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Simulation Study of Pd Submonolayer Films on Au(hkl) and Pt(hkl) and Their Relationship to Underpotential Deposition M. I. Rojas, M. G. Del Po´polo, and E. P. M. Leiva* INFIQC, Unidad de Matema´ tica y Fı´sica, Facultad de Ciencias Quı´micas, Universidad Nacional de Co´ rdoba, 5000-Co´ rdoba, Argentina Received June 8, 1999. In Final Form: June 20, 2000 The structure and stability of palladium adlayers on Au(hkl) and Pt(hkl) were studied at different coverage degrees by means of Monte Carlo simulations using the interatomic potentials of the embedded atom model. In all cases the Pd films were found to grow epitaxially and pseudomorphically with the crystallographic orientation of the substrate. The differences and similarities of the adlayer with the substrate were analyzed.
Introduction The unique chemical and physical properties exhibited by ultrathin films of Pd deposited on Au and Pt singlecrystal faces have strongly motivated experimental research in the area of electrochemistry and the related field of surface science. On the other hand, theoretical and computational studies have left far behind the requirements of experimentalists. In addition to providing by itself an interesting field for basic research, the modification of gold and platinum electrodes by palladium deposition offers a new alternative in the catalysis of organic reactions due to the high resistivity of these electrodes against CO poisoning. In fact, Pd adlayers on Au(hkl) or Pd on Pt(hkl) exhibit in general a high catalytic activity and they are better than the massive Pd(hkl) ones.1 Underpotential deposition (upd) of Pd on Au(111) or on Au(100) has been observed in a potential range between 0.53 and 0.65 V vs SCE previous to the massive deposition which occurs at 0.50 V.2 The occurrence of Pd upd on Au(110) was mentioned as possible but it has not been studied so far. A preliminary study of ultrathin Pd films on Au(111) employing scanning tunneling microscopy (STM) has revealed a two-dimensional growth during the initial stage of the deposition.2,3 The morphology of the Pd superlattice on Au(hkl) has been investigated by cyclic voltammetry measurements for a Cu upd monolayer taken as a structural probe. The fact that these films show an electrochemical behavior similar to Pd(hkl) supports the idea that their texture is similar to that of the substrate.1-3 The Pd/Pt upd shift is not reported in the literature but this system grows in a layer-by-layer mechanism which is characteristic of an upd system.9 Attard4 and Clavilier5 have studied the electrochemical behavior of irreversible Pd films on Pt(111), while Baldauf and Kolb1 have studied the catalytic activity of Pd/Pt(hkl) electrodes. Low-energy electron diffraction (LEED) measurements showed a (1 × 1) structure for the monolayer which extended in the (1) Baldauf, M.; Kolb, D. M. J. Phys. Chem. 1996, 100, 11375. (2) Baldauf, M. Ph.D. Thesis, Ulm, Germany, 1996. (3) Baldauf, M.; Kolb, D. M. Electrochim. Acta 1993, 38, 2145. (4) Attard, G. A.; Bannister, A. J. Electroanal. Chem. 1991, 300, 467. (5) Clavilier, J.; Llorca, M. J.; Feliu, J. M.; Aldaz, A. J. Electroanal. Chem. 1991, 310, 429. (6) Han, M.; Mrozek, P.; Wieckowski, A. Phys. Rev. B 1993, 48, 8329. (7) Attard, G. A.; Price, R.; Al Akl, A. Electrochim. Acta 1994, 39, 1525. (8) Inukai, J.; Ito, M. J. Electroanal. Chem. 1993, 358, 307. (9) Lorenz, W. J.; Staikov, G. Surf. Sci. 1995, 335, 32.
multilayer range, thus providing evidence for pseudomorphic growth.6,7 The Pd adlayer structure deposited on Pt(111) or on Pt(100) electrodes has also been studied through the carbon monoxide (CO) adsorption by means of IR reflection adsorption spectroscopy (IRAS), delivering simultaneous structural information about the platinum substrate and the palladium overlayer.8 The results obtained in this latter work also suggested that epitaxial Pd growth on Pt(111) and Pt(100) should be pseudomorphic. It is also worth mentioning that in both systems, Pd/Au and Pd/Pt, the adsorbate and the substrate belong to the transition metal group, with very similar atomic radii which give a small lattice misfit. It is the purpose of this study to provide energetic and structural information concerning the systems Pd/Au(hkl) and Pd/Pt(hkl) from computer calculations. To do this we performed Monte Carlo (MC) and molecular dynamics (MD) simulations with the potentials of the embedded atom model (EAM).10,11 This type of simulations has been widely employed in the study of condensed matter, because they allow the direct evaluation of structural properties. On the other hand, the EAM is particularly suitable for metallic systems, due to the fact that this model takes into account many body effects characteristic of the metallic binding. Recently, some of us13 have performed similar studies on the interaction of Cu adatoms with a Ag(111) surface at different coverage degrees employing MC/EAM simulations. The present work is organized as follows. First, we briefly discuss the underpotential deposition phenomenon and the details of the model. Second, we discuss the structure of the adsorbed monolayer and substrate relaxation upon adsorption at different coverage degrees. Underpotential Deposition To quantify energetic aspects of the system, we used the underpotential shift ∆φupd as originally defined by Kolb et al.15 From an experimental point of view, this corresponds to the potential difference between the desorption peak of a monolayer of a metal M adsorbed on (10) Daw, M. S.; Baskes, M. I. Phys. Rev. 1983, 50, 1285. (11) Foiles, S. M.; Baskes, M. I.; Daw, M. S. Phys. Rev. B, 1986, 33, 7983. (12) Liu, C. L.; Cohen, J. M.; Adams, J. B.; Voter, A. F. Surf. Sci. 1991, 253, 334. (13) Del Po´polo, M.; Leiva, E. J. Electroanal. Chem. 1997, 440, 271. (14) Rojas, M.; Del Po´polo, M.; Leiva, E.; Manuscript in preparation. (15) Kolb, D. M.; Przasnyski, M.; Gerischer, H. J. Electroanal. Chem. 1974, 54, 25.
10.1021/la990731g CCC: $19.00 © 2000 American Chemical Society Published on Web 10/10/2000
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a foreign substrate S and the current peak corresponding to the dissolution of the bulk metal M. To compare the deposition of Mz+ ions on the substrate S with the corresponding reaction on the bulk metal M, the following reactions are considered
ze0(S) + Mz+ + nsS h MΘ(S) M(M) h Mz+ + ze0(M) where MΘ(S) denotes the atom M adsorbed on S at the coverage degree Θ, ze0(S) and ze0(M) represent the electrons in the metals S and M, respectively, M(M) indicates the bulk metal M, Mz+ represents the dissolved metal ion, and ns denotes the number of substrate atoms per adsorbate atom. The use of suitable equilibrium conditions for the system and neglection of entropic contributions lead to17
∆φupd )
1 (U bulk - UM/Sads) ze0 M
(1)
where UM/Sads is the adsorption energy of M on S at the coverage degree Θ and UMbulk is the cohesive energy of bulk M. The two thermodynamic quantities on the righthand side of eq 1 were obtained from the MC simulations described below. The Model The System. The substrates employed in the Monte Carlo simulations were two different sets for each face. In the case of the (111) substrate face, a 5-layer slab with 36 atoms per layer and a 6-layer slab with 72 atoms per layer were employed. In the case of the (100) face a 5-layer slab with 32 atoms per layer and a 6-layer slab with 72 atoms per layer were used with the same purpose. For the (110) face the substrates were a 5-layer slab with 36 atoms per layer and a 6-layer slab with 81 atoms per layer. The larger systems were employed to obtain the adsorption energies, the remaining properties were calculated with smaller ones. Test runs comparing the behavior of both types of systems were also performed. Periodic boundary conditions were imposed to the supercell in the x and y directions. While the position of the atoms in the two surface layers was allowed to vary, the remaining ones were fixed at their bulk equilibrium configuration to simulate the presence of a semi-infinite crystal. The substrate surface was assumed to be smooth without consideration of reconstruction or steps. Different coverage degrees were emulated employing a variable number of Pd atoms on the Au(hkl) and Pt(hkl) substrates. Comparative simulations were run by depositing a variable number of Pd atoms on Pd(hkl) substrates. Simulation Method. The simulations were of the canonical Monte Carlo type. That is, the runs were performed in the (NVT) ensemble at 300 K, allowing for the positions of the adsorbate and surface substrate atoms to explore the whole configuration space. Also, no lattice model was assumed neither for the two surface layers of the substrate nor for the location of the surface atoms. In this way, we could study the relaxation of the adsorbate atoms at different adsorbate surface concentrations. In the usual continuum Monte Carlo simulations, the attempts to change the x, y, and z coordinates of the particles are usually made according to
xi′ f xi + ∆(Ran - 0.5) yi′ f yi + ∆(Ran - 0.5) zi′ f zi + ∆(Ran - 0.5) where primed and unprimed coordinates denote new and old (16) Leiva, E. P. M. Curr. Top. Electrochem. 1993, 2, 269. (17) Sa´nchez, C. G.; Del Po´polo, M. G.; Leiva, E. P. M. Surf. Sci. In press.
Figure 1. Monte Carlo simulation for a single atom of Pd on (a) Au(111) and (b) Au(100) surfaces. The positions of the adatoms are shown in dark grey. The black spots show the position of the atoms in the first lattice plane of the substrate, and the gray ones indicate the positions of the Au atoms in the second lattice plane. The evaluation run was of 15 000 MC steps after 5000 equilibration steps. The snapshots were taken every 20 MC steps, and the simulation temperature was 300 K. values, ∆ is a small displacement and Ran are random numbers uniformly distributed between 0 and 1. For each trial move, the move is accepted or rejected depending on the change of the energy of the system, according to the Metropolis algorithm or similar. As long as the energy barriers for atomic motion are not very large as compared with the thermal contribution kT, this provides a very efficient equilibration procedure. However, as it is the case of the present systems, and especially in the case of the more open surfaces, relatively large barriers may preclude the correct equilibration of the systems. This occurs for example, for the migration of an atom from a position close to its equilibrium location at a hollow place to a neighboring hollow place, or for its detachment/attachment motion from/to clusters. That is, although a neighboring position is available with an equivalent energy, its access is precluded by a barrier. To overcome this kind of problems, we allowed the adatoms to perform attempts for long jumps on the surface, with displacements ∆r such as
∆r ) n1b s 1 + n2b s2 s1 and b s2 label the primitive where n1 and n2 are integers and b vectors of a two-dimensional Bravais lattice, suitably chosen for each substrate surface. These “long” jumps are important to get a proper equilibration of the system, especially in the case of the more open surfaces where the surface barriers are of the order of 1 eV. On the other hand, the “short” jumps usually employed in continuum Monte Carlo simulations, also present in our studies, adequately describe the vibrational motion of the adsorbate atoms in the neighborhood of their equilibrium positions.
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Figure 2. Island formation of Pd on Au(111) surfaces after equilibration through 5000 MC steps of a system with several adsorbate atoms: (a) 12 adatoms; (b) 24 adatoms. Evaluation run as in Figure 1. The crosses denote the initial position of the adsorbate atoms. The simulation temperature was 300 K. Some molecular dynamics (MD) runs were performed in order to compare the distribution functions obtained by our present MC simulation with those employing the XMD program developed by Rifkin.18 In the case of MD runs, the substrates employed consisted of a 7-layer slab with 196 atoms per layer for the (111) faces and an 8-layer slab with 200 atoms per layer for the (100) faces. Interatomic Potentials. The interatomic potentials are the key elements of every simulation. In this work we adopted the EAM potentials which take into account the many body interactions characteristic of metallic systems.10,11 With this method, the total energy of the system Etot is expressed in terms of two contributions: N
Etot )
∑Fi(F
h,i)
+ 1/2
i)1
∑ ∑ φ (r ) ij
i
ij
(2)
j*i
In this expression, Fh,i is the host electron density at atom i due to the remaining atoms of the system. Fi(F), an attractive term, is the energy to embed atom i into the background electron density F. φij(rij) is the core-core pair repulsion between atom i and j separated by the distance rij. The electron density is approximated by the superposition of the atomic densities
Fh,i )
∑F (r ) j
ij
j*i
where Fja(r) is the contribution of atom j to the electronic density. In all cases we used the parametrization of Foiles et al.11
Results and Discussion Adatom Distribution on the Metal Surface. The first point tested was the motion of a single adatom on the (18) Rifkin, J. Center for Materials Simulation, University of Connecticut, http://www.ims.uconn.edu/centers/simul/. (19) Cahn, R. W.; Haasen, P.; Kramer, E. J. In Materials Science and Technology; Vol. 1, Structure of Solids; Gerold, V., Ed.; VCH: Weinheim, 1993; Chapter 8. (20) Boisvert, G.; Lewis, L. J. Phys. Rev. B 1996, 54, 2880.
Figure 3. Dot diagram showing the position of the adsorbate atoms and the position of the first layer substrate adatoms for adsorption of a Pd monolayer on (a) Au(111), (b) Au(100), and (c) Au(110). Simulation conditions as in Figure 1.
surface of a compact (111) and an open (100) face, as shown in Figure 1 for Pd on Au. It can be clearly seen that the atom is able to reach all regions of the substrate surface, although the qualitative features for the (111) and (100) faces are very different. In fact, while the former show a more even distribution, the latter are strongly concentrated on the adsorption sites. This picture reflects the very different characteristics of the potential energy for
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Figure 4. Adsorption energy Eads as a function of the coverage degree for a Pd adlayer on Pd, Au, and Pt. Circles, squares, and triangles represent the (111), (100), and (110) faces, respectively.
the adatom on these substrates. Similar studies with two atoms show the considerably larger mobility of Pd on the Au(111) surface. In the case of three adatom, the mobility is further reduced on both types of surfaces, the appearance of ring-like structures being very typical for the (111) substrates. The evolution of many-adatoms systems offers also interesting aspects, as shown in Figure 2. A random distribution of the adatoms on the surface was assumed at the beginning of the simulation, as denoted by crosses in the figures. It can be noticed that after equilibration the system evolves toward island formation the ring-like structures mentioned above appear very often. In the case of the (111) surface, island formation on both fcc and hcp adsorption sites are built, as expected from the small difference between the adsorption energies for both types of sites. Structure of the Adsorbed Monolayer. Figure 3 shows, as a dot diagram, the position of the adsorbate atoms and the position of the first layer substrate adatoms for adsorption of a Pd monolayer on Au(hkl). In all cases a (1 × 1) structure is apparent, similar results being obtained for Pd adsorption on Pt(hkl). This is by no means a trivial result, as we can conclude from a comparison with the behavior of other systems. For example, in the case of Cu adsorption on Ag(111) we have found that due to the smaller size of the adsorbate, this delivers a rather compressed structure.13 On the other hand, in the case of other systems involving large adsorbates on small substrates, the simulations show that some of the adsorbate atoms are kicked out of the surface.14
Adsorption Energy and Underpotential Shifts. Figure 4 shows the adsorption energy of palladium atoms at different coverages on several substrates. We can see that the adsorption energy decreases with coverage in different amounts for the different types of substrates, converging to a limiting value that depends on the nature of the substrate. For the Pd/Au system this value, close to -3.7 eV, is very similar for all single-crystal faces. Although the differences are small, it appears that the adsorption on the more open faces is energetically favored, following the expected trend for a metallic adsorbate on a foreign surface. For Pd/Pt the binding energies spread around -4.09 eV, following the same ordering as in Au. In the case of Pd on Pd, all types of substrates lead to an adsorption energy of -3.87 eV, which is in the order of kT over the bulk static binding energy. At first sight this result may seem rather amazing, since the surface energies of Pd for (111), (100), and (110) planes are noticeably different, as reflected by the calculations of Foiles et al.11 and Liu et al.12 The reason for the adsorption energy of Pd on Pd(hkl) to be independent of the surface type can be understood in Figure 5, where we have represented the adsorption of a layer of a metal M on a single crystal face of a metal of the same nature. Since the new surface layer being built is exactly equivalent to the original surface layer of the substrate, the energetic change per atom EadsM produced by adsorbing a layer of M on an M(hkl) surface should be exactly equal to the energetic change produced by adding a lattice plane to the bulk metal. It is clear that the total energy change produced by adding a lattice plane to a surface M(111) will be greater than the
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Figure 5. Scheme showing that the addition of a new lattice plane to a single-crystal surface (upper part) is equivalent to adding a bulk lattice plane (lower part). Table 1. Adsorption Energy Per Adatom Eads in eV for Pd Adsorption on Au(hkl), Pt(hkl), and Pd(hkl) at Monolayer Coverage Degree
Table 2. Theoretical Underpotential Shifts ∆Oupd for Pd Adsorption on Au and Pt Single-Crystal Surfaces (a valence of 1 was assumed for Pd)
face/system
Pd/Au
Pd/Pt
Pd/Pd
face/system
Pd/Au
Pd/Pt
111 100 110
-3.70 -3.73 -3.73
-4.02 -4.09 -4.14
-3.87 -3.87 -3.87
111 100 110
-0.17 -0.14 -0.14
0.15 0.22 0.27
corresponding change generated by adding a lattice plane to a surface, i.e., M(100), because a larger number of atoms is added in the former case. However, the energetic change per atom EadsM should be the same, since in all cases bulk atoms are added. The Eads values for Θ ) 1 are reported in Table 1. According to these figures, the Pd monolayer is less stable on Au than on Pd. It should be noted that the energy required to stretch the Pd monolayer to fit on the Au substrate is considerably larger than the corresponding energy to fit the Pd monolayer on a Pt substrate,17 thus contributing to the greater stability of the latter system. In fact, gold has a lattice parameter (aAu ) 4.08 Å) that is larger than that of palladium (aPd ) 3.89 Å). According to the present results, and based only on energetic grounds, upd is not expected for the system Pd/Au(hkl). The fact that this phenomenon is experimentally observed could indicate that the present EAM potentials are not accurate enough to describe the present surfaces. However, we have previously found17 that other contributions, such as anion adsorption, may in principle strongly change the energetics of the system and even induce upd if anions are more strongly adsorbed on the adsorbate than on the substrate. First-principles calculations that are in progress will give a definite answer to the question whether upd takes place on energetic grounds in the systems of this study. On the other hand, adsorption of Pd on Pt(hkl) yielded in all cases a positive underpotential shift, indicating that this process should be possible on energetic grounds. The values of ∆φupd for the systems considered here are included in Table 2. The drastic change of Eads with Θ at low Θ in the case of the (111) surfaces observed in Figure 4 indicates that on the more compact faces the effective interaction parameter between adsorbed atoms is considerably larger (and negative) than in the case of the more open ones. This important attractive contribution is not unexpected,
Table 3. Adsorption Energy in eV for Θ f 0 of a Pd Atom on Au and Pt Single-Crystal Surfaces face/system
Pd/Au(hkl)
Pd/Pt(hkl)
Pd/Pd(hkl)
111 100 110
-2.76 -3.23 -3.48
-3.13 -3.58 -4.06
-2.69 -3.19 -3.73
since the adsorbate atoms are closer to each other in the case of the more compact faces. Table 3 shows the adatom adsorption energy for Θ f 0 on different substrates, denoting the metal-adsorbate interaction without the adsorbate-adsorbate contribution. The qualitative trend is again that the adsorbate atom is more stable on the more open surfaces. We must finally point out that due to finite size effects, the present results for Eads vs Θ have only a qualitative value because the relatively small number of adatoms employed in our simulations can hardly represent the status of the real surface. The Structure of the Adatom Monolayer. The structure of a simple monatomic fluid containing N particles can be characterized by a set of distribution functions for the atomic positions, the simplest of which b2) is the pair distribution function g(r b1,r
g(r b1,r b2) ) g(r) )
N(N - 1) F2ZNVT
∫ drb3 drb4....drbN exp(-βV(r b1,r b2...b r N))
where F denotes particle density, ZNVT is the canonical r1|, and the integral partition function, β ) 1/kT, r ) |r b2 - b is carried out over the coordinates of all particles but b r1 and b r2. This function gives the probability of finding a pair of atoms at a distance r apart, relative to the probability expected for a completely random distribution at the same density. In the case of the fluid mentioned above, the particle density is a constant over the system and g
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Figure 6. Pd-Pd pair distribution functions obtained from MC simulations for Pd adsorbed on (a) Au(111), (b) Au(100), and (c) Au(110) at different coverage degrees as indicated in the figure. The simulation temperature was 300 K.
is only a function of the distance r. Furthermore, g(r) is constructed through an average over spherically symmetric shells surrounding each of the particles of the system according to
g(r) )
V
〈 N2
δ (r - |r bij|)〉 ∑i ∑ j*1
A different situation arises in the present simulation, since the adsorbate atoms are expected to be more or less confined to a plane parallel to the surface defined by the substrate atoms. Thus, we shall rather define the following pair distribution function as
g(r|) )
S
〈 N2
δ (r| - |r bij|)〉 ∑i ∑ j*1
where b rij| is the projection onto the plane parallel to the ri and S denotes the surface of surface of the vector b rj - b
the system. Thus, the averages are now taken over cylindrical shells and the distribution function is referred to an ideal gas with the average surface density N/S. Since the atoms actually move in three dimensions, the distance |r bij| will be somewhat smaller than the corresponding |r bij| and thus g(r|) may not reflect the exact physical situation. For this reason, we shall use this function only for qualitative purposes to compare the results for different coverage degrees by the adsorbates. In the present case, the average was calculated from histograms for distances in the range 0 < r| e L/2.21 Figures 6(a-c) shows g(r|) for Pd on Au(111), Au(100), and Au(110), respectively, at different coverage degrees, and the results of MC and MD simulations are compared in Figure 7. The maxima correspond to the position of the first, second, etc., nearest neighbors. It can be seen in Figure 6 that, with increasing coverage degree, the peaks slightly shift toward larger values, thus denoting a slight (21) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1992.
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Figure 7. Comparison between Monte Carlo (‚‚‚) and molecular dynamics (s)pair distribution functions for Pd adsorbed on (a) Au(111) and (b) Au(100) at Θ ) 1. The simulation temperature was 300 K.
expansion of the adsorbate which is particularly evident in the case of the more compact (111) face. This effect is a consequence of the many body interactions accounted for in the EAM potential. At low coverage degrees the average coordination decreases with a concomitant increase in the bond order between the atoms, making the distance between neighboring atoms shorter. This stress is released as the coverage degree increases and the monolayer coverage is approached. This can also be interpreted in terms of eq 2, where the energy of the system is written as the sum of one atom terms Ei of the form
Ei ) Fi(Fh,i) +
1
∑ φij(rij)
2j*1
(3)
If we now roughly think of the adsorbate atoms as having each N nearest neighbors and consider only the interaction with them, we can write
Ei ≈ C + Fi(Fh,i) +
1 Nφij(rnn) 2
(4)
where we have absorbed in the constant C the repulsive interaction with the substrate atoms and rnn represents the distance between nearest neighbors. While the repulsive term in eq 4 grows linearly with the number of nearest neighbors, the embedding part shows a weaker dependence, typically of the square root type. Thus, we
Figure 8. Average atomic density perpendicular to the surface F⊥(z) for Pd adsorption on (a) Au(111), (b) Au(100), and (c) Au(110). The curves were obtained from MC simulations, and the arrows denote the curves for increasing coverage degree. The simulation temperature was 300 K. The inset shows the average position of each lattice plane ∆Z in angstroms referred to its value for Θ ) 1. Triangles label the adsorbate and circles the first and squares the second substrate lattice plane, respectively.
see that the minimization of the energy of the system with respect to rnn envisaged as a sum of terms of the type 4 should deliver a larger distance between nearest neighbors for increasing N (that is, for increasing coverage degree). Note that the height of the peaks of g(r|) should not be
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Table 4. Nearest Neighbor Distances in Angstroms between Adsorbate Atoms dθnn at Different Coverage Degrees of Pd on Different Substratesa distance/surface
Pt(111)
Pt(100)
Pt(110)
Au(111)
Au(100)
Au(110)
Pd(111)
Pd(100)
Pd(110)
dΘ)0.25nn dΘ)1nn
2.70 2.78
2.74 2.78
2.78 2.78
2.67 2.89
2.75 2.89
2.79 2.89
2.61 2.76
2.69 2.76
2.72 2.76
a d nn in the case of Θ ) 0.25, only atoms with two neighbors were considered. The nearest neighbor distances between surface substrate Θ atoms are annAu 2.88 Å, annPt 2.77 Å, and annPd 2.75 Å respectively.
used to compare the distribution functions at different coverage degrees, since these are referred to ideal gases with different concentrations. Pd adsorption on the different single-crystal faces of Pt presents a similar behavior. A comparative analysis of the distribution functions for the systems Pd/Au(111), Pd/Pd(111), and Pd/Pt(111) at full coverage denotes a strong similarity between the two latter systems, where the substrates exhibit very similar lattice constants. The expansion effect of the adsorbate with increasing Θ can also be analyzed in terms of the average nearest neighbor distances between Pd adsorbate atoms dnn. Table 4 compiles dnn at different coverage degrees. This quantity is a function of both, the coverage degree and the number of neighbors nnn surrounding the atom considered for the average. With the purpose of comparing extreme cases, we chose on one side dnn for Pd atoms with nnn at Θ ) 0.25 and on the other side nnn ) 6 at Θ ) 1. In agreement with the observation for g(r|), a noticeable increase of dnn with Θ takes place in the case of the (111) face. The effect is more pronounced in the case of Au, which is considerably larger than Pd. Both MC and MD results indicate that at full coverage and for both metallic systems and the three low-index single-crystal faces, the adlayer should grow pseudomorphically, that is, with the same lattice constant as the substrate. Interlayer Spacing Relaxation. According to the chemical intuition concerning bond order conservation, it is expected that the expansion of the adsorbate should be accompanied by some change in the bonding perpendicular to the surface. The average atomic density perpendicular to the surface F⊥ may be employed to analyze this point. This quantity is defined according to
F⊥(z) )
∫AF(x,y,z)dx dy A
where F(x,y,z) is the one particle density and A is the surface area. Figure 8 shows F⊥(z) for different coverage degrees for the Pd/Au(hkl) system. While the F⊥ profile of the second atomic layer of the substrate remains essentially unaltered upon adsorption, changes are evident in the first substrate layer and in the adsorbate. The (111) and the (100) faces present common features. Both the first substrate layer and the adsorbate show an outward relaxation. This effect is stronger for the adsorbate layer, so that the net effect for increasing coverage is a separation of the adsorbate from the first substrate layer. The inset of Figure 8 shows the average position of each of the atomic planes, taking as a reference the position of each plane at Θ ) 1. The increase of Θ implies an increase in the coordination of the surface atoms with the concomitant increase of the bond length in both directions, parallel and perpendicular to the surface. The (110) face behaves differently. Although both the first substrate layer and the adsorbate relax outward, in this case the relaxation of the former is remarkably larger, and the net effect is that the adsorbate becomes closer to the first layer of the substrate with
increasing Θ. This effect can be understood in the following terms. In the case of the (110) face the distance of the adsorbate atoms to the substrate atoms in the first plane is almost equal to the distance from the substrate atoms in the second lattice plane, so that an isolated adsorbate atom is already coordinated to 5 atoms, which is an important number compared with the maximal coordination of 7 at a full monolayer coverage. On the other hand, the coordination number of the substrate atoms in the first layer change from 7 at ΘPd ) 0 to 11 at ΘPd ) 1, which is a rather important change. Furthermore, the adsorption site on this face is located just on top of the nearest neighbor belonging to the second substrate layer, so that the inward relaxation of the adsorbate is also expected to be hindered by the presence of the substrate atoms in the second layer. Similar results were obtained for the Pd/Pt(hkl) system. This type of phenomenon may also be operative in the case of the experimental observation of the outward relaxation of a Rh(110) surface upon hydrogen adsorption22 and other systems, as has been pointed out by Somorjai.23 Conclusions The Pd films grow pseudomorphically with the same lattice constant and crystallographic orientation as the substrate on all substrate types investigated. These facts are in agreement with the experimental data in the literature. The adsorption energy decreases with the coverage degree and converge to a limit which depends on the nature of the substrate. While upd is predicted for the Pd/Pt(hkl) system, the opposite occurs in the case of Pd/Au(hkl). In this respect, we remark that our model does not take into account anion adsorption or electric field effects. A relaxation of the adsorbate layer in the direction perpendicular to the surface is predicted as a function of the coverage degree for the (111) and (100) faces. For the (110) faces, the relaxation should take place for the first lattice plane of the substrate. Acknowledgment. This work was supported by CONICOR (Consejo de Investigaciones Cientı´ficas de la Provincia de Co´rdoba), SECyT (Secretarı´a de Ciencia y Te´cnica de la Universidad Nacional de Co´rdoba), CONICET (Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas, PIP and PEI 86/98), and Program BID 802/OCAR PICT no. 06-04505, Argentina. M. G. Del Po´polo thanks CONICOR for a fellowship. The authors are grateful to the Alexander von Humboldt Foundation for the donation of a Digital workstation. We thank J. Rifkin for useful assistance concerning the use of the XMD simulation program and M. I. Baskes for providing the tables with the potential functions. Language assistance from P. Falcon is also acknowledged. LA990731G (22) Jona, F.; Marcus, P. M. Surface Structures from LEED: Metal Surfaces and Metaestable Phases; Springer Series in Surface Sciences; Vol 11; Van der Veen, J. F., Van Hove, M. A., Eds.; Springer: Berlin, 1988. (23) Somorjai, G. A. Surf. Sci. 1995, 335, 10.
