12718
J. Phys. Chem. 1995,99, 12718-12722
Dilution and Clustering in Model Clusters of Small Bimetallic RuGe and RuSn Aggregates: A Density Functional Study Annick Goursot,* Luca Pedocchi? and Bernard Coq Laboratoire de Mattriaux Catalytiques et Catalyse en Chimie Organique URA 418 CNRS, ENSCM, 8 rue de I'Ecole Normale, 34053 Montpellier Ctdexl, France Received: February 28, 1995; In Final Form: June 13, 1995@
Density Functional Calculations (DFT) are reported for 13 atom model clusters of RuSn and RuGe bimetallic particles with cubooctahedral structure. The purpose of this study is to analyze the major factors which govern the dilution effect for Sn or Ge, which is one of the two aspects of their topological segregation on the Ru surface, the other one being the site preference. Site preference controls the location of the atoms of the second element at low- or high-coordination sites, whereas the dilution effect is governed by their capacity to make preferentially homonuclear or heteronuclear bonds. This study has shown that island formation is controlled by a preparation step which defines the most stable facet. In the case of Ge3 and Sn3 clusters, a (1 11) facet is less favorable than a (100) facet and the energetics preference for the (100) geometry is far more pronounced for Ge than for Sn. Combined with preparation, stabilizing Ru-M bonds depends on the electronic interactions between both metal elements and on the morphologies of the island and of the particle. For the cubooctahedral model we have chosen, the Ru-M interactions favor the (1 11) island for Ge and the (100) island for Sn. Finally, island formation with respect to a diluted topology must also be discussed in terms of the binding energy between M atoms. The stabilization induced by M-M bonding is shown to be the most favorable for Ge3 (100).
Introduction Among metal catalysts, metal alloys have become a very important class, especially for reforming reactions. The investigation of factors controlling their activity and morphology has led to the development of a large variety of mixed-metal systems, not only for catalysis but also for metallurgy, electrochemistry, and microelectronics. Bulk metals can be characterized by the presence of a large number of valence orbitals that can donate or accept electrons. However, results of photoelectron spectroscopy measurements for monometallic solids indicate that the electronic properties of bulk and surface metal atoms are different.' It is known that a reduction in the atomic coordination number produces a narrowing of the valence band at the surface. Moreover, heterogeneous catalysts are most often supported metallic aggregates, and their selectivity in catalytic reactions generally depends on the size of the metal particle, Le., on the proportion of atoms of low c~ordination.~,~ For bimetallic catalysts, both electronic4 and geometric effect@ can be invoked in order to explain the role of the additional element on their catalytic behavior. Indeed, alloying induces modifications in the surface structure and thus in its adsorption properties. As a consequence, the topology of the surface is of major importance. Surface segregation of one component is now well e~tablished,~-'~ and theoretical models have correlated this phenomenon with the lower heat of sublimation or the larger atomic volume of this comp~nent.~-l~ Experimental evidence for a topological segregation of one element (Cu, Pb, Sn, Ge) has been obtained for well-dispersed bimetallic Ru and Rh particles on the basis of alkane hydrogenolysis as probe reactions, which are shown to have different properties with
' Permanent address: Laboratorio di Chimica Fisica delle Interfasi, via Cavour 82, 50129 Firenze, Italy). * Author to whom correspondence should be addressed. @Abstractpublished in Advance ACS Abstracts, August 1, 1995. 0022-3654/95/2099-12718$09.00/0
respect to monometallic particle^.^,'^-'^ Quantum chemical studies of Ru model clusters incorporating one Ge or Sn atom have indicated the existence of a site preference for the second element.I4 Both the nature of the heteronuclear bond (electronic effect) and the atomic volume of the second element (geometric effect) are at the origin of this topological preference: (i) a Ge or Sn atom with four valence electrons, in the s and p shells, is more easily accomodated in a cluster of Ru atoms if its coordination number is low (54); (ii) the large Sn/Ru size mismatch forces Sn to segregate to a comer site. Site preference is one of the two aspects of topological segregation; the other one is often called the dilution effect. This effect corresponds to the tendency of the atoms of the second element to either form islands or distribute themselves among the surface atoms. In other words, the dilution effect is controlled by the preference of the atoms of the second element to make homonuclear or heteronuclear bonds. In order to complete the analysis of the site preference in RuGe and RuSn clusters, we have undertaken the study of the dilution effect, using the same type of quantum chemical approach. In the present work, we report density functional theory (DFT)calculations on RuGe and RuSn model clusters chosen in order to analyze this complementary aspect of the topological segregation. Thirteen atom clusters with cubooctahedral structure have been chosen because all surface atoms have the same low coordination number of five, which allows us to rule out any interference between dilution and site preference effects. This study aims to clarify (i) the bonding properties of Ge(Sn) within homonuclear or heteronuclear bonds and (ii) their relations to the geometric structure of the clusters. As was the case for the site segregation study, the interaction with the support has not been considered.
Methods Computational Details. These DFT calculations have been performed using the deMon ~ r o g r a m ' ~in - ' ~which the molecular 0 1995 American Chemical Society
Dilution and Clustering in RuGe and RuSn
J. Phys. Chem., Vol. 99, No. 34, 1995 12719 the three Ge(Sn) atoms are on a (111) facet, C3" symmetry; (iii) the three Ge(Sn) atoms are on a (100) facet, C, symmetry. EXAFS measurements of small suppported particles with approximately a dozen Ru atoms have revealed an average RuRu bond length of 2.60 A?4*25We have thus assumed that the related Ru13 cubooctahedron, where all Ru-Ru bonds are equal, can be properly described with bond lengths of 2.60 A. This assumption allows a considerable gain in computer time, since only the positions of the three Ge(Sn) atoms are to be optimized while the Ru atoms are kept fixed. All clusters have been calculated in singlet states. Ge3 and Sn3 (M3) Clusters. In order to understand the M-M bonding properties in the R U I O Mmodels, ~ Ge3 and Sn3 clusters have also been studied. Two different kinds of M3 clusters have been considered: (i) free molecules with optimized geometries for three different conformers (linear, D3h and C2" triangles); (ii) models at the geometries of the M3 fragments in the optimized structures of RuIoM~.
Results for Three RuloM3 Models (c)
(0
Figure 1. Geometric structures of RuloM3 and Rule model clusters with M = Ge, Sn: (a) R U I O Mwith ~ three diluted M atoms; (b) R U I O M ~ ~ an M3 (100) facet; (d) with an M3 (111) facet; (c) R U I O Mwith Rule substrate corresponding to structure a; (e) Rule substrate corresponding to structure b; (f) Ruio substrate corresponding to structure c.
orbitals are developed as a combination of Gaussian type orbitals. All calculations have been performed using a local spin density (LSD) potential, with the Vosko-Wilk-Nusair (VWN) parameterization for the correlation term.'* After selfconsistency, the total energy was then calculated at a nonlocal level using the Perdew and Wang functional for exchange19and the Perdew functional for correlation.20 For all atoms, the core electrons were replaced by model core potentials; for the Ru atom, the (4p, 4d, 5s) electrons were included in the valence shell, whereas the (3d, 4s, 4p) electrons for Ge and the (4d, 5s, 5p) electrons for Sn were treated as valence electrons, leading to 14 valence electrons for all atoms. In a short notation, the patterns for the orbital basis sets are (611/511/51*) for Sn and (5 1/41/41) for Ge, whereas the associated auxiliary basis sets were (3,5;3,5) for both elements.21 As described previou~ly,'~ a Ru(+14) MCP has been used associated with (2211/3111/ 311) and (3,4;3,4) orbital and auxiliary basis sets, respectively.22 Bond orders (BO), which will be used to compare bonding properties in the different clusters, have been calculated according to Mayer's d e f i n i t i ~ n .The ~ ~ DIT approach deals with the electronic density of a system, but Kohn-Sham orbitals can always be used, as well as Hartree-Fock orbitals, in order to build a Slater determinant which constitutes the approximate ground-state wave function. Bond orders, calculated from this wave function, are very useful quantities which allow discussion of chemical properties. Their comparison within a cluster or their evolution in different clusters helps us to analyze the RuRu, Ru-M and M-M bond strengths. RuGe and RuSn Clusters. Cubooctahedral model clusters of 13 atoms have been chosen because they include both (100) and (111) facets and display surface atoms with the same coordination number of 5. In order to model the chemical composition of real RuGe(Sn)/A1203 catalysts studied in the same project,24a ratio of 3 Ge(Sn) atoms to 10 Ru atoms has been adopted. Three model clusters with the following characteristics have then been studied (Figure la-c): (i) the Ge(Sn) atoms have only Ru first neighbors, C3" symmetry; (ii)
Diluted M Atoms (M = Ge, Sn). Figure l a illustrates the RuloGe3 and RuloSn3 clusters in which the three M atoms are equivalent, each one being surrounded by five Ru atoms. Optimization of their positions keeps the Ge atoms at 2.60 A from all Ru neighbors. The calculated Ru-Ge bond order (BO) has an average value of 0.60. For the Sn analog, optimization leads to Ru-Sn bonds of 3.05 A with the central Ru atom and 2.85 8, with the surface Ru neighbors. The Ru-Sn bonds have an average BO of 0.55. These Ru-Ge and RuSn bond lengths are in line with the atomic radii, Le., 1.25, 1.30, and 1.45 A for Ge, Ru, and Sn, respectively. The bond order values show that Ge and Sn atoms have comparable bonding strength with Ru atoms when they have only Ru as first neighbors. This was already the case for corner Ge or Sn atoms in Ru8M models with a single M atom.I4 This result can be interpreted in terms of a comparable accomodation of diluted Ge or Sn atoms onto a Ru surface at rather lowcoordination sites. M Atoms on a (111) Facet. Figure l b displays the R U I O M ~ clusters where three Ge(Sn) atoms are located on a (1 11) facet. Each M atom has then two M and three Ru first neighbors. Optimization of the Ge positions (keeping C3" symmetry) led to a cluster where the three equivalent Ge atoms have mi rated farther from each other, yielding Ge-Ge bonds of 2.89 and closer to their surface Ru neighbors (Ru-Ge bond = 2.42 A). The bond distance with the central Ru remains almost unchanged (2.57 A). This relaxation shows that short Ge-Ge bond distances are not favorable for this (1 11) structure. This result seems in contradiction with the small value of the Ge atomic radius from which one would have anticipated a shortening rather than a lengthening of the Ge-Ge bond with respect to 2.60 A. The Ge-Ge calculated BO is only 0.29, whereas the Ru-Ge BO is 0.71. If the five bond orders around each Ge atom are averaged, a value of 0.54 is found, which gives some indication of the bond strength between this Ge atom and the rest of the cluster. This value is lower than for the diluted case (0.60), confirming the existence of less favorable bonding interactions. The situation looks somewhat different for the Sn analog. Indeed, in the optimized cluster, the Sn-Sn bond length is 3.06 8, and the Sn-Ru bond length is 2.64 A with Ru surface atoms and 2.85 8, with the central Ru atom. In contrast to Ge, the increase of the Sn-Sn bond distance with respect to 2.60 8, was expected on the basis of the large Sn atomic radius. As for the Ge analog, there are two short bonds with the surface
1,
12720 J. Phys. Chem., Vol. 99,No. 34, 1995 Ru atoms and a longer one with the central Ru atom. The SnSn BO is 0.40, whereas the average Ru-Sn BO is 0.55, which is similar to the value obtained for a diluted Sn surrounded by five Ru atoms. Averaging the five BO values around Sn atoms yields a value of 0.49 which is smaller, as was the case for Ge, than the value of 0.55 when Sn atoms are diluted. For both Ge and Sn clusters, the M-M bonding interactions are less favorable than the Ru-M interactions but the difference is more pronounced in the case of Ge models. M Atoms on a (100) Facet. Since small metal particles display different kinds of facets, it was interesting to study also clusters with three M atoms substituted in a less dense facet (Figure IC). In this case, the three M atoms are no longer equivalent; one M atom has two M-M and three Ru-M bonds, and the two others have only one M-M bond and four Ru-M bonds. Globally, the cluster now displays two M-M bonds instead of three. After optimization of the Ge positions (keeping C, symmetry), a value of 2.65 8, is obtained for the Ge-Ge bonds while the Ge-Ru distances are all very close to 2.61 A, except the distance between the unique Ge and the central Ru atom which is 2.67 8,. The bond angle between the three Ge atoms (89’) is very close to a right angle. The Ge-Ge bond order is calculated to be 0.50 while the BO values for Ru-Ge bonds are 0.56 for the unique Ge and 0.62 for the others. The average BO value per Ge atom (also averaged over the three Ge) is evaluated to be 0.59, larger than for the (1 11) facet (0.54) and almost similar to the value obtained when Ge is diluted (0.60). Substitution in a (100) facet leads thus to much less distorted Ge-Ge and Ru-Ge bond lengths than does substitution in a (1 11) facet, and the overall bonding interactions in terms of bond distances and bond orders are very similar to those in the diluted case. For the related Sn cluster, the conclusion is different in the sense that the bonding interactions are not so different from those from the substitution in the (1 11) facet. Indeed, although Sn-Sn bonding is stronger and Ru-Sn bonding is weaker, compared to a (111) substitution, both structures look less favorable than dilution in the Ru surface: (1) The Sn-Sn bond lengths are 2.97 A while the Ru-Sn bond distances for the unique Sn atom are 2.85 (surface Ru atoms) and 3.04 8, (central Ru), and those for the two other atoms are 2.75 and 2.88 8, with the surface and central Ru atom(s), respectively. (2) The Sn-Sn bond order is 0.50 and the Ru-Sn BO values are 0.47 and 0.50 for the unique and nonunique atoms, respectively. Averaging the five BOs for all Sn atoms leads to a value of 0.49 per Sn atom. These results conceming three different topologies of clusters containing 10 Ru and 3 Ge(Sn) atoms show that the dilution effect (or, conversely, island formation) is a rather complex phenomenon which depends on both the M-M and Ru-M bonding interactions. Another way to compare substitutionin (1 11) and (100) facets is to consider the M3 fragment as an adsorbate on a Ru substrate and to analyze how the M atoms are accomodated on the Ru particle. For this purpose, we have performed calculations on two different kinds of M3 clusters: (i) isolated Ge3 and Sn3 molecules with optimized structures; (ii) Ge3 and Sn3 fragments fixed at the geometries obtained in the Ru1oGe3 and RuloSn3 models, both at (1 11) and (100) facets. Comparison of these two sets of M3 clusters (labelled below as “molecule” and “fragment”) will allow the effects of alloying with a substrate to be delineated and the influence of the M-M
.Goursot et al.
TABLE 1: Geometries and Relative Energies of Ge3 Molecules and Fragments isolated molecules structure linear D3h viplet hisinglet
(1 11)
C2“(100)
bond length (angle)” 2.33 2.5 1 2.51 2.36 (84)
energyb 8.7 0.8 11.2
0.0
fragments from RuloGe3 bond length (angle)”
energyb
2.90 2.65 (89)
14.5 0.0
“Bond lengths are in angstroms and bond angles in degrees. Energies are in kcal mol-I.
TABLE 2: Geometries and Relative Energies of Sn3 Molecules and Fragments isolated molecules
fragments from RuloGe3
structure
bond length (angle)”
energyb
bond length (angle)”
energyb
linear D3h triplet D3h singlet ( 1 1 1) C2”(100)
2.70 2.91 2.9 1 2.74 (80)
7.6 0.6 7.7 0.0
3.07 2.97 (87)
0.0
2.2
a Bond lengths are in anstroms and bond angles in degrees. Energies are in kcal mol-I.
and Ru-M bonding interactions on the relative stabilities of the different R u & f 3 models to be determined.
Results for M3 Clusters The three possible structures for isolated M3 molecules, Le., linear (Dmh), equilateral triangle (&), and isosceles triangle (CzV),have been studied. The highest occupied molecular orbital (HOMO) of the D3h structure is degenerate (e symmetry) and partially occupied by 2 electrons. According to Hund’s rule, the triplet state is more stable than the singlet state (as shown in Tables 1 and 2). However, in the following developments, the singlet state will only be considered for comparison with M3 (1 11) facets on RUI& clusters. Indeed, in these clusters, the Ge and Sn levels are at the bottom of the valence band and filled with paired electrons. Moreover, Ru particles have no magnetic properties, and the model clusters have thus been studied as singlet states. Ge3 Clusters. The optimized bond lengths and relative energies of the molecules are presented in Table 1. Analysis of this table shows that the ground-state structure is the CzV molecule, the equilateral triangle being the least stable. Both linear and C2” molecules have two short Ge-Ge bonds with comparable values, whereas the D3h structure has three strongly elongated Ge-Ge bonds (20.15 A). The calculated relative energies between the Ge3 fragments of the (1 11) and (100) facets are given in Table 1, together with their geometries. Examination of Table 1 allows the following remarks to be formulated: (1) the open structure (CzVor (100)) is the most stable for both kinds of models; (2) the fragments have strongly elongated bonds with respect to the isolated molecules, with the largest effect for the (1 11) structure (+0.39 A) compared to that for the (100) model (f0.29 A); (3) the energy difference between the (100) and (1 11) fragments (14.5 kcal mol-’) is larger than the difference for the isolated molecules (11.2 kcal mol-’). Sn3 Clusters. The optimized structures and relative energies of the Sn3 molecules are presented in Table 2. The D3h molecule has strongly elongated bonds (20.17 A) with respect to the linear and CzVmolecules, as found above for Ge3. In the same way, the C2” molecule is the most stable, but the two other conformers are less destabilized than for Ge3.
Dilution and Clustering in RuGe and RuSn
J. Phys. Chem., Vol. 99, No. 34, 1995 12721
+ 3M - Ru,,M3 (diluted) + Ae, Ru,, ( 111) + M3 (111) --. Ru,,M3 ( 111) + Ae2 Rule (100) + M3 (100)-Ru,,M3 (100) + Ae3 3M + 10 Ru Ru,,M3 (diluted) + AE,
TABLE 3: Energy Differences between M3 Molecules, Fragments, and RUIOMJ Clusters for (100) and (111) Structures (M = Ge or Sn) energy difference“ Ge 3
Ru,, (diluted) Sn
3
[(loo)fragment] - [(loo) molecule] [( 11 1) fragment] - [( 111) molecule] [(lll)fragment] - [(loo) fragment] [(I 11) RuIoM~I RuioM31
16.7 8.8 20.1 3.3 14.5 2.2 10.0 14.0 a Energy difference (kcal mol-’) = .!?[lessstable system] - E[more stable system]. Comparison between the Sn3 molecules and fragments shows that the presence of the RUIOsubstrate has caused bond elongations (0.23 8, for (100) and 0.16 8, for (111) clusters) that are less pronounced than for Ge3. Moreover, in contrast to Ge3, this elongation is smaller for the (1 11) structure. Finally, the energy difference between the Sn3 (100) and (111) fragments only amounts to 2.2 kcal mol-’, whereas it was 14.5 kcal mol-’ for Ge3.
-
+
+ AE2 -Ru,,M3 (100) + AE3 Ru,,M3 (1 11)
where
+ de, AE, = Ae2 + de, + de, AE3 = Ae3 + de, + de’, AE, = Ae,
Bond formation energies are thus easily separated into Ru-Ru (dei), Ru-M (AeJ, and M-M (de,, de’,) energy terms. The total formation energies are AEi ( i = 1,3), which give, by In order to delineate the different factors which control island difference, the relative stabilities of the R U I O M clusters. ~ All formation, relative stabilities between M3 molecures and fragthese values are collected in Table 4. ments for (100) and (1 11) structures have to be compared with Their analysis allows comparison of the three types of the corresponding RUI& energy differences. These values are clusters. Their relative energies reveal a different behavior for collected in Table 3. RuGe and RuSn bimetallic particles: diluted Sn atoms corComparison between M3 molecules and M3 fragments gives respond to the most stable structure whereas the cluster information on the modifications which are necessary to transcontaining three diluted Ge atoms has a total energy comparable form a Ge3 or a Sn3 molecule into a small (11 1) or (100) fragto that which includes a Ge3 (100) facet. However, the M3 (1 11) ment “adapted” to its Rulo substrate. In other words, it provides island is the least stable topological situation for both Ge and a description of the “preparation” which M3 has to undergo in Sn clusters. These findings are the results of the combined order to permit its bonding to the Rule particle. We have seen effects of M-M, Ru-M, and Ru-Ru bonding stabilization. above that this preparation induces a smaller distortion for Sn3 The stabilization of M3 fragments with respect to isolated than for Ge3, which means a lower energy cost. Moreover, these atoms is comparable for three of the clusters, with a bond two fragments have opposite behaviors concerning preparaformation energy of around 120 kcal mol-], but substantially tion: the Ge3 (100) fragment needs less energy to be prepared larger for the Ge3 (100) fragment. In fact, a comparison with (16.7 kcalmol-’)thantheGe3 (1ll)fragment (20.1 kcalmol-I). the corresponding (111) cluster shows that this particular In contrast, it is easier to adapt Sn3 to a (111) facet (3.3 kcal stability is the decisive factor which makes the RuloM3 (100) mol-’) than to a (100) facet (8.8 kcal mol-’). cluster as stable as the diluted model. There is no equivalent Preparation of the M3 “adsorbate” has cost energy. This situation for the RuSn bimetallics. energy has to be compensated by bonding interactions with the Analysis of the Ru-Ru bonding interactions reveals that the Rule substrate, leading to the formation of a stable R U I O M ~ most stable Rulo substrate is the cluster related to a (1 11) island cluster. Energy differences between the (1 11) and (100) (Figure le), whereas the least stable is the cluster from which structures for fragments and the related RuloM3 clusters give the three diluted M atoms have been removed (Figure Id). The information on this bonding stabilization. It is seen from Table other model has an intermediate stability (Figure If). In fact, 3, that for Ge3, this energy difference decreases from 14.5 to the relative stabilities of these Rulo particles are strongly 10.0 kcal mol-’, which means that the Ge-Ru interactions favor correlated to the bulkiness of their structure: the most compact the (1 11) island, whereas Sn-Ru interactions stabilize more is the most stable and the least stable cluster displays three large the (100) island (increase from 2.2 to 14.0 kcal mol-’). These holes. The stability criterion is more likely compactness, results show that island formation depends on both M3 preparaalthough the total number of Ru-Ru bonds is also increasing tion and bonding interactions with the Ru atoms. However, a with increasing cluster stability (the average coordination complete description of the factors controlling the choice number increases being 4.2, 4.3, and 4.8 for the Rulo clusters between dilution and island formation requires the evaluation represented in Figure Id-f, respectively). of the relative stabilities of the Rulo particles, which are It is worth noting that when three M atoms (diluted or as an illustrated in Figure Id-f. Indeed, starting from isolated M M3 fragment) are added to the RUIO framework to complete the and Ru atoms, one can describe the formation of the studied cubooctahedron, the Ru-M bonding energy decreases while the RUIOM clusters ~ using the following equations: Ru-Ru stabilization increases. In other words, the less stable the Rule substrate, the larger the energy gain through “alloying” 3M-M3(111)+de, to yield a 13-atom particle. The very strong stabilization M3 (100) de’, induced by filling the holes of the Ru substrate (diluted case) is compensated by M-M bonding energies only for the Ge3 10Ru Ru,, (diluted) de, (100) facet. Comparison between RuloGe3 and RuloSn3 models shows that -Ru,,(111)+de2 the Ru-Sn bonding interactions are always weaker, yielding Ru,, (100) de3 smaller formation energies, for the Sn clusters. Moreover, Sn
General Discussion
-
+
-.
-
+
+
12722 J. Phys. Chem., Vol. 99, No. 34, 1995
Goursot et al.
TABLE 4: Interaction, Bond Formation and Relative Energies for the RuloM~Clusters (kcal mol-’) clusters RuloGe3 (diluted) RuloGe3(100) RuloGe3 (111) RuloSn3 (diluted) RuloSn3(100) RuloSn3(1 11)
Ru-Ru Ru-M M-M total AE bonding bonding bonding bond relative energy energy energy formation energy 757.0 777.7 814.9 757.0 777.7 814.9
338.3 180.2 147.7 317.2 163.8 114.0
136.4 121.9 122.0 119.8
1095.3 1094.3 1084.5 1074.2 1063.5 1048.7
0.0 1.0 10.8
0.0 10.7 25.5
islands are always more destabilizedthan Ge islands with respect to a diluted topology. This study has been performed without optimizing the positions of the Ru atoms, but we believe that the main conclusions would also hold if Ru atoms were allowed to relax. This relaxation should be limited since the Ru-Ru bonds have been fixed to the value determined experimentally for a Ru particle of comparable size. Moreover, since Ge and Sn atoms are allowed to adjust to the different Ru substrates, the Ru-M interactions should be described rather realistically. The relaxation of the clusters is limited by symmetry constraints, which are larger for the C3v symmetry. Consequently, the RUIOM~ (100) models, with a low C,symmetry, are those which should display the largest relaxation effects and thus undergo the largest stabilization.
Conclusion This study has shown that the topology of a bimetallic particle is a complex property which involves intricate electronic and geometric factors. Comparison with M3 model clusters has led to the concept of a necessary adaptation of the atoms or clusters (islands) of the second element to the framework of the pure metal particle. This adaptation can be described as a combination of the most favorable Ru-M and M-M bonding interactions for a given morphology of the Ru particle. We have seen that island formation is controlled by a preparation step which defines the most stable facet. In the case of Ge3 and Sn3 clusters, the D3h symmetry of a (1 11) facet is less favorable than the CzVsymmetry ((100) facet)). The energetic preference for the (100) geometry is far more pronounced for Ge than for Sn. Along with this preparation energy, Ru-M and Ru-Ru bonding interactions represent intricate factors that also govern island formation. Their stabilizing effect depends on the electronic interactions between both metal elements and also on the morphologies of the island and of the particle. Compact metal particles are more stable, which induces larger stabilization when the atoms of the second element fill holes. There is thus a balance between stability of the pure metal particle (larger if more compact) and the energy gain due to Ru-M bonding (larger for less compact Ru particles). For the cubooctahedral model we have chosen, these interactions favor the (100) island with respect to the (11l), with a larger efficiency for Sn clusters.
Island formation with respect to a diluted topology also has to be discussed in terms of the binding energy between M atoms, which has been shown to be a predominant factor for the stabilization of Ru1oGe3(100). This overall picture shows how the nature of the two metals involved in the “alloy”, as well as the shape of the particle, may change the topological segregation on the surface of the bimetallic particle. If the relaxation of the framework is considered as roughly comparable for the three topologies (diluted, (loo), and (111) facets), some qualitative trends can be predicted for small RuGe and RuSn particles: (i) Ge atoms have no clear preference either for dilution on the Ru surface or for aggregation into (100) islands; (ii) Sn is more likely to be distributed on the Ru surface; (iii) for a larger Sn/Ru ratio, (100) facets will be preferred.
Acknowledgment. This work has been supported by the European Economic Community in the form of a Stimulation Action Science (No. SC1* - CT91 - 0681), which funded study visits of L. Pedocchi to our laboratory. We are grateful to CSCS (Manno, Switzerland) for a grant of computer time. References and Notes (1) Purcell, K. G.; Pupille, J.; King, D. A. Surf: Sci. 1989, 208, 245. (2) Coq, B.; Bittar, A.; Figubras, F. Stud. Sutf Sci. Catal. 1989, 48, 327. (3) Coq, B.; Bittar, A.; Dutartre, R.; Figubras, F. J. Catal. 1991, 128, 275. (4) Verbeek, H.; Sachtler, W. M. H. J. Catal. 1976, 42, 257. (5) Ponec, V. Advances in Catalysis; Academic Press: London, New York, 1983; Vol. 32, p 149. (6) Martin, G. A. Catal. Rev. Sci. Eng. 1988, 30, 519. (7) Hauen, R.; Oelhafen, P.; Guntherodt, H. J. Surf: Sci. 1989, 220, 341. (8) Clarke, J. K. A.; Creaner, A. C. M. Ind. Eng. Chem. Prod. Res. Dev. 1981, 20, 574. (9) Williams, F. L.; Nason, D. Surf: Sci. 1974, 45, 377. (10) McLean, D. In Grain Boundaries in Metals; Clarendon: Oxford, 1957. (1 1) Sundaram, V. S.; Wyndblatt, P. Sutf Sci. 1975, 52, 569. (12) Coq, B.; Goursot, A.; Tazi, T.; Figubras, F.; Salahub, D. R. J. Am. Chem. SOC.1991, 113, 1485. (13) Smale, M. W.; King, T. S. J. Catal. 1990, 125, 335. (14) Goursot, A.; Pedocchi, L.; Coq, B. J. Phys. Chem. 1994,98,8747. (15) St-Amant, A.; Salahub, D. R. Chem. Phys. Lett. 1990, 169, 387. (16) St-Amant, A. Ph.D. Thesis, Universiti de Montrbal, Montreal, Canada, 1991. (17) Daul, C.; Goursot, A.; Salahub, D. R. In Numerical Grid Methods and Their Application to Schrodinger Equation; Cejan, C., Ed.; NATO AS1 Series; Kluwer Academic Publishers: Dordrecht, Netherlands, 1993; p 153. (18) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (19) Perdew, J. P.; Yue, W. Phys. Rev. B 1986, 33, 8800. (20) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (21) Goodwin, L. Unpublished results. (22) Musolino, V.; Russo, N. Unpublished results. (23) Mayer, I. Chem. Phys. Lett. 1983, 97, 270. (24) Coq, B.; Crabb, E.; Warawdekar, M.; Bond G. C.; Slaa, J. C.; Galvagno, S.; Garcia Ruiz, J.; Sanchez Sierra, C. J. Mol. Catal. 1994, 92, 107. (25) Vlaic, G.; Bart, J. C.; Caviglio, W.; Furesi, A.; Ragaini, V.; Cattania Sabadini. M. G.; Burattini, E. J. Catal. 1987, 107, 263. JP950560Y
