ) 2 0

@-@ H~

HAB

HBB

@--HAs

Fig. 2. Schematic representation of the formatmn of a hemispherical particle from a close-packed lattice. A t o m s w~th their centre within the semi-orcle are counted as belonging to the particle The various interactions are indicated by lines

+ 3( H A A / 2 -- H a B / 2 -- 0 ) ;

(5)

and the interchange of a bulk A atom with a surface B atom: AE2 = (nab - nAB + 6 ) 2 0 +(12--ZB)(HaA/2--HBa/2--O

).

(6)

12

O.L.J. Gtjzeman / Surfacesegregatton m small supportedparttcles

Only if the surface were a perfect (111) plane z B equals 9 and then the two expressions will be identical. Physically the difference arises from the fact that the interface is a plane where all A and B atoms have always 9 A or B nearest neighbours, whereas at the surface the number of nearest neighbours may have any value between 1 and 11. The calculations were performed according to the standard Monte Carlo rules [32]. An interchange of a randomly selected A - B pair is attempted. If the energy change A E associated with this interchange is negative, the move is accepted, if the energy change is positive the move is accepted with probability e x p ( - A E / k T ) . After equilibration of the system various averages can be computed. They are P[A] (or X[A]), the probability that a surface atom is of type A and P[AA] and P[AB], the probability that a pair of neighbouring surface atoms consists of A - A and A - B , respectively. These numbers represent the fraction of surface sites and surface doublet sites where singly and doubly coordinated adsorption may take place. Alternatively, they are proportional to the turn-over numbers for reactions supposed to take place on these sites. Higher-coordinated sites are evaluated as follows. An empty fcc site near the surface is chosen first, where supposedly adsorption may take place. This site may have up to 11 neighbouring surface atoms. If

at least three of these are A atoms the number of A - A - A adsorption sites is incremented by one. A similar count is done for A - A - B , A - B - B and B - B - B sites. The probabilities P[AAA], etc., are then formed by dividing the number of A - A - A sites by the number of surface atoms. Note that in this case these probabilities do not add up to one since a given empty fcc site may offer several environments at the same time. Nevertheless, this is the number of sites that may be involved in threefold-coordinated bonds with adsorbates which is the chemically relevant number. Alternatively, these numbers are proportional to the turn-over numbers calculated on a surface area basis for reactions involving a threefold-coordinated site. Apart from these data we can also extract from the simulations for all A and B atoms the average number of A, B or support atoms around them. This number is the quantity that is measured in E X A F S experiments on small particles [33].

3. Results and discussion The shape of a hemispherical particle constructed according to our rules is shown in fig. 3 for two different radii, R = 3.16 and R = 7.07 in units of the nearest-neighbour distance. These

1 Fig 3. Shape of a hemispherical particle On the left a particle with radms R = 7 07 in units of the nearest-neighbour distance, on the right a particle with R = 3 14 in units of the nearest-nelghbour distance. These parUcleswould have a radius of about 17 and 8 A, respectively.

O.L.J. Gtjzeman / Surface segregatton m small supportedparticles Table 1 Bond strengths (in k c a l / m o l ) used m the calculation for C u - N i and A g - P d alloys System

HAA

Hnn

Cu-NI

- 13.0

- 17.5

O

Ag-Pd

-11.33

-14.97

HAS

HBS

0 126

- 12.0

- 12.0 -6.0 -3.0

-0.400

-12.0

- 12.0 -60 -30

13

approximation used. Whereas for the Cu-Ni system O is positive (which leads to phase separation) the Ag-Pd system has a negative value of O (which leads to ordered structures). The bond strengths between the Cu and Ag atoms and the substrate were fixed at - 1 2 kcal/mol and the bond strength of the non-segregating component (Ni or Pd) was chosen to be - 1 2 , - 6 and - 3 kcal/mol. This reflects an increasing tendency of the segregating component to accumulate at the interface and may thus lead to a decrease in surface segregation. All calculations were done for a temperature of 500 K. Fig. 4 shows the surface concentration of copper atoms in a Cu-Ni particle as a function of the particle radius for three different overall compositions of 0.1, 0.5 and 0.8, respectively. Lines have been drawn between two adjacent points. The apparent scatter in the data for a given composition is real and caused by two factors. Especially for small particles the given composition may not be possible, e.g. for a particle with an odd number of atoms a composition of 0.5 would lead to a non-integral number of copper atoms (in which case the number is rounded off). Also the depen-

T h e first component is denoted by A and the second by B. The support is denoted as S.

would represent particles of about 16 and 35 ,~ diameter and contain 119 and 1155 atoms, respectively. Their shape is fairly regular with large low-index planes exposed as well as steps. The similarity with field-ion microscopy pictures of etched tips is striking, as is to be expected since these are also believed to be hemispherical entities. The calculations for the two alloy systems investigated were done with the parameters listed in table 1. In all cases the first compound (Cu or Ag) is expected to segregate to the surface in the

0.8 0.8

0.6

0.,5

0.4

0.2-

0.1 0.0

RADIII8

o

i

~

a

4

s

e

7

S

a

~'o

Fig. 4. ( [] ) Mole fraction of copper in the surface atoms of a hemispherical particle as a function of the particle radius, expressed in terms of the nearest-neighbour distance at three overall concentrations. The calculation was done wath a bond strength of - 12 k c a l / m o l for the bond between nickel and the support. T h e wavy lines for mole fractions 0 1 and 0.5 represent the results if this bond strength is changed to - 6 or - 3 kcal/mol.

14

O.L.J Gtjzeman / Surface segregation m small supported parttcles

seen to have a small maximum for X[Cu] = 0.1 as a function of the particle radius, but otherwise appears to be almost independent of the particle radius. A similar effect of the bond strength of nickel to the support is seen for X[Cu] = 0.5, where the copper concentration in the surface is decreased for small radii, compared to the case of equal bond strengths. Physically this is again understandable from the increased tendency of copper to accumulate at the interface and the limited supply of copper atoms. This leaves less copper to cover the surface. Decreasing the bond strength of nickel to - 3 k c a l / m o l does not alter this general appearance of the curves shown. The results for the A g - P d system show the same effects as can be seen in fig. 5. Segregation for the concentrations X[Ag] = 0.1 and 0.5 is less severe than in an infinite system, where the values for the surface concentration are 0.56 and 0.97, respectively. The amount of segregation increases with particle size but is counteracted by a decreased bond strength of palladium to the interface for X[Ag] = 0.1 and X[Ag] = 0.5 if the radius is not too large. Of course, these results may be a consequence of the chosen geometry of the particle, which

dence of the total number of atoms in the particle is not a smooth, continuous, function of the particle radius. As can be seen, the extent of segregation increases with particle radius. This implies that any chemical reaction involving only one copper site must have a larger rate (on a per site basis) if larger particles are employed. W h e n the surface consists completely of copper, as is found for mole fractions of 0.5 and 0.8, this size effect disappears of course. It should be noted that a plane alloy surface (in this same approximation) is composed solely of copper for all three mole fraction considered. It may thus appear that segregation in small particles is less severe than in bulk crystals. The physics behind this observation is simply that for a small, originally uniform particle, segregation leads to a decrease in the "bulk" composition and, since the number of surface atoms is so large, there are just not enough copper atoms to cover the surface completely while maintaining thermodynamic equilibrium. A different effect is also shown in fig. 4 by the drawn wavy lines. H e r e we have assumed that binding of nickel to the interface is less strong ( - 6 as compared to - 1 2 kcal/mol). Now the mole fraction of copper at the surface is actually

1.0- X[.,a~] 0.8

0.6

~

.\ / i ~'

0.5 ~ / "~

S/-,'

/

//"--.~

0.4 0.2-

~ "~'~"~'~'~

0.1 0.C --

o

" ~' - - - ~ - ~ - ~ P,.ADIUS

~

-2

S

-4

s

e-

7

s-- 9

~o

Fig 5. ([]) Mole fraction of sliver m the surface atoms of a hemispherical particle as a function of the parttcle radius, expressed in terms of the nearest-nelghbour d~stance at three overall concentrations The calculation was done with a bond strength of - 12 kcal/mol for the bond between palladmm and the support. The wavy lines for mole fractions 0.1 and 0.5 represent the results If this bond strength is changed to - 6 or - 3 kcal/mol.

O.L J. Gozeman / Surface segregatton m small supported parttcles

15

1.0 X [ ~ U ]

0.5 0.8

0.8

0.4

0.1

__.a__---a---

0.2ATOMS

°'°soo

lOOO

1~o

~o

~

Fig. 6. ([]) The mole fraction of copper in the surface of a particle with constant radms of 9.49 n n. units as a function of the number of atoms in the particle. The highest number of atoms shown corresponds to a hemisphere, whose height decreases in going to a lower number of atoms. The calculation was done with a bond strength of - 12 kcal/mol for the bond between nickel and the support. The wavy lines represent the results if this bond strength is changed to - 6 or - 3 kcal/mol.

keeps a fixed surface-to-interface ratio. Theref o r e , w e i n v e s t i g a t e d p a r t i c l e s in t h e s h a p e o f a

s u r f a c e a r e a (figs. l a a n d l b ) . T h e s a m e e f f e c t s a r e s e e n h e r e , a s s h o w n in figs. 6 a n d 7 f o r

spherical cap with fixed interface area and a fixed

Cu-Ni. (The Ag-Pd

1.0-

system behaves similarly and

X[OI] 7.

0.8

0.6

0.5

0,4 C~-

0

0

--0

~

0.2

'

-

~

0.1

INTERFACE RADIUS 0.0

~,

9

1'0

Fig. 7. ( [] ) Mole fraction of copper m the surface of a particle with constant surface area as a function of the interface radius. The lowest interface radius corresponds to a hemisphere, whose height decreases upon increasing the interface radius. The calculation was done with a bond strength of - 12 kcal/mol for the bond between nickel and the support. The wavy lines represent the results if this bond strength is changed to - 6 or - 3 kcal/mol.

O.L.J Gtjzeman / Surface segregation m small supportedparttcles

16

1.o PIG~a-NI

0.8

0.6

O.5 0.4

0.2

0.0 Fig. 8. (13) The probability of finding a mixed Cu-Ni site in the surface of a hemispherical particle as a function of the parUcle radius, expressed in terms of the nearest-neighbour distance at two overall concentrations. The strength for the Ni-support bond was taken as - 12 kcal/mol. The wavy line represents the results if this bond strength is changed to - 6 or - 3 kcal/mol.

is not shown here.) For a fixed interface area and e q u a l b o n d s t r e n g t h s t o t h e i n t e r f a c e (fig. 6) segregation increases with the number of atoms in t h e p a r t i c l e . W e h a v e c h o s e n t o p l o t t h e n u m -

1.0

ber of atoms in the particle on the x-axis in this case, as the interface area does not change. This trend is reversed for the low-concentration alloy when copper is assumed to bind more strongly to

P[Cu-Nil

{}.8

0.6-

0.4 -

0.1

02.

0.( Fig. 9 (13) Probability of finding a mixed Cu-Nl site m the surface of a particle with constant radius of 9.49 n.n. umts as a function of the number of atoms in the particle. The strength for the Ni-support bond was taken as - 1 2 kcal/mol. The wavy line represents the results if this bond strength is changed to - 6 or - 3 kcal/mol.

O.L.J. Gijzeman / Surface segregation m small supported parttcles

1.0-

17

HC'.-Ni]

0.8-

0.6-

0.4 ~

-- ~

----_

0.1

o~

RPACE RADIUS 0.0

~

~

1()

Fig. 10. ([]) Probability of finding a mixed Cu-Ni site in the surface of a particle with constant surface area as a function of the number of atoms in the particle. The strength for the Ni-support bond was taken as - 12 kcal/mol. The wavy line represents the results if this bond strength is changed to - 6 or - 3 kcai/mol.

atoms in the particle decreases in this case in going from left to right). Thus we may reach a somewhat general conclusion for surface segrega-

t h e s u p p o r t . K e e p i n g t h e s u r f a c e a r e a at a cons t a n t v a l u e (fig. 7) b u t c h a n g i n g o n l y t h e i n t e r f a c e radius

shows the

same

1.0

trend

(the

number

of

P[Cu-Ni-Nil

o.a

0.5

0.6

0.4 0.1

0.0

0

i

2

~

.

4

.

.

5

.

.

e

7

8

a

~

10

Fig. 1I. ( [ ] ) Probability of finding an fcc empty site with at least one copper and two nickel neighbours in a hemispherical panicle surface as a function of the particle radius. The strength for the Ni-support bond was taken as - 12 kcal/mol. The wavy line represents the results if this bond strength is changed to - 6 or - 3 kcal/mol.

0 L.J. Gtjzeman / Surface segregatwn m small supported partwles

18

B- N[A-BI

5-

4-

3. o

2. m

o

o/~/oT.,r~ooooOoo_~

o

[]

0.8 " / / ~ /

RADIUS

Fig 12. ( [ ] ) Average number of mckel atoms around a copper atom and ( * ) palladium atoms around a silver atom as a function of the particle size. The wavy lines represent the results for a purely random distribution of atoms at the indicated concentrations of component A.

tion in small particles, namely that segregation increases with the number of constituent atoms in the particle if both components bind equally strongly to the support. This trend can be reversed, however, if the segregating component 10-

has a higher tendency to accumulate at the interface. For several catalytic reactions on small particles the surface composition is not the only important parameter. Rather the occurrence of cer-

N[A-A]

9-

7-

4

0.8

-

-

-

-

3

2-

0.5

--/-

o

~ -'2

•

~

-

-

•

mm

e

R

. •

W

4

-

~

s

RADIUS

6

r

e

9

lo

Fig. 13. (E3) Average number of copper atoms around a copper atom and ( * ) sdver atoms around a silver atom as a funcUon of the particle size. The wavy lines represent the results for a purely random distribution of atoms at the indicated concentrations of component A.

O.L.J. Gijzeman / Surface segregatton m small supported partlcles

tain specific sites, consisting of an ensemble of several atoms is required to produce the desired product. It is thus necessary to consider the abundance of specific clusters of surface atoms. Some results for doublet sites in a hemispherical particle with varying radius are shown in fig. 8, which shows the probability that two neighbouring surface atoms form a C u - N i mixed site. In the semi-infinite system this number would be zero, since the surface is composed exclusively of copper. As can be seen this probability is certainly non-zero for the concentrations shown of X[Cu] --- 0.1 and 0.5. Also an appreciable and somewhat unexpected size dependence can be seen in this figure, one probability increasing and the other decreasing with particle size. This trend may be reversed for the low-concentration system by decreasing the bond strength of nickel with the surface. Again this effect arises from the interplay between the large number of surface atoms, the limited amount of copper present and the presence of an interface with different binding properties for both components. The A g - P d system (not shown here) exhibits the same features. Again, using the two different particle shapes considered previously, the same trends hold as shown in figs. 9 and 10. The situation with higher-coordinated sites is similar for low mole fractions of copper. Fig. 11 shows the probability of finding an empty fcc site with at least one copper and two nickel atoms adjacent to it. Recall that the probability used here is defined as the number of these sites divided by the number of surface atoms and represents the reaction rate per surface atom for a reaction that requires one such site. Note that the probabilities are high, in contrast to the expectation for a flat surface where these numbers would be negligible. The size dependence is again increasing or decreasing with particle radius depending on the choice for the nickel-interface binding energy. The situation for the A d - P d system is qualitatively the same. A different property that may be calculated easily is the average number of like or unlike nearest neighbours to a given atom. This number is obtained from EXAFS experiments as the coordination number. Fig. 12 shows the result for

19

the average number of nickel atoms around a copper atom and the average number of palladium atoms around a silver atom. As expected the C u - N i system shows a smaller coordination due to the fact that copper and nickel effectively repel each other, whereas the interaction between silver and palladium is attractive. The results for a random distribution of atoms in the particle at the same mole fraction are also indicated by the drawn wavy lines. The results are fairly insensitive to the particle radius, especially when taking into account the known experimental uncertainties in these types of experiments. So, even assuming that the particle is indeed hemispherical, its size may not easily be deduced from these considerations alone. The coordination of atoms by like atoms shows a much larger particle size effect as shown in fig. 13, but now the numbers are always close to that of a random distribution for all concentrations investigated and again it seems that no particle size can be deduced from a measurement of just this quantity.

4. Conclusions The results presented above lead to some general conclusions concerning segregation in small alloy particles, anchored to a support. In agreement with previous studies we find that in systems were segregation of one component is expected for semi-infinite systems the segregation in small particles will be less, especially for low mole fractions of the segregating component. We also find that the extent of segregation increases with particle size, if both components bind equally strongly to the support. If this is not the case, an increase in particle size may actually lead to a decrease in the amount of segregation, if the segregating component has a stronger bond with the interface than the non-segregating component. Size effects on the number of available adsorption sites with a higher coordination number are large. Even for equal bond strengths of both components a decrease or an increase in a certain type of sites may occur depending on the overall concentration. Since catalytic reactions often pro-

20

0 L.J. Gljzeman / Surface segregatton m small supported parttcles

ceed on an ensemble of more than one atom it seems difficult to predict a general trend for the effect of particle size on such reactions. The average coordination numbers of atoms by unlike atoms in a hemispherical particle do not depend heavily on the particle size and may even be seemingly close to random for both ordering and non-ordering systems. The coordination of atoms by like atoms shows a large particle size effect but is probably within experimental error indistinguishable from that of a random distribution.

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