Interaction between Catalyst and Support. 3. Metal ... - ACS Publications

Nucleation, clustering, and multilayer growth of metals on oxide surfaces are processes which influence the stability and function of many catalysts. ...
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9230

J. Phys. Chem. B 2001, 105, 9230-9238

Interaction between Catalyst and Support. 3. Metal Agglomeration on the Silica Surface Qisheng Ma and Kamil Klier* Department of Chemistry and Zettlemoyer Center for Surface Studies, Lehigh UniVersity, Bethlehem, PennsylVania 18015

Hansong Cheng,* John W. Mitchell, and Kathryn S. Hayes Air Products and Chemicals, Inc., 7201 Hamilton BouleVard, Allentown, PennsylVania 18195-1501 ReceiVed: April 10, 2001; In Final Form: June 25, 2001

Nucleation, clustering, and multilayer growth of metals on oxide surfaces are processes which influence the stability and function of many catalysts. In this work, we have examined initial stages of these processes by means of modeling involving calculations of energies and optimum structures of Co and Ni on a silica surface. Surface concentrations of Co and Ni with metal-to-oxygen ratios ranging from 1:3 to 5:3 (one-third of a monolayer to multilayer) were investigated. The positions of the metal, surface oxygen, and subsurface silicon atoms were optimized, and energies of the metal-oxide and metal-metal interactions in each optimization step as well as in stable geometries were calculated on a two-dimensional periodic slab model with hexagonal unit cell of composition Con(Nin)O3(top)Si2(OH)2. The methodology employed the periodic density functional theory (DFT) at the full-potential linearized augmented plane wave (FP-LAPW) level with spin-polarization taken into account. At the lower coverage with n ) 1, the Co and Ni metals were bonded to various adsorption sites with energies ranging between 1.0 and 2.0 eV. The 3-fold oxygen hollow sites of the siloxane 6-ring were found to be energetically most favored for the adsorption of either metal, more so than 3-fold sites with Si underneath. For n ) 2-3, several nearly equally stable configurations were identified. A further increase of metal coverage resulted in metal clustering due to the stronger metal-metal interaction that ranges around 4.0 eV per metal atom. With n > 3, i.e., metal:oxygen ratios exceeding 1:1, the Co and Ni metals formed layered structures with strong metal-metal bonds and relatively weak metal-silica surface bonds.

1. Introduction Highly dispersed transition metal clusters supported on oxides have broad applications in many areas, such as heterogeneous catalysis, ceramics, and microelectronic devices.1,2 Great attention has been devoted both experimentally and theoretically to the understanding of the interaction between metals and supports.3,4 From a theoretical point of view, metal-support interaction encompass microelectronic phenomena for which quantum mechanical calculations, especially the density functional theory (DFT), have been widely applied to provide theoretical insights to many physical and chemical processes. On the other hand, the systems involved are complex such that certain degrees of approximations and modeling have to be imposed in studying the metal-support effects. The approaches generally included simulating the metal clusters with a few atoms and modeling the supporting substrate as a terminated cluster or a truncated slab. The interaction of Ni and Cu atoms as well as Ni4 and Cu4 clusters with the MgO(100) surface by a cluster model has been investigated by Pacchioni and Ro¨sch5 using the linear combination of Gaussian-type orbitals density functional (LCGTO-DF) method. Yudanov et al.6 also performed the LCGTO-DF study of Pd atoms and Pd4 clusters on MgO(100). The authors found that the metal square cluster is almost perfectly accommodated to the MgO substrate, suggesting a preference for pseudomorphic growth of large metal particles. A DFT calculation of Wn (n ) 1-4) clusters on the ideal MgO(100) surface has also been carried out by Cai et al.7 using the cluster model embedded in

a large array of point charges (PCs) with spin-polarization taken into account. The tetrahedron shape of W4, most stable in the gas phase, is calculated to be energetically preferred also in the adsorbed state. Larger metal clusters up to Cu13 adsorbed on the MgO surface have also been simulated by Musolino et al.8 using the Car-Parrinello approach. The authors found that for n g 5, three-dimensional cluster formation is preferred to twodimensional coverage of the surface. A good understanding of the structural information about the supporting surface is crucial for modeling the substrate in terminated cluster calculations, for which the MgO(100) has been generally adopted in these calculations because magnesium oxide has a rocksalt lattice, the simplest metal-oxide crystal structure. Co(Ni)/SiO2(Al2O3) are of particular interest because they are the active heterogeneous catalysts for, among others, amination reactions.9,10 In our previous studies,11,12 adsorption of low submonolayer coverages Co and Ni on SiO2 and Al2O3 surfaces has been calculated using the slab models. While lower metal coverage studies have revealed a significant insight into the primary metal-support interactions, a better understanding of the adhesive force of metals to the supporting substrate requires a study of higher coverages and metal clusters on the supporting surface. Well-separated periodical slabs have been widely used in the surface calculations. In general, the slab model reduces the artificial termination effects and provides more reliable models for substrate which otherwise would have to be simulated by clusters of unrealistically small size. Another significant difference between the cluster model and the slab

10.1021/jp011341h CCC: $20.00 © 2001 American Chemical Society Published on Web 08/29/2001

Metal Agglomeration on the Silica Surface

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Figure 1. Four different configurations of two Co metals adsorbed on the silica substrate with 2:3 metal:oxygen ratio. (a) the H+H1 configuration; (b) the H+H1_opt configuration; (c) the stand-up configuration; and (d) the side-on configuration. Both the top view and the side view renditions have been shown. The shadowed areas indicate the hexagonal unit cells. The vertical distances of Co atoms to the oxygen plane are also shown.

model is that adsorbed atoms are laterally repeated due to the periodical arrangements of the unit cell. The concept of metal clusters is no longer valid when the number of adsorbed atoms increases. Instead, we define the metal coverage by the ratio of number of metal atoms to the number of oxygen atoms of the top layer of slab within a unit cell. With three oxygen atoms on the top layer in the unit cell, up to a 5:3 metal:oxygen ratio of Co and Ni adsorption on the silica surface has been studied, and the geometrical and energetic properties of these heterostructures are reported herein. 2. Computational Details The DFT calculations were performed using the WIEN97.9 code with the full-potential linearized augmented plane-wave (FP-LAPW) method.13 The SiO2 slab was taken initially from a truncated (111) surface of β-cristobalite silica, containing three layers with the silicon layer sandwiched by two layers of oxygen. An additional fourth layer formed by hydrogen atoms was also included to terminate the dangling oxygen atoms. The hexagonal unit cell (a ) b ) 0.53 nm and c ) 2.0 nm) contains the stoichiometry O3(top)Si2(OH)2. The geometry of the slab has been fully optimized before the metal adsorption; the coordinates of optimized SiO2 slab were listed in our previous publication.11 The first O layer and second Si layer were allowed to relax with metals adsorbed, while the dangling (OH) groups were fixed. The basic features of this two-step optimization are (i) an inward movement of the O atoms toward the center of the H site (Figure 1a) in the metal-free SiO2 slab and (ii) adsorption of the metal atom into a stable position near the center of the H site, with metal-oxygen distances 0.195 nm (Co) and 0.190 (Ni), elevations 0.071 nm (Co) and 0.070 nm (Ni) above the O3(top) plane, and O-M-O angles 106.9° (Co) and 107.1° (Ni). Partial optimization14 was carried out by calculating the forces acting on the atoms after each convergence of SCF cycle. A modified Newton damping dynamic scheme15 was applied to move the specified atoms. Optimization convergence was assumed when the forces on specified atoms were less than 5

mRy/au. A set of four special k-points with 2 × 2 × 1 k-mesh in the irreducible wedge of the hexagonal Brillouin Zone (BZ) has been used. The following quantities are defined to characterize the geometrical and energetic properties of the metal adsorption. (1) The metal adsorption energy: ads Eads Me[n] ) (1/n)(EMen - Eslab - nEMe1)

(1)

ads is the calculated total energy of n metal atoms in where EMe n the unit cell of the adsorbed-substrate system, Eslab is the calculated energy of the SiO2 slab, and EMe1 is the single atom energy calculated with one metal atom in a 1 × 1 × 1 nm3 unit cell. The metal adsorption energy Eads Me[n] measures the adsorption strength of metals on the silica substrate from isolated atomic states, which includes the metal-substrate as well as metal-metal interactions. (2) The metal-layer adsorption energy:

ads free Eads Layer[n] ) EMen - Eslab - EMen

(2)

free is the total calculated energy of the “free” metal where EMe n layer. This energy is obtained by optimizing the structure of the metal layer starting from the geometry of the adsorbed layer on the surface.8 The metal-layer adsorption energy Eads Layer[n] measures the ability of adsorption of a preformed metal layer on the substrate, which reflects the metal-substrate interaction alone. (3) The one-metal adsorption energy

ads ads Eads Atom[n] ) EMen - EMen-1 - EMe1

(3)

is also defined to measure the energy associated with the addition of one metal atom to the adsorbed metal cluster or layer.

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ads ads TABLE 1: Adsorption Energies of Co and Ni Multilayers on the Silica Substrate. the Energies Eads Me [n], ELayer[n], EAtom[n] are Defined in Equations 1-3 Accordingly

metal:oxygen ratio 1:3

2:3

3:3

Eads Me[n] (eV/atom)

adsorption configuration

Co -1.28 -1.31 -1.45 -1.90 -3.34 -3.59 -3.98 -4.03 -4.04 -4.64 -4.30 -4.89

Top site (T) Bridge site (B) 3-fold site (H1) 3-fold hollow site (H) H+H1 H+H1_opt side-on stand-up without substrate relaxation with substrate relaxation

4:3 5:3

ads ELayer [n] (eV)

Eads Atom[n] (eV)

Ni

Co

Ni

-1.19 -1.24 -1.40 -1.74 -3.59 -3.78 -4.00 -3.82 -3.89 -4.03 -4.24 -4.79

-1.28a

Co

-1.19 -1.24a -1.40a -1.74a -0.81 -1.20 -1.28 -1.63 -1.02 -1.01 -0.98 -0.34

-1.31a -1.45a -1.90a -0.92 -1.42 -2.21 -2.32 -1.12 -1.08 -1.26 -0.62

Ni

-1.28 -1.31a -1.45a -1.90a -3.15 -3.66 -4.44 -4.55 -4.05 -4.35 -5.09 -6.25

a

a

-1.19a -1.24a -1.40a -1.74a -3.28 -3.67 -4.10 -3.75 -3.68 -3.84 -5.30 -5.95

The numbers for single atom adsorption presented here are identical with those in column 3 and 4 for Eads Me[n] because for n ) 1, EMe1 of free ads eq 1 ) EMe of eq 2 ) E Me1 of eq 3, and En-1 of eq 3 ) Eslab of eqs 1 and 2. n a

TABLE 2: Geometry of Co and Ni Multilayers on the Silica Substratea geometry (nm) metal:oxygen ratio

adsorption configuration

1:3

T B H1 H H+H1 H+H1_opt side-on stand-up without relaxation with relaxation

2:3

3:3 4:3 5:3

d(Me-Me)

d(Me-O)

Co

Ni

Co1

Co2

Co3

Co4

Co5

Ni1

Ni2

Ni3

Ni4

Ni5

0.339 0.306 0.219 0.213 0.239(0.053 0.229(0.048 0.228(0.130 0.226(0.183

0.338 0.301 0.221 0.218 0.233(0.045 0.227(0.042 0.221(0.124 0.223(0.168

0.189 0.219 0.205 0.195 0.190 0.384 0.277 0.213 0.197 0.201 0.374 0.420

0.280 0.398 0.284 0.377 0.347 0.343 0.439 0.620

0.313 0.284 0.562 0.576

0.637 0.461

0.645

0.188 0.212 0.203 0.190 0.188 0.381 0.281 0.211 0.193 0.206 0.371 0.410

0.286 0.394 0.274 0.378 0.360 0.334 0.443 0.660

0.307 0.290 0.551 0.551

0.664 0.446

0.493

a The average metal-metal distances d(Me-Me) and the average metal-oxygen distances d(Me-O) are defined in eqs 4 and 5 accordingly. Structure files with exact positions of all individual atoms in each of the calculation are available from the authors upon request.

(4) Average metal-oxygen distance:

d(Me-O) ) (1/3)[d(Me-O1) + d(Me-O2) + d(Me-O3)] (4) In most of cases, metal adsorbed at the 3-fold oxygen sites. It is thus convenient to measure the average distance of metal to the nearest three oxygen atoms. (5) Average metal-metal distance:

d(Me-Me) ) (1/n/(n - 1))

d(Mei-Mej) ∑ i*j

(5)

where Mei-Mej is the distance between ith and jth metals (i, j ) 1, 2, ... n). 3. Results and Discussion 3.1. Surface Metal:Oxygen Ratio 1:3 (0.33 Monolayer). Adsorption of one Co or Ni atom on the silica substrate has been studied in our previous work.11 Four possible adsorption sites have been found, namely, the top site (T), the bridge site (B), the 3-fold site with one Si underneath (H1), and the 3-fold hollow site without Si below (H). The Co/Ni metal atom has been found bonded most strongly at the H site with significantly large adsorption energies of -1.90 eV for Co and -1.76 eV for Ni, respectively. 3.2. Surface Metal:Oxygen Ratio 2:3 (0.67 Monolayer). Several metastable configurations of two Co atoms adsorbed

on the SiO2 surface have been found. In a first attempt, two Co atoms were placed on the H and H1 sites together without further geometry optimization (the H+H1 configuration, Figure 1a). The metal adsorption energy defined by eq 1, Eads Me[2]_(H+H1) ) -3.34 eV/atom is greater than that of a single Co atom adsorbed at the H (-1.90 eV) or the H1 (-1.45 eV) site. This suggests that an additional metal-metal interaction has taken place. Furthermore, examination of forces on the Co atoms indicates that both Co atoms are not stable in the H+H1 configuration. When the geometry optimization of the “H+H1 configuration” was performed, both Co atoms moved vertically away from the substrate surface, resulting in a new stable configuration (the H+H1_opt configuration, Figure 1b), with a metal adsorption energy Eads Me[2]_(H+H1_opt) ) -3.59 eV/atom. Geometrically, both Co atoms have much longer average Co-O distances in the H+H1_opt configuration (0.341 and 0.411 nm) than in the H+H1 configuration (0.071 nm and 0.217 nm), while the CoCo distance was reduced from 0.339 to 0.306 nm. A third configuration was initialized by adding one Co atom on top of another Co atom initially adsorbed at the H site, followed by a geometry optimization. A stable configuration (the stand-up configuration, Figure 1c) was found with the second Co atom sitting on top of the first Co atom. Note that the first Co atom adsorbed on the H site relatively strongly with the adsorption energy of -1.90 eV. The stand-up configuration of two Co atoms reflects the competition between the metal-metal interaction and the metal-substrate interaction, such that the Co-Co interaction is not strong enough to pull

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Figure 2. Geometry of Co metals adsorbed on the silica substrate with metal:oxygen ratios larger than or equal to 1:1. (a) Co3 adsorption with the silica substrate frozen; (b) Co3 adsorption with the silica substrate relaxed; (c) the tetrahedron-type Co4 adsorption; and (d) the “W”-type with a “butterfly”-like connection of the Co5 adsorption.

the first Co atom from the surface. A metal adsorption energy Eads Me[2]_(stand-up) ) -4.03 eV/atom results from both stronger metal-metal interaction (Co-Co distance 0.213 nm) and the metal-substrate interaction (average Co1-O distance of 0.212 nm and Co2-O of 0.377 nm) makes this stand-up configuration more energetically favored than the H+H1_opt configuration. The last metastable configuration (the side-on configuration in Figure 1d) was found by starting with two Co atoms near the silica surface. Two Co atoms lie nearly parallel to the surface with Co atoms located closer to two on-top (T) sites. The metal adsorption energy Eads Me[2]_(surface) ) -3.98 eV/atom is comparable to but slightly smaller than that of the stand-up configuration, resulting from a relatively weaker metal-metal interaction (Co-Co distance of 0.219 nm) and the similar metalsubstrate interactions. The distances of the first Co atom (labeled A in Figure 1) to the nearest three oxygen atoms are 0.209, 0.296, and 0.343 nm (an average 0.283 nm) and 0.210, 0.319, and 0.323 nm for the second Co atom (labeled B in Figure 1) (an average 0.284 nm). The energies and properties of two-atom clusters of Ni adsorbed on the silica surface have also been calculated and compared with the Co2 adsorption. Four metastable configurations such as those in the Co2 adsorbed have been found again. A single Ni atom, as pointed out in our previous studies, interacts with the silica substrate slightly weaker than a Co atom. However, the metal-metal interaction of the Ni atoms is comparable to that of Co atoms, associated with very close values of cohesive energy of bulk metals (4.39 eV/atom for Co and 4.44 eV/atom for Ni).16 The combination of the metalmetal interaction and the metal-substrate interaction results in a very similar adsorption pattern of Ni atoms and Co atoms. However, the stand-up configuration, which is the most energetically favored for the Co adsorption, becomes less stable than the configuration of two Ni atoms parallel to the surface. Figure 1 illustrates the geometry of the four different configurations of the Co2 adsorption on the silica substrate, with the geometries and energies of four different configurations

listed in Tables 1 and 2. In general, the single Co and Ni atoms were bonded to oxygen atoms near the silica surface at various sites quite strongly with energies ranging from -1.0 to -2.0 eV, as shown in Table 1, the rows labeled 1:3. Subsequently, the metal-metal interaction between the second “incoming” metal, and the first adsorbed metal in both the Co2 and Ni2 clusters ranged around -4.0 eV, as indicated in Table 1, columns 5 and 6. These metal-metal interactions dominated the entire adsorption pattern. 3.3. Surface Metal:Oxygen Ratios from 3:3 to 5:3 (Effective Monolayer to Multilayers). Only one stable configuration was found when 3 Co atoms per unit cell were adsorbed. To study the effect of relaxation of the substrate, two optimization steps have been performed. First, only the Co atoms were allowed to relax with the silica substrate frozen (Figure 2a). Subsequently, the top oxygen and second layer silicon atoms of the slab were relaxed, together with the Co atoms (Figure 2b). In the optimized geometry, the first two Co atoms remained nearly in their stand-up configuration, as in the 2:3 coverage, while the third Co atom adsorbed close to the H1 site (Figure 2a) or near the on top T site (Figure 2b). Three Co atoms formed a triangular cluster with metal-metal distances of 0.214, 0.220, and 0.282 nm, for an average d(Me-Me)) 0.239 nm. This geometry was slightly distorted from its stable configuration without the presence of the silica slab, i.e., a perfect triangular cluster with Co-Co distances of 0.223 nm. By allowing the substrate to relax with the Co atoms, the third Co atom was able to move closer to the other Co atoms by forming stronger metal-metal bonds with metal-metal distances of 0.224, 0.219, and 0.245 nm, for an average d(Me-Me)) 0.229 nm, but fewer metal-oxygen interactions with longer d(Me-O) distances (viz. Table 2), resulting in an additional metal adsorption energy of -0.60 eV/atom. Once the metal:oxygen ratio exceeded 1:1, i.e., when four and five metal atoms were added in the unit cell, the Co and Ni atoms started to agglomerate by forming layer structures somewhat more remote from the silica surface. At the 4:3

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Figure 3. Total charge densities and net spin densities of selected Co atoms adsorbed on the silica slab. (a-1 and a-2) One Co atom adsorbed at the H site; (b-1 and b-2) two Co atoms adsorbed in the stand-up configuration; (c-1 and c-2) two Co atoms adsorbed in the side-on configuration; (d-1 and d-2) three Co atoms adsorbed with substrate relaxation; (e-1 and e-2) four Co atoms adsorbed; and (f-1 and f-2) five Co atoms adsorbed. The projected side view renditions with 2-times of the unit cell are presented. The electronic densities cover 11/2 unit cell from the left with a bare 1/ unit cell from the right in each figure. 2

coverage, four Co atoms formed a near tetrahedral Co4 cluster within the unit cell with relatively large cluster-cluster separations. The smallest Co-Co distance from different cells, 0.303 nm, was greater than the average Co-Co distance in the Co4 cluster within the same unit cell, 0.228 nm. The Co4 cluster formed a multilayer structure, with the first two atoms (labeled

A and B in Figure 2) at the H and H1 sites and the other two atoms (labeled C and D in Figure 2) above the first two Co atoms forming a near tetrahedral structure. This is in general agreement with the results of Cai et al.7 and Musolino et al.8 that the three-dimensional cluster formation is preferred to the formation of two-dimensional raft-like surface structures. Even

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Figure 4. Densities of states (DOS) of selected Co atoms adsorbed on the silica slab. (a) One Co atom adsorbed at the H site; (b) two Co atoms adsorbed with the stand-up configuration; (c) three Co atom adsorption; (d) four Co atom adsorption; (e) five Co atom adsorption; and (f) the hcp bulk Co metal. Both spin-up (top) and spin-down (bottom) portions are presented with the Fermi level, indicated as EF. The locations of the Co 3d levels in both the spin-up and spin-down have also been labeled.

though the Co4 cluster was further away from the silica surface (at an average metal oxygen-plane distance of 0.465 nm), its shape was distorted from a perfect tetrahedral structure in the substrate-free environment. This indicates that the relatively weak metal-substrate interaction defined by eq 2, Eads Layer[4] = -1.0 eV, still affects the cluster geometry in a significant way, The lateral interactions among the metal atoms became stronger at the coverage 5:3. Instead of forming larger metal clusters, the fifth Co atom bridged the nearest Co4 clusters to form a “W”-type multilayer structure with a “butterfly”-like

connection between the nearest Co5 metal clusters (viz. Figure 2). The first two atoms (labeled A and B in Figure 2) were located at the H and H1 sites, as in the Co4 adsorption. The smallest Co-Co distance from different cells of 0.236 nm is comparable with the average Co-Co distance of 0.226 nm within the same unit cell, while the average metal oxygen-plane distance becomes even larger (0.508 nm). Compared with the Co4 adsorption, the Co5 layer undergoes a relatively smaller distortion from its substrate-free structure, resulting in the smaller metal-layer adsorption energy of Eads Layer[5] = -0.6 eV.

9236 J. Phys. Chem. B, Vol. 105, No. 38, 2001 3.4. Spin States. The state-of-the-art computational method employed here is unbiased with respect to spin multiplicity, and it was found that the lowest energy configurations for the adsorbed metals have the highest possible spin states, indicating a ferromagnetic coupling involved in the metal-metal interactions. The electronic charge density in the density functional theory (DFT) calculation has been decomposed to the spin-up (FR) and the spin-down (Fβ) portions by performing spinpolarization calculations. The total charge density F is then equal to FR + Fβ, and the net spin density is defined as Fspin ) FR Fβ. The silica slab without the presence of metals is spin-free (Fspin ) 0), while the Co atom has Fspin ) 3 with 5 spin-up d electrons and 2 spin-down d electrons in its atomic state and a doubly occupied, spin-paired 4s shell. Figure 3 represents graphically the calculated total charge densities F and the net spin densities Fspin of selected Co atoms adsorbed on the silica slab. Overall, the net spin densities are nearly equally distributed among the Co atoms, with a relatively small portion extended into the top-layer oxygen atoms, particularly at lower coverages (n e 3). This suggests that the presence of the Co metals polarize the silica surface, even though the magnitude of the polarization is relatively small. Metalmetal interactions, on the other hand, are much more dependent on the distribution of net spin densities. As can be seen from the Figure 3b-2,c-2, an antibonding sigma*-like bond is formed with a node between the two Co atoms. The densities of states (DOS) of both the spin-up and the spin-down portions in clusters with Co:O ratios 1:3 to 5:3 are given in Figure 4. The DOS are presented only for the most stable configuration at each Co:O ratio calculated, i.e., the standup configuration for Co2 and the Co3 adsorption with substrate relaxation configuration for Co3. The Fermi level EF passes through a set of partially filled metal 3d spin-down orbitals, while the fully occupied metal 3d spin-up orbitals are in general 1.0-2.0 eV below the Fermi level (cf. Figure 7). This fairly large energy separation between the spin-up and the spin-down of metal 3d levels prevents spin flipping among the 3d electrons, resulting in the most energetically stable highest possible spin states for the Co and Ni atom adsorption. For comparison, the DOS’s of hcp bulk Co metal (a ) 0.251 nm and c ) 0.407 nm) have also been calculated and are shown in Figure 4f. As the cluster size increased, the Co 3d DOS became more similar to that of the bulk Co metal, especially in the fully occupied spin-up portion. Similar DOS patterns were obtained for Ni clusters and the fcc Ni metal. A further regular property change is that of the magnetic moment, which progressively decreased with increasing cluster size. The magnetic moments µat per metal atom in free clusters, adsorbed clusters, and bulk metals were estimated from the net spin S, calculated as the difference of spin-up and spin-down values for all atomic spheres and the interstitial space in the unit cell, as µat ) geSµB/n, where ge ) 2.0023 is the free electron value, µB is the Bohr magneton, and n is the number of metal atoms in the unit cell. Since each unit cell contained just one cluster, n is also the number of atoms in the metal cluster. The values of µat steadily decreased from the near spin-free values 3 for Co and 2 for Ni in the single atom11 to lower values for the clusters (∼2.4 for Co5 and ∼1.2 for Ni5), with the limits for the bulk metals calculated at 1.57 for hcp Co (experiment gives 1.72)17 and 1.0 for fcc Ni (compared to experimental 0.61).17 Furthermore, the adsorbed clusters had slightly lower magnetic moments than their counterparts separated from the substrate oxide, indicating that the effect of the metal adsorption on magnetic properties of the metal particles is very small and

Ma et al.

Figure 5. Calculated magnetic moments µat per metal atom in the Con and Nin (n ) 1-5) clusters in the “free” space and in the adsorbed states.

Figure 6. Energy relations vs the cluster size. The adsorption energies ads ads Eads Me[n], ELayer[n], and EAtom[n] defined in eqs 1-3 accordingly for both Co and Ni atoms with the relation to the number of metal atoms per unit cell are presented.

if anything, antiferromagnetic in its nature due to induced spin polarization of the support by the metal. These relationships are summarized in Figure 5. The tendency of magnetic moment to decrease with cluster size is attributed to the polarization of increasingly overlapping 4s orbitals with increased itinerant antiferromagnetic coupling and for larger agglomerates to the evolution of band structure with overlapping spin-up and spindown 3d manifolds. 3.5. Patterns and Trends with Cluster Size. 3.5.1. Structures. The cluster structures are determined by the interplay between adsorption energy and metal-metal interactions. As the cluster size increases, the nearest metal to oxygen-plane distance dramatically increases from ∼0.08 nm for a single adsorbed metal atom to >0.4 nm for the supra-monolayers (viz. Figures 1 and 2). At the same time, the metal-metal distance is already short in the stable adsorbed dimers, ∼0.22 nm, with but a little change upon cluster growth to stable trimers, tetramers, and supra-monolayers, ∼0.22-0.23 nm. These

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Figure 7. Schematic relations of orbital energies of Co 2p1/2, 2p3/2, and 3p levels with the size of the Co clusters. The numbers near each line indicate the average energy levels with the dispersion in eV. The differences between Co 2p1/2 and Co 2p3/2, 2p3/2, and 3p levels are also shown. The energy reference is chosen to be the O 1s of the bottom oxygen layer of the silica slab, then shifted to the experimental -531.0 eV value.17 All other calculated levels (Co 2p and Co 3p) were shifted by the same amount. Note that the results do not include the final-state calculations and a constant energy shift due to the work function.

interatomic distances fall close to but are smaller than those in bulk metals, about 0.25 nm for both hcp Co and fcc Ni,16 which have also been verified by the same level of calculations as presently used for the adsorbed clusters. Stabilization of clusters with n > 2 is provided by the tendency to maximize the number of nearest neighbors, giving rise to triangles of Co3, tetrahedra of Co4, and the “W”-type multilayer structure with a “butterfly”like connection between the nearest metal clusters of Co5. The clusters are not free, however, and adsorption forces, although about half the strength of the metal-metal bond, change the cluster shapes by anchoring one or two metal atoms on the oxide surface. As a result, the Co3 triangles are elongated with one apical atom toward the surface, the Co4 tetrahedra are puckered from an ideal Td- to D2V-like shapes, and even the weakly bonded Co5 supramonolayers are held essentially by one metal atom down to the surface. In fact, all the “first cluster atoms” (labeled A in Figure 2) are sited in the 3-fold hollow (H) sites which provide the highest adsorption energy for a single adatom, and the “second cluster atoms” (labeled B in Figure 2) find positions near the 3-fold (H1) sites which afford the next highest adsorption energy for a single atom (viz. Table 1). 3.5.2. Total Energies. Intertwined with the structural patterns, the total cluster and adsorption energies exhibit corresponding trends. The adsorption energy per metal atom defined by eq 1, Eads Me[n], dramatically increases with cluster size primarily due to the metal-metal bond formation (viz. Table 1). At the same time, adhesion of the metal cluster or layer to the oxide defined by eq 2, Eads Layer[n], becomes progressively weaker. These relations are demonstrated in Figure 6. The adsorption energy of a single metal atom onto a precursor cluster defined by eq 3, Eads Atom[n], also increases with cluster size due to the increased number of metal atoms available for bonding. The overall trends shown in Figure 6 are similar for both metals, with the metalsupport interaction slightly stronger for Co than Ni. The metalmetal interaction is also stronger in the Co2 and Co3 than in the Ni2 and Ni3 clusters but becomes nearly equal in larger clusters and bulk metals. 3.5.3. Orbital Energies. Orbital energies in the valence-band (VB) and core-level (CL) regions are closely related to the initial states in X-ray photoelectron spectroscopy (XPS). Their variations calculated here are sufficiently large to provide a diagnostic tool for identification of the cluster size from the following parameters: (1) the metal 2p3/2, 2p1/2, and 3p binding energies referenced, e.g., to the O 1s photoemission from “far away” oxygen atoms in the support structure; (2) the metal 3d spindown and 3d spin-up supra-VB binding energies referenced to the top of the O2p VB. The corresponding patterns are illustrated

Figure 8. Schematic relations of orbital energies the spin-up and spindown portions of the average Co 3d level with the size of the Co clusters. The energy references are chosen from the top of valence band (VB) which mainly consists of O-2p levels.

in Figures 7 and 8. The fully relativistic core region calculations of the WIEN program provide reliable core level energy (The experimental energy difference between Co 2p1/2 and Co 2p3/2 is 14.97 eV).18 The calculated binding energy (BE) shifts are 1-2 eV (Figure 7) in the CL region and 2-3 eV (Figure 8) in the VB region. In particular, the very small clusters (n ) 1-3) show the 3d energies well above those of the O 2p valence band while, in the larger cluster,s the 3d levels merge with the top of the O 2p VB. This theoretical prediction is verifiable by XPS in the VB region. For n g 2, the widths of the Co 3d levels have been dramatically broadened (1.5-2.5 eV) due to the presence of the metal-metal interactions compared to that in the n ) 1 case (∼0.5 eV) (viz. Figure 7). 4. Conclusions Nucleation, clustering, and multilayer growth of metals on oxide surfaces are processes which influence the stability and function of many catalysts. Metal agglomeration deactivates the catalyst, resulting in expensive catalyst replacements. Our calculations suggested that a clean siloxane surface of silica does not provide a strong enough adhesive force for higher coverages of Co and Ni metals. Even though the metals interact with the silica substrate fairly strongly (1-2 eV/atom) at lower coverage, the stronger cohesion (3-4 eV/atom) results in clustering and further agglomeration at higher metal coverages, with concomitant loss of surface area of the metal and its reactivity for catalytic processes. The spin-polarization calculations indicate the antibonding “ferromagnetic” coupling of the partially filled metal 3d orbitals is the major contribution to the stronger metal-metal interaction, which in turn dominates

9238 J. Phys. Chem. B, Vol. 105, No. 38, 2001 the metal adsorption on the silica surface. Anchoring of the metal particles on a weak support such as the presently studied silica has to employ other methods, such a specially designed “mechanical trapping”,19 bonding to the unreducible transition metal ions,20 to the defect sites of substrate surface,21 or even using a strong chemical interaction with the oxide.22 The methodology employed here has given consistent and reliable results for all the properties of bulk metals, and is verifiable by experiment for clusters in terms of their geometry (EXAFS, electron microscopy, photoelectron diffraction), valence-band and supra-valence band electronic structure (UPS and VB-XPS), chemical shifts in CL-XPS, and magnetic moment measurements. Acknowledgment. This research was carried out under the Grant PPDO-001 of the Pennsylvania Infrastructure Technology Alliance (PITA) program with financial support from PITA and Air Products and Chemicals, Inc. (APCI). Support of scientists Drs. K. Anselmo, J. Armor, J. Tao, R. Pierrantozzi, and C. Valenzuela and their commitment to computational approaches to practical aspects of material science of catalysis are highly appreciated. References and Notes (1) Lambert, R. M.; Pacchioni, G., Eds. In Chemisorption and ReactiVity of Supported Clusters and Thin Films; NATO ASI Series E., Vol. 331; Reidel: Drodrecht, The Netherlands, 1997. (2) Sinfelt, J. H. Bimetallic Catalysts; John Wiley & Sons: New York, 1983.

Ma et al. (3) Stevenson, S. A.; Dumesic, J. A.; Baker, R. T. K.; Ruckenstein, E. Metal-Support Interactions in Catalysis, Sintering, and Redispersion; Van Nostrand Reinhold Company Inc.: New York, 1987. (4) Stakheev, A. Yu.; Kustov, L. M. Appl. Catal. A 1999, 188, 3. (5) Pacchioni, G.; Ro¨sch, N. J. Chem. Phys. 1996, 104, 7329. (6) Yudanov, I. V.; Vent, S.; Neyman, K.; Pacchioni, G.; Ro¨sch, N. Chem. Phys. Lett. 1997, 275, 245. (7) Cai, S.; Neyman, K. M.; Hu, A.; Ro¨sch, N. J. Phys. Chem. 2000, 104, 11506. (8) Musolino, V.; Selloni, A.; Car, R. Surf. Sci. 1998, 413, 402. (9) Sewell, G. S.; O’Connor, C. T.; van Steen, E. Appl. Catal. A 1995, 125, 99. (10) Gardner, D. A.; Clark, R. T. Catalytic Process for Preparing Ethyl Amines. U.S. Patent 4,255,357, March 10, 1981. (11) Ma, Q.; Klier, K.; Cheng, H.; Mitchell, J. W.; Hayes, K. S. J. Phys. Chem. B 2000, 104, 10618. (12) Ma, Q.; Klier, K.; Cheng, H.; Mitchell, J. W.; Hayes, K. S. J. Phys. Chem. B 2001, 105, 2212. (13) Blaha, P.; Schwarz, K.; Luitz, J. WIEN97, A Full Potential Linearized Augmented Plane WaVe Package for Calculating Crystal Properties; Technische Universita¨t: Wien, Austria, 1999. (14) Yu, R.; Singh, D.; Krakauer, H. Phys. ReV. B 1991, 43, 6411. (15) Stumpf, R.; Scheffler, M. Comput. Phys. Commun. 1994, 79 447. (16) Kittel, C. Introduction to Solid State Physics, 6th ed.; John Wiley & Sons: New York, 1986. (17) Buschow, K. H. J. Handbook of Magnetic Materials; NorthHolland: Amsterdam, 1993. (18) Moulder, J. F.; Stickle, W. F.; Sobol, P. E.; Bomben, K. D. In Handbook of X-ray Photoelectron Spectroscopy; Chastain, J., Ed.; PerkinElmer Corporation: 1992. (19) Sachtler, W. M. H.; Zhang, Z. C. AdV. Catal. 1993, 39, 129. (20) Contreras, J. L.; Fuentes, G. A. Stud. Surf. Sci. Catal. 1996, 101, 1195. (21) Ferrari, A. M.; Pacchioni, G. J. Phys. Chem. 1996, 100, 9032. (22) Louis, C.; Cheng, Z. X.; Che, M. J. Phys. Chem. 1993, 97, 9022.