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On the Stability of Ag/Au(111) Expanded Structures C. G. Sa´nchez* Atomistic Simulation Group, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, United Kingdom
S. A. Dassie and E. P. M. Leiva Universidad Nacional de Co´ rdoba, Facultad de Ciencias Quı´micas, Unidad de Matema´ tica y Fı´sica, INFIQC, 5000 Co´ rdoba, Argentina Received April 2, 2002. In Final Form: June 7, 2002 In this work, we present a series of first-principles calculations on the stability of expanded silver monolayers adsorbed on a gold (111) substrate. The main result obtained is that none of the structures that are more expanded than the (1 × 1) compact monolayer is more stable than the bulk silver phase and hence should not be underpotentially deposited. A possible explanation for the discrepancy between experimental and theoretical results may lie in the strong work function shift generated by the adsorbate. This may produce large electric fields at the interface, modifying the binding energy and promoting anion adsorption through a negative shift in the potential of zero charge.
1. Introduction Underpotentially deposited Ag on Au(111) expanded structures has been the subject of numerous electrochemical studies. In situ techniques such as atomic force microscopy,1 scanning tunneling microscopy,2-4 lowenergy electron diffraction,5 and others (for a review see ref 8) have allowed the study of a wide range of structures. All these studies report the existence of a compact p(1 × 1) structure at potentials very close to the bulk silver deposition and a series of more open structures at higher potentials up to 0.60 V more positive than the bulk deposition. These superlattice structures that are commensurate with the substrate but present overlayer structures larger than the (1 × 1) one will be addressed as expanded structures.9 The purpose of this work is to study the stability of these expanded monolayers from a theoretical point of view and to shed light on the physical reasons for their stability. The existence of expanded structures is sometimes ascribed to repulsive interactions between adsorbate atoms. In the case of two interacting particles, the term repulsive or attractive can be easily defined in terms of the forces (or minus the gradient of the potential energy) acting between them, and these forces deliver a direct criterion for the relative mechanical stability of two different configurations of the system. In the present case, however, we are dealing with a different criterion of stability, the thermodynamic one, which will be formulated below in terms of differences of the binding energies. (1) Chen, C.; Vesecky, S. M.; Gewirth, A. J. Am. Chem. Soc. 1992, 114, 451. (2) Ogaki, K.; Itaya, K. Electrochim. Acta 1995, 40, 1249. (3) Garcia, S.; Salinas, D.; Mayer, C.; Schmidt, E.; Staikov, G.; Lorenz, W. Electrochim. Acta 1998, 43, 3007. (4) Esplandiu, M. J.; Schneeweiss, M. A.; Kolb, M. A. Phys. Chem. Chem. Phys. 1999, 1, 4847. (5) Mrozek, P.; Sung, Y. E.; Wieckowski, A. Surf. Sci. 1995, 335, 44. (6) Venables, J. S. Introduction to Surface and Thin Film Processes; Cambridge University Press: Cambridge, 2000. (7) Neugebauer, J.; Scheffler, M. Phys. Rev. B 1992, 46, 16067. (8) Herrero, E.; Buller, L. J.; Abrun˜a, H. D. Chem. Rev. 2001, 101, 1897. (9) Budevski, E.; Staikov, G.; Lorenz, W. J. Electrochemical Phase Formation and Growth; VCH: Weinheim, 1996.
Furthermore, the many-body properties of the metallic binding make a separate discussion of adsorbatesubstrate and adsorbate-adsorbate interactions considerably difficult.10 In the present case, we shall rather use the term repulsive(attractive) in the sense that the binding energy of the adatoms to the surface increases (decreases) when the coverage degree by adatoms increases. Thus, when a decrease in the average distance between neighboring adsorbate atoms is accompanied by an increase in the binding energy we shall be speaking of repulsive interactions, and vice versa. This definition is coherent with the electrochemical jargon, where the species occurring at higher potentials are ascribed to be more stable. With this convention, repulsive interactions cannot stabilize a structure and the only way in which expanded structures can be more stable than the (1 × 1) one is that they present a more negative binding energy. We shall see below that for the present system this is not the case. 2. Model and Calculation Method Underpotential deposition (UPD) involves the electrosorption of metal ions on foreign substrates at potentials more positive than the reversible Nernst deposition potential of the adsorbate. Underpotentially deposited phases are more stable than the bulk phase of the adsorbate. A measure of this relative stability is given by the so-called underpotential shift ∆φupd originally defined by Kolb et al.11 as
∆φupd )
1 (µ[(M)M] - µ[(S)Mθ]) ze0
(1)
where µ[(M)M] is the chemical potential of the adsorbate in the bulk phase and µ[(S)Mθ] is the chemical potential of the adsorbate adsorbed over S at a coverage degree θ. The underpotential shift is available from experiment as the potential difference between the adsorption and bulk deposition peaks in a cyclic voltammogram. (10) Stampfl, C.; Neugebauer, J.; Scheffler, M. Surf. Sci. 1994, 307, 8. (11) Kolb, D. M.; Przasnyski, M.; Gerischer, H. J. Electroanal. Chem. 1974, 54, 25.
10.1021/la020312a CCC: $22.00 © 2002 American Chemical Society Published on Web 07/24/2002
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Table 1. Comparison between Theoretical Predictions (th) and Experimental Results (exp) for the Lattice Constant (a), Bulk Modulus (B), and Surface Energies of the (111) Face (σ) for the Metals Considered in This Worka metal ath/Å aexp/Å Bth/Mbar Bexp/Mbar σth/J m-2 σexp/J m-2 Ag Au a
4.04 4.06
4.09 4.08
1.30 2.17
1.04 1.67
1.39 1.54
1.25 1.52
Experimental values were taken from ref 20.
To explain the stability of expanded structures, we need a model that allows us to calculate the underpotential shift as a function of the coverage degree for several adsorbed structures. The first approximation in our model is to neglect entropic contributions to ∆φupd and attempt to calculate it at 0 K:
∆φupdT)0
1 ) [U bulk - UM/Sads(θ)] ze0 M
(2)
bulk
is the cohesive energy of the bulk adsorbate where UM and UM/Sads(θ) is its adsorption energy on the substrate as a function of the coverage degree. Under these conditions, ∆φupd is reduced to a purely energetic quantity. UM/Sads(θ) is a particularly complex magnitude since it contains contributions coming from adsorbed molecules at the interface, double-layer charging, and possibly also the influence of specific adsorbing ions. We may simplify all this by dividing UM/Sads(θ) into two parts, one that comes from the bond formed between the substrate and the adsorbate and the other that represents the change in the structure of nonmetallic species present at the interface before and after adsorption (e.g., species that adsorb on the monolayer but not on the substrate). The contribution of this last part to the underpotential shift may be considered to be small if the charge of the surface does not change appreciably between the clean and metallic adsorbate covered states. The change in surface charge is difficult to estimate a priori, but we will further elaborate on this point later. To calculate the energy difference in eq 2, we take a first-principles approach. The method used has been described in detail elsewhere.12 We use the local density approximation (LDA) of density functional theory as implemented in the code SIESTA.18,19 This program uses a numerical localized basis set to represent the KohnSham orbitals and nonlocal norm conserving pseudopotentials to avoid dealing with core electrons. The basis set used for the calculations presented here was of double-ζ plus polarization (DZP) quality; all the parameters used and the validation tests performed are described in detail in ref 12. Results for the properties of bulk Ag and Au obtained from this model are shown in Table 1. The agreement between calculated and experimental values is good and in the range expected for LDA. For the study of substrate-adsorbate systems, we use a supercell approach where the substrate is represented by a slab of 5 (111) layers of gold atoms and a metal layer, representing the adsorbate, is placed on both sides of the slab. The amount of vacuum between periodic images of the slab (7 (111) layers) and the thickness of the slab representing the substrate are appropriate according to our previous studies.12-14 The position of adsorbate atoms within the surface unit cell was relaxed for all the studied (12) Sa´nchez, C. G.; Kohanoff, J. J.; Leiva, E. P. M. Langmuir 2001, 17, 219. (13) Sa´nchez, C. G.; Leiva, E. P. M. J. Electroanal. Chem. 1998, 458, 183. (14) Sa´nchez, C. G.; Leiva, E. P. M. Electrochim. Acta 1999, 45, 691.
Figure 1. ∆φupdT)0K as a function of the coverage degree for different expanded structures of Ag adsorbed on Au(111). Table 2. Coverage Degree (θ), Underpotential Shift (∆OupdT)0K), Change in Work Function Produced by the Adsorbate (∆Φ), and Equilibrium Distance between the Adsorbed Layer and the Substrate in Units of the Substrate’s (111) Interlayer Distance (dAgAu/dAu111) structure
q
∆φupdT)0K/V
∆Φ/eV
dAgAu/dAu111
p(1 × 1) (3 × 3) p(x3 × x3 )R30° p(2 × 2) p(3 × 3) p(4 × 4)
1.00 0.44 0.33 0.25 0.11 0.07
+0.03 -0.73 -1.04 -1.09 -0.99 -1.30
-0.35 -1.39 -1.21 -1.05 -0.64 -0.49
0.98 0.90 0.89 0.89 0.88 0.88
expanded structures by first performing an exhaustive search over a grid of adsorbate positions and then relaxing the lowest energy geometries by means of conjugate gradients. 3. Results and Discussion The results obtained for ∆φupdT)0K for the most stable structures found at each coverage are presented in Figure 1 and Table 2. Results were obtained for six expanded structures that present coincidence cells with the substrate p(1 × 1), (3 × 3), p(x3 × x3)R30°, p(2 × 2), p(3 × 3), and p(4 × 4). The convergence with respect to the k-point sampling over the (nearly) two-dimensional Brillouin zone of the supercell is better than 0.08 eV for the p(1 × 1) and (3 × 3) structures and better than 0.03 eV for the remaining ones. From the values obtained for the underpotential shift, it is clear that the only structure that may present UPD is the p(1 × 1); all other structures more expanded than the compact monolayer are unstable with respect to the bulk metal and should not present UPD in terms of a simple energetic analysis. The underpotential shift is not a monotonic function of the coverage degree but presents an arrest for coverages close to 1/5. From the viewpoint of the effective interaction defined in the Introduction, we can conclude from Figure 1 that it is strongly attractive at high coverage degrees, being slightly repulsive or neutral in the region 0.125 < θ < 0.33. It could be expected that the adatom-adatom interaction should become repulsive in the limit of very low coverage degrees, because in this region charge transfer from the adsorbate to the substrate should become maximal. This limit, however, cannot be reached with the present calculation procedure and computer capabilities. Moreover, the long-range interaction between adatoms on metallic surfaces has been found to be oscillatory, with a period of half the Fermi wavelength, with identification of several minima and
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maxima up to distances as large as 70 Å.15 In the field of density functional calculations, nonmonotonic behavior of the pair interaction between adatoms has been observed by Fichthorn for adsorption of Ag on Ag(111) strained and unstrained surfaces.16,17 The distance between the monolayer and the substrate in terms of the interlayer distance of the substrate is also shown in Table 2. This distance decreases monotonically with the decrease in coverage. This relaxation is expected, since the effective coordination of the adsorbate is lower for the more expanded structures, a fact that is compensated by decreasing the distance to the substrate. Since the work function is an experimental magnitude often used to characterize the UPD phenomenon from a phenomenological point of view, the changes in work function upon adsorption were calculated for all the systems considered. The work function of a metallic surface can be expressed as
Φ ) χ - f
(3)
where f is the Fermi level and χ is the surface dipole that can be calculated from the surface charge density by integration of the Poisson equation. We may assume that the Fermi level remains the same after adsorption since it is a bulk property and should not be affected by changes in the surface. This is not exactly true for our calculation in which the metal is represented as a finite slab, but since we are interested in an estimation of the changes in work function this assumption should not affect our results. Thus, changes in the work function upon adsorption can be ascribed purely to the change in surface dipole. This change in surface dipole can be calculated from the corresponding change in the electronic density profile across the surface. We define the planeaveraged electronic density of the system as
n(z) )
∫∫n(x, y, z) dx dy ∫∫dx dy
(4)
where z is the axis perpendicular to the surface and the integral is carried out over the area of the surface unit cell. The change in electronic density or differential density is defined as
δn(z) ) n(z)M/S - n(z)S - n(z)M
(5)
where n(z)M/S is the electronic density for the metalsubstrate system, n(z)S is that for the clean substrate, and n(z)M is that for the adsorbate monolayer isolated in a vacuum. On account of the above, the change in surface dipole can be calculated from the dipole moment of δn(z), since n(z)M is symmetric in z and thus has no dipole moment. This dipole moment can be directly calculated from the electrostatic potential generated by the change in elec(15) Repp, J.; Moresco, F.; Meyer, G.; Rieder, K.-H. Phys. Rev. Lett. 2000, 85, 2981. (16) Fichthorn, K. A.; Scheffler, M. Phys. Rev. Lett. 2000, 84, 5371. (17) Fichthorn, K. A.; Scheffler, M. In Collective Diffusion on Surfaces: Collective Behaviour and the Role of Adatom Interactions; Tringides, M. C., Chvoj, Z., Eds.; Kluwer: Dordrecht, The Netherlands, 2001; p 225. (18) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcı´a, A.; Junquera, J.; Ordejo´n, P.; Sa´nchez-Portal, D. http://www.arXiv.org/abs/cond-mat/ 0111138, 8 Nov 2001. (19) http://www.uam.es/departamentos/ciencias/fismateriac/siesta/
tronic density by integration of the corresponding Poisson equation. We thus have the equality
∆Φ ) ∆χ )
∫ab δn(z)(a - z) dz
(6)
where a and b are points well inside and outside the metal, respectively. The averaged electronic densities, differential densities, and electrostatic potential generated by the differential density are plotted in Figure 2a,b for the p(1 × 1) and p(2 × 2) structures. Differential density profiles are useful to analyze the charge rearrangement produced at the interface upon adsorption. Note that the absolute values of the redistributed charge are very small, in general 2 orders of magnitude lower than the valence electronic density values. However, the effects that this small charge rearrangement has on the electrostatic potential difference across the interface are very important. For the p(1 × 1) structure, the differential density induces a positive electrostatic potential (relative to vacuum) in the region that goes from the first substrate layer to the vacuum. This is related to an induced positive charge density in front of the adsorbate. On the other hand, the changes in the electrostatic potential are negative inside the substrate. This must be contrasted with the behavior of the changes in the electrostatic potential for all the other structures, which are always negative (as can be seen in Figure 2b for the p(2 × 2) structure). The values for the change in work function calculated for all the structures are shown in Table 2 and plotted in Figure 3. Similar to the observation for the UPD shift, the work function change is not a monotonic function of the coverage degree, and it attains a minimum for a coverage close to 4/9. This plot resembles very closely the behavior of the work function of metals such as W when covered by alkali adsorbates, as predicted by the jellium model.21 Wieckowski et al.5 have determined a number of twodimensional phases after immersion and transfer of the electrodes to the ultrahigh vacuum environment. Since expanded structures appear to be stable under these conditions, experimental measurements of the work function of the system should be possible to allow comparison with the present theoretical predictions. Phenomenological approaches6 relate the changes in the work function to a dipole layer, each of the dipoles having an effective dipole moment µ according to the equation
∆Φ ) e0 µN/0
(7)
where N is the number of dipoles per unit surface and 0 is the permeability of a vacuum. We have calculated µ taking for N the number of adsorbate atoms per unit surface and obtained the results shown in Figure 4. From this plot, it can be observed that even at the lowest coverage degree, µ is still changing very rapidly with θ; this denotes that the dipole-dipole interactions responsible for the depolarization of the adatoms are still strong under these conditions. Although the effective dipoles are small in comparison with those observed with alkali metals on high work function substrates6 (about 1 order of magnitude less), they are important. On the other hand, our values of µ are similar to those calculated by Neugebauer and Scheffler for Na adsorption on Al(111).7 Assuming a typical surface-adatom distance (∼4 atomic units), they cor(20) Foiles, S. M.; Baskes, M. I.; Daw, M. S. Phys. Rev. B 1986, 33, 7983. (21) Lang, N. D. Phys. Rev. B 1971, 4, 4234.
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Figure 2. Average electronic density (top panel), differential electronic density (middle panel), and electrostatic potential induced by the differential density (lower panel) for p(1 × 1) (a) and p(2 × 2) (b) monolayers of Ag on Au(111).
Figure 3. Work function change as a function of the coverage degree for different expanded structures of Ag adsorbed on Au(111).
respond to an effective transfer of ca. 0.15 electrons at the lowest coverage degree. In section 2, we posed as a necessary condition to be able to calculate the underpotential shift from our model that the structure of the double layer, including adsorbed water molecules and anions, remain unchanged upon adsorption. This condition requires in a first approximation that surface charge remain the same. However, our results for the change in the work function indicate that this condition should not be fulfilled. Work function and potential of zero charge are roughly linearly related with a slope of 1:22
ψpzc = Φ + constant
(8)
Figure 4. Effective dipole moments as a function of the coverage degree for Ag atoms adsorbed on Au(111). These were evaluated from the work function changes and the surface atomic density according to eq 7.
Our results for work function changes of about 1.2 eV for the most expanded structures suggest changes of the surface potential of zero charge of that magnitude. This change in potential of zero charge would mean a drastic change in surface charge upon adsorption and hence in the structure of the double layer. The change in the structure of the double layer should provide the energy necessary to stabilize expanded structures, since the sole adsorbate-substrate bond is not able to explain by itself the positive UPD shifts observed. (22) Trasatti, S. In Electrified Interfaces in Physics, Chemistry and Biology; Guidelli, R., Ed.; Kluwer Academic: Dordrecht, The Netherlands, 1992; p 245.
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At least three different effects related to changes in the double layer may contribute to stabilize the expanded structures. One of them is the additional adsorption of anions upon formation of the UPD adlayer. This hypothesis has been discussed in a more general context in a previous work12 and is related to the fact that the enhanced adsorption of anions may cooperate to stabilize the foreign adatoms. However, experiments carried out in F-containing electrolytes, an slightly adsorbing anion,5 also delivered a number of expanded structures. Furthermore, in the case of SO42- containing solutions the surface is already covered by anions before silver adsorption,4 so this effect may be somewhat decreased. Thus, other effects are worthy of being considered. The second source of stabilization may also be related to the negative shift in the potential of zero charge. The produces a concomitant positive charging of the surface, inducing the stabilization of water molecules on the surface. Finally, a third point to be considered is the effect of the electric field on the binding energy. This has been observed in the case of the homoatomic adsorption of Pt on Pt(001) by Feibelman.23 (23) Feibelman, P. J. Phys. Rev. B 2001, 64, 125403.
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Work is in progress to consider this effect for the present system. 4. Conclusions The observed stability of expanded monolayers of silver deposited at underpotentials cannot be explained by the sole metal-substrate bonding energy. Calculations in a vacuum show that all expanded monolayers are more unstable than the bulk silver phase and hence should not present underpotential deposition. The rearrangement energy of the double layer upon adsorption may provide the necessary stabilization. This hypothesis is supported by strong work function changes that may signify drastic changes in surface charge upon adsorption. Acknowledgment. Fellowships for C. Sa´nchez and S. A. Dassie from CONICET, financial support from CONICET, Agencia Co´rdoba Ciencia, Secyt-UNC, Program BID1201/OC-AR PICT No. 06-04505, and language assistance by Pompeya Falco´n are gratefully acknowledged. LA020312A
