Relevance of Heterometallic Binding Energy for Metal Underpotential

If the M atoms are more stable when they are adsorbed on metal S than when they are ..... those of a previous calculation employing the embedded atom ...
0 downloads 0 Views 132KB Size
Download PDF
Langmuir 2001, 17, 2219-2227

2219

Relevance of Heterometallic Binding Energy for Metal Underpotential Deposition C. G. Sanchez and E. P. M. Leiva* Unidad de Matema´ tica y Fı´sica, Facultad de Ciencias Quı´micas, INFIQC, Universidad Nacional de Co´ rdoba, 5000 Co´ rdoba, Argentina

J. Kohanoff Atomistic Simulation Group, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland Received November 27, 2000 We present first-principles calculations for a number of metals adsorbed on several different metallic substrates. Some of these systems are very relevant in electrochemistry, especially in the field of underpotential deposition phenomena. The present studies reveal the existence of a relationship between the excess binding energy and the surface energy difference between substrate and adsorbate. Comparisons with experimental underpotential shifts show that excess binding energies are systematically underestimated. By analyzing experimental information on different systems, we conclude that this discrepancy between our vacuum calculations and experiments carried out in an electrolytic solution is likely to be due to anion adsorption and/or solvent effects.

1. Introduction The deposition of a metal on a foreign metal surface in the submonolayer and monolayer range has been the subject of extensive work in the field of surface science as well as in the related area of electrochemistry. Although in the former case sophisticated equipment is required to perform experiments under controlled coverage conditions, in the latter the experimental arrangement simply involves an electrochemical cell and a potential source. In electrochemistry, potential control is equivalent to controlling the chemical potential of the adsorbates, and because of the exponential relationship between potential and activities, changes in the degree of coverage can be produced that in the gas phase would require pressure modifications of several orders of magnitude. The price to pay for the flexibility of the electrochemical system is the presence of two contaminants, namely the solvent and the electrolyte. This implies that all the energetic information that can be experimentally obtained will be, in principle, affected by the contribution of these two factors. A third factor to mention is the charging of the electrochemical double layer, which indirectly affects the previous two. For instance, the location of the point of zero charge contributes to stimulate or inhibit processes such as ion or solvent adsorption. Thus, a relevant question to be posed is whether the information that can be obtained from electrochemical experiments can be extrapolated to the metal/vacuum interface. This is one of the motivations of the present work. A special chapter within metal deposition in electrochemistry is the so-called underpotential deposition. This involves the deposition of one (occasionally two) metal monolayers at potentials more positive than the reversible Nernst potential. This phenomenon attracted the interest of many experimentalists, who tried to rationalize its occurrence in terms of some physical properties of the specific metals involved, for example, lattice constant,1 * Corresponding author. E-mail: [email protected]. (1) DeGeiso, R. C.; Rogers, L. B. J. Electrochem. Soc. 1959, 106, 433.

electronegativities,2 and work function.3,4 The status of this field prior to the 1980s has been reviewed by Kolb,2 comprising information mainly on polycrystalline surfaces. Another review by one of us5 is concerned with theoretical models for this phenomenon. From the analysis of the existing models, it appeared rather difficult to formulate a general theory for underpotential deposition, which would allow for the determination of general trends in terms of a few simple properties of the isolated constituent metals. In this respect, some general trends have been proposed by Schmickler et al.6-8 by using density functional theory (DFT) applied to the adsorption of an spmetal on a high-work-function substrate. Among other recent theoretical approaches to underpotential deposition are band structure calculations from first principles,9 statistical thermodynamical models,10-12 extensions of the Anderson-Newns model for adsorption from the gas phase,13,14 and quantum-mechanical semiempirical methods.15,16 Very recently, we applied the embedded atom method (EAM) to analyze systematically a number of (2) Kolb, D. M. In Advances in Electrochemistry and Electrochemical Engineering; Gerischer, H., Tobias, C. W., Eds.; Wiley: New York, 1978; Vol. 11, p 125. (3) Kolb, D. M.; Przasnyski, M.; Gerischer, H. J. Electroanal. Chem. 1974, 54, 25. (4) Trasatti, S. Z. Phys. Chem. NF 1975, 98, 75. (5) Leiva, E. Electrochim. Acta 1996, 41, 2185 and references therein. (6) Leiva, E.; Schmickler, W. Chem. Phys. Lett. 1989, 160, 75. (7) Schmickler, W. Chem. Phys. 1990, 141, 95. (8) Lehnert, W.; Schmickler, W. J. Electroanal. Chem. 1991, 310, 27. (9) Kramar, T.; Podloucky, R.; Neckel, A.; Erschbaumer, H.; Freeman, A. J. Surf. Sci. 1991, 247, 58. (10) Blum, L.; Huckaby, D. A. Proceedings of the Symposium on Microscopic Models of Electrode-Electrolyte Interfaces, 1992. Proc.s Electrochem. Soc. 1993, 93-5, 232. (11) Blum, L.; Huckaby, D. A. J. Electroanal. Chem. 1994, 375, 69. (12) Blum, L.; Legault, M.; Turq, P. J. Electroanal. Chem. 1994, 379, 35. (13) Schmickler, W. Chem. Phys. Lett. 1985, 115, 216. (14) Kornyshev, A.; Schmickler, W. J. Electroanal. Chem. 1986, 202, 1. (15) Lopez, M. B.; Estiu, G. L.; Castro, E. A.; Arvia, A. J. THEOCHEM 1990, 210, 353. (16) Lopez, M. B.; Estiu, G. L.; Castro, E. A.; Arvia, A. J. THEOCHEM 1990, 210, 365.

10.1021/la001639j CCC: $20.00 © 2001 American Chemical Society Published on Web 03/09/2001

2220

Langmuir, Vol. 17, No. 7, 2001

Sanchez et al.

systems18 and performed more accurate density functional calculations20,21 for some specific cases. It is the purpose of this work to present a systematic study of the energetics of the adsorption of several d-metals, popular among electrochemists, on a foreign metallic substrate. We then analyze some ideas formulated on the basis of simpler models and point out the coincidences and limitations. Finally, we discuss the present results in the light of available experimental data and present our conclusions. 2. Some Thermodynamic Considerations Underpotential deposition involves the electrosorption of metal ions on foreign substrates at potentials more positive than the reversible Nernst deposition potential of the adsorbate. A meaningful concept in underpotential deposition theory is the so-called underpotential shift, ∆φupd, which was originally defined by Kolb et al.3 as the potential difference between the desorption peak of a monolayer of a metal M adsorbed on a foreign substrate S and the current peak corresponding to the dissolution of the bulk metal M. A more general definition of ∆φupd2,5,17 can be stated in terms of the chemical potential of the atom adsorbed on a foreign substrate at coverage Θ and the chemical potential of the same species in the bulk:

∆φupd(Θ) )

1 (µ[(M)M] - µ[(S)MΘ]) ze0

(1)

At T ) 0 K, eq 1 reduces to a purely energetic contribution and can be rewritten as

∆φT)0 upd )

1 (Ubulk - U ˜ ads M/S) ze0 M

(2)

˜ ads where U M/S is the adsorption energy of M on S in the electrochemical system at the coverage degree Θ and Ubulk M is the cohesive energy of bulk M. The reason for the tilde is explained later. To reach a better understanding of the meaning of the various terms in eq 2, we briefly revisit the cycle proposed by Schmickler7 for the present problem. In Figure 1, we show a scheme of an electrochemical cell, where an electrode of metal S is covered by metal M, and the applied potential difference ΨM - ΨS maintains equilibrium (no overall electron flow) in the system. Both metals are connected to a piece of a third metal M2. The ionic cores Mz+ are free to flow from the surface of S to the pure M electrode through the electrolytic solution containing Mz+ ions. Therefore, the free energy of transferring the ions from the surface of S to the bulk of M is zero. This can be formally written as z+ Mz+ ad f M M bulk

∆GT ) 0

(3)

An alternative cycle for this same transfer can be devised in terms of another set of physical quantities, as shown in Figure 1. Steps 1-7 are as follows: (1) adatom desorption, (2) adatom ionization, (3) electron incorporation into metal M2, (4) transfer of the Mz+ ions from the outer potential ΨS to ΨM, (5) electron extraction from metal (17) Leiva, E. In Current Topics in Electrochemistry; Council of Scientific Information: Trivandrum, India, 1993; Vol. 2, p 269. (18) Del Po´polo, M.; Sa´nchez, C.; Leiva, E. Surf. Sci. 1999, 421, 59. Rojas, M. I.; Sa´nchez, C.; Leiva, E. Surf. Sci. 2000, 453, 225. (19) Trasatti, S. In Electrified Interfaces in Physics, Chemistry and Biology; Guidelli, R., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992; p 245. (20) Sa´nchez, C.; Leiva, E. J. Electroanal. Chem. 1998, 458, 183. (21) Sa´nchez, C.; Leiva, E. Electrochim. Acta 1999, 45, 691.

Figure 1. Thermodynamic cycle employed to calculate the underpotential shift.

M2, (6) reduction of ion Mz+, and (7) incorporation of atom M to bulk M. Because the overall effect of the cycle is the same as that of eq 3, then 7

∆Gi ) ∆GT ∑ i)1

(4)

So, using condition 3 and the fact that work function and ionization energy terms compensate each other (steps 2-6) we obtain

1 ψS/M - ψM ) [∆G7 + ∆G1] z

(5)

∆G7 is exactly the free energy of cohesion of the metal, so at T ) 0 it reduces to Ubulk M . On the other hand, although ∆G1 may be in principle related to the binding energy of the M atoms in the adsorbed sub(monolayer) Uads M/S, it may be quite a complex quantity because of the nature of the electrochemical interface. In fact, ∆G1 contains the influence of the solvent molecules adsorbed at the interface, the contribution of the double-layer charging, and possibly also the influence of specific adsorbing ions. It is for this ads ˜ ads reason that we have written U M/S instead of UM/S in eq 2. Only upon neglecting all these three effects, at T ) 0 K, can we write

∆G1≈ -Uads MS Therefore, eq 5 takes the form

∆Uex 1 (ψS/M - ψM)T)0 ≈ [Ubulk - Uads M/S] ) z M z

(6)

where in the second equality we have defined the excess binding energy as ∆Uex. If the M atoms are more stable when they are adsorbed on metal S than when they are part of the bulk of metal M, then ∆Uex is a positive quantity. In the present work, we concentrated on the calculation of ∆Uex for the (111) surface of several popular singlecrystal face-centered cubic (fcc) electrochemical systems. 3. Calculation Method: The Model Our aim in this work is to extract general conclusions for different heteroepitaxy systems. Therefore, for calculating the energy of substrate-adsorbate systems we shall consider a compact adsorbed monolayer commen-

Heterometallic Binding Energy

Langmuir, Vol. 17, No. 7, 2001 2221

surate with the substrate surface unit cell with a 1 × 1 cell of coincidence. It is well-known that expanded and even incommensurate adsorbate structures are formed in some M/S systems,22 which are more stable than the corresponding compact commensurate monolayers. However, this type of structure will not be analyzed in the present calculations. Expanded commensurate structures are characterized by very large unit cells, which are well beyond present computational capabilities. Incommensurate layers are not even compatible with currently available methodologies. On the other hand, no explicit experimental information exists on the energetics and structure of the adsorbed monolayer for many of the systems analyzed here. It is possible that, in many of them, expanded and incommensurate structures are more stable than 1 × 1 structures, especially in the case of relatively large adsorbates. In those cases, our calculated underpotential deposition shifts are expected to be more negative than the experimental ones. Therefore, we believe that in some of the systems for which we predict a very small or negative ∆Uex the phenomenon could still take place. In addition, it has already been proposed by some of us18 that if the adsorbate’s potential of zero charge (pzc) is considerably more negative than that of the substrate, then the adsorption of anions may play a very important role in stabilizing the adsorbed metal monolayer. This leads to an effect similar to that of expanded monolayers. Reciprocally, a destabilization of the adsorbed monolayer can also occur upon anion adsorption if the corresponding pzc follows the opposite trend. In the present work, all the electronic properties will be calculated by means of density functional theory.23,24 Within this framework, the energy of a many-electron system, described by the electronic density n(r), in an external potential v(r) corresponds to the minimum of the energy functional

∫ v(r) n(r) dr + n(r) n(r′) 1 dr dr′ + Exc[n(r)] ∫ ∫ 2 |r - r′|

E[n(r)] ) Ts[n(r)] +

(7)

subject to the constraint of constant number of electrons. In eq 7, Ts[n(r)] is the kinetic energy of a noninteracting electron gas of density n(r). The functional Exc[n(r)] is the exchange-correlation energy and contains information about the many-body character of the electronic system. In the present work, we shall use the local density approximation (LDA) for exchange and correlation:

Exc[n] )

∫ xc(n(r)) n(r) dr

(8)

where xc(n(r)) is the exchange-correlation energy per particle of a homogeneous gas of density n(r). Because metals usually exhibit quite uniform electron densities, the LDA turns out to be a rather good approximation. We shall use here the parametrization proposed by Perdew and Zunger,25 based on Ceperley and Alder’s26 quantum Monte Carlo results. The electronic density and the kinetic energy functional are obtained through the solution of (22) Budevski, E.; Staikov, G.; Lorenz, W. J. In Electrochemical Phase Formation and Growth, An Introduction to the Initial Stages of Metal Deposition; VCH Publishers: New York, 1996. (23) Kohn, W.; Sham, L. J. Phys. Rev. A 1965, 140, 1143. (24) Hohenberg, P.; Kohn, W. Phys. Rev. B 1964, 136, 153. (25) Perdew, J. P.; Zunger, A. Phys. Rev. B 1981, 23, 5048. (26) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 567.

Kohn-Sham self-consistent equations,23

{

-

∇2 2

+

ZI

n(r′)

}

∑I |r - R | + ∫ |r - r′| dr′ + vxc(r) I

ψi(r) )

iψi(r) (9)

where

vxc(r) )

dExc dn(r)

(10)

is the exchange-correlation potential. The electronic density is constructed from the Kohn-Sham orbitals in the following way:

n(r) )

∑i fi|ψi(r)|2

(11)

where fi are the occupation numbers of the different electronic bands. The kinetic energy functional is given by

Ts[n(r)] )

∑i fi ∫ ψ/i (r)(-∇2/2) ψi(r) dr

(12)

The numerical solution of eq 9 requires the expansion of the Kohn-Sham orbitals in a suitable basis set. If we treat all the electrons explicitly, the vast majority of the basis functions will be used to describe core wave functions, which are largely unaffected by chemical processes. To circumvent this problem, the effect of core electrons plus nuclei on the valence electrons is represented by normconserving pseudopotentials. These were constructed according to the prescription of Troullier and Martins.27 This reduces conveniently the number of functions in the basis set. All our calculations have been carried out using the program SIESTA,28-30 a code designed for DFT calculations in systems with a large number of atoms. We have used a basis set composed of pseudoatomic orbitals for expanding the Kohn-Sham orbitals. This set is constructed using a generalization of the method proposed by Sankey and Niklewski,31 which consists of solving the problem of the pseudoatom with the boundary condition that the electronic valence wave functions vanish beyond a certain cutoff radius. In this way, the number of nonzero Hamiltonian matrix elements to calculate is dramatically reduced. To give more flexibility to the basis set, a second group of valence orbitals and a set of polarization orbitals are added to the valence set. This corresponds to a double-ζ plus polarization (DZP) basis set in the usual quantum chemistry terminology. For each of the transition metals considered in this paper, a total of 15 numerical basis orbitals is used, 2 s and 10 d orbitals (the doubled valence set) and 3 p orbitals (the polarization functions). The procedure used to construct this set is described in detail elsewhere.29,30 To verify the transferability of the pseudopotentials and the suitability of the basis set, we calculated some equilibrium properties for the metals, namely, the lattice (27) Troullier, M.; Martins, J. L. Phys. Rev. B 1993, 43, 1991. (28) Ordejo´n, P.; Artacho, E.; Soler, J. M. Phys. Rev. B 1996, 53, 10441. (29) Sa´nchez-Portal, D.; Ordejo´n, P.; Artacho, E.; Soler, J. M. Int. J. Quantum Chem. 1997, 65, 453. (30) Artacho, E.; Sa´nchez-Portal, D.; Ordejo´n, P.; Garcı´a, A.; Soler, J. M. Phys. Status Solidi 1999, 215, 809. (31) Sankey, O. F.; Niklewski, D. J. Phys. Rev. B 1998, 40, 3979.

2222

Langmuir, Vol. 17, No. 7, 2001

Sanchez et al.

Table 1. Comparison between Theoretical Predictions (th) and Experimental Results (exp) for the Lattice Constant a (in Bohr), Bulk Modulus B (in Mbar), and Surface Energies σ (in eV/Å2) of the Metals Considered in This Worka metal

ath

aexp

Bth

Bexp

σth

σexp

Ag Au Cu Pd Pt

7.61 7.75 6.71 7.30 7.44

7.73 7.71 6.82 7.35 7.41

1.33 2.06 1.80 2.22 2.78

1.04 1.67 1.38 1.95 2.83

0.091 0.090 0.134 0.128 0.145

0.077 0.094 0.111 0.125 0.155

a

Experimental values are taken from ref 33.

constant and bulk modulus of the bulk metal, and the surface energy. The results are shown in Table 1. It can be observed that the agreement with experimental values is comparable to what is usually obtained from planewave calculations. The average relative errors in lattice parameters and bulk moduli are 0.9% and 19%, respectively. The localization radius of the basis set (corresponding to an energy shift of 0.136 eV28-30) was chosen as a compromise between a reasonable accuracy and a sufficiently low computational cost. To verify this, we repeated the calculation for a much larger localization radius, corresponding to an energy shift of 0.05 eV, which produced average relative errors of 0.7% and 20% in lattice parameters and bulk moduli, respectively, although the computational cost grows by 1 order of magnitude. The k-point summation was done in all cases on a 36 point Monkhorst-Pack32 mesh in the Brillouin zone which corresponds a 6 point mesh in its irreducible part. This k-point sampling ensures an energy convergence better than 1 meV. For the study of substrate-adsorbate systems, we use a slab geometry and periodic boundary conditions, as shown in Figure 2. For the substrate (S), we consider a stack of (111) planes, each plane containing n atoms within the supercell. This arrangement of n atoms is periodically replicated in order to take into account infinite planes. This substrate slab, composed of m layers, is terminated by adsorbate planes (M) on both its sides. Periodic boundaries in the direction orthogonal to the surface imply that we actually consider a periodic arrangement of slabs separated by vacuum regions. According to test calculations with a small number of substrate slabs, adsorption is expected to take place on highly coordinated adsorption sites. Therefore, we have chosen a (1 × 1) adsorption geometry, which is reflected in our choice of the calculation supercell (n ) 1). To ensure that our setup accurately represents isolated surfaces, the width of the vacuum region was varied until satisfactory convergence of the total energy was reached. We found that a distance equivalent to six lattice planes was adequate for the present purposes. The position of the adsorbate lattice plane was relaxed in the calculations. No attempt was made at relaxing the first lattice plane of the substrate. Test calculations indicate that neglecting the above relaxation represents an uncertainty of the order of 0.01 eV in excess binding energies. Therefore, we will report only two significant figures in our results. We consider now the calculation of the energy difference ∆Uex in eq 6. This quantity is the difference between the binding energy of M on S, Uads M/S, and the corresponding cohesive energy of M, Ubulk M . Although each of these quantities involves the energy of an isolated M atom, the calculation of this single atom energy is not necessary to obtain ∆Uex because it cancels upon addition in eq 6. (32) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 3979.

Figure 2. Schematic illustration of the supercell geometry employed in this work to represent the substrate/adsorbate system. dhkl denotes the distance between (hkl) lattice planes. The metal slabs extend over planes perpendicular to the plane of the page, by periodic replication.

Therefore, we obtained ∆Uex in the following way. First, an energy calculation was performed with a slab taking m ) 5, covered on both sides with a monolayer of adsorbate. Let us denote this quantity as US+M. Second, an energy calculation was performed for the same slab but without the adsorbate. Let us denote this with US. Finally, a calculation was made with a supercell containing 13 atomic planes of the adsorbate, without any vacuum region. With the energy obtained in the latter calculation denoted as UbM, the excess energy was obtained from b

UM 1 ∆Uex ) (US - US+M) + 2 13

(13)

Working with a basis set of atom-centered functions introduces a basis set superposition error (BSSE) when comparing the energies of different structures. This is true in the present case, where we compare the energies of a covered and a clean substrate. The BSSE can be corrected by recalculating the energies in the presence of appropriately chosen extra basis functions, centered in the missing atoms (counterpoise correction). We have calculated this correction in the case of Ag/Pt(111) and found that the original calculation underestimated ∆Uex by 0.06 eV. In the following, we report the noncorrected excess binding energies, bearing in mind that error bars are on the order of 0.05 eV. 4. Results and Discussion 4.1. Excess Binding Energies and Surface Energies. The excess binding energies ∆Uex for adsorption of different adsorbates on the fcc (111) face of single crystals of several substrates are given in Table 2. The metals are sorted according to increasing surface energy, from left to right and from top to bottom. In this matrix format, it can

Heterometallic Binding Energy

Langmuir, Vol. 17, No. 7, 2001 2223

surface energies σM and σS of the metals involved, we go through the lower cycle, making some approximations. For the first primed step, we have the compression (expansion) of the adsorbed monolayer. We shall neglect this contribution, although in some cases it is quite important, especially if the lattice mismatch between the two metals is important (see below). Thus, we write for ∆UI′

∆UI′ ≈ 0

(14)

In the second primed step, we annihilate the free surface of the compressed (expanded) M monolayer and the corresponding surface of the pure metal M. We approximate this by

∆UII′ ≈ -2σMAM

(15)

In the third primed step, we create two new free surfaces. Depending on the compressed or expanded status of the adsorbate, this energy change can be approximated by Figure 3. Two alternative thermodynamic cycles to calculate the excess binding energy of a monolayer of metal M adsorbed on S. The upper cycle involves detachment of the M monolayer, disassembly into isolated M atoms, and reassembly into bulk metal M. The lower cycle consists of compressing or expanding the M monolayer, putting it into contact with bulk S, and separating the S/M metal junction to form free S and M surfaces. Table 2. Excess Binding Energies ∆Uex (in eV) for Different Adsorbates on Different (111) Substrates adsorbate substrate Ag Au Cu Pd Pt

Ag

Au 0.17

0.00 -0.38 0.27 0.33

-0.51 0.32 0.32

Cu

Pd

Pt

-0.55 -0.50

-0.13 -0.24 0.00

-0.15 -0.40 -0.15 0.02

-0.02 0.06

0.08

be observed that, with some notable exceptions, for a given substrate the excess binding energy tends to decrease for increasing surface energy of the adsorbate. Conversely, a given adsorbate usually exhibits larger excess binding energies on high surface energy substrates. These results support the same general trend already found within the framework of the jellium model,6 that is, the simplest approach to bulk metals and metal surfaces that takes into account explicitly the electronic component. In the above work, it was suggested that the underpotential shift should be related to the surface energy differences ∆σM-S between the substrate and the adsorbate. This was based in the observation that deposition involves replacing a surface (of metal S) by another of a different nature (metal M). We illustrate this point in Figure 3 by considering a thermodynamic cycle. In the upper part, we show the cycle usually employed to calculate the energetic contribution to the underpotential shift. This involves (I) detachment of the M monolayer from the S substrate, (II) disassembly of the M monolayer into the component atoms, and (III) reassembly of the M atoms to yield bulk M. In the lower part, we show an alternative cycle starting from the same initial conditions and leading to the same final state: (I′) the M adsorbed monolayer is compressed (or stretched) so that the lattice parameter corresponds to that of bulk M, (II′) the substrate and compressed (stretched) monolayer are brought into contact with bulk metal M, and (III′) bulk M is separated from bulk S to yield clean surfaces of M and S. To find a relationship between ∆Uex and the

{

∆UIII′ ≈

AM(σM + σS) AS(σM + σS)

aS > aM aS e aM

(16)

where σM and σS denote the surface energies of substrate and adsorbate, respectively, AS and AM are the atomic areas of substrate and adsorbate, respectively, and aS and aM denote the corresponding lattice parameters. The excess binding energy can then be calculated by adding up all the contributions of the second cycle, in place of the more natural first cycle, in the following way:

∆Uex ) ∆UI′ + ∆UII′ + ∆UIII′

(17)

Replacement of the approximations (eqs 14-16) into eq 17 leads to

∆Uex ) f(σS, σM) ≈

{

AM(σS - σM) aS > aM AS(σS - (AM/AS)σM) + σM(AS - AM)

aS e aM (18)

The first approximation involves the assumption that the M monolayer is not significantly stressed on the surface of S. The second approximation assumes that a single layer of M is sufficient to screen the influence of the substrate. Finally, the third approximation implies that a semiinfinite crystal of M behaves like bulk M when it is in contact with a semiinfinite crystal of S and conversely. Although the first and the third assumptions are particularly strong, the second one is rather reasonable because of the ability of metals to screen the presence of a perturbation. For example, typical screening lengths of Cu and Ag are 0.55 and 0.59 Å, values that are smaller than interplanar distances. Figure 4 shows the correlation between ∆Uex and f(σS, σM) arising in the present calculations. A linear regression with a slope close to unity is apparent, although two systems, Ag/Cu(111) and Au/Cu(111), exhibit a strong deviation from this line. It is remarkable that these are the metal pairs which exhibit the larger lattice misfits, thus questioning the validity of the first approximation -∆UI′ ≈ 0. Smaller, but meaningful, deviations from the linear correlation are also observed for Cu/Ag(111) and Cu/Au(111). The reason these deviations are somewhat smaller is understandable, because it is usually easier to stretch a monolayer than to compress it.

2224

Langmuir, Vol. 17, No. 7, 2001

Sanchez et al.

Figure 4. Excess binding energy vs difference of surface energies between substrate and adsorbate. Figure 6. Contributions of kinetic + electrostatic energy (left bar) and exchange and correlation energy (middle bar) to the excess binding energy (left bar) for the different systems considered in this work. Table 3. Comparison between the Present Results ∆Uloc for the Excess Binding Energies and Those Employing a PW Basis Set (∆Upw), Obtained Using the fhi96md Packagea adsorbate/substrate

∆Uloc (eV)

∆Upw (eV)

Ag/Au(111) Au/Ag(111) Cu/Ag(111) Cu/Au(111)

0.00 0.17 -0.55 -0.50

0.02 0.12 -0.56 -0.46

a Bockstedte, M.; Kley, A.; Neugebauer, J.; Scheffler, M. Comput. Phys. Commun. 1997, 107, 187.

Figure 5. Excess binding energy calculated from firstEAM principles results, ∆UDFT ex , vs EAM results, ∆Uex , for the different metal pairs considered in this work.

Finally, for negligible lattice misfit eq 18 reduces to ∆Uex ≈ A(σS - σM), which was the correlation found by using the jellium model.6 4.2. Comparison with Other Theoretical Results. A systematic study for the same systems considered here has been performed using the embedded atom method.18 To appreciate the correlation between previous and present theoretical results, we plotted in Figure 5 our first-principles results for the excess binding energies, EAM ∆UDFT ex , versus the corresponding EAM results, ∆Uex . A linear fitting of the data for 20 systems yields the following correlation:

∆UDFT ex

) (-0.04 ( 0.04) + (0.96 (

0.15)∆UEAM ex

which can be interpreted fairly well as a linear correlation with a slope of unity. This is a strong indication that the EAM is a rather good approximation, so results obtained within this model are, at least, qualitatively reliable. We emphasize the fact that the EAM parameters have been taken directly from ref 33 and that no attempt at fitting to the present first-principles results has been made.

We also present in Table 3 the comparison of the present DFT results with other calculations performed for some selected pairs of metals, employing the same exchangecorrelation functional but a plane wave basis set to expand the Kohn-Sham orbitals. As can be seen, the two sets of results are very similar, the largest disagreement being smaller than 50 meV (4 mRy). Because the plane wave basis can be considered as a fully converged benchmark, the above results serve as a validation of the size of the basis set and the localization radii of the basis functions chosen for the present calculations. 4.3. Energetic Contributions to the Underpotential Shift. As stated above, the excess binding free energy related to underpotential deposition can be written as bulk ∆GT)0 - Uads upd = (UM M/S) ) ∆Uex

(19)

where the energy of the electronic system can be split into the contributions due to kinetic (k), electrostatic (e), and exchange and correlation (xc): xc ∆Uex ) ∆Uk+e ex + ∆Uex

In Figure 6, we show these two contributions to the excess binding energy for the systems considered here. It (33) Foiles, S. M.; Baskes, M. I.; Daw, M. S. Phys. Rev. B 1986, 33, 7983.

Heterometallic Binding Energy

Langmuir, Vol. 17, No. 7, 2001 2225

Figure 7. Contributions of kinetic + electrostatic energy and exchange and correlation energy to the binding energy of bulk Ag, as a function of the lattice parameter. Table 4. Sign of the Contribution of Exchange and Correlation Energy to the Excess Binding Energy M S

Ag

Ag Au Pt Pd Cu

+ + + +

Au

Pt

Pd

Cu

+

-

+

+ +

+ + +

+

+

Table 5. Sign of the Contribution of Kinetic + Electrostatic Energy to the Excess Binding Energy M S Ag Au Pt Pd Cu

Ag -

Au

Pt

Pd

Cu

-

+ +

+ + +

+ -

-

+ -

-

is clear that ∆Uex is the result of a delicate balance between two quantities which are, in absolute value, considerably larger. The present results can be better understood by looking at the relative importance of the k + e and xc contributions to the bulk cohesive energy, Ucoh, of a metal. In Figure 7, xc we show the two contributions, Uk+e coh and Ucoh, as a function of the lattice parameter a for bulk Ag. It can be seen that the minimum in the cohesive energy arises as a consequence of a monotonic increase of Uxc coh and a with a. Similar results are monotonic decrease of Uk+e coh obtained for the other metals. According to this and reasoning exclusively in terms of lattice constants, ∆Uk+e bind is expected to be positive for systems involving adsorbates whose bulk lattice constant is smaller than that of the corresponding adsorbed monolayer and vice versa. A similar reasoning indicates the opposite sign for ∆Uxc bind. xc and ∆ U are given in Tables 4 and 5 The signs of ∆Uk+e ex ex for all the systems studied in this work. The metals have been ordered by decreasing bulk lattice constant. It is observed that the signs deduced from the above geometric reasoning are mostly confirmed by theoretical results,

Figure 8. Thermodynamic cycle illustrating the role of adsorbed water molecules in determining the excess binding energy in the case of underpotential deposition. The step numbers denote (1) desorption of water molecules from the surface of the adsorbate into the vacuum, (2) desorption of metal M from the surface of the substrate to deliver isolated M atoms in the vacuum, (3) combination of the adsorbate atoms from the vacuum to deliver bulk metal M, and (4) adsorption of water molecules from the vacuum onto the surface of the naked substrate S.

except for a few cases where specific chemical effects are xc more important. For instance, ∆Uk+e ex and ∆Uex are both positive in Pd/Pt(111). 4.4. Comparison with Experimental Results. Most electrochemical experiments are performed under conditions where the specific adsorption of anions cannot be ruled out. Moreover, it can even play an essential role in determining whether underpotential deposition can happen. In our previous work,18 we argued that the influence of anion specific adsorption may be particularly important in cases where the potential of zero charge shifts toward negative potentials upon the formation of the adsorbate layer. Let us consider the thermodynamic cycle of Figure 8, which has been previously used to illustrate the role of the solvent in underpotential deposition phenomena.18 That is, in step 1 some free enthalpy must be invested in order to desorb water in contact with the adsorbate, and in step 4 some amount of free enthalpy is recovered as a consequence of water adsorption on the naked substrate. Thus, depending on this difference of free enthalpy the adsorption of M may be stimulated or hindered. For example, a strong interaction of water with the adsorbate atoms (and a weak one with the substrate) will increase the stability of the monolayer. Anions are likely to play a role similar to that of the water molecules. An additional fact that must be considered is the change of the work function of the system upon building of the foreign adatom monolayer. In most underpotential deposition systems, the adsorbate is known to have a lower work function than the substrate, so that the deposition of the monolayer is accompanied by a decrease of the work function of the system. As previously shown,21 this decrease may be even more dramatic if the adsorbate is expanded with respect to its bulk structure, as is the case of the underpotential deposition of Cu on Au single-crystal surfaces. On the other hand, the work function of the surface, say Φ(ΘM)S/M, is approximately related to the potential of zero charge ∆ψpzc of the system according to19

1 ∆ψpzc ≈ (Φ(ΘM)S/M - Φref) e

(20)

2226

Langmuir, Vol. 17, No. 7, 2001

Sanchez et al.

where Φref is the so-called work function of the reference electrode. This equation shows that a lowering of the work function implies a negative shift of the potential of zero charge. Let us consider now a system where the potential at which the foreign monolayer is deposited is negative with respect to the potential of zero charge. Hence, before the building of the underpotential deposition monolayer the surface bears a negative charge and anion adsorption is precluded on electrostatic grounds. However, when the underpotential monolayer is deposited at the same potential, Φ(ΘM)S/M decreases with a concomitant shift of the ∆ψpzc. If this shift is important enough, the surface may acquire a positive charge, thus promoting the adsorption of anions. Therefore, anions appear to play a stabilizing role. In the cycle of Figure 8, this would imply that step 1 begins with an anion-covered surface, whereas at the end of step 4 the surface is anion-free. We believe that this stabilization mechanism is operative in the case of Cu underpotential deposition on Au(111), which is discussed below. The information concerning excess binding energies for metal/vacuum interfaces, which would be straightforwardly comparable to the present calculations, is actually rather sparse. A remarkable exception is the system Ag/ Pt(111), which has been characterized in both surface science34 and electrochemistry.35 Analysis of thermal desorption spectra in a vacuum34 leads to the conclusion that Ag is bound to Pt(111) about 0.17 eV more strongly than to Ag(111). In electrochemical experiments,35 a deposition peak is observed at an underpotential of about 0.35 V, although the existence of a pseudomorphic layer was confirmed by X-ray scattering at least up to an underpotential of ca. 0.2 V, but no measurements could be undertaken at higher potentials. Our calculated excess binding energy of 0.33 eV reported in Table 2 can thus be considered in fair agreement with the experimental result in a vacuum, especially taking into account that this was an indirect measurement obtained at high temperatures, whereas our calculation is a zero-temperature energetic comparison. The system Ag/Au(111) has been the subject of extensive research in the electrochemical environment. In situ atomic force microscopy,36 tunneling microscopy,37-39 and low-energy electron diffraction (LEED) techniques40 identified a wide variety of adlattices. Very recent experiments in H2SO4 electrolytic solution39 showed the existence of multiple structures. In the underpotential range between 0.5 and 0.2 V, a sequence of increasingly closely packed hexagonal structures was observed. The appearance of a (1 × 1) structure was detected only at underpotentials between 0.13 and 0.2 V. The authors argued that the open structures reflected the repulsive effect of coadsorbed anions. They also pointed out that a shift of the potential of zero charge has to be assumed in order to explain the observed flow of charge during the experiments. Thus, we can assume that in the presence of SO42- related anions the excess binding energy for the system Ag(1 × 1)/Au(111) is close to 0.2 eV.

LEED experiments using HF as electrolyte,40 where the influence of anions is supposed to be minimal, also yielded six different expanded structures. In these experiments, the (1 × 1) structure was identified at underpotentials lower than 0.06 V. This is, then, the upper limit for the excess binding energy of the (1 × 1) structure in HF solution. Hence, the SO42- anions present in the above H2SO4 solutions must be responsible for more than 0.14 eV of excess binding energy. Our prediction for ∆Uex is actually a very small, or even zero, underpotential shift (see Tables 2 and 3). Therefore, if we assume that anions in HF do not affect significantly the energetics of the system, some other source should be responsible for the remaining 0.06 eV. A very plausible hypothesis is that this difference is due to water adsorption. The interaction of water with the metal surface may be stimulated by the increase in positive charge upon building up of the adsorbate layer. In fact, as pointed out by Esplandiu et al.,39 the system should show experimentally a strong shift in the potential of zero charge. This is also supported by our calculations of work function for Au(111) and Ag(1 × 1)/Au(111), where we found that the formation of the Ag monolayer should be accompanied by a lowering of the work function of 0.60.7 eV. If anions do not play any role in the case of the HF experiments, then some water species must be responsible for the existence of expanded structures. There are also two strong physical arguments against the existence of expanded structures without some “external aid” for the system Ag/Au(111). The first is that Ag and Au have a practically negligible lattice mismatch, so adsorbing Ag on Au should not introduce appreciable stress on the surface. Recent calculations41 indicate that the change in surface stress induced by the adsorption of a pseudomorphic monolayer is about one-third of that induced by the adsorption of Ag on Pt(111). Because Ag/ Pt(111) does not exhibit expanded adsorbed monolayers,35 it is very unlikely that Ag/Au(111) will do so. The second argument regards the energetics. It has been reasonably claimed that some positive charge resides on the Ag atom,40 thus giving rise to repulsive Ag-Ag interactions which would promote the existence of expanded structures. This repulsion, however, should be operative only at long distances (i.e., at several nearest neighbor distances), as recently shown by Fichthorn and Scheffler42 for adsorbates on Ag(111). At shorter distances, attraction should prevail, and the system must become increasingly more stable as long as the adsorbate layer becomes more compact. Thus, expanded structures should be less stable than pseudomorphic ones. But if they are less stable, why do they occur at higher potentials? The deposition of Cu on Pt(111) has been carried out in different electrolytes.43-47 Our prediction for the excess binding energy is relatively small (0.06 eV) when compared to the large experimentally measured underpotential shift (≈ 0.4 V). However, the result of our calculations should be compared to the underpotential shift of the pseudomorphic structure, which is difficult to infer from the

(34) Paffett, M. T.; Campbell, C. T.; Taylor, T. N. Langmuir 1985, 1, 741. (35) Wang, J. X.; Marinkovic, N. S.; Adzic, R. R.; Ocko, B. M. Surf. Sci. 1998, 398, L291. (36) Chen, C.; Vesecky, S. M.; Gewirth, A. J. Am. Chem. Soc. 1992, 114, 451. (37) Ogaki, K.; Itaya, K. Electrochim. Acta 1995, 40, 1249. (38) Garcia, S.; Salinas, D.; Mayer, C.; Schmidt, E.; Staikov, G.; Lorenz, W. J. Electrochim. Acta 1998, 43, 3007. (39) Esplandiu, M. J.; Schneeweiss, M. A.; Kolb, D. M. Phys. Chem. Chem. Phys. 1999, 1, 4847. (40) Mrozek, P.; Sung, Y.-E.; Wieckowski, A. Surf. Sci. 1995, 335, 44.

(41) Leiva, E. P. M.; Del Po´polo, M. G.; Schmickler, W. Chem. Phys. Lett. 2000, 320, 393. (42) Fichthorn, K. A.; Scheffler, M. Phys. Rev. Lett. 2000, 84, 5371. (43) Markovic, N. M.; Ross, P. N. Langmuir 1993, 9, 580. (44) Markovic, N. M.; Ross, P. N. J. Vac. Sci. Technol., A 1993, 11, 2225. (45) Markovic, N. M.; Gasteiger, H. A.; Ross, P. N. Langmuir 1995, 11, 4098. (46) Michaelis, R.; Zei, M. S.; Zhai, R. S.; Kolb, D. M. J. Electroanal. Chem. 1992, 339, 299. (47) Bludau, H.; Wu, K.; Zei, M. S.; Eiswirth, M.; Over, H.; Ertl, G. Surf. Sci. 1998, 402-404, 786.

Heterometallic Binding Energy

experiment. In this respect, it has to be remarked that the LEED pattern of ref 43 which identified the (1 × 1) structure was obtained by emersion of the electrode at a potential close to the bulk deposition potential of Cu. Auger electron spectroscopy measurements, instead, indicated the formation of a monolayer at the Nernst potential. In analogy with the Ag/Au(111) case, we argue that in Cu/ Pt(111) some water species may play a role in stabilizing the adsorbate. Inspection of voltammograms indicates that in the potential region where a Cu monolayer is desorbed (at the concentration usually employed in experiments) the Pt surface already shows evidence of the formation of some reversibly oxidized species. Clearly, the oxygen comes from the aqueous environment. Because Cu is less noble than Pt, it would be rather strange if the Cu adatoms would not form an oxidized species in this potential region. In fact, along with the deposition of the Cu monolayer, some reaction formally of the type

Cu + H2O h CuOH + H+ + e could take place, the electron being absorbed by the metallic substrate. As in the case of the early stages of the oxidation of the Pt surface, this reaction would not involve the whole Cu monolayer but rather would produce an incomplete coverage of the surface by some oxygen-containing species. In this case, the OH-, or some related species, would play the same role as the anions in stabilizing expanded adsorbed (sub)monolayers. We finally address the Cu/Au(111) system, which is the prototypical experimental underpotential deposition system. As in our previous EAM18 and first-principles calculations,21 we have not obtained a positive excess binding energy. The reasons for the strong disagreement between experimental and theoretical results have been examined in our previous work21 and must also be considered in the framework of the discussion given above. From the experimental viewpoint, the importance of anion adsorption on the system Cu/Au(111) has been shown by Shi et al.48 These authors have measured the (48) Shi, Z.; Wu, S.; Lipkowski, J. Electrochim. Acta 1995, 40, 9.

Langmuir, Vol. 17, No. 7, 2001 2227

surface excess of Cu and SO42- as a function of the electrode potential, finding a strong cooperative character between the adsorption of Cu and this anion. In the case of SO42containing electrolytes, the 1 × 1 Cu structure on Au(111) is covered by sulfate anions at a concentration of 2.2 × 1014 ions cm-2, which is very close to the limiting sulfate concentration on Au(111). On the contrary, specific anion adsorption on Au(111) is practically absent in Cu2+ free solutions at the potentials where the 1 × 1 structure occurs. Experiments in the absence of specific adsorbing anions as well as comparison with results from the metal/vacuum interface would be very useful to shed some light on the present problem. 4.5. Conclusions. We have performed systematic firstprinciples calculations for the energetics of a number of systems involving a d-metal adsorbate on a d-metal substrate. Some of the systems considered here are of common use among electrochemists, especially in the field of the so-called underpotential deposition phenomena. Our results of binding energies confirm those of a previous calculation employing the embedded atom model. In addition, the present studies reveal the relationship between the excess binding energy and the difference of surface energy between substrate and adsorbate, postulated some time ago on the basis of the simpler jellium model. First-principles results appear to underestimate the excess binding energies, which are experimentally obtained from underpotential shifts. Analysis of experimental data indicates that this discrepancy is likely to originate in an excess binding energy produced by anion and/or solvent specific adsorption. Work is in progress to assess directly the influence of these factors, by explicitly considering adsorbed anions and water molecules. Acknowledgment. E.P.M.L. and C.G.S. thank CONICET, CONICOR, Secyt UNC, and Program BID 802/ OC-AR PICT No. 06-04505 for financial support. J.K. thanks Ruth Lynden-Bell for valuable comments on the manuscript. We thank Pablo Ordejo´n and E. Artacho for facilitating and assisting with the use of the SIESTA package. LA001639J