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Surface Stress and Electrocapillarity of Solid Electrodes C. Friesen,† N. Dimitrov,† R. C. Cammarata,‡ and K. Sieradzki*,† Arizona State University, Tempe, Arizona 85287-6106, and Johns Hopkins University, Baltimore, Maryland 21218 Received June 29, 2000. In Final Form: October 31, 2000 There are two fundamental excess thermodynamic parameters that characterize a surface, the surface free energy and the surface stress. The surface free energy is the reversible work per unit area to form new surface while maintaining a constant equilibrium density of surface atoms. The surface stress is the reversible work per unit area required to form new surface by elastic deformation of a preexisting surface, and thus the atom density is altered. For a fluid surface the surface free energy is equal to the surface stress, but for a solid this is in general not true. We develop thermodynamic arguments that describe proper interpretations of wafer curvature experiments that are typically used in electrocapillarity experiments of solid electrodes. Additionally, we consider stress evolution during underpotential deposition. The sources of stress relate to electrocapillarity differences between overlayer and substrate, interface stress, and coherency stress. Experimental results are presented for the systems Pb2+/Au(111), Pb2+/ Ag(111), and Ag+/Au(111). We show how it is possible to use the experimental data to extract results for the interface stresses in each of these systems. The following values of interface stress were determined: for the incommensurate Pb/Au(111) interface, 1.76 ( 0.04 N/m; for the incommensurate Pb/Ag(111) interface, 0.9 ( 0.04 N/m; and for the coherent Ag/Au(111) interface, -0.08 ( 0.04 N/m. Finally, we employ the thermodynamic arguments developed to consider two important problems in the electrocapillarity of solids. The first is a comparison of the magnitude of the change in surface free energy and surface stress that result from pure double - layer effects. The second is the potential-induced 23 × x3 S (111) reconstruction that occurs on Au surfaces. Here, we calculate the difference in surface stress between the reconstructed and unreconstructed surface, obtaining -0.43 N/m, which compares favorably with recently published experimental results.
1. Introduction This paper is concerned with the measurement and interpretation of stress evolution during the electrodeposition of ultrathin films. One aspect of this problem relates to the electrocapillarity behavior of a solid and exactly which quantities are measured in a so-called wafer curvature experiment. In such experiments, the metal electrode in the form of a thin sheet or cantilever bends in response to an applied variation in potential. This bending is measured as a change in curvature of the solid electrode with potential and is often described in terms of a surface stress variation. There are various sources that can contribute to the measured changes in surface stress, including electrocapillarity, coherency stress, and interfacial stress. This paper considers each of these sources in detail and describes a thermodynamic framework within which we can interpret wafer curvature experiments. The electrocapillarity behavior of solid electrodes is described by the modified Lippmann equation, yet over the years, there has been some confusion in the literature concerning the proper usage and interpretation of this equation. In section 2, we discuss this and demonstrate that it does accurately describe the electrocapillarity behavior of solid electrodes. Two important and related examples are considered at the end of this paper. The first addresses the electrocapillarity of Au(111) surfaces. Here we use a thermodynamic argument to estimate the change in surface stress with potential that is to be expected owing to double-layer charging effects. The second example that we consider is the potentialinduced 23 × x3 S (111) reconstruction. We use the modified Lippmann equation to estimate the change in † ‡
Arizona State University. Johns Hopkins University.
surface stress that occurs owing to the reconstruction and compare this result to recent measurements of this quantity. The Stranski-Krastanov (SK) thin film growth mode is characterized by the formation of one or several initial wetting layers followed by three-dimensional (3D) cluster growth. A number of electrochemical overlayer/substrate systems that display underpotential deposition (upd) undergo this form of growth. We have previously used in situ scanning tunneling microscopy to study the system 5 × 10-4 M Ag+ + 0.1 M HClO4/Au (111).1 This work showed that two underpotentially deposited wetting layers of Ag form in this system and that subsequent growth occurs by kinetically driven 3D islanding and coalescence. Recently we used ion channeling to characterize the epitaxy between a 200 nm thick Ag overlayer grown on a Au(111) single crystal in the same electrolyte.2 These results demonstrated that there was a high degree of lattice matching between overlayer and substrate, even though the formation and coalescence of 3D islands dominate growth. The lattice misfit, em, is defined by
em )
aS - af af
(1)
where af is the lattice parameter of the film and as is the lattice parameter of the substrate. For the system Ag/ Au(111), the misfit is -0.0019. The purpose of the experimental study reported on herein is to examine stress evolution during the initial stages of electrochemical thin film growth in systems that display upd. We have examined stress evolution for the systems Pb2+/Au(111), Pb2+/Ag(111), and Ag+/Au(111) by (1) Corcoran, S. G.; Chakarova, G. S.; Sieradzki, K. Phys. Rev. Lett. 1993, 71, 1585. (2) Brankovic, S. R.; Dimitrov, N.; Sieradzki, K. Unpublished results.
10.1021/la000911m CCC: $20.00 © 2001 American Chemical Society Published on Web 01/06/2001
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using an in situ cantilever beam deflection technique that measures strain as a function of film thickness. In section 2, we discuss thermodynamic issues associated with wafer curvature or beam deflection type measurements in electrolytes, and in section 3 the experimental details of our measurements are provided. The results are presented and analyzed in section 4 and discussed in section 5, and in section 6 we summarize our results. 2. Preliminary Considerations and Thermodynamic Issues Associated with Wafer Curvature or Beam Deflection Measurements in Electrolytes The reversible work per unit area involved in forming a surface (exposing new atoms) is the surface free energy γ. This parameter describes the reversible work per unit area to form new surface by adding area or atoms at the equilibrium interatomic spacing. An example of such a process is cleavage. The surface stress, f, is associated with the reversible required to elastically deform a surface. In this process, surface area is altered by changing the density of atoms on the surface. When a fluid surface is stretched, new atoms or molecules arrive at the surface such that the time-average number of atoms per unit area remains constant. As a result, for a fluid, the surface free energy is equal to the surface stress. On the other hand, when a solid surface is elastically stretched, the actual number of atoms per unit area is altered and, in general, f * γ. At the atomic scale the origin of the surface stress is easily seen by the following heuristic argument. Consider a half-space of a metal single crystal. The surface atoms reside in a lower electron density compared to the bulk atoms and therefore wish to adopt an equilibrium spacing different from the bulk. The bulk atoms, however, impose the constraint that the surface atoms are forced into registry with the underlying lattice. In this sense the surface atoms are strained and the surface has a stress being exerted on it by the underlying lattice. Generally, for low-index metal surfaces the atoms would prefer to adopt a smaller equilibrium spacing than the bulk in order to increase the local electron density, so that the coherency constraint results in a surface tensile stress. Since the surface is free of normal stresses, relaxation normal to the surface occurs resulting in a variation of the nearsurface interplanar spacing. For a very few metals, the constraint imposed by the bulk is energetically too costly and the surface adopts a lower free energy state by undergoing a reconstruction that increases the surface density of atoms. In many ways this reconstruction is similar to the coherent/incoherent transition of an epitaxial monolayer on a solid substrate.3 In the thermodynamics of surfaces as formulated by Gibbs,4 the amount of reversible work dw performed to form new area dA of a fluid or solid surface can be expressed as
dw ) γ dA
(2)
The total work needed to create a planar surface of area A (equivalently, the total excess free energy of the surface) is equal to γA. Gibbs4 noted that in the case of solids there is a second type of quantity, called the surface stress, associated with the reversible work needed to elastically (3) Cammarata, R. C.; Sieradzki, K. Annu. Rev. Mater. Sci. 1994, 24, 215. (4) Gibbs, J. W. The Scientific Papers of J. Williard Gibbs, Vol. 1; Longmans-Green: London, 1906; p 55.
deform a preexisting surface. The surface stress, fij, is a tensor quantity and is defined by the expression describing the reversible work dwsur to introduce a surface strain, i.e., dwsur ) d(γA) ) Afij dij. The relationship between the surface stress and the surface free energy is described by the Shuttleworth equation:5
fij ) γδij + ∂γ/∂ij
(3)
where ij is the surface strain tensor and δij is the Kronecker delta. For a general surface, the surface stress tensor can be referred to a set of principal axes such that the offdiagonal components are equal to zero. For a surface possessing a 3-fold or higher rotation axis of symmetry, the surface stress is isotropic and can be taken as a scalar, i.e., f ) γ + ∂γ/∂. For most solids, f is generally of the same order of magnitude as γ and can be positive or negative. Theoretical calculations of surface stresses generally involve calculating the surface free energy and its derivative with respect to elastic strain. Both first-principles and semiempirical atomic potential calculations involving computer simulations have been attempted; however, only first-principles approaches yield accurate values for surface stress.3 Tabulated values of the surface stress and surface energy for a variety of metals, ionic solids, and semiconductors can be found in the recent review by Cammarata and Sieradzki.3 Experimentally, surface stress is a difficult parameter to measure. Two primary techniques that have been used are lattice parameter measurements (involving transmission electron microscopy) as a function of particle size6-8and wafer curvature. Wafer curvature techniques have the advantage that they can be used under a variety of experimental conditions, e.g., during thin film growth in a vacuum or electrolytes. Here, as discussed below, a thin rectangular wafer whose top and bottom surfaces have different surface stresses will bend in response to that difference. By measuring the radius of curvature of the bent wafer, the difference in the surface stresses of the two surfaces, ∆f, can be determined. Couchman and Davidson9 were the first to obtain a version of the Gibbs adsorption equation appropriate for plane solid/electrolyte interfaces:
dγ ) -s dT + 2(f - γ) d - q dV -
∑i Γi dµi
(4)
where T is the temperature, is the linear elastic strain, µi is the chemical potential of species i, and s, Γi, and q denote, respectively, per unit area, surface excesses of entropy, species i, and charge. At fixed T and µi
dγ (dV )
T,µi
) -q + 2(f - γ)
d (dV )
T,µi
(5)
which is the electrocapillarity equation for solid electrodes in analogy with the standard Lippmann equation for fluid/ fluid electrochemical interfaces. This relation describes how the solid/electrolyte interfacial free energy changes with electrode potential under the indicated constraints assuming ideal polarized electrode behavior. Note that (5) Shuttleworth, R. Proc. R. Soc. 1950, A63, 445. (6) Mays, C. W.; Vermaak, J. S.; Kuhlmann-Wilsdorf, D. Surf. Sci. 1968, 12, 134. (7) Wassermann, H. J.; Vermaak, J. S. Surf. Sci. 1970, 22, 164. (8) Wassermann, H. J.; Vermaak, J. S. Surf. Sci. 1972, 32, 168. (9) Couchman, P. R.; Davidson, C. R. J. Electroanal. Chem. 1977, 85, 407.
Solid Electrode Surface Stress and Electrocapillarity
the standard equation appropriate for a liquid metal electrode is recovered by setting f ) γ. Lin and Beck10 reported perhaps the first measurements for the change in surface stress, ∆f, with electrochemical potential for polycrystalline thin Au ribbons in electrolytes. As discussed below, in such experiments one typically measures a change in f with respect to an arbitrary reference zero stress state. A sensitive extensometer method was used to measure ribbon extension as a function of the electrochemical potential (measured with respect to the potential of zero charge). In Appendix B of their paper they argued that the dγ/d term makes a negligible contribution to the change in surface stress, so that ∆γ = ∆f. This conclusion results from an error in their analysis. Following integration of their eq B5, they considered the asymptotic behavior of γ as approaches zero, resulting in the erroneous conclusion that ∆γ = ∆f. If one evaluates the constants of integration and performs a Taylor series expansion about ) 0, an entirely different conclusion is reached, i.e., that the dγ/d term is not negligible and that ∆γ ) (f - γ). We note that several other researchers11-14 have assumed that ∆γ = ∆f (citing Lin and Beck’s work) in the interpretation of their own experiments related to electrocapillarity of solids. We revisit this issue in some detail at the end of this paper. In experiments such as those of Lin and Beck,10 or others where wafer curvature is employed,11,12 measurement of electrode strain (or curvature) as a function of potential yield results for ∆f (via elastic constitutive relations) as a function of electrode potential. A typical value of ∆f for Au(111) surfaces in these experiments for potential changes of 0.5 V is 0.5 J m-2. For the same change in electrode potential, the order of magnitude of strain involved in any of these experiments10-13 is 10-6. Since (f - γ) is of order unity,3 the (f - γ) d/dV term in the electrocapillarity equation makes a negligible contribution to dγ/dV compared to q, which is of order 0.1 C m-2 over the same 0.5 V change in electrode potential, i.e., ∆γ ∼ 0.05 J m-2.. In the case of solid/electrolyte interfaces, the quantity ∆γ can be determined (assuming that there is no change in surface structure) as for liquid-metal/ electrolyte interfaces, by measuring the charge density (at fixed strain) as a function of the electrode voltage, i.e., q(V) can be obtained via on-line integration of the current. Electrochemically induced alterations in surface stress also occur in processes such as monolayer adsorption or underpotential deposition (upd). Wafer curvature or similar techniques are typically used to measure the change in surface stress associated with overlayer formation. In general, this change will include stress contributions from the solid/solid and solid/electrolyte interface as well as the elastic energy per unit area associated with the coherency strain in the overlayer. Cammarata et al.15 have described the appropriate thermodynamic work terms for this epitaxy problem. Since in electrochemical deposition ∆f ) ∆f(∆V), the surface stress of the overlayer and substrate surfaces must be evaluated separately at a fixed value of potential corresponding to the deposition potential. An interface between two solid phases has two interface stresses since each of the phases can be independently (10) Lin, K. F.; Beck, T. R. J. Electrochem. Soc. 1976, 123, 1145. (11) Raiteri, R.; Butt, H.-J. J. Phys. Chem. 1995, 99, 15728. (12) Haiss, W.; Sass, J. K. J. Electroanal. Chem. 1996, 410, 119. (13) Ibach, H.; Bach, C. E.; Giesen, M.; Grossman, A. Surf. Sci. 1997, 375, 107. (14) Brunt, T. A.; Chabala, E. D.; Rayment, T.; O’Shea, S. J.; Wellend, M. E. J. Chem. Soc., Faraday Trans. 1996, 92, 3807. (15) Cammarata, R. C.; Sieradzki, K.; Spaepen, F. J. Appl. Phys. 2000, 87, 1227.
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strained. Cahn and Larche16 define two strains, ij and eij, associated with a general deformation of the interface. The strain ij corresponds to straining both phases equally, while eij is the strain associated with stretching one phase with respect to the other. We note that eij will cause an alteration in the interface structure corresponding to the introduction or removal of misfit dislocations. A reference area, A, also needs to be defined,3,15 which can be taken as
A ) A0(1 + eijδij + ijδij)
(6)
where A0 is the area at zero strain. Once a reference area is set, we define an interfacial free energy σ as the reversible work to form the unit area of interface. Associated with the two strains are two interface stresses related to the reversible work per unit area to elastically stretch the interface. The total reversible work per unit area to deform the interface can be expressed as3,15
dwint ) A(gij deij + hij dij)
(7)
where the interface stresses g and h are defined by
gij ) σδij + ∂σ/∂eij
(8)
hij ) σδij + ∂σ/∂ij
(9)
and
In analogy with the situation for a surface, if the interface has a 3-fold or higher rotation axis of symmetry, g ) σ + ∂σ/∂e and h ) σ + ∂σ/∂. Consider an interface formed by placing an overlayer on a substrate. We take the reference state of the system to be that defined by a fully relaxed incoherent interface, so that the film and substrate display their bulk equilibrium lattice parameters. The structure of the interface is a two-dimensional array of edge dislocations in which the Burgers vectors lie in the plane of the interface. The interfacial free energy per unit area can be expressed as3
σ0 ) RCb
(10)
where C is a composite elastic modulus, C ) 2[(1 - νf)/µf + (1 - νS)/µS]-1, b is the magnitude of the of the Burgers vector of the interface dislocations, and R ) |em|/2π[ln (R/ b) + 1]. The quantities ν and µ are the Reuss average Poisson’s ratio and shear modulus for the film and substrate.17 Note that this model of the interface energy only accounts for the structure and neglects the energy associated with chemical differences across the interface; i.e., a coherent interface has zero energy in this model. In a more complete model of the interface energy, there would also be a chemical term added to eq 10 corresponding to the energy of a coherent interface. If the overlayer is strained by an amount e with respect to the substrate (as would be the case if part of the misfit were uniformly accommodated as coherency strain) the interfacial free energy can be expressed as
σ ) σ0|1 - (e11 + e22)/2em|
(11)
where e11 and e22 are the in-plane (coherency) strain components. We are now in a position to write a general expression for the energy per unit area, dwint, involved (16) Cahn, J. W.; Larche, F. Acta Metall. 1982, 30, 51. (17) Hirth, J. P.; Lothe, J. In Theory of Dislocations, 2nd ed.; John Wiley and Sons Inc.: New York, 1982; p 836.
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with the introduction of a coherency strain in the overlayer:
dwint ) 2(f - γ) de + 2(g - σ) de + 2Σcohtf de
(12)
The factor of 2 appearing in the coefficients comes from straining the overlayer along two orthogonal directions (i.e., biaxially). The second term describes the change in film/substrate interface energy with strain [(∂σ/∂e) de], altering the dislocation density in the interface. This change in interface structure alters the coherency strain energy in the overlayer by an amount 2Σcoh de. The coherency stress, Σcoh, (in units of newtons per square meter) is expressed as an equivalent surface stress by multiplying by the film thickness, tf. This term may also be written as the product Yte de, where Y is the biaxial modulus of the overlayer. At fixed T, V, and µi
dwint ) 2(f - γ) de + 2(g - σ) de + 2Yte de (13) Integration of this equation at fixed T, V, and µi yields3,15
wint ) 2(f - γ)e + 2(g - σ)e + Yte2
(14)
In a wafer curvature experiment one measures a change in curvature, ∆κ, or alternatively uniform strain (i.e., ∆) of the substrate and overlayer. The Stoney equation is derived by writing the total energy of two terms: (1) the surface work of uniform stretching involving all the sources of surface stress and (2) the bulk strain energy (related to the bending) of the deformed wafer. By minimizing this energy with respect to the uniform strain , one obtains an expression for the total measured change in surface stress, ∆F:
∆F ) ∆Σinttf ) (1/6)MStS2∆κ ) (2/6)MStS
(15)
where tf is the film thickness, ts is the substrate thickness, and Ms is the biaxial modulus of the substrate. The quantity Σint (in units of newtons per square meter) contains all the sources of intrinsic stress associated with overlayer formation. The sources of the measured induced uniform strain (equal to ∆κts/2) are the following: the difference between intrinsic surface stresses of overlayer and substrate ∆f, the interface stress ∆h, and the surface stress Σcohtf. The measured change in surface stress, ∆F, may be written as
∆F ) ∆f + ∆h + ∆Σcohtf
(16)
We note that the ∆f term is the difference of the intrinsic surface stress of overlayer and substrate including an electrocapillarity correction related to the difference in the potential of zero charge (pzc) of the overlayer and substrate. There is no contribution of the surface stress parameter g to the measured ∆κ. Wafer curvature techniques have been used to measure surface stress changes during upd of metals onto foreign metal substrates. Brunt et al.14,17 measured the change in surface stress for Au(111) during Pb upd from a 0.1 M HClO4 + 10-3 M Pb(ClO4)2 electrolyte. At full monolayer coverage this system is fully incommensurate.18,19In this case, there should be no contribution of coherency stress to the measured change in surface stress. They found that during the Pb upd process the total surface stress decreased by about 1 N m-1. In a region following the (18) Melroy, O. R.; Toney, M. F.; Borges, G. L.; Samant, M. G.; Kortright, J. B.; Ross, P. N.; Blum, L. Phys. Rev. 1988, B38, 10 962. (19) Toney, M. F.; Gordon, J. G.; Samant, M. G.; Borges, G. L.; Melroy, O. R.; Yee, D.; Sorenson, L. B. J. Phys. Chem. 1995, 99, 4733.
deposition of the full Pb upd monolayer and prior to bulk Pb deposition, they found an almost linear decrease in the surface stress (0.3 N m-1) over the voltage range of 0-150 mV vs Pb/Pb2+. In separate grazing incidence X-ray scattering experiments (GIXS), Toney et al.19 determined that in this potential region the Pb monolayer was compressing by about 2%. These results demonstrate the magnitude of surface stress changes that occur during upd processes. Brunt et al.14 also examined stress generation during deposition of Ag on Au(111) in the upd regime; however, they made no attempt to understand the detailed nature of their results. 3. Experimental Section Silver and gold films of 200 nm nominal thickness were prepared by evaporation onto freshly cleaved mica substrates at 340 °C at a deposition rate of 0.02 nm/s. The depositions produced films with exclusively {111} textures.1 These structures served as cantilevers in the experiments described below. All glassware, Teflon holders, and electrochemical cells used in the experiments and preparation of electrolytes were cleaned by immersion in concentrated HNO3 and H2SO4 at 70 °C and then rinsed with doubly distilled and Barnstead Nanopure (18.3 MΩ) water. The Pt counterelectrode was prepared just before each experiment by immersion in HNO3 at 70 °C for 5 min followed by hydrogen flame annealing for 2 min. It was then rinsed in Nanopure water for 30 s. In the experiments involving Pb deposition, a 99.99% pure Pb wire served as a pseudo-reference electrode. It was prepared by placing it in HNO3 at 70 °C for 1 min followed by rinsing with Nanopure water. In the electrocapillarity experiments and for the depositions of Ag on the Aucoated mica cantilevers, a standard calomel electrode in conjunction with a salt bridge containing 5 × 10-4 M Ag+ + 0.1 M HClO4 served as the reference electrode. All cyclic voltammetry was performed with a Bioanalytical Systems CV-27 potentiostat. The data were collected with a Nicolet 310 oscilloscope. The working and reference electrodes were both placed 1 cm from the working electrode. Pb deposition experiments were performed in an electrolyte containing 0.01 M Pb2+ + 0.1 M HClO4. Unless otherwise noted, all results are reported with respect to the 0.01 M Pb2+/Pb pseudo-reference electrode. In situ stress monitoring of the electrochemical processes was performed in a 150 mL flat-bottomed rectangular cell. The (cantilever) working electrode surface area was 3 cm2. It protruded out of its holder 3 cm and was struck by the laser beam at a distance of 2.0 cm from the clamp. Electrical contact with the thin film was made with a thin piece of gold foil. The foil was coated on one side with enamel and placed between the clamp and the working electrode. To limit clamping effects, the Teflon clamp was tightened with the minimum force required to hold the electrode in place. A beam from a 30 mW diode pumped laser was reflected from the cantilever and the deflection was measured with a bi-celltype photodetector. The current that was produced in each detector was amplified and appropriate electronic circuit components were employed to develop a signal representing the sum and difference of incident light on the two detectors. The difference signal was then divided by the sum signal and amplified. The resulting voltage was measured with the oscilloscope. Calibration of the deflection measurement was done by utilizing the stepping motor of a Digital Instruments AFM base to deflect the beam by a prescribed amount. After each experiment the appropriate biaxial modulus of the wetted cantilever was determined by measuring the deflection of the cantilever resulting from the application of a prescribed force. The elastic modulus, Ms, was then calculated by use of small displacement beam theory. Unless otherwise noted, the error in all the surface stress change measurements is (0.04 N/m. McNeil and Grimsditch20 used Brillouin scattering to measure the 13 independent elastic constants of mica. Mica is a layered (20) McNeil, L. E.; Grimsditch, M. J. Phys.: Condens. Matter 1993, 5, 1681.
Solid Electrode Surface Stress and Electrocapillarity
Figure 1. Electrocapillarity curve for Au (111) in 0.1 M HClO4. Sweep rate 10 mV s-1. monoclinic material that has highly anisotropic elastic properties. However, they reported that the anisotropy in the basal plane is small. If the hexagonal basal plane was isotropic, C66 ) (C11 - C12)/2, one would expect C66 ) 65.2 GPa, which is to be compared to the measured value of 70.7 ( 0.6 GPa. Thus the degree of anisotropy in the basal plane is small. Using the Cij values that they report, we find that for a mica substrate Ms ) 221 ( 1.0 GPa. Our calibration procedure yielded a value of Ms ) 230 ( 10 GPa, and we consider this agreement to be adequate.
4. Results and Analysis 4.1. Electrocapillarity Behavior of Au(111). Figure 1 shows our results for the electrocapillarity behavior for Au(111) in 0.1M HClO4. The equilibrium structure of the as-deposited Au(111) surface is the reconstructed 23 × x3 structure. Numerous experiments have demonstrated that a similar reconstruction exists in electrolytes and that potential excursions to about 0.2 V positive of the pzc lifts the reconstruction and results in a bulk-terminated (111) surface.21,22Potential excursions negative of the pzc eventually result in recovery of the reconstructed surface. The results shown in Figure 1 were obtained after six potential cycles and are representative of a surface that is bulk-terminated. The right ordinate scale has the surface stress maximum referenced to 2.77 N/m obtained from first-principles calculations for the bulk-terminated Au(111) surface.3 4.2. Surface Stress Evolution during upd for the system Pb2+/Au(111). Figure 2 shows the cyclic voltammetry and change in surface stress as a function of potential during upd of Pb for the system Pb2+/Au (111). The labeled regions on the stress-potential curve have the following interpretations that we base on the X-ray scattering results of Toney et al.19: A - B corresponds to a rotation of the incommensurate Pb adlayer by 2.5°, B - E is the electrocompression behavior of the adlayer in the cathodic scan direction, E - C is the electrocompression behavior of the adlayer in the anodic scan direction, and C - D is the collapse of the rotation back to 0°. We note that, over the time scale of our experiments, in situ scanning tunneling microscopy for this system23,24has (21) Kolb, D. M. Prog. Surf. Sci. 1996, 51, 109. (22) Wang, J.; Ocko, B. M.; Davenport, A. J.; Isaacs, H. S. Phys. Rev. B 1992, 46, 10231. (23) Tao, N.; Pan, J.; Li, P.; Oden, P.; Derose, J.; Lindsay, S. Surf. Sci. 1992, 271, L338.
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Figure 2. Cyclic voltammetry (dashed line) and surface stress potential (solid line) behavior for upd for the system Pb2+/ Au(111) in 0.01 Pb(ClO4)2 + 0.1 M HClO4. Scan rate 50 mV s-1; arrows indicate direction.
shown that no roughening of the Au surface occurs after the Pb adlayer is stripped from the surface, and we have obtained similar results in our own laboratory. Therefore, in what follows, we neglect the possibility of surface alloying in interpreting our results. The relaxation of the Pb adlayer observed in Figure 2 (A - B) occurs in the range of 210-180 mV prior to the completion of the full monolayer. This result differs from that found by Toney et al.,19 who observed the relaxation in the potential range 160-130 mV where a full coverage Pb monolayer is present. We attribute this to the different in-plane mosaic spreads likely present in the Au thin films owing to differences in vacuum deposition parameters. Point D with coordinates (0.249, -0.21) corresponds to a fully relaxed Pb adlayer (see below) in the anodic scan direction. At 0.249 mV the Au(111) electrode shows a change in electrocapillarity-induced surface stress of -0.03 N/m (electrocapillarity correction), so at point D, ∆F ) -0.18 N/m. This ∆F includes contributions related to interface stress h and the surface stress difference ∆f between Pb and Au. The pzc (vs 0.01 M Pb2+/Pb) for bulk-terminated Au(111) is 657 mV,21 and the pzc for Pb(111) is -433 mV. We should in principle make a similar electrocapillarity correction for the Pb adlayer; however, since the intrinsic f value for Pb is small (see below) this correction would fall within the measurement error. The behavior shown in Figure 2 is independent of scan rate in the range 2-200 mV s-1 except for the region describing the rotation of the adlayer in the anodic scan direction. Figure 3 shows results for the region C - D of Figure 2 as a function of scan rate. As the scan rate is lowered the relaxation associated the counterrotation of the adlayer becomes more pronounced and the stresswave positions shift slightly to lower potentials. These results indicate that the counterrotation process is slow and likely involves adatom diffusion over small distances. We now discuss the electrocompression region (E - C) of Figure 2. The origin of the electrocompression is incorporation of Pb atoms into the adlayer with decreasing potential. We have used the results of Toney et al.19 to convert the stress change-potential curve in this region (24) Chen, C.; Washburn, N.; Gewirth, A. J. Phys. Chem. 1993, 97, 9754.
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Figure 3. Results for region C - D of Figure 2 as a function of scan rate. Scan rates are (in sequential order from solid top curve to dotted bottom curve) 1, 10, 30, 50, and 200 mV s-1.
Figure 5. Cyclic voltammetry (dotted line) and surface stress potential behavior (heavy solid line) for the system Pb2+/ Ag(111) in 0.01 Pb(ClO4)2 + 0.1 M HClO4. Electrocapillarity curve of Ag in 0.1 M HClO4 is shown as the light solid line. Scan rate was 50 mV s-1. The stress axis is referenced to that of Au(111); see Figure 7.
Figure 4. ∆F - curve in the electrocompression region (anodic sweep) E - C of Figure 2. The data have been fit to a straight line (shown as a dashed line) of slope 9.42 N/m and intercept -0.19 N/m.
to a stress-strain curve, and the results are shown in Figure 4. The change in surface stress plotted on the ordinate corresponds to ∆F in eq 16. This equation can be written in terms of strain by noting that Σcoh)Y111e, where Y111 is the biaxial modulus defined by Y111 ) E111/ (1 - ν111), where E111 ) 4/(2S11 + 2S12 + S44) and ν111) (2S11 + 10S12 - S44)/12 and the Sij values are the elastic compliances. Here we treat the electrocompression stress as a coherency stress. Substituting appropriate compliance values for Pb17 yields a value of Y111 ) 5.92 × 1010 Pa. Rewriting eq 16 yields
∆F ) ∆f + ∆h + Ytfe
(17)
This equation can be used to interpret the results of Figure 4. The quantity Ytf can be viewed as the biaxial modulus of the layer, which is defined by the slope of the line in Figure 4. This is equal to 9.42 N/m and can be compared to the result of Toney et al.19 They reported a twodimensional compressibility of the Pb adlayer on Au(111), κ2D = 1.7 Å2/eV, corresponding to a layer biaxial modulus of 9.43 N/m [i.e., κ2D ) (Ytf)-1]. Another quantity that we can compare the layer biaxial modulus against is the product of the bulk Y111 () 5.92 × 1010 Pa) and the (111) Pb interplanar spacing (0.2856 nm), which turns out to be 16.9 N/m. This significant overestimate of the layer modulus (by almost a factor of 2) is not surprising since
the calculation uses the modulus for a layer in the bulk solid rather than a layer at a free surface. Finally, we determine the magnitude of the interface stress h for this system at point E in Figure 2, where the interface is fully incoherent. This is just prior to where bulk deposition of Pb occurs. Now, according to eq 16, ∆F ) ∆f + ∆h. To determine ∆f, we make use of available first-principles results for the surface stress of clean unreconstructed Pb(111) and Au(111) surfaces.3 The surface stress for Au(111) is 2.77 N/m and that of Pb(111) is 0.82 N/m, so ∆f ) -1.95 N/m. At point E, ∆F ) -0.48 N/m, so that ∆h ) 1.47 N/m. 4.3. Surface Stress Evolution during upd for the System Pb2+/Ag(111). Figure 5 shows the cyclic voltammetry and surface stress as a function of potential during upd of Pb for the system Pb2+/Ag (111). These results will be analyzed in an analogous manner to those presented in Figure 2. We note that the upd Pb layer is incommensurate and rotated by 4.5° with respect to Ag(111)19 and that under the conditions employed in these experiments interfacial alloying in this system does not occur.25,26The surface stress change associated with going from the Ag(111) surface to the Pb(111) surface plus the interface term (∆h) is 0.2 N/m. Figure 6 shows the electrocompression region with a slope of 8.80 N/m. This behavior was independent of scan rate over the range 2-200 mV s-1. Toney et al.19 reported a two-dimensional compressibility of the Pb adlayer on Ag(111) of 1.25 Å2/ eV, which corresponds to a layer biaxial modulus of 12.8 N/m. This difference is somewhat surprising in view of the excellent agreement obtained for the layer biaxial modulus between our stress measurements and X-ray work19 for the system Pb/Au(111). Presently, we can offer no explanation for this. Our results indicate a layer modulus of 8.80 N/m, which is significantly closer to the value found for the Pb adlayer on Au(111). Again as before, we estimate the interface stress, ∆h, at point A, which is just prior to where bulk Pb deposition occurs. Unfortu(25) Vitanov, T.; Popov, A.; Staikov, G.; Budevski, E.; Lorenz, W. J.; Schmidt, E. Electrochim. Acta 1986, 31, 981. (26) Carnal, D.; Oden, P. I.; Muller, U.; Schmidt, E.; Siegenthaler, H. Electrochim. Acta 1993, 40, 1223.
Solid Electrode Surface Stress and Electrocapillarity
Figure 6. ∆F - curve in the electrocompression region (anodic sweep) for Pb2+/Ag(111). The data have been fit to a straight line (shown as a dashed line) of slope 8.80 N/m and intercept -0.28 N/m.
nately there are no first-principles results for the surface stress of Ag(111); however, we have an experimental value of 2.0 N/m (as discussed below in reference to Figure 7), resulting in a ∆f ) -1.2 N/m. At point A (Figure 5), ∆F ) 0.20 N/m, so that ∆h ) 1.40 N/m. Since the pzc values of Ag(111) and Pb(111) differ by only 140 mV, electrocapillarity corrections to these values do not seem warranted. 4.4. Surface Stress Evolution during upd for the System Ag+/Au(111). To examine the stress evolution for the system Ag+/Au(111), experiments were designed in the following manner. First the surface stress behavior was studied in a solution containing 5 × 10-5 M AgClO4. Subsequently 10-3 M Pb2+ ions were added as Pb(ClO4)2, and Pb upd was performed on the system 10-3 M Pb2+/ Ag(111)wetting/Au(111). The sweep rate for this set of experiments was 10 mV s-1. The results of these experiments are summarized in Figure 7. The dashed line is the electrocapillarity curve for Au(111) in 1 M HClO4 (from Figure 1). The light solid line shows the upd behavior of 0.01 M Pb2+/Au(111) (from Figure 2). The heavy solid lines (arrows indicate the scan direction) show the upd behavior of two wetting layers, Ag+/Au(111), followed by upd of Pb2+ on the (underpotentially) deposited Ag adlayers. The Pb2+/Ag(111)wetting part of this surface stress curve is virtually identical to that shown in Figure 5. The charge associated with Ag stripping was 550 µC cm-2, corresponding to about 2.5 ML of Ag. The voltammetry clearly shows two waves in the vicinity of 800 mV that correspond respectively to stripping of the overpotentially deposited Ag and stripping of the second upd Ag monolayer. We have compared the electrocompressibilty of the incommensurate Pb adlayer in Figure 7 to that in Figure 6 and they are in agreement to within 0.04 N/m, which represents the uncertainty in our surface stress change measurements. At 0 mV, the Pb/Au(111) surface stress curve is separated from the Pb/Ag(111)wetting/Au(111) stress change curve by 0.12 N/m. We have found that continued deposition of Pb (in the overpotential deposition regime) results in these two curves asymptotically approaching one another. Recall that we determined that, at 0 V (vs Pb2+/Pb), h for the system Pb/Au(111) is 1.47 N/m and h for the system Pb/Ag(111) is 1.4 N/m. The surface stress difference of
Langmuir, Vol. 17, No. 3, 2001 813
Figure 7. Cyclic voltammetry (dotted line) and change in surface stress (heavy solid line) for the sequential upd of Ag+/ Au(111) followed by upd of Pb2+/Ag(111)/Au(111). Arrows indicate scan direction. The surface stress difference, ∆f, between Au(111) and Ag(111) at 200 mV is 0.72 N/m. Electrocapillarity curve for Au (dashed line), from Figure 1, and upd of Pb2+/Au (111) (light solid line), from Figure 2, are shown for comparison.
0.12 N/m indicated in Figure 7 corresponds to a combination of the epitaxial surface stress and the interface stress, h, for Ag(111)/Au(111) and the difference between the interface stresses for Pb/Au(111) and Pb/Ag(111). Previous work1,27 has demonstrated that no interfacial alloying occurs for this system. Additionally, owing to S-K growth for Ag+/Au(111), we ignore the contribution of the partially completed third Ag layer to the coherency stress. Y111 for Ag has a value of 1.73 × 1011 Pa and the misfit strain is -0.0019, resulting in a coherency stress of -3.3 × 108 Pa. The product of the coherency stress and the film thickness [corresponding to twice the Ag(111) interplanar spacing] yields a surface stress of -0.156 N/m. Setting up a balance of surface stresses (in newtons per meter)
-0.12 + (∆f + ∆h)Pb/Au(111) ) (∆f + ∆h)Ag/Au(111) + (∆f + ∆h)Pb/Ag(111) + Σcohtf -0.12 - 0.48 ) -0.72 + ∆hAg/Au(111) + 0.2 - 0.156 allows us to conclude that h for the coherent Ag(111)/ Au(111) is very small, i.e., on the order of 0.08 ( 0.04 N/m. 5.0 Discussion Our estimates of the interface stress, h, assume that the magnitude of the intrinsic surface stresses are not significantly altered by specific adsorption effects. Assuming this to be the case, one can always make appropriate electrocapillarity corrections. Equation 5 describes how the surface free energy changes with the intensive parameters, T, , V, and µi, which allows us in principle to determine how adsorption alters γ, given the adsorption isotherm, i.e., Γ ) Γ(µi). To ascertain whether adsorption processes are affecting electrocapillarity behavior, we need an estimate of the magnitude of the doublelayer-induced change in intrinsic surface stress. Consider (27) Corcoran, S. G.; Chakarova, G. S.; Sieradzki, K. J. Electroanal. Chem. 1990, 377, 85.
814
Langmuir, Vol. 17, No. 3, 2001
Friesen et al.
eq 4 at fixed T, e,and µi
dγ ) -q dV + 2(f - γ) d
(17)
and the Maxwell relation that we derive from it:
( ) (
∂q ∂
)
∂(f - γ) )2 V ∂V
(18)
∂γ (∂V∂f ) ) (∂V ) - 21(∂q∂)
(19)
V
The first term on the right-hand side of eq 19 is equal to -q. The second term can be evaluated as follows. Since 2d ) dA/A, 1/2(∂q/∂)V ) A(∂q/∂A)V. Upon taking derivatives and recognizing that the charge density is defined as the charge, Q, per unit area, A, i.e., q ) Q/A, and q ) cV, where c is the capacitance, C, per unit area, we obtain
A
∂q (∂A )
) -q + V
(∂Q ∂A )
V
) -q + cV + C
( ∂V∂A)
V
) 0 (20)
The last term on the right-hand side of this equation is zero, and since cV ) q, we arrive at the interesting result under the indicated constraints:
∂γ (∂V∂f ) ) (∂V )
(21)
Owing to double-layer effects, over a potential variation of 0.5 V, we expect a charge accumulation on the order of 0.1 C/m2. In the region of almost constant slope of Figure 1, the magnitude of the ∂(F)/∂V term is about 1 C/m2. On the basis of these arguments, we expect that specific adsorption of (ClO4)- must be responsible for the relatively large changes in surface stress shown in Figure 1. We note that weak adsorption of this anion on Au(111) has been reported by Hammelin et al.28 Apparently, this weak adsorption causes significant alterations in the surface stress behavior. It is important to point out that our result, (∂f/∂V) ) (∂γ/∂V), is technically different from the erroneous result arrived at by Lin and Beck10 and discussed in the Introduction. We can easily see that in general ∆f * ∆γ by the following argument. We expand in a Taylor series in strain to first-order both the surface energy and the surface stress
γ() ) γ( ) 0) +
(∂γ∂)
) (f - γ)
)0
f() ) f( ) 0) +
dγu ) -qu dV + 2(f - γ)u de
(24)
dγr ) -qr dV + 2(f - γ)r de
(25)
The reconstruction is defined by the condition dγu ) dγr or γr - γu ) 0:
Upon expanding eq 18, we obtain
argument is developed here. Consider two modified Lippmann equations, at fixed T, µi, and , one for the bulkterminated unreconstructed surface (u), and the other for the 23 × x3 reconstructed surface (r):
(∂∂f)
)0
(22) (23)
and determine that ∆γ ) (f - γ) and ∆f ) (∂f/∂))0. For close-packed metal surfaces, the (f - γ) term is on the order of 1 N/m and the (∂f/∂) term is on the order of -10 N/m,3 so that (∆f/∆γ) = -10. Finally, we consider eq 4 at fixed T, , and µi, which describes the case relevant to the 23 × x3 S (111) Au surface reconstruction. We treat the reconstruction as a first-order phase transition as there is a discontinuous appearance of the reconstructed phase with applied potential. In the thermodynamics of solids, such transitions are described by the Clapeyron equation. A similar (28) Hammelin, A.; Vitanov, T.; Sevastyanov, E.; Popov, A. J. Electroanal. Chem. 1983, 145, 225.
1 ∂V ∆f ) fr - fu ) + (qr - qu) 2 ∂e
( )
(26)
The (∂V/∂e) term on the right-hand side of eq 26 physically corresponds to the change in pzc associated with the -0.045 strain of the reconstruction. Kolb and Schneider29 determined that the reconstructed surface has a pzc that is 0.090 V larger than the bulk-terminated (111) surface, so we estimate the (∂V/∂e) term as (0.09/-0.045) = -2 V. Wang et al.22 have determined that at a surface charge density of about +0.07 electron/atom the reconstruction starts to form, and after charge of +0.2 electron/atom the structure is fully formed. The q for this process is about 0.45 C m-2, so that we estimate ∆f ) (f23×x3 - f(111)) ) -0.45 N/m. Bach et al.30 reported a value of ∆f ) -0.43 N/m. 6.0 Summary and Conclusions To our knowledge, the measurements reported on herein represent the first estimates for the interface stress, h, of a single solid/solid interface. Other measurements of this quantity were made on multilayer structures where the total stress was determined as a function of the multilayer wavelength.31-36To date these measurements were made on multilayer structures where interfacial-alloying issues could not be strictly ruled out,37 so the magnitude as well as the sign of the interface stress seems to be in question. As discussed in the paper, under our experimental conditions and for the systems that we considered, Pb/ Au(111), Pb/Ag(111), and Ag/Au(111), interface alloying effects can be strictly ruled out. We have described thermodynamic formalisms for the interpretation of surface stress evolution during underpotential deposition. Changes in surface stress result from three contributions: the change in intrinsic surface stress ∆f between overlayer and substrate, the interface stress ∆h associated with the formation of the film/substrate interface, and the product of the coherency stress and the film thickness, Σcohtf. Wafer curvature measurements yield results for the total change in surface stress that includes contributions from each of these terms as described by eq (29) Kolb, D. M.; Schneider, J. Electrochim. Acta 1986, 31, 929. (30) Bach, C. E.; Giesen, M.; Ibach, H.; Einstein, T. L. Phys. Rev. Lett. 1997, 78, 4225. They actually measured -0.43 N/m but argued that their entire surface was not reconstructed and did an area correction that yielded a ∆f ) -0.61 N/m. (31) Josell, D.; Bonevich, J. E. J. Mater. Res. 1999, 14, 4358. (32) Ruud, J. A.; Witvrouw, A.; Spaepen, F. J. Appl. Phys. 1993, 74, 2517. (33) Scweitz, K. O.; Geisler, H.; Chevallier, J.; Bottiger, J.; Feidenhans’l, R. In Thin FilmssStresses and Mechanical Properties VII; Cammarata, R. C., Nastasi, M. A., Busso, E. P., Oliver, W. C., Eds.; Materials Research Society Symposium Proceedings 505; Materials Research Society: Warrendale, PA, 1998; p 559. (34) Gladyszewski, G.; Labat, S.; Gergaud, P.; Thomas, O. Thin Solid Films 1998, 319, 78. (35) Labat, S.; Thomas, O.; Gergaud, P.; Charai, A.; Alfonso, C.; Barrallier, L.; Gilles, B.; Marty, A. J. Phys. IV 1996, 6, C7. (36) Clemens, B. M.; Eesley, G. L. Phys. Rev. Lett. 1988, 61, 2356. (37) Clemens, B. M.; Nix, W. D.; Ramaswamy, V. J. Appl. Phys. 2000, 87, 2816.
Solid Electrode Surface Stress and Electrocapillarity
17. Since first-principles calculations exist for the surface stress for Au(111) and Pb(111), we were able to determine the magnitude of the interface stress h for this system as 1.47 ( 0.04 N/m. Similar measurements for the system Pb/Ag(111) yields a value of h ) 1.40 ( 0.04 N/m. The relative magnitude of these interface stresses is indicative of the similarity of the structure of the incoherent Pb/ Au(111) and Pb/Ag(111) interface. Our results also demonstrate that we were able to measure the coherency stress for two coherent epitaxial wetting layers of Ag/ Au(111). The measurements indicate that the stress h
Langmuir, Vol. 17, No. 3, 2001 815
associated with this coherent interface is very small and likely below the resolution of our measurement. Acknowledgment. K.S., N.D., and C.F. gratefully acknowledge the National Science Foundation, Division of Materials Research (Contract DMR-0090079) for support of this work. R.C.C. gratefully acknowledges support from the National Science Foundation administered through the Materials Research Science and Engineering Center at Johns Hopkins University. LA000911M
