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Interaction of silver adatoms and dimers with graphite surfaces
Surface Science 541 (2003) 91–100 www.elsevier.com/locate/susc
Interaction of silver adatoms and dimers with graphite surfaces Guan Ming Wang a, Joseph J. BelBruno a
a,*
, Steven D. Kenny b, Roger Smith
b
Center for Nanomaterials Research and Department of Chemistry, Burke Chemical Laboratory, Dartmouth College, Hanover, NH 03755, USA b School of Mathematics and Physics, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK Received 18 December 2002; accepted for publication 6 June 2003
Abstract The energetics and surface relaxation of silver adatoms and dimers and carbon adatoms on graphite are investigated using an ab initio density functional theory description. The energy landscape sketched along [1 1 0] indicates that the sites favored by silver adatoms are near carbon b-sites, but the insignificant energy differences among binding sites means that atomic mobility on the graphite surface is very high. These results are consistent with the available experimental data from scanning tunneling microscopy. The energy difference between binding sites for silver dimers is found to be even smaller than that for adatoms, indicating high surface mobility for dimers as well as atoms. The deformation of graphite surfaces by silver adatoms is small and limited to those adjacent carbon atoms in the top layer. The preferred carbon adatom binding site is over a carbon–carbon bond. Larger surface deformations result from carbon adatoms on the graphite surface. The effect of different variables, such as the number of layers in the slab, supercell size and the size of the basis set, were also examined and these results are included. 2003 Elsevier B.V. All rights reserved. Keywords: Silver; Graphite; Adatoms; Surface energy; Surface relaxation and reconstruction; Density functional calculations; Surface chemical reaction
1. Introduction Increasing interest has been shown in recent years in the study of atom and cluster deposition on surfaces using different techniques under a variety of experimental conditions. This interest is driven by the need to understand phenomena such as fragmentation [1–3] diffusion-limited aggregation [4–6] and self-assembly [7] on substrates. Likewise, an understanding of the interactions between adsorbed particles and the surface is *
Corresponding author. Fax: +1-603-646-3946. E-mail address: [email protected] (J.J. BelBruno).
helpful in the interpretation of STM experiments and the surface deformation accompanying STM. The details of these adsorbate–surface interactions are also essential to the development of nanoscale electronic devices. One of the model systems studied for understanding the basic science involved in the process is that of silver atoms and clusters deposited on graphite [8–13,19]. Graphite is widely used as a substrate due to its unique structure and electronic properties. It is characterized by strong sp2 in-plane bonding and weak van der Waals coupling between atomic planes. Graphite is chemically inert, generally homogeneous and usually free of defects.
0039-6028/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0039-6028(03)00837-9
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The extensive interest in the silver–graphite system, in particular, has been fueled by the available body of experimental results [3,8–12]. Ganz et al. [13,19] observed silver adatoms distributed in small groups of flat islands using STM after evaporation of the metal onto a graphite surface. Although single atoms were rarely observed, they reported single adatoms pinned to the substrate near b-sites, and in addition, determined that the Ag–Ag interaction plays an important role or even dominates the interactions, if the silver atoms are close together on the surface. On the other hand, much less work has been carried out theoretically regarding binding energetics and surface relaxation for the silver–graphite system. Reasons for this relative neglect might include the intensive computational effort required for ab initio calculations and the difficulty in coping with the weak part of the interactions in graphite. Duffy and Blackman [14] employed the Dmol v4.0.0 [15] package of programs and followed a cluster approach with a fixed graphite surface. Their calculations, the only previous computational report involving silver on graphite, located the b-site as the favored binding location for a silver adatom. However, surface contraction [16] is possible in graphite and the adatoms interact with the surface, potentially giving rise to surface reconstruction. This surface relaxation might only affect the lattice geometry slightly, but could significantly change the energy differences among different binding sites [17]. In related computational work, Moullet [18] simulated Al clusters on graphite with a monolayer of carbon atoms and obtained over-bond binding sites as most favored, but found only minor binding energy differences. These conflicting results, albeit for different chemical systems, and the simplifications in the earlier silver adatom study led us to explore the silver graphite system in detail, using a more accurate computational technique and additional layers of graphite. In this paper, we investigate the interactions in the silver–graphite system using the package for linear-combination of atomic type orbitals (PLATO) [20]. This package has been previously applied to the study of atoms and molecules on surfaces [21,22]. PLATO employs a numerical basis of atomic-like functions, which allows the use of
relatively small basis sets and, thus, a high computational efficiency to be obtained. This turns out to be critical to the silver–graphite system. It has been reported [23] that STM tips may induce elastic deformations of a graphite surface. We have included in our calculations starting geometries with initially distorted graphite surfaces and allowed the silver atom and surface to relax from initial points both above the defects and away from the defects. The landscape of the binding energy along [1 1 0], centered around a bsite, on the surface was determined. These results provide information on the ability of the silver atoms to form locally ordered patterns as observed by STM [13] after evaporation. In order to probe the influence of surface effects, carbon adatoms on graphite surfaces were similarly investigated. These results reveal a significantly different response of the graphite surface. The graphite ABAB stacking pattern observed by experiment [16] is used for the initial configuration of the surface. A supercell approach is adopted throughout all calculations with PLATO. This approach is especially convenient for the observation of the Ag–Ag interaction, which emerged most distinctly as the Ag atoms become closer (supercell becomes smaller). In Section 2, PLATO will be explained briefly. Major results and a discussion will be presented in Section 3, and followed by the conclusions in Section 4.
2. Methods The calculations were carried out using the program PLATO. This is a density functional theory code in which the Kohn–Sham eigenvectors are expanded in numeric atomic-like orbitals with a finite range. Electron–ion interactions are represented by the pseudopotentials of Goedecker et al. [24]. The pseudopotentials (and exchange and correlation functional) of Hartwigsen et al. [25] are employed. The integrals for orbital overlap, kinetic energy, one and two center neutral potential terms, non-local pseudopotential and ion–ion interactions are calculated and tabulated prior to use and interpolated during a calculation. The remaining integrals are calculated numerically
G.M. Wang et al. / Surface Science 541 (2003) 91–100
on an atom-centered mesh. Forces are obtained by differentiation of the total energy. The use of finite ranged atomic-like orbitals can yield high quality results with relatively small basis sets, provided that the orbitals are optimized [20]. A modest basis set consisting of double numeric plus polarization is used throughout the calculations. This basis set is constructed from orbitals of the neutral atom and the doubly positively charged atom, supplemented by higher orbital angular momentum orbitals. The orbitals are forced to go to zero at a selected cutoff radius; the equivalent of confining the atom to a square well. In principle, there are three degrees of freedom available to optimize the orbitals; the charges on the ions, the cutoff radius and a smoothing distance. The neutral atoms and the doubly positive ions are always used and the smoothing distance is kept to the minimum value needed to have the orbitals and their derivatives go to zero in a smooth fashion at the cutoff radius. The cutoff radius is chosen so as to optimize the orbitals. This procedure keeps the number of orbitals in the basis set as well as their range to a minimum, while providing a reliable basis set for a wide range of molecular systems. The first trials were made with shorter cutoff radii, 6.0 and 7.0 a.u. for carbon and silver, respectively. Subsequent calculations were significantly improved by extending the cutoff radii to 7.0 a.u. for carbon and 8.0 a.u. for silver.
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Fig. 1. The computational supercell that contains 3 · 3 · 2 primitive cells of graphite with a vacuum above and below. The bottom two atomic layers (darker balls) are fixed and the top two layers (white balls) are allowed to relax. A silver dimer (black balls) stays above the surface.
3.1. PLATO parameters
Similar testing was performed on a graphite slab where the number of layers was also varied. The optimum graphite supercell was found to contain 3 · 3 · 2 primitive cells of graphite with four atomic layers as shown in Fig. 1. There was a vacuum region, with half the thickness of the slab, above and below the graphite. The bottom two layers of carbon atoms were fixed, while the top two layers were allowed to relax to accommodate any relaxations on bonding to the adatoms. There were 72 carbon atoms for calculations with the 3 · 3 in-plane size.
In addition to isolated atoms and dimers, the PLATO package was applied to silver adatoms, carbon adatoms and silver dimers at binding sites on graphite surfaces. Initial studies focused on the optimal supercell size required for the calculations. Equivalent supercells with in-plane sizes of 2 · 2, 3 · 3 and 10 · 10 were tested on silver adatom and dimers, without the graphite surface. The 3 · 3 inplane size was found large enough to decouple the interactions of silver atoms among repeated cells. The binding energy change for a silver atom with 3 · 3 and 10 · 10 in-plane sizes was negligible.
3.1.1. Isolated Ag2 PLATO was applied to both an isolated silver atom and an isolated silver dimer. The bond dis, in tance for a free dimer was obtained as 2.533 A excellent agreement with the experimental value [26] from laser spectroscopy. The Ag2 2.530 A binding energy was calculated to be 2.48 eV, which should be compared with an experimental value of 1.66 eV [27]. However, the LDA has been shown to result in over-binding in small, isolated molecules, so that discrepancies of this magnitude in the isolated dimer energy are to be expected.
3. Results and discussion
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3.1.2. Isolated graphite surface The PLATO package was applied to the fourlayer graphite surface. The first trial was made with the shorter cutoff radii, but the surface contraction, Dd12 , indicates the decrease of the distance d12 between the top and second layers was , a value greater than experifound to be 0.22 A . We believe this discrepancy is due mental, 0.05 A to the fact that the weak van der Waals interaction is difficult to handle with density functional theory methods, especially when coupled with strong covalent in-plane carbon–carbon bonding. This discrepancy is significantly improved by extending the cutoff radii. The value of Dd12 is decreased . Therefore, the longer cutoff from 0.22 to 0.12 A radii were employed for all remaining calculations involving Ag–graphite systems. 3.2. Silver on graphite 3.2.1. Silver adatoms on a relaxed graphite surface Once the graphite surface is relaxed, a silver atom is added above the surface at different binding sites, as shown in Fig. 2, for further relaxation. Results for silver atoms are listed in Table 1. b-sites are preferred for single silver atoms, but the differences in binding energy are not significant. Within experimental error, all of the different types of binding sites are energetically equivalent. These results are consistent with STM observations [19] indicating that single silver atoms are visible near b-sites, but only for a brief observation time. Then, presumably due to the absence of barriers along carbon–carbon bonds, adatoms move until they are stabilized by a large island, a particle, a defect or the edge of the sub-
Fig. 2. A silver atom (black ball) at different binding sites above the graphite surface with only the top two atomic layers drawn. White balls are the top layer and darker balls are the second layer. (a) a-site; (b) b-site; (c) over-bond (OB); and (d) over-hole (OH).
strate. The energy difference between the b-site and the over-hole (OH) site, the least well bound of the binding sites, is only 0.05 eV. The distance between the surface and the second layer, d12 , changes slightly and the closest atom below the silver atom is dragged slightly out of the surface by the binding, as indicated by DhC . This result is consistent with the solution phase alkene chemistry of Agþ . While formation of g2 complexes with benzene is the preferred reaction, the Agþ is free to roam over the entire carbon skeleton [28]. This Agþ –benzene reaction is a simple, but apt model for the chemistry we report here. 3.2.2. Silver adatoms on fixed surfaces The results in the previous section differ from the lone study previously reported in the literature [14]. The order of preference in binding sites, and
Table 1 The interactions between a silver atom and the graphite surface using PLATO with a 3 · 3 · 2 supercell ) ) ) Site EB (eV) hAg (A DhC (A d12 (A Surface a b Over-bond Over-hole
– 0.430 0.439 0.434 0.392
– 2.543 2.539 2.544 2.613
– 0.046 0.050 0.038 0.002
3.223 3.237 3.270 3.204 3.199
Ag charge – 0.026 0.025 0.057 0.073
EB is the binding energy, hAg the height of the silver atom above the average level of the top layer and DhC denotes the height of the closest carbon atom(s) to the binding site above the average level of the surface layer.
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more importantly, the magnitude of the differences in binding energy are at variance. Moreover, the magnitude of the binding energy differences in the earlier study is too large to explain the apparent mobility of the silver atoms in the STM experiment. Contrary to our results, the earlier report also found significant charge on the adatoms. There are three possible causes of error in the earlier calculations: the use of small carbon clusters for the graphite surfaces (and different size clusters for the study of each binding site), the use of fixed surface layers and the nature of the basis set. We have attempted to explore the effect of these parameters on the binding of silver atoms to graphite, since they are of fundamental importance for any study of this type. First, we employed fixed surfaces with the bulk value of the carbon plane distance as in Ref. [14] in order to compare with our relaxed case and with existing data. Results are listed in Table 2. The binding energies and the heights of silver atoms above the surface are not significantly changed compared with our relaxed silver–graphite case. However, the larger distance between the surface and second layers makes the electronic distinction between aand b-sites even less significant. The heights of silver atoms above the surface in the previous work [14], are close to these fixed graphite layer results, the energy differences between binding sites are much greater in the previous work and no close correlation is found in our study between the charge and the binding energy. A fixed graphite surface clearly influences the final results, but does not account for the differences between Ref. [14] and the current work. We conclude that fixed layers of graphite will be acceptable for qualitative adsorption results, but detailed calculations will require that the layers be allowed to relax.
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The calculations in Ref. [14] employed a double numeric basis set, similar in concept to that used in PLATO. However, the cutoff radii for the carbon and silver atoms were significantly shorter than those used in the current work and in addition, the basis set was smaller. We have already shown that the cutoff radii must extend to significantly longer distances in order to satisfactorily account for the isolated graphite surface as well as isolated silver atoms and dimers. This effect, difficult to quantify, should have a significant influence on the final results. 3.2.3. Silver adatoms on a monolayer of graphite To explore the role of the underlayer(s) in the energetics of the silver–graphite system, we relaxed silver adatoms on a 4 · 4 in-plane monolayer of graphite as used by Moullet with Al adatoms [18]. The over-bond, or bridge site, becomes the (marginally) most stable binding site for silver with the energy only 0.002 eV lower than the top sites, equivalent to both a- and b-sites. Again, all sites are energetically equivalent, within experimental error. This result is similar to that observed for aluminum on graphite using an ab initio molecular dynamics approach [18]. It appears that beyond two layers, additional layers of graphite have no significant effect on the surface structure, but play a role in the determination of the binding energy. Our results indicate that, in general, monolayers are not good models for the substrate surface. 3.2.4. Surface defects and atom–atom interactions Terrace steps are known to be preferred aggregation sites for deposited silver atoms, but the effect of surface defects on the binding of silver to graphite is not documented. We examined cases
Table 2 The binding energy EB and the height of the silver atom above the surface calculated using PLATO in comparison with previous work Site a b Over-bond Over-hole
This work
Ref. [14]
EB (eV)
) h (A
EB (eV)
) h (A
0.423 0.425 0.420 0.391
2.570 2.568 2.571 2.614
0.27 0.54 0.23 0.33
2.50 2.46 2.48 2.46
Graphite surfaces are fixed for both sets of results.
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with an initially deformed surface caused by pulling up the carbon atom designated as the . The silver adatom above b-binding site by 0.9 A this site is monotonically driven towards the surface, along with the initially elevated carbon atom, and the system returns to the geometry described above as the b-site case. Other cases shown in Fig. 3 include allowing the silver atom to start from either the over-hole or over-bond sites (near a bsite) and then relax. The silver atom is found to move towards the b-site and its final height above the surface is nearly identical with that reported in Table 1. By combining these data with those for different binding sites described in previous sections above, the energy landscape may be sketched along [1 1 0] for a silver adatom on a graphite surface. This is shown in Fig. 4. Barriers between binding sites have not been directly calculated as might be done in a dynamics calculation. Rather, the silver atom binding energy at various points along the surface has been calculated and plotted. However, any barriers would be expected to be revealed by these DFT calculations along the expected pathway. There appear to be no transition barriers for movement of the atom along the surface. The binding energies around the b-site are asymmetrical. The relatively flat well around the bsite ranging to the over-bond site and finally to the a-site provides considerable freedom for the silver atom to aggregate after deposition. Since a carbon–carbon bond lies between two holes, the bottom of the well is in fact a deep valley, from a three-dimensional perspective. This constrains the silver atom to preferentially move along the bond and motion towards the holes is unlikely. Such
Fig. 3. A silver atom (black ball), initially set away from the most favored b-site, moves towards to the b-site through the relaxation process: faster from (a) the over-hole side than from (b) the over-bond side. White balls are top layer and darker balls are the second layer of graphite. Third and fourth atomic layers are not shown.
Fig. 4. The binding energy of a silver atom on the graphite surface along [1 1 0]. OB is over-bond and OH is over-hole.
Table 3 The binding energy and the height above the surface of silver atom for a 2 · 2 in-plane size ) Site EB (eV) h (A a b Over-bond Over-hole
0.401 0.402 0.399 0.396
2.591 2.584 2.593 2.614
limitations to mobility are the reason silver adatoms are observed on the bond or near b-sites by STM, and that the observed patterns are not all locally ordered. To determine the extent of silver–silver interaction, we performed calculations with a smaller, 2 · 2, in-plane size. Silver atoms may not form a reconstructed lattice while they aggregate in this simulation, however, the results shown in Table 3 indicate that the interactions between silver adatoms due to the periodic boundary conditions play more important roles in the formation of 2-D islands as they become closer. The energy differences decrease rapidly, by one order of magnitude, when the in-plane size shrinks from 3 · 3 to 2 · 2. This increase in the importance of silver–silver interactions is consistent with the stable islands formed with local patterns once those silver atoms aggregate, as observed by STM [13].
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3.2.5. Ag2 on graphite surfaces PLATO has also been applied to silver dimers on graphite surfaces. Results are collected in Table 4 for the possible configurations of dimers shown in Fig. 5. The center of a silver dimer is set initially above the sites listed in the first column. The hole A site means that the dimer is oriented along the diagonal of the hexagon while hole B is almost spanning the two opposite over-bond sites (plots (e) and (f) in Fig. 5). Also, there are two cases for the over-bond site, one perpendicular and the other parallel to the bond as shown by (c) and (d) in Fig. 5. For the a-site case, one silver atom is over a hole and the other is over the b-site that is on the opposite side. A similar situation applies to the b-site case, one silver atom lies over an a-site and the other over a hole. The most favored site is the hole A site, which is in agreement with the adatom case since the two silver atoms lie close to one a- and one b-site each. The dimer binding energy for all sites is approximately 3 eV. This energy includes both the dimer bond energy and the adsorption energy. If the free dimer bond energy, 2.48 eV, is subtracted from this energy, then the surface binding energy per atom is approximately 0.25 eV, less than that for single adatoms. One may also see, from the table, that the maximum energy difference between adjacent sites is even smaller than that for the adatom sites given in Table 1. This implies that the dimers should be at least as mobile over the graphite surface as the adatoms. Experimentally, the observation of dimers was a rare event, which is consistent with a mobile adsorbed species that is almost free to move over the surface and eventually aggregates
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Fig. 5. Typical configurations of silver dimers (black balls) on graphite surfaces over different binding sites. (a) a-site; (b) bsite; (c) over-bond and perpendicular; (d) over-bond and parallel; (e) over-hole and diagonal (hole A); (f) over-hole and spanning opposite bonds (hole B). White balls are top layer and darker balls are the second layer of graphite. Third and fourth atomic layers are not shown.
into the experimentally observed islands. When compared with single adatoms, dimers reside at a higher distance above the surface. The listed height in Table 4 is actually an averaged value for the two atoms. The two atoms of Ag2 are not at the same height if they encounter different surroundings, as they generally do. In Table 4, DhAg2 denotes the height difference that results between the two
Table 4 The interactions between silver dimers and graphite surfaces using PLATO and a 3 · 3 in-plane supercell size with four atomic layers in the supercell ) ) ) ) ) Site EB (eV) h (A dAg (A DhAg (A DhC (A d12 (A 2
Surface a b Bond? Bondk Hole A Hole B b2
– 2.993 2.991 3.003 2.983 3.032 3.023 3.008
– 2.974 2.982 2.967 2.971 2.861 2.870 2.873
– 2.590 2.592 2.593 2.582 2.592 2.596 2.596
2
– 0.099 0.091 0.000 0.002 0.005 0.005 0.000
– )0.01 )0.015 )0.028 )0.014 )0.011 )0.01 )0.017
3.211 3.212 3.228 3.228 3.225 3.237 3.234 3.231
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G.M. Wang et al. / Surface Science 541 (2003) 91–100
Fig. 6. Two atoms of a silver dimer initially above two b-sites are relaxed to a position near to the b-sites. White balls are top layer and darker balls are the second layer of graphite. Third and fourth atomic layers are not shown.
atoms. The parameter dAg2 is the bondlength of the dimer and this does not significantly change among all sites considered. For the graphite surface, the top layer is deformed to some extent, but the second layer of the graphite is seldom disturbed at all. DhC denotes the displacement of those closest carbon atoms below the dimer; negative values mean surface carbon atoms are depressed by the dimers. The last row of Table 4 contains the special case where the two silver atoms are initially placed above two adjacent b-sites. Recall that a b-site is slightly favored by a silver adatom. As expected, the two atoms move nearer to the two b-sites, but are constrained by the Ag–Ag bond distance and move to final positions that are slightly off from both b-sites. This is the case plotted in Fig. 6, one can see similar pictures obtained by STM in Fig. 3(b) of Ref. [19]. 3.3. Carbon on graphite 3.3.1. Carbon adatoms on graphite Surface corrugation induced by STM tips has been reported by several different research groups [13,19,23,29]. This surface deformation has been attributed to many factors: experimental settings such as the STM mode, tunneling current, bias
voltage and the environment (nascent or vacuum) during the scanning. Dirty tips and surfaces, especially in the case of carbon tips, are apparently two of the most important factors resulting in surface corrugation. There is neither experimental data with clean tips and surfaces available for comparison, nor computational results available to test the effect of tip composition on corrugation. We suspected that, due to the obviously greater carbon–carbon interaction, carbon tips could experimentally induce larger corrugations than metallic tips with similar tunneling current and bias voltage, even though the extent of such corrugation remains experimentally uncertain. As a model to indicate whether this hypothesis regarding corrugation was valid, we applied PLATO to carbon adatoms on graphite surfaces. Since the binding energy of carbon adatoms was expected to be higher than that of silver, a shorter cutoff radius of 6.0 a.u. and a 3 · 3 in-plane size with three atomic layers were assumed sufficient to capture the major features of the system and to reduce the cpu times. Results are shown in Table 5. There are significant differences in the binding of carbon and silver adatoms to graphite surfaces. The binding energies are much greater for carbon compared to those for silver atoms; the carbon adatom has a much stronger interaction with the surface than the silver adatom at all sites. This interaction is due to the under-coordination of the carbon adatoms which have some p-character in the dangling bonds. The over-bond site is most favored by carbon adatoms with an energy difference of 1.55 eV with respect to the over-hole site, the least favored. Unlike the case with silver adatoms, this energy difference is much greater than any potential error in the calculations. Carbon adatoms develop a large negative charge compared with the silver adatoms shown in Table 1. In ad-
Table 5 Binding energy and the height of carbon adatoms above a graphite surface ) Site EB (eV) h (A a b Over-bond Over-hole
2.384 2.532 3.448 1.898
1.81 1.73 1.61 1.47
) DhC (A
C charge (e, Mulliken)
0.27 0.22 0.29 0.04
)0.436 )0.466 )0.683 )0.366
G.M. Wang et al. / Surface Science 541 (2003) 91–100
dition, carbon adatoms induce one order of magnitude greater surface distortion than silver atoms, except at the over-hole site. Simulation of carbon adatoms on graphite surfaces with defects was also completed. Results show that carbon adatoms on distorted surfaces (surface atoms elevated above the plane of the surface) relaxed to the corresponding cases with ÔnormalÕ surfaces, indicating that the defects are elastic.
4. Conclusions For the first time, surface relaxation and multiple atomic layers are introduced to density functional theory calculations on silver–graphite systems. In this paper, we report results from extensive calculations involving silver and carbon adatoms and silver dimers on graphite surfaces that were carried out using the PLATO software package. Several important issues regarding related experiments and computer simulations for supported clusters on solid surfaces are successfully addressed. The adatom–surface interactions and surface deformation from silver and carbon adatom calculations are found to be significantly different. The calculations indicate that single silver adatoms have a preference for b-sites, but the energy differences among binding sites are small; experimentally, these adatoms are found near bsites by STMs. The silver atoms remain mobile on the surface as indicated by the insignificant differences in binding energies among the different types of binding sites. The calculations suggest that silver atoms are expected to travel along the carbon– carbon bonds until they are stabilized by a defect or other particles and aggregate. Silver dimers are found to be as mobile as adatoms. A sufficiently large supercell or cluster surface is critical to successful structural modeling. The Ag–Ag interaction is strengthened and the interaction between particles and surfaces is weakened when the size of the supercell is reduced from 3 · 3 · 2 to 2 · 2 · 2. Together with the results for binding energy of the dimers at different sites, these results indicate that the Ag–Ag interactions become important, or even dominant, during aggregations from initially
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evaporated atoms. The methodology demonstrated in this paper may be applied to larger silver clusters on surfaces and to various cluster-surface systems. Acknowledgements The technical assistance of the Kiewit Computation Center at Dartmouth College and the financial assistance of the NATO Division of Scientific and Environmental Affairs through a Collaborative Linkage Grant, PST.CLG.978441, are gratefully acknowledged.
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Interaction of silver adatoms and dimers with graphite surfaces Guan Ming Wang a, Joseph J. BelBruno a
a,*
, Steven D. Kenny b, Roger Smith
b
Center for Nanomaterials Research and Department of Chemistry, Burke Chemical Laboratory, Dartmouth College, Hanover, NH 03755, USA b School of Mathematics and Physics, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK Received 18 December 2002; accepted for publication 6 June 2003
Abstract The energetics and surface relaxation of silver adatoms and dimers and carbon adatoms on graphite are investigated using an ab initio density functional theory description. The energy landscape sketched along [1 1 0] indicates that the sites favored by silver adatoms are near carbon b-sites, but the insignificant energy differences among binding sites means that atomic mobility on the graphite surface is very high. These results are consistent with the available experimental data from scanning tunneling microscopy. The energy difference between binding sites for silver dimers is found to be even smaller than that for adatoms, indicating high surface mobility for dimers as well as atoms. The deformation of graphite surfaces by silver adatoms is small and limited to those adjacent carbon atoms in the top layer. The preferred carbon adatom binding site is over a carbon–carbon bond. Larger surface deformations result from carbon adatoms on the graphite surface. The effect of different variables, such as the number of layers in the slab, supercell size and the size of the basis set, were also examined and these results are included. 2003 Elsevier B.V. All rights reserved. Keywords: Silver; Graphite; Adatoms; Surface energy; Surface relaxation and reconstruction; Density functional calculations; Surface chemical reaction
1. Introduction Increasing interest has been shown in recent years in the study of atom and cluster deposition on surfaces using different techniques under a variety of experimental conditions. This interest is driven by the need to understand phenomena such as fragmentation [1–3] diffusion-limited aggregation [4–6] and self-assembly [7] on substrates. Likewise, an understanding of the interactions between adsorbed particles and the surface is *
Corresponding author. Fax: +1-603-646-3946. E-mail address: [email protected] (J.J. BelBruno).
helpful in the interpretation of STM experiments and the surface deformation accompanying STM. The details of these adsorbate–surface interactions are also essential to the development of nanoscale electronic devices. One of the model systems studied for understanding the basic science involved in the process is that of silver atoms and clusters deposited on graphite [8–13,19]. Graphite is widely used as a substrate due to its unique structure and electronic properties. It is characterized by strong sp2 in-plane bonding and weak van der Waals coupling between atomic planes. Graphite is chemically inert, generally homogeneous and usually free of defects.
0039-6028/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0039-6028(03)00837-9
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The extensive interest in the silver–graphite system, in particular, has been fueled by the available body of experimental results [3,8–12]. Ganz et al. [13,19] observed silver adatoms distributed in small groups of flat islands using STM after evaporation of the metal onto a graphite surface. Although single atoms were rarely observed, they reported single adatoms pinned to the substrate near b-sites, and in addition, determined that the Ag–Ag interaction plays an important role or even dominates the interactions, if the silver atoms are close together on the surface. On the other hand, much less work has been carried out theoretically regarding binding energetics and surface relaxation for the silver–graphite system. Reasons for this relative neglect might include the intensive computational effort required for ab initio calculations and the difficulty in coping with the weak part of the interactions in graphite. Duffy and Blackman [14] employed the Dmol v4.0.0 [15] package of programs and followed a cluster approach with a fixed graphite surface. Their calculations, the only previous computational report involving silver on graphite, located the b-site as the favored binding location for a silver adatom. However, surface contraction [16] is possible in graphite and the adatoms interact with the surface, potentially giving rise to surface reconstruction. This surface relaxation might only affect the lattice geometry slightly, but could significantly change the energy differences among different binding sites [17]. In related computational work, Moullet [18] simulated Al clusters on graphite with a monolayer of carbon atoms and obtained over-bond binding sites as most favored, but found only minor binding energy differences. These conflicting results, albeit for different chemical systems, and the simplifications in the earlier silver adatom study led us to explore the silver graphite system in detail, using a more accurate computational technique and additional layers of graphite. In this paper, we investigate the interactions in the silver–graphite system using the package for linear-combination of atomic type orbitals (PLATO) [20]. This package has been previously applied to the study of atoms and molecules on surfaces [21,22]. PLATO employs a numerical basis of atomic-like functions, which allows the use of
relatively small basis sets and, thus, a high computational efficiency to be obtained. This turns out to be critical to the silver–graphite system. It has been reported [23] that STM tips may induce elastic deformations of a graphite surface. We have included in our calculations starting geometries with initially distorted graphite surfaces and allowed the silver atom and surface to relax from initial points both above the defects and away from the defects. The landscape of the binding energy along [1 1 0], centered around a bsite, on the surface was determined. These results provide information on the ability of the silver atoms to form locally ordered patterns as observed by STM [13] after evaporation. In order to probe the influence of surface effects, carbon adatoms on graphite surfaces were similarly investigated. These results reveal a significantly different response of the graphite surface. The graphite ABAB stacking pattern observed by experiment [16] is used for the initial configuration of the surface. A supercell approach is adopted throughout all calculations with PLATO. This approach is especially convenient for the observation of the Ag–Ag interaction, which emerged most distinctly as the Ag atoms become closer (supercell becomes smaller). In Section 2, PLATO will be explained briefly. Major results and a discussion will be presented in Section 3, and followed by the conclusions in Section 4.
2. Methods The calculations were carried out using the program PLATO. This is a density functional theory code in which the Kohn–Sham eigenvectors are expanded in numeric atomic-like orbitals with a finite range. Electron–ion interactions are represented by the pseudopotentials of Goedecker et al. [24]. The pseudopotentials (and exchange and correlation functional) of Hartwigsen et al. [25] are employed. The integrals for orbital overlap, kinetic energy, one and two center neutral potential terms, non-local pseudopotential and ion–ion interactions are calculated and tabulated prior to use and interpolated during a calculation. The remaining integrals are calculated numerically
G.M. Wang et al. / Surface Science 541 (2003) 91–100
on an atom-centered mesh. Forces are obtained by differentiation of the total energy. The use of finite ranged atomic-like orbitals can yield high quality results with relatively small basis sets, provided that the orbitals are optimized [20]. A modest basis set consisting of double numeric plus polarization is used throughout the calculations. This basis set is constructed from orbitals of the neutral atom and the doubly positively charged atom, supplemented by higher orbital angular momentum orbitals. The orbitals are forced to go to zero at a selected cutoff radius; the equivalent of confining the atom to a square well. In principle, there are three degrees of freedom available to optimize the orbitals; the charges on the ions, the cutoff radius and a smoothing distance. The neutral atoms and the doubly positive ions are always used and the smoothing distance is kept to the minimum value needed to have the orbitals and their derivatives go to zero in a smooth fashion at the cutoff radius. The cutoff radius is chosen so as to optimize the orbitals. This procedure keeps the number of orbitals in the basis set as well as their range to a minimum, while providing a reliable basis set for a wide range of molecular systems. The first trials were made with shorter cutoff radii, 6.0 and 7.0 a.u. for carbon and silver, respectively. Subsequent calculations were significantly improved by extending the cutoff radii to 7.0 a.u. for carbon and 8.0 a.u. for silver.
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Fig. 1. The computational supercell that contains 3 · 3 · 2 primitive cells of graphite with a vacuum above and below. The bottom two atomic layers (darker balls) are fixed and the top two layers (white balls) are allowed to relax. A silver dimer (black balls) stays above the surface.
3.1. PLATO parameters
Similar testing was performed on a graphite slab where the number of layers was also varied. The optimum graphite supercell was found to contain 3 · 3 · 2 primitive cells of graphite with four atomic layers as shown in Fig. 1. There was a vacuum region, with half the thickness of the slab, above and below the graphite. The bottom two layers of carbon atoms were fixed, while the top two layers were allowed to relax to accommodate any relaxations on bonding to the adatoms. There were 72 carbon atoms for calculations with the 3 · 3 in-plane size.
In addition to isolated atoms and dimers, the PLATO package was applied to silver adatoms, carbon adatoms and silver dimers at binding sites on graphite surfaces. Initial studies focused on the optimal supercell size required for the calculations. Equivalent supercells with in-plane sizes of 2 · 2, 3 · 3 and 10 · 10 were tested on silver adatom and dimers, without the graphite surface. The 3 · 3 inplane size was found large enough to decouple the interactions of silver atoms among repeated cells. The binding energy change for a silver atom with 3 · 3 and 10 · 10 in-plane sizes was negligible.
3.1.1. Isolated Ag2 PLATO was applied to both an isolated silver atom and an isolated silver dimer. The bond dis, in tance for a free dimer was obtained as 2.533 A excellent agreement with the experimental value [26] from laser spectroscopy. The Ag2 2.530 A binding energy was calculated to be 2.48 eV, which should be compared with an experimental value of 1.66 eV [27]. However, the LDA has been shown to result in over-binding in small, isolated molecules, so that discrepancies of this magnitude in the isolated dimer energy are to be expected.
3. Results and discussion
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3.1.2. Isolated graphite surface The PLATO package was applied to the fourlayer graphite surface. The first trial was made with the shorter cutoff radii, but the surface contraction, Dd12 , indicates the decrease of the distance d12 between the top and second layers was , a value greater than experifound to be 0.22 A . We believe this discrepancy is due mental, 0.05 A to the fact that the weak van der Waals interaction is difficult to handle with density functional theory methods, especially when coupled with strong covalent in-plane carbon–carbon bonding. This discrepancy is significantly improved by extending the cutoff radii. The value of Dd12 is decreased . Therefore, the longer cutoff from 0.22 to 0.12 A radii were employed for all remaining calculations involving Ag–graphite systems. 3.2. Silver on graphite 3.2.1. Silver adatoms on a relaxed graphite surface Once the graphite surface is relaxed, a silver atom is added above the surface at different binding sites, as shown in Fig. 2, for further relaxation. Results for silver atoms are listed in Table 1. b-sites are preferred for single silver atoms, but the differences in binding energy are not significant. Within experimental error, all of the different types of binding sites are energetically equivalent. These results are consistent with STM observations [19] indicating that single silver atoms are visible near b-sites, but only for a brief observation time. Then, presumably due to the absence of barriers along carbon–carbon bonds, adatoms move until they are stabilized by a large island, a particle, a defect or the edge of the sub-
Fig. 2. A silver atom (black ball) at different binding sites above the graphite surface with only the top two atomic layers drawn. White balls are the top layer and darker balls are the second layer. (a) a-site; (b) b-site; (c) over-bond (OB); and (d) over-hole (OH).
strate. The energy difference between the b-site and the over-hole (OH) site, the least well bound of the binding sites, is only 0.05 eV. The distance between the surface and the second layer, d12 , changes slightly and the closest atom below the silver atom is dragged slightly out of the surface by the binding, as indicated by DhC . This result is consistent with the solution phase alkene chemistry of Agþ . While formation of g2 complexes with benzene is the preferred reaction, the Agþ is free to roam over the entire carbon skeleton [28]. This Agþ –benzene reaction is a simple, but apt model for the chemistry we report here. 3.2.2. Silver adatoms on fixed surfaces The results in the previous section differ from the lone study previously reported in the literature [14]. The order of preference in binding sites, and
Table 1 The interactions between a silver atom and the graphite surface using PLATO with a 3 · 3 · 2 supercell ) ) ) Site EB (eV) hAg (A DhC (A d12 (A Surface a b Over-bond Over-hole
– 0.430 0.439 0.434 0.392
– 2.543 2.539 2.544 2.613
– 0.046 0.050 0.038 0.002
3.223 3.237 3.270 3.204 3.199
Ag charge – 0.026 0.025 0.057 0.073
EB is the binding energy, hAg the height of the silver atom above the average level of the top layer and DhC denotes the height of the closest carbon atom(s) to the binding site above the average level of the surface layer.
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more importantly, the magnitude of the differences in binding energy are at variance. Moreover, the magnitude of the binding energy differences in the earlier study is too large to explain the apparent mobility of the silver atoms in the STM experiment. Contrary to our results, the earlier report also found significant charge on the adatoms. There are three possible causes of error in the earlier calculations: the use of small carbon clusters for the graphite surfaces (and different size clusters for the study of each binding site), the use of fixed surface layers and the nature of the basis set. We have attempted to explore the effect of these parameters on the binding of silver atoms to graphite, since they are of fundamental importance for any study of this type. First, we employed fixed surfaces with the bulk value of the carbon plane distance as in Ref. [14] in order to compare with our relaxed case and with existing data. Results are listed in Table 2. The binding energies and the heights of silver atoms above the surface are not significantly changed compared with our relaxed silver–graphite case. However, the larger distance between the surface and second layers makes the electronic distinction between aand b-sites even less significant. The heights of silver atoms above the surface in the previous work [14], are close to these fixed graphite layer results, the energy differences between binding sites are much greater in the previous work and no close correlation is found in our study between the charge and the binding energy. A fixed graphite surface clearly influences the final results, but does not account for the differences between Ref. [14] and the current work. We conclude that fixed layers of graphite will be acceptable for qualitative adsorption results, but detailed calculations will require that the layers be allowed to relax.
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The calculations in Ref. [14] employed a double numeric basis set, similar in concept to that used in PLATO. However, the cutoff radii for the carbon and silver atoms were significantly shorter than those used in the current work and in addition, the basis set was smaller. We have already shown that the cutoff radii must extend to significantly longer distances in order to satisfactorily account for the isolated graphite surface as well as isolated silver atoms and dimers. This effect, difficult to quantify, should have a significant influence on the final results. 3.2.3. Silver adatoms on a monolayer of graphite To explore the role of the underlayer(s) in the energetics of the silver–graphite system, we relaxed silver adatoms on a 4 · 4 in-plane monolayer of graphite as used by Moullet with Al adatoms [18]. The over-bond, or bridge site, becomes the (marginally) most stable binding site for silver with the energy only 0.002 eV lower than the top sites, equivalent to both a- and b-sites. Again, all sites are energetically equivalent, within experimental error. This result is similar to that observed for aluminum on graphite using an ab initio molecular dynamics approach [18]. It appears that beyond two layers, additional layers of graphite have no significant effect on the surface structure, but play a role in the determination of the binding energy. Our results indicate that, in general, monolayers are not good models for the substrate surface. 3.2.4. Surface defects and atom–atom interactions Terrace steps are known to be preferred aggregation sites for deposited silver atoms, but the effect of surface defects on the binding of silver to graphite is not documented. We examined cases
Table 2 The binding energy EB and the height of the silver atom above the surface calculated using PLATO in comparison with previous work Site a b Over-bond Over-hole
This work
Ref. [14]
EB (eV)
) h (A
EB (eV)
) h (A
0.423 0.425 0.420 0.391
2.570 2.568 2.571 2.614
0.27 0.54 0.23 0.33
2.50 2.46 2.48 2.46
Graphite surfaces are fixed for both sets of results.
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with an initially deformed surface caused by pulling up the carbon atom designated as the . The silver adatom above b-binding site by 0.9 A this site is monotonically driven towards the surface, along with the initially elevated carbon atom, and the system returns to the geometry described above as the b-site case. Other cases shown in Fig. 3 include allowing the silver atom to start from either the over-hole or over-bond sites (near a bsite) and then relax. The silver atom is found to move towards the b-site and its final height above the surface is nearly identical with that reported in Table 1. By combining these data with those for different binding sites described in previous sections above, the energy landscape may be sketched along [1 1 0] for a silver adatom on a graphite surface. This is shown in Fig. 4. Barriers between binding sites have not been directly calculated as might be done in a dynamics calculation. Rather, the silver atom binding energy at various points along the surface has been calculated and plotted. However, any barriers would be expected to be revealed by these DFT calculations along the expected pathway. There appear to be no transition barriers for movement of the atom along the surface. The binding energies around the b-site are asymmetrical. The relatively flat well around the bsite ranging to the over-bond site and finally to the a-site provides considerable freedom for the silver atom to aggregate after deposition. Since a carbon–carbon bond lies between two holes, the bottom of the well is in fact a deep valley, from a three-dimensional perspective. This constrains the silver atom to preferentially move along the bond and motion towards the holes is unlikely. Such
Fig. 3. A silver atom (black ball), initially set away from the most favored b-site, moves towards to the b-site through the relaxation process: faster from (a) the over-hole side than from (b) the over-bond side. White balls are top layer and darker balls are the second layer of graphite. Third and fourth atomic layers are not shown.
Fig. 4. The binding energy of a silver atom on the graphite surface along [1 1 0]. OB is over-bond and OH is over-hole.
Table 3 The binding energy and the height above the surface of silver atom for a 2 · 2 in-plane size ) Site EB (eV) h (A a b Over-bond Over-hole
0.401 0.402 0.399 0.396
2.591 2.584 2.593 2.614
limitations to mobility are the reason silver adatoms are observed on the bond or near b-sites by STM, and that the observed patterns are not all locally ordered. To determine the extent of silver–silver interaction, we performed calculations with a smaller, 2 · 2, in-plane size. Silver atoms may not form a reconstructed lattice while they aggregate in this simulation, however, the results shown in Table 3 indicate that the interactions between silver adatoms due to the periodic boundary conditions play more important roles in the formation of 2-D islands as they become closer. The energy differences decrease rapidly, by one order of magnitude, when the in-plane size shrinks from 3 · 3 to 2 · 2. This increase in the importance of silver–silver interactions is consistent with the stable islands formed with local patterns once those silver atoms aggregate, as observed by STM [13].
G.M. Wang et al. / Surface Science 541 (2003) 91–100
3.2.5. Ag2 on graphite surfaces PLATO has also been applied to silver dimers on graphite surfaces. Results are collected in Table 4 for the possible configurations of dimers shown in Fig. 5. The center of a silver dimer is set initially above the sites listed in the first column. The hole A site means that the dimer is oriented along the diagonal of the hexagon while hole B is almost spanning the two opposite over-bond sites (plots (e) and (f) in Fig. 5). Also, there are two cases for the over-bond site, one perpendicular and the other parallel to the bond as shown by (c) and (d) in Fig. 5. For the a-site case, one silver atom is over a hole and the other is over the b-site that is on the opposite side. A similar situation applies to the b-site case, one silver atom lies over an a-site and the other over a hole. The most favored site is the hole A site, which is in agreement with the adatom case since the two silver atoms lie close to one a- and one b-site each. The dimer binding energy for all sites is approximately 3 eV. This energy includes both the dimer bond energy and the adsorption energy. If the free dimer bond energy, 2.48 eV, is subtracted from this energy, then the surface binding energy per atom is approximately 0.25 eV, less than that for single adatoms. One may also see, from the table, that the maximum energy difference between adjacent sites is even smaller than that for the adatom sites given in Table 1. This implies that the dimers should be at least as mobile over the graphite surface as the adatoms. Experimentally, the observation of dimers was a rare event, which is consistent with a mobile adsorbed species that is almost free to move over the surface and eventually aggregates
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Fig. 5. Typical configurations of silver dimers (black balls) on graphite surfaces over different binding sites. (a) a-site; (b) bsite; (c) over-bond and perpendicular; (d) over-bond and parallel; (e) over-hole and diagonal (hole A); (f) over-hole and spanning opposite bonds (hole B). White balls are top layer and darker balls are the second layer of graphite. Third and fourth atomic layers are not shown.
into the experimentally observed islands. When compared with single adatoms, dimers reside at a higher distance above the surface. The listed height in Table 4 is actually an averaged value for the two atoms. The two atoms of Ag2 are not at the same height if they encounter different surroundings, as they generally do. In Table 4, DhAg2 denotes the height difference that results between the two
Table 4 The interactions between silver dimers and graphite surfaces using PLATO and a 3 · 3 in-plane supercell size with four atomic layers in the supercell ) ) ) ) ) Site EB (eV) h (A dAg (A DhAg (A DhC (A d12 (A 2
Surface a b Bond? Bondk Hole A Hole B b2
– 2.993 2.991 3.003 2.983 3.032 3.023 3.008
– 2.974 2.982 2.967 2.971 2.861 2.870 2.873
– 2.590 2.592 2.593 2.582 2.592 2.596 2.596
2
– 0.099 0.091 0.000 0.002 0.005 0.005 0.000
– )0.01 )0.015 )0.028 )0.014 )0.011 )0.01 )0.017
3.211 3.212 3.228 3.228 3.225 3.237 3.234 3.231
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G.M. Wang et al. / Surface Science 541 (2003) 91–100
Fig. 6. Two atoms of a silver dimer initially above two b-sites are relaxed to a position near to the b-sites. White balls are top layer and darker balls are the second layer of graphite. Third and fourth atomic layers are not shown.
atoms. The parameter dAg2 is the bondlength of the dimer and this does not significantly change among all sites considered. For the graphite surface, the top layer is deformed to some extent, but the second layer of the graphite is seldom disturbed at all. DhC denotes the displacement of those closest carbon atoms below the dimer; negative values mean surface carbon atoms are depressed by the dimers. The last row of Table 4 contains the special case where the two silver atoms are initially placed above two adjacent b-sites. Recall that a b-site is slightly favored by a silver adatom. As expected, the two atoms move nearer to the two b-sites, but are constrained by the Ag–Ag bond distance and move to final positions that are slightly off from both b-sites. This is the case plotted in Fig. 6, one can see similar pictures obtained by STM in Fig. 3(b) of Ref. [19]. 3.3. Carbon on graphite 3.3.1. Carbon adatoms on graphite Surface corrugation induced by STM tips has been reported by several different research groups [13,19,23,29]. This surface deformation has been attributed to many factors: experimental settings such as the STM mode, tunneling current, bias
voltage and the environment (nascent or vacuum) during the scanning. Dirty tips and surfaces, especially in the case of carbon tips, are apparently two of the most important factors resulting in surface corrugation. There is neither experimental data with clean tips and surfaces available for comparison, nor computational results available to test the effect of tip composition on corrugation. We suspected that, due to the obviously greater carbon–carbon interaction, carbon tips could experimentally induce larger corrugations than metallic tips with similar tunneling current and bias voltage, even though the extent of such corrugation remains experimentally uncertain. As a model to indicate whether this hypothesis regarding corrugation was valid, we applied PLATO to carbon adatoms on graphite surfaces. Since the binding energy of carbon adatoms was expected to be higher than that of silver, a shorter cutoff radius of 6.0 a.u. and a 3 · 3 in-plane size with three atomic layers were assumed sufficient to capture the major features of the system and to reduce the cpu times. Results are shown in Table 5. There are significant differences in the binding of carbon and silver adatoms to graphite surfaces. The binding energies are much greater for carbon compared to those for silver atoms; the carbon adatom has a much stronger interaction with the surface than the silver adatom at all sites. This interaction is due to the under-coordination of the carbon adatoms which have some p-character in the dangling bonds. The over-bond site is most favored by carbon adatoms with an energy difference of 1.55 eV with respect to the over-hole site, the least favored. Unlike the case with silver adatoms, this energy difference is much greater than any potential error in the calculations. Carbon adatoms develop a large negative charge compared with the silver adatoms shown in Table 1. In ad-
Table 5 Binding energy and the height of carbon adatoms above a graphite surface ) Site EB (eV) h (A a b Over-bond Over-hole
2.384 2.532 3.448 1.898
1.81 1.73 1.61 1.47
) DhC (A
C charge (e, Mulliken)
0.27 0.22 0.29 0.04
)0.436 )0.466 )0.683 )0.366
G.M. Wang et al. / Surface Science 541 (2003) 91–100
dition, carbon adatoms induce one order of magnitude greater surface distortion than silver atoms, except at the over-hole site. Simulation of carbon adatoms on graphite surfaces with defects was also completed. Results show that carbon adatoms on distorted surfaces (surface atoms elevated above the plane of the surface) relaxed to the corresponding cases with ÔnormalÕ surfaces, indicating that the defects are elastic.
4. Conclusions For the first time, surface relaxation and multiple atomic layers are introduced to density functional theory calculations on silver–graphite systems. In this paper, we report results from extensive calculations involving silver and carbon adatoms and silver dimers on graphite surfaces that were carried out using the PLATO software package. Several important issues regarding related experiments and computer simulations for supported clusters on solid surfaces are successfully addressed. The adatom–surface interactions and surface deformation from silver and carbon adatom calculations are found to be significantly different. The calculations indicate that single silver adatoms have a preference for b-sites, but the energy differences among binding sites are small; experimentally, these adatoms are found near bsites by STMs. The silver atoms remain mobile on the surface as indicated by the insignificant differences in binding energies among the different types of binding sites. The calculations suggest that silver atoms are expected to travel along the carbon– carbon bonds until they are stabilized by a defect or other particles and aggregate. Silver dimers are found to be as mobile as adatoms. A sufficiently large supercell or cluster surface is critical to successful structural modeling. The Ag–Ag interaction is strengthened and the interaction between particles and surfaces is weakened when the size of the supercell is reduced from 3 · 3 · 2 to 2 · 2 · 2. Together with the results for binding energy of the dimers at different sites, these results indicate that the Ag–Ag interactions become important, or even dominant, during aggregations from initially
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evaporated atoms. The methodology demonstrated in this paper may be applied to larger silver clusters on surfaces and to various cluster-surface systems. Acknowledgements The technical assistance of the Kiewit Computation Center at Dartmouth College and the financial assistance of the NATO Division of Scientific and Environmental Affairs through a Collaborative Linkage Grant, PST.CLG.978441, are gratefully acknowledged.
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