Optical Second Harmonic Generation as a Probe of Selective

May 22, 1995 - as a diagnostic tool of Zn dissolution from brass. A previously proposed model of selective dissolution is incorporated in this framewo...
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Langmuir 1995,11, 3457-3466

3457

Optical Second Harmonic Generation as a Probe of Selective Dissolution of Brass G. Nagy and D.Roy* Department of Physics, Clarkson University, Potsdam, New York 13699-5820 Received May 22, 1995. In Final Form: July 5, 1995@ A phenomenological framework is developed to explorethe potential of surface second harmonic generation as a diagnostic tool of Zn dissolution from brass. A previously proposed model of selective dissolution is incorporated in this framework and tested experimentally by using a brass electrode (a-Cu0.63Zn0.37)in 0.1 M NaC104. This electrode is subjected to voltage-controlled selective dissolution of its Zn sites, and the morphology of the dissolving surface is monitored with optical second harmonic generation employing two fundamental wavelengths, 1064 and 532 nm. At both wavelengths, the second harmonic intensities exhibit strong correlations with the electrochemicalcurrents for Zn dissolution. These observed correlations are consistent with the theory presented. The results demonstrate how time-resolved information about surface reactions on binary alloys can be obtained with combined electrochemical and second harmonic generation techniques. 1. Introduction Selective dissolution (SD) of binary alloys is a classic problem of applied e1ectrochemistry.l The core of this problem lies in the complicated kinetics of the “early” stages of surface reactions, where the less noble component of the alloy begins to ionize for a cumulative disordering of the ~ u r f a c e . ~The - ~ traditional electrochemical techniques for studying this problem usually provide data for the interfacial currents and impedances. The analyses of such data commonly require several fitting parameters, such as various unknown rate constants and diffusion c0efficients.l With such analyses, often it becomes difficult to obtain a reliable, time-resolved description of the morphological evolutions of the reactive surface. On the other hand, it is the evolving surface structure during the early stages of SD that governs the cumulative decay of the a l l ~ y . ~In- problems ~ like these, where electrochemical methods alone can only partially address the central issue, supplementary optical surface probes become useful. Potentially, optical second harmonic generation (SHG), an intrinsically surface-sensitive technique, is a strong candidate for such an accompanying probe of alloy electrochemistry.aJ1 Nevertheless, while most of the electrochemical SHG experiments reported so far concentrate on metals and semiconductors,a-14SHG studies of alloys are considerably rare.15J6 To apply SHG to alloy electrodes, however, first it is necessary to develop a theoretical framework correlating

* To whom correspondence should be addressed. e-Mail: [email protected],clarkson.edu. * Abstract published in Advance A C S Abstracts, September 1, 1995. (1)Kaiser, H.In Corrosion Mechanisms; Mansfeld, F., Ed.; Marcel Dekker: New York, 1987;p 85. (2)Pickering, H.W.; Kim, Y. S. Corrosion Sci. 1982,22,621. ( 3 )StevanoviC, J.; Skibina, L. J.; StefanoviC, M.; DespiC, A.; JoviC, V. D. J . Appl. Electrochem. 1992,22,172. (4)El-Rahaman, H.A. A. Corrosion 1991,47,4242. (5)Pashley, D. W. Philos. Mag.1969,4, 324. (6)Pickering, H.W.; Wagner, C. J . Electrochem. Soc. 1967,114,698. ( 7 )Durkin, P.;Forty, A. J. Phil. Mug. A 1992,45, 95. (8)Richmond, G.L.; Robinson, J. M.; Shanon, V. L. Prog. Surf. Sci. 1988,28,1. (9)Richmond, G. L. Electroanul. Chem. 1991,17,87. (10)Biwer, B.M.; Pellin, M. J.;Schauer, M. W.; Gruen, D. M. Surf. Interface Anal. 1989,14,635. (11)Biwer, B. M.; Pellin, M. J.; Schauer, M. W.; Gruen, D. M. Langmuir 1988,4,121. (12)Corn,R. M.; Higgins, D. A. Chem. Reu. 1994,94,107. (13)Shen, Y. R. Annu. Rev. Muter. Sci. 1988,16, 69. (14)Liebsch, A. Surf Sci. 1994,307-309, 1007. (15)Nagy, D.; Roy, D. Langmuir 1996,11,711.

0743-7463/95/2411-3457$09.00/0

the electrochemical and nonlinear optical properties of the alloy surface. To our knowledge, no detailed theory on this particular subject is available at this time. Therefore, a considerable portion of this paper is devoted to the development of a theoretical guideline to design and analyze surface SHG experiments from a reactive binary alloy. Here, our goal is to select a relatively simple surface reaction with an available model for its mechanism, develop a theoretical treatment so that the model can be tested with SHG, and perform this test with combined electrochemical and SHG measurements. For this surface reaction, we focus on the early stages of SD of brass in neutral media. A previously proposed model of SD,17suitable for this experimental system, is chosen as the basis for our theoretical considerations. The essential features of this model and those of electrochemical SD ofbrass are outlined in section 2. In sections 3.i and 3.ii, this model is further extended and correlated with the appropriate electrochemical variables of our experimental system. Using the same model, we also develop a theoretical description of the SH response of the dissolving brass surface. Our approach to this theory is strictly phenomenological, concentrates on the typical experimentally measurable quantities, and is presented in 3.iii and 3.iv. In our experiments, we use a polycrystalline a-Cuo,63Zno,37 brass sample in 0.1 M NaC104with a standard potential sweep method to control the SD of Zn (at moderate levels). The dissolving brass surface is probed with SHG at 532 and 266 nm, using fundamental wavelengths of 1064 and 532 nm, respectively. The experimental results are presented in section 5 and analyzed in section 6 by using the theoretical considerations of section 3. With these analyses, we demonstrate the possibility of further expanding SHG experiments to applied electrochemical studies. 2. Background

(i)Electrochemistry of Brass Dissolution in Neutral Solutions. We refer to a standard three-electrode cell at room temperature, where the dissolution of the brass working electrode is introduced with an anodic voltage scan using linear sweep voltammetry (LSV).laWe (16)Joseph, M.;Klenerman, D. J . Electroanal. Chem. 1992,340, 301. (17)Forty, A.J.; Rowlands, G. Phil. Mag. A 1981,43,171. (18)Bard, A. J.;Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications; Wiley: New York, 1980.

0 1995 American Chemical Society

Nagy and Roy

3458 Langmuir, Vol. 11, No. 9,1995 also consider only moderate amounts of SD, where the brass surface is not entirely depleted of Zn atoms. Zn, the less noble component of brass, dissolves via the reaction1

leading to a positive dc Faradaic current density, Zzn. On a saturated calomel electrode(SCE)scale, the equilibrium potential, Vzn, for this reaction is -1.00 V.18 As the applied voltage, V, is scanned to more positive values, this reaction persists, and in addition, at the so-called “corrosion”voltage, V,, the Cu sites begin to oxidize, giving In the absence rise to a second Faradaic current, of specifically adsorbing ions, V, * -0.1 V.15J8 A third Faradaic component, IC,, due to Cu dissolution (Cu/Cu2+) would appear in the observed LSV current at even more positive voltages, V 2 VC, =VY 0.14 V, were VC, is the equilibrium voltage for Cu dissolution. Our present experiments are performed in 0.1 M NaC104 (to avoid specific adsorption effect~’~*~l) in the voltage range Vzn < V < VC,. As discussed above, in the first segment (VZ, < V < V,) in this range, the predominant surface process is SD of Zn. In the second segment (V, 5 V < VC,), both SD of Zn and corrosion of Cu are allowed. In section 5, we show that in both of these voltage regions, the SH response of the brass surface follows the Faradaic current profiles. In section 6, we concentrate strictly on the first voltage range (Vzn < V < V,) to study the mechanism of SD. The main features of the theoreticalmodel chosen for this study are briefly discussed below. (ii)Layer-by-LayerReordering Model of Selective Dissolution. In the currently available theoretical models, SD from binary alloys is often characterized in terms of a surface diffusion mechanism. In this description, the neighboring more noble-metal atoms of the lost less noble sites diffuse along the surface and combine to create islandlike surface structures. Forty and Rowlands have described this surface diffision mechanism of SD with a “layer-by-layer reordering“ (LLR) model of the alloy.17 In their model, SD is considered to be a process always occurring at the topmost surface layer, while the inward damage propagation is treated as “sinking“of the reactive surface into the bulk. Previously, this model has provided satisfactory explanations for complicated electrochemical data for SD of Ag-Au alloys. To our knowledge, the application of LLR has not been extended to other alloys. At the same time, we note that no specific model has been previously proposed for SD of brass in neutral media in the absence of SA. We also note that with appropriate analysis, the evolution of surface morphologies described in LLR can be conveniently checked with SHG. Hence, while using SHG experiments in this work, we choose to examine this LLR model as a possible description of the early stages of SD of brass. In the LLR model, the kinetics ofbrass SD are described as follows. As SD of Zn starts,the topmost layer of brass begins to re-form itself, with growing Cu islands surrounded by decreasing areas of unchanged brass. These islands are formed around so-called defect sites where, after diffusing along the surface, loose Cu adatoms released from the regions of SD stabilize themselves, nucleate, and aggregateinto larger structures. An island and its surrounding region described in this fashion are schematicallyshown in Figure 1A. In this figure, c is the

I*

-

lc.4J9920

(19) Pchelnikov, A. P.; Sitnikov, A. D.; Marshakov, I. K; Losev, V. V. Electrochim. Acta 1981,26, 591. (20) Polunin, A. V.; Pchelnikov, A. P.; Losev, V. V.; Marshakov, I. K.

Electrochim. Acta 1982,27,467. (21) Chervyakov, V. N.; Pchelnikov, A. P.; Losev, V. V. Sou. EZectmhem. 1991,27,1457.

Figure 1. Schematic representation of a dissolving brass surface in terms of the layer-by-layer reordering model of selective dissolution. A shows a cross-sectional view of a surface island and its neighboring regions resulting from selective dissolution of Zn from brass. B shows a view from the top of the island sites arranged in a hexagonal array on the brass surface (the scales are slightly different in A and B). In both A and B, c is the nucleation center for island formation, R(n) is the radius of an island after the reorderingof n atomic layers from a surrounding surface of radius Ro, and Rfrepresentsan effective range of the electromagneticfield associated with the island. In A, md is the height of the Cu island after the reorganizationof the first surface layer, d is the atomicdiameter of Cu, and nd corresponds to the depth of dissolution of the brass surface. Also in A, the dashed elliptical line represents the structural approximation of the islands that is used in the electromagneticenhancement calculations.

nucleation center where m number of Cu layers are deposited after the first layer of brass from a surrounding circular zone of radius Ro is reordered by SD. This Ro can be interpreted as the effective range of island formation (maximumdistance traveled by a diffusingCu atom before encountering a nucleation site). The height of the island resulting from the reordering of the first layer of brass is approximated as md, where d is the atomic diameter of Cu. According to Forty and Rowlands, reordering of successive layers of the alloy facilitates growth only on the side walls of the island. These authors justify this assumption by noting that the less densely packed faces surrounding the nucleation center are likely to grow most ra~id1y.l~ Thus, in LLR, the islands are considered to growth predominantly in a ’lateral” mode, being surrounded by unaltered brass sites exposed from the next layer. This lateral growth leaves uneven regions of brass within the island, but they are always completelycovered by Cu layers (Figure 1A). After n layers of brass are reordered, the island radius expands to R(n) and the surrounding brass regions shrink accordingly. At the same time, these brass regions sink to a depth H: In an equivalent description, this latter effect can be taken as a vertical growth of the island by the height H on a flat bass substrate. Sincen describes the extent of cumulative surface reordering, we refer to n as the “reordering parameter ”. The LLR model results for these dimensions are as follows:17

H(n) = (m

+ n)d

(2)

Optical SHG as a Probe

of

Brass

Langmuir, Vol. 11, No. 9, 1995 3459 this expression with eq 6, g can be expressed without involving the unknown rate constant:

where T(m)is the gamma function and x is the fractional concentration of Cu in the original brass sample. The dashed semiellipsein Figure 1Aindicates how the surface island can be approximated as a hemispheroidal structure of aspect ratio HIR. A circular region of radius R f i s also shown in Figure 1A. The hemispheroidal geometry and the region defined by R(n) < Rf < Ro are relevant to the optical response of the island and are discussed later in this paper. R and H (hence, m and n ) are the relevant parameters of the LLR model. The coverage of surface islands is indicated by R . By measuring this coverage during SD, one can obtain the rate of the lateral spreading of surface damage. Similarly, time-resolved measurements ofH would indicate the rate of damage propagation into the bulk alloy. The issue of electrochemically measuring R and H i s not addressed in the original LLR model. In the following section, we discuss how these parameters can be probed with LSV and apply these considerations to those of SHG measurements. 3. Theory (i) Coverage of Surface Structures. In a simple extension of the LLR model, the brass surface can be described as a collection of circular zones of radius Ro. At a given stage of SD (determined by the value of n),each of these zones concentrically encircles a hemispheroidal isoland of average radius R(n) and average height H(n). Packing the surfacewith circular zones leads to void areas. To account for these void areas, we model the surface with a hexagonal close packed geometry where each hexagon is centered around a circular zone of radius Ro. The area of such a hexagon is 6R02tan(nl6). A top view of this surface scheme is shown in Figure 1B. The surface density, NO,of nucleation centers (number of growing islands per unit area) is written as

No = [6R02tan(~c/6)]-’

(4)

The fraction, g,of the original electrode surface covered by the islands is then expressed as

g = N0[nR21

(5)

In LSV, the electrode voltage, V, is scanned linearly in time t at a rate of r, starting from an initial voltage Vi so that V(t)= Vi rt. The corresponding Faradaic current density, Z ( 0 , can be integrated to obtain the cumulative Faradaic charge, Q(V). By using these data, it is possible to measure g as a function of V. In the corrosion-free voltage region (Z = ZZ,), the observed Faradaic current density results entirely from the reaction of eq 1and can be written asz2

+

IW = K[I - VI exp[CP(V - V091

(6)

where k and Vo)are the rate constant and the standard potential for the reaction of eq 1,respectively;j3 = 1- a; a and ,B are the Faradaic transfer coefficients (05 a 5 1); 5 = WIR,T; F is the Faraday constant; R, is the gas constant; and T is the ambient temperature. Experimentally, a reference voltage, VO,can be chosen where VO is greater than but close to Po).Since the surface reaction is minimal at Vo, it can be assumed that g(V0) % 0. Then, Combining according to eq 6, Z(V0)= k exp[5/3(Vo- PO))l. (22)Bockris, J. O’M.; Rubin, B. T.; DespiC, A.; Lovrecek, B. Electrochim. Acta 1972,17, 973.

By appropriately choosing or measuring j3 for eq 8, J(V) and, hence, g(V)can be measured with LSV. Note that due to the voltage-dependent coverage term g(V)in eq 6, it is difficult to obtain j3 with the usual method of Tafel plots. Here, the measurement of j3 requires an independent set of data related to the coverage of surface islands; later in this paper, we show that SHG can serve this purpose. (ii) Reordering Parameter in Terms of Electrochemical Quantities. Once g(V) is determined, the reordering parameter, n, of the LLR model can also be obtained as a function of V. Substituting for R from eq 3 in eq 5 and comparing the resulting expression for g with that of eq 7, we obtain

When only the first monolayer (ML) of brass is re-formed ( n = l),eq 9 takes the f o r d 7 (10) where we have used the expression for N Ofrom eq 4, with

Here, VMLis the voltage at which reordering of the first brass ML is completed and Z(VML)is the current observed at that voltage. Whenj3 is determined, eqs 10 and 11can be used to obtain m. Then, with an appropriate estimate for Ro, eq 9 can be used to obtain n from the LSV data. Considering the measurement of m, we note that

(12) where QMLis the cumulative Faradaic charge due to the reordering of the first layer of brass. In view of eq 1and Figure lB, this charge can be also expressed as follows:

(13) whereN& is the surface density of Zn atoms for the original sample and e is the electroniccharge. Denoting the atomic masses of Cu and Zn as Mc, and Mz,, respectively, we obtain Nzn = [(@abr) - (McuN~u)llMzn.Here, N c , is the surface density of Cu atoms, abr is the depth of a brass monolayer, and is the mass density for the original ~~,~~ sample. In the absence of surface s e g r e g a t i ~ n ,NcJ Nz, % N’cU/N”’,= x/(l - x); the primed quantities denote bulk atomic densities. Under this condition,

A combination of eqs 4, 13, and 14 leads to the result (23) Somojai, G. A. Principles of Surface Chemistry; F’rentice Hall: Englewood Cliffs, NJ, 1972. (24) Kumar, V.; Kumar, D.;Joshi, S. K. Phys.Reu. B, 1979,19,1954.

Nagy and Roy

3460 Langmuir, Vol. 11, No. 9, 1995

a fixed cross section are affected by this extra area. In this latter case, the appropriate surface fraction of the islands is evaluated as With the known quantities on its right-hand side, eq 15 can be used to obtain Qm, and this result can be substituted in eq 12. Subsequently, by utilizing LSV data for I(V),one can solve for VMLfor eq 12. This would give J M Lfrom eq 11 and then m from eq 10. (iii)Phenomenological Treatment of Surface SHG from DissolvingBrass. Now we enquire how the surface morphologies described in the LLR (as shown in Figure 1 ) should respond to SHG. For this discussion,we consider a standard 45” reflection geometry in a p-in-p-out polarization configuration for surface SHG. We also assume the hemispherical geometry (Figure 1A) of the SD-generated islands. For an incident optical frequency, w , the SH signal, SQ,from brass at the frequency 8 (Q = 2w) has the form13 (16) where xf’ is the local optical-field-influenced effective second-order surface susceptibility of brass and E ( w ) is the incident optical field. As shown in Figure 1, the dissolving brass electrode has surface regions of different chemical makeups. All these regions contribute toxf). In the electric dipole approximation, these contributions arise only from the topmost surface layers of the optically relevant sectors on the reactive e l e c t r ~ d e . ~ , Therefore, ~J~J~ as far as SHG effects are concerned, the Zn cores of the Cu-covered islands (Figure 1A)can be neglected. In this view, while considering their SHG responses, we treat the surface structures described in the LLR model simply as Cu islands. In the LLRdescription, the dissolving brass always has two distinct types ofsectors: expanding regions of Cu islands and shrinking areas of brass surrounding these islands. These two chemically distinct sectors represent three optically different surface regions:26(I) Cu islands occupying a surface fractiong’;(11)brass surface of a total coverage g’fin the immediate neighborhoods of, and optically affected by these, islands; (111)the rest, 1(g‘ +g’f),ofthe brass sites that are far from, and optically unaffected by, the rough Cu structures. According to a recently reported simple “three-region model” of surface SHG, xf’ for such a surface can be written asz5

xg:, xr),

xg)

where and are the effective second-order susceptibilitiesof surfaceregions I, 11,and 111,respectively. The optical enhancement factor, u,has the form

I4 = IL(W)121L(Q)I

(18)

where L(w) and L ( 8 ) are the complex local field factors for the input and output channels of SHG, respectively. Note that the optically-sensitive island coverage, g‘, is different from the electrochemical coverage, g . This difference arises from the fact that the effective electrode area, A,, increases with the growing island radius as

A, = A ( 1 + N f l R 2 )

(19)

where A is the original electrode area. This growth does not contribute to the electrochemical data because the Cu-covered extra areas do not participate in SD of Zn. However, the optical data generated by a laser beam of (25)Nagy, G.;Roy, D.J.Phys. Chem. 1994,98,6592.

g‘ = N&2nR2)/A,

(20)

Combining eqs 5, 19, and 20, the coverage of region I is found to be

g‘ = 2g/&

+ 1)

(21)

The coverage, g’f, of region I1 is written as g’f = AdA,, where Af is the total surface area occupied by region 11. As indicated in Figure lB,

A, = n(Rf2 - R2)N,,A

(22)

Using eqs 19, 20, and 22, we obtain

g ’ f = (g‘/2)[(RdR)’- 11 = fg’

(23)

where f represents a subfraction ofg’, with f = (1/2)[(Rd R)2 - 13. The magnitude ofL is governed by two electromagnetic rod effect at the sharp (EM)p h e n ~ m e n a : ~(1) ~ , lightning ~’ edges of the surface structures and (2) surface plasmon resonance within these structures. The strengths of these effects depend on the shape and wavelength-dependent dielectric functions of the interfacial materials.26 The , Cu for the relevant wavelengths dielectric functions, E C ~ of of the typical SHG experiments are listed in Table 1.28 Considering only aqueous electrolytes, we also include in Table 1the wavelength-dependent dielectric function, E’, of water.29 As evident from these listed values, E’ can be taken essentially as a real number within the wavelength range considered. Under this c o n d i t i ~ n , ~ ~ , ~ ~

where E C ~and , ~ E C ~represent , ~ the real and imaginary parts of ccu, respectively. B is the depolarization factor that governs the amplitude of the lightning rod effect (0 B 1). Neglecting the relatively weak plasmon damping criteria,3OB depends only on the shape of the surface island. In EM theories of SHG, such an island is modeled as a hemispheroid as shown in Figure lA, and the shape of the island is characterized in terms of the aspect ratio (HIR) of the hemi~pheroid.~~ In eq 24, L is amplified via the lightning rod effect, where B 0. This latter condition holds only for sharp structures (prolate hemispheroids with H/R * 1). Amplification of L via surface plasmon resonance occurs when EC~,,JE‘ 1 - (UBI. For the dielectric functions listed in Table 1, this resonance condition cannot hold if the value of B approaches one. Such large values of B are found for very oblate (flat) he mi spheroid^.^^ Thus, if the assumed hemispheroidal islands are highly oblate in nature, neither one of the two EM enhancement effects can be significant. This is also evident from eq 24 where L 1, as B 1. It is this latter

-

-

-

-

(26)Boyd, G.T.;Rasing, Th.;Leite, J. R. R.; Shen, Y. R. Phys. Rev. B 1984,30,519. (27)Leitner, A.Mol. Phys. 1990, 70, 197. (28)Johnson, P.B.; Christy, R. W. Phys. Rev. B 1970,6, 4370. (29)Hale, G.M.;Querry, M. R. Appl. Opt. 1973,12, 555. (30)Wokaun, A.;Gordon, J. P.; Liao, P. Phys. Rev. Lett. 1982,48, 957. (31)Gersten, J.; Nitzan, A. J. Chem. Phys. 1980, 73,3023. (32)Chang, R. K.,Furtak, T. E., Eds. Surface Enhanced Raman Scattering; Plenum: New York, 1982.

Langmuir, Vol. 11, No.9, 1995 3461

Optical SHG as a Probe of Brass

Table 1. Optical Parameters Relevant to the SHG Response of Dissolving Brass wavelength, nm

photon energy, eV

1064 532 266

1.17 2.34 4.68

ECu

scenario that emerges from the LLR description of alloy dissolution, because the surface islands for LLR are considered to grow predominantly in a lateral model. In other words, the LLR model predicts that even if the brass surface is roughened with SD, this roughness cannot support EM enhancements. This would imply that ILI 1, with 1u1 1. Therefore, if LLR provides a valid description of the dissolving brass, we expect that the surface roughness caused by SD would not drastically amplify the surface SHG signal. For its comparison with experimental data, x(t) (eq 16) is usually normalized as follows:

-

-

(25) where s is an optically measurable quantity

s(v) = I[s,(v)/s,(v,)11/21 - 1

E’

-49.13 + i4.91 -5.50 + i5.76 -0.78 + i4.80

(26)

A theoretical expression for s is found for eqs 17 and 25:

(27)

xp’

where is a measure of the relative susceptibility contributions to SHG from the three surface regions of dissolving brass

The voltage dependence of s comes from those of the different terms on the right-hand sides of eqs 27 and 28. Detailed information about the electronic and morphological changes in surface conditions is contained in these terms. The following discussion outlines a possible method to access this information. (iv) Combining Electrochemical and SHG Methods. In section 3.i, we have discussed the LLR-predicted island coverage,g(V),in terms of the electrochemical Z(V) data. The discussion of section 3.iii also uses the LLR model and relates this coverage with the optical s(V)data. By testing for consistency between the coverages found from these two types of measurements, we can test the validity of LLR. This, in turn, requires that the possible voltage dependencies off, x:~), and o in eq 27 be resolved. By using EM boundary conditions, the susceptibilities of regions I1 and I11 can be related as xi2’ = Zxk:), where I is an EM scalingfactor that contains the interfacial dielectric function^.^^^^^ Following previous calculations,this factor can be written as 1 = [6c~(SZ)6c~(w)]/[E’(SZkbr(w)l,were 6br is the dielectric function of brass and the other dielectric functions have been defined earlier.26i31-34From these considerations, eq 28 can be expressed as

1.76+ i1.36 x 1.78+ i4.00 x 1.80+ i7.27x

Acu

Abr

0.52 0.12

0.00

0.48

This observation allows for the assumption of a sharp boundary (discrete Rf)between regions I1 and 111. Moreover, from the results of those calculations, a phenomenological relationship between Rf and R can be noted: CL3l With the assumption of perfectly Rf GZ F(1 conducting islands, the factor C is independent of the interfacial dielectric functions, as well as of R. Then, according to eq 23,

+

f = (l/2)[(C

+ u2- 11

(30)

where f is independent of R and, hence, of V. Next we consider the intrinsic voltage dependencies of and As we have reported recently, this particular effect can arise from surface-charge-inducedStark shifts of interband transitions in Cu and brass.15 These surface charge variations originate from the non-Faradaic doublelayer charging process as a result of changing V. In our earlier works, by probing the non-Faradaic voltage regions of Cu and brass, we have examined the relationships of $: and with variations in surface charge densities, q.15935936 Those relationships contain various Stark energy parameters. In a rigorous treatment of SHG, these parameters should be calculated by using appropriate perturbation techniques. In this work, we analyze the voltage-dependent susceptibilitiesfrom phenomenological observations concentrating only on the NaC104 environment. With this electrolyte, when the susceptibilities of Cu and brass (square roots of observed SHG signals) are plotted against V(and not against q),the resulting graphs appear to be essentially linear. 15,35 Satisfactory linear fits to these graphs are obtained with resulting slopes expressed in the form

xf:

x:).

x:,’

(31) where V, is the potential of zero charge of polycrystalline Cu. From such linear fits, the following empirical expressions are found for the voltage-dependent susceptibilities of Cu and brass:

xg:

where AcUand Abr represent the slopes of the - Vand - V graphs, respectively. Since anion-specific adsorption is not favored in NaC104, the surface charge densities of Cu and brass are relatively insensitive to moderate variations in the concentrationof this electrolyte. Consequently, for both Cu and brass, A shows almost negligible variations in the 0.05-0.1 M range of NaC104 Ix$’l = A l l + [lxg:I~lx;31 (29) concentration^.^^,^^^^^ AcU and Abr obtained for NaC104 concentrations in this range with fundamental waveNow we focus on the term f. Previous calculations show lengths of 1064 and 532 nm are listed in Table 1. The that the local field of an island remains uniform over a reasons for the observed wavelength dependencies of A certain distance from the island wall (Rf from the are discussed in our earlier work.15 Here, we assume that nucleation center) and then falls off rather ~ h a r p l y . ~ ~ ~ ~ ~ ~

(33) Wokaun, A. Mol. Phys. 1986,56,1.

(34)Chen, C. K.; Heinz, T. F.; Ricard, D.; Shen, Y. R. Phys. Rev. B 1963,27,1965.

~~

(35)Hewitt, T. D.; Gao, R.; Roy, D. S u ~Sei. . 1993,291, 233. (36)Gao, R.; Hewitt, T. D.; Roy, D. J.Phys. Chem. Solids 1993,54, 685.

(37) Nagy, G. Ph.D. Thesis, Clarkson University (in progress).

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3462 Langmuir, Vol. 11, No. 9, 1995

the linear empirical equations (32) and (33) can be extrapolated into the voltage region of SD of brass and can be used to analyze the voltage effects on xp' in eq 29. As evident from eqs 29,32, and 33, such an analysis would also require an estimate for the V-independent quality x~~(V,)&'(V,). This latter issue is further discussed in section 6.i. Next we consider the possibility of voltage effects on u and 1. The expression for u via e s 18 and 24 can be effective only after large-scale (> 10- ) surface roughness is e s t a b l i ~ h e d .The ~ ~ game criterion applies to 1. In LSVcontrolled SD of brass, the threshold voltage for the activation of u (and 1)can be identified as that where the cumulative surface reordering reaches the above-mentioned critical dimensions of the surface islands. Considering typical brass dissolution experiments in the LLR description and using simple arguments of mass conservation, it can be shown that, usually, for this threshold to be operative, at least one ML of brass must be reordered.37 We roughly approximate V m to be the voltage where the u and I contributions to SHG become active. For V -= V n , the presently used forms of these parameters become questionable, making it difficult to follow their behaviors in this range. For V > VML,u and 1 can be V dependent if ccu and Ebr respond to the voltage variations. However, the incident and SH frequencies considered here are considerably below the plasmon frequency of Cu. At these frequencies, it is reasonable to assume that EC,, and Ebr are voltage i n d e ~ e n d e n t .According ~~ to eq 24, u can be additionally voltage dependent if the depolarization factor ( B )changes with changing V. This can occur if B is measurably larger than zero and the shape ofthe surface island also changes with its size. In the LLR model, all the surface islands are characterized with one average shape, and thus, possible variations in B with cumulative SD are neglected here. However, even if a variation in B is present in SD of brass, the impact of this variation on the SHG signal would be insignificant. The latter argument follows from one of the main predictions of the LLR model-that due to the lateral growth of surface islands, B remains nearly 1throughout the early stages of SD. In other words, the LLR condition, 10) 1,should not be perturbed considerably with voltage changes that are responsible for moderate levels of SD. From the above discussion, certain relevant features of the LLR model can be summarized: (a) SHG analysis of brass dissolution should focus mainly on the SQ(V) data collected in the region, V > VML.(b) Both lightning rod and surface plasmon effects should have negligible contributions to S p when the brass surface is roughened with SD. (c) The dependence of S p on the surface island coverage should be consistent with the electrochemical results expressed in terms of eq 7. Feature a should be incorporated in the procedure for data analysis. This can be done by normalizing s(V)(eq 26) and g(V)(eqs 7 and 8)with respect to their respective values at V m . Features b and c can be used as test indicators for the validity of the LLR model. This can be achieved by combining the electrochemical and SHG data in an appropriate design that would search for these particular signatures of LLR indicated in b and c.

1

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4. Experimental Section The experimental setup for this work is described elsewhere.35~39~40 In brief, 7-11s light pulses at 10 Hz and 1064- or 532-nm wavelength from a Nd:YAG laser are incident on the (38)McIntyre, J. D.E . Adv. Electrochem. Electrochem. Eng. 1973, 9,61. (39)Hewitt, T.D.; Roy, D. Chem. Phys. Lett. 1991, 181, 407. (40) Nagy, G.; Roy, D.Langmuir 1993,9,1868.

-0.5

-0.2

0.1

-0.2

-0.5

V (vs. SCE)

Figure 2. Interfacial current, Z (in A), and SHG intensity, SQ (in B and C), of a brass electrode during the voltage cycle -0.65 V 0.1 V -0.65 V in 0.1 M NaC104. Here, VOis the initial voltage corresponding to the original brass surface and V, is the corrosion voltage where the Cu sites of brass oxidize. In B and C, the incident wavelengths used for SHG are 1064 and 532 nm, respectively. "he solid lines in A and B represent typical single-voltagescans, and the dotted lines represent the averages of several SH scans performed under identical conditions.

-.

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brass sample at an angle of 45". The reflected SH signal at 266 nm or at 532 nm is collected in a p-in-p-out geometry, with a cooled photomultiplier tube, and processed with conventional electronics. The polycrystalline a-brass electrode (Cu0.63Zn0.37; 1.00 cm in diameter with 8.45 g/cm3density) is used with a Pt counter electrode and a SCE reference. A thoroughly Ar-purged neutral aqueous electrolyte (pH 7) of 0.1 M NaC104 is used. Our trial LSV data show that in the positive scans,the SD current for Zn becomes noticeablenear -0.5V, at a considerably larger voltage than Vh. Thus,the relevantvoltage range for the present system lies between -0.6 and 0.1 V. The applied cell voltage is scanned within this limit with a potentiostat at a rate of 2 mV/s. A fresh solution and a thoroughly polished sample are used with each new voltage scan. "he electrochemical and SH data are simultaneouslyrecorded and stored on a microcomputer. Since the SH signalis relativelyweak, about five data scans are usually taken under identical conditionsand averaged to obtain the final data.

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5. Results The Faradaic current ( I ) and the SH signal (SQ)from the dissolving brass surface under voltage (V) control are shown in Figure 2. In A, the horizontal arrow shows the direction of the scan. Vo and V,indicate the lower limit of the voltage scan and the corrosion voltage, respectively. Since the SD current is negligible below VO,we take this voltage as the reference point in our LSV scans where the sample surface can be considered as essentially unchanged. As mentioned in section 2, Z % IZn for Vo IV I V,. As the voltage is increased in this latter range, the SD current increases and, as a result of Zn removal from the brass surface, eventually drops to lower values.1,21 This voltage-specific peak of 4,is seen in Figure 1A. For V r V,, we detect I =Izn+I,, while&,, continues to decrease as Vis increased. While using a stationary electrolyte (as in this experiment), it is difficult to separately measure these two components of Nevertheless, it is known that with increasing voltages in this range, I, should ~ -observed ~~ in increase and I% should d e c r e a ~ e . ~ JAs Figure 2A, I, exhibits a predominant control over the behavior oflin the corrosion region. This increasing trend of Z, and, hence, of Z continues for a detectable interval after the voltage scan is reversed to the cathodic mode. Moreover, since the surface layer of brass becomes considerably Zn-free during the anodic voltage scan, no measurable signature of ZZ,,is found in the cathodic scan.

Optical SHG as a Probe of Brass

Langmuir, Vol. 11, No.9, 1995 3463

Parts B and C of Figure 2 show the normalized SH signals [SQ(V)/SQ(VO)I collected from the brass surface under the voltage treatment of Figure 2A. Here, tiW = 1.17 eV in B and 2.34 eV in C. In parts B and C of Figure 2, the solid lines represents the SH data for typical singlevoltage scans. The corresponding dotted lines indicate average data from multiple scans. A striking feature of these SHG data is that they do not exhibit any large enhancements,with the surface roughening occurringwith the SD process. As discussed in section 3.iv, this is also an expected feature of the LLR model. This observation indicates how LLR might present a feasible description of the dissolving surface in the present system. Although the SHG signals in Figure 2 are not enhanced, their variations display noticeably close correlations with those of I(V). It is this correlation that indicates the unenhanced optical response of the evolving surface morphologies during SD. The Sa-I correlations are most pronounced in the region of strongest SD (-0.6 V -0.2 V) during the anodic voltage scan. The surface SHG response continues to change in the remaining portion of the anodic scan (-0.2 V I VI 0.1 V). In this latter range (V > V,), SD is accompanied by Cu corrosion, and oxide layers of Cu are developed on the ~ u r f a c e . The ~ , ~observed ~ SH signals for V > V, are most likely affected by additional contributions from such oxide layers. The predominant species of these oxides are expected to be CuO and C U ~ O . The ~ ~electronic - ~ ~ structures of these oxide species indicate that their SH responses should be different for the 1.17- and 2.34-eV incident photons.41 The different voltage dependencies of the SH data for -0.2 V IV 5 0.1 V in parts B and C of Figure 1 display these expected optical features of such copper oxides. Furthermore, these oxide layers remain largely unreduced when the voltage scan is reversed and, cumulatively, lead to surface passivation The SH data in the cathodic scan (0.1 V to -0.6 V) of parts B and C of Figure 1 contain information about the voltage dependencies of the coverages, as well as of the structural and electronic properties of these layers.40 Continued SD of the Zn sites remaining on the top layer and from those exposed in the successive layers ofbrass also contributes to the SHG effects observed in these cathodic scans. The cumulative Faradaic charge, Q(V), of SD is obtained by applying eq 12 to the I(V) data of Figure 2A and is presented in Figure 3. The charge, &(VML),required to reorder the first brass ML is obtained by applying eqs 12 and 15 to these data.47 The corresponding voltage, Vm, is identified in Figure 3. In the following section, we analyze the electrochemical and optical results of Figures 2 and 3.

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6. Discussion

(i)Role of SurfaceSusceptibility. SD in the presence of surface corrosion presents a relatively complicated scenario. To understand the SH response of brass in this region, it is necessary to first analyze the optical data in the absence of corrosion. This primary stage of SD without (41)Lenglet, M.;Kartouni, K.; Delahaye, D. J.Appl. Electrochem. 1991,21, 697. (42)DiQuarto, F. I.; Piazza, S.; Sunseri, C. Electrochim.Acta 1986, 30. 315. -->

(43)Hamilton, J.C.; Farmer, J. C.; Anderson, R. J. J.Electrochem.

Soc. 1986,133,739.

(44)Marchiano, S.; Elsner, C. I.; M a , A. J. J.Appl. Electrochem. 1980,10,363. (45)Deutscher, R.L.;Woods, R. J.App1. Electrochem. 1986,16,413. (46)Collisi, U.;Strehblow, H.-H. J.Electroanal. Chem. 1986,210, 213. (47) Pearson, W. B. A Handbook o f h t t i c e Spacings and Structures of Metals a n d Alloys; Pergamon: London, 1967;Vol. 2.

Figure 3. Faradaic charge ( Q )of Zn dissolution from brass in the voltage range of -0.64 V to -0.27 V. Here, V m = -0.565 V represents the voltage at which all Zn from one monolayer of brass has been dissolved.

corrosion is the main focus of our present report. Therefore, leaving the corrosion effects for future studies, here we concentrate only on the corrosion-free voltage region, -0.65 to -0.10 V. To analyze the experimental results in this voltage region, we follow the discussion of 3.iv and scale the SHG data with respect to those recorded at VML:

The theoretical expression for the optical quantity defined in eq 34 is found by using eqs 16 and 17:

where g’(V) and g’(vML) are related to the Z(V) data of Figure 2Avia eqs 7,8, and 21. The scaled susceptibilities are defined from eqs 28 and 29 as follows:

and a similar expression for X:~’(VML), with Vreplaced by VMLin eq 36. On the right-hand side of eq 35,x;”(V) contains the signatures of xgL(V) and &)(V); g‘(V) contains the information about island coverages. In order to compare the behaviors ofs(V)andg‘(V),first it is necessary to resolve how much contribution the former quantity receives from x;”(V). The followingdiscussion focuses on this susceptibility term. As noted in 3.iv, the susceptibility contributions can be resolved by using eqs 30-33, with an appropfiate estimate for the ratio, ~~~(V,)/xg)(V,)]. Considering this latter quantity, we noted that the normalized data format of eq 34 allows for simple order of magnitude estimates for the V-independent quantities, without introducing considerable errors in the data analyses. Such an estimate for the above-mentionedratio of susceptibilities is available from the simple anharmonic oscillator model of SHG. SQfrom both Cu and brass are dominated by bound electron effects, and this model provides a reasonable account for these effects. According to this (48)Boyd, R. W.Nonlinear Optics; Academic: San Diego, 1992.

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3464 Langmuir, Vol. 11, No. 9, 1995

where Dcu(w)= wcu2- w2 - ( i d t ) ,&(O) = Wb? - O2 (iw/t), T is the electron relaxation time (assumed to be the same in Cu and brass), and ncu and n b r are the bulk densities of the available electrons (from the d or p bands, as applicable with the the incident wavelength) for resonance transitions in Cu and brass, respectively. We have defined a b r in the context of eq 14, acu is the lattice constant of Cu, WC, and Wbr are the corresponding resonance frequencies, and me is the electron mass. According to our previously published results,15 for the 1.17-eV fundamental, wcU= ~ ~ d SZ and i Wbr = ~ ~ # i SZ. The E terms represent energy thresholds of various transitions involving the d and p bands of Cu and brass. The unprimed and primed subscripts of E denote filled and empty electronic states in the corresponding bands, respectively. For the 2.34-eV fundamental, wcU 6 d p . h w and Wbr E d p , h 0. Furthermore, since c u and Zn (and, hence, brass) atoms have the same d and p shell configurations, we assume nC&br % W&N”br,whereN”cu and w b r are the bulk atomic densities of Cu and brass, respectively. Using this approximation, with the abovenoted resonance conditions in the expressions of DcUand Dbr, and applying the resulting expression to eqs 37 and 38, respectively, we obtain

-

-

-

-

where the subscripts associated with the square brackets denote incident photons frequencies in electronvolts. In view of the LLR model, if we assume that lul is on the order of one and does not depend on V, eqs 36 and 39 can be combined in the following expressions:

Figure 4. Surface susceptibility function of brass (defined in eq 40) for incident photons at 1064 nm (in A) and 532 nm (in B)under the voltage-induced dissolution treatment of Figure 2A.

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t 1 P S , ~ O we obtain 5 from eq 42. With a similar calculation including the experimental V from Figure 2 in eq 41, we obtain as a function of Vin the range -0.65 V 5 V -0.10 V. Combining these calculations, the normalized susceptibility term (first square-bracketed quantity on the right-hand side of eq 40) is obtained for each incident photon energy as a function of V. The results are plotted in Figure 4. The behaviors ofthe susceptibility function are considerably different for the two incident photon energies (1.17 eV in A and 2.34 eV in B). This difference comes from the two strong wavelength-dependent quantities, Abr and 7, included in eqs 40-42. By incorporating the results of Figure 4 in eq 35, it is now possible to draw a direct comparison between the optical and electrochemical measurements. This topic is considered next. (ii)Relative Roles of Coverage and Roughness of Surface Structures. The unenhanced SHG signals in Figure 2, consist with the LLR scenario of flat surface structures, imply a relative passive role of surface roughness in SHG from dissolving brass. This description is also embedded in the calculations for Figure 4, where we have assumed the condition Iu( 1 to derive eq 40. Here, we use the results of Figure 4 as a bridge between the electrochemical and optical data, analyze the island coverage dependency of SHG, and further examine the surface roughness criteria for LLR. From eqs 7, 8, 21, and 21, we obtain

-

where q = 1 for Rw = 1.17 eV and 7 = (wd2) for b = 2.34 eV. Equations 40-42 present the LLR-model-predicted voltage dependencies of the Cu and brass susceptibilities. We evaluate the right-hand side of eq 40 in the following steps. We use C = 0.034 (from the published results in 17 ref 32) in eq 12 to obtain f % 0.0345. By using ~ b ~ ( l . eV) = -36.1 i5.32 (from ref 49) and the values of ccu and E‘from Table 1, we calculate Z(ho = 1.17 eV) % 6.12 and l(hw = 2.34 eV) sz 3.42. We also use acu % d = 3.60 A, abr = 3.69 A, w’cu = 8.45 X loz8m-3, and P b r = 7.86 X lo2’ m-3, all from ref 47; VML= -0.565 V from Figure 2; V,= -0.96 V from ref 15; and wavelength-dependent AcUand Abr from Table 1. With these values and assuming that

where J(V)is expressed in eq 8 and J(VML) is also found from the same equation by replacing V with VML. All quantities but j3 in eq 43 are either known or electrochemically obtained in Figures 1A and 2. Here, we treat pas avariable parameter to fit the electrochemical results with the optical ones. If LLR applies to the present system, we expect a reasonable fit, yielding a single value of ,/3 for the entire experimental voltage range with the requirement that 0 < ,/3 < 1. To check this possibility, we combine eqs 7,8, and 43 with Figures 2A, 3, and 4 to form a complete expression for the right-hand side of eq 35. This expression , and the measured quantities of contains the unknown E Figures 2A, 3, and 4. Usingp as an adjustable parameter, we numerically fit this expression with the measured optical quantity on the right-hand side of eq 40. In this procedure, we find that a complete fit results if we allow

(49) Sasovskaya, I. I.; Korabel, V. P. Phys. Stat. Solid. B 1986,134, 621.

(50)Shen, Y. R. The Principles York, 1984.

+

of

Nonlinear Optics; Wiley: New

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I

I

-0.6

-0.5

I

-0.3

-0.4

-0.6

V (vs. SCE)

-0.4

-0.3

respectively. The dashed lines represent a point-by-point numerical fit of eq 35 to these data points. In these fits, eq 35 is evaluated with the results of Figures 2A,3, and 4 with /3 (embedded in g') as an adjustable parameter.

1

Figure 7. Calculated values of the aspect ratio H/R of Cu islands (circles) and the resulting depolarization factor B (triangles) as a function of voltage for Ro = 200Od (in A) and RO= 2500d (in B). The open and solid symbols represent calculationsbased on the 1064-and 532-nmincidentwavelength data, respectively.

the corresponding SHG data processed in the same LLR framework . Figures 5 and 6 support the view that the optical response of dissolving brass in our present system is strongly governed by lateral growths of surface islands. The relatively passive optical role of surface roughness has been already noted earlier in this paper and emerges again from the results of Figures 5 and 6. These latter results also allow us to further clarify the magnitude of the EM enhancement factor, u. As indicated in eqs 18 and 21, the magnitude of 0 is determined by that of the depolarization factor, B. So far in this paper, we have assumed that B rz 1to justify the approximation lul 1. Having the results ofFigures 5 and 6,we can now calculate the expected magnitude of this depolarization factor. The steps of this calculation are summarized below. We use /3 from Figure 6 and I(V) from Figure 2A to obtain J(Vw)from eq 11. Subsequently, from eq 10, we obtain m = 3.35 (averaged for the two incident photon energies). We take this value of m and J(V)from eq 8 to numerically solve eq 9. An estimate of Ro is also needed for this calculation. In their study of SD from Ag-Au alloys, Forty and Rowlands have used electron micrographs for Ag-Au surfaces subjected to strong SD and corrosion treatments-l7 By measuring the spacings between the corrosion spots, these authors estimated Ro 250d~,, where d ~ is, the atomic diameter of Au. The electron micrograph for a similarly treated brass electrode shows such spacings that are about an order of magnitude larger than those observed by Forty and Rowland on AuAg.' Thus, for brass, we estimate ROto be in the range of 2000d-2500d. We obtain numerical solutions for n(V) from eq 9 for both limits of this range of Ro. Using these n(V)with the now known m, we calculate H(V) from eq 2 andR(V) from eq 3. The voltage-dependent aspect ratio, H(V)fR(V),obtained from these calculations is shown by the triangles in Figure 6. As expected from the LLR model and EM theories of SHG, these aspect ratios are wavelength independent and remain close to zero, varying only between 0 and 0.08 throughout the experimental voltage range. By using thesevalues ofH(V)/R(V)in the analytical formulas published by Osborn, we obtain B(me5l This latter quantity is plotted with circles in Figure 7. We find that B is also wavelength independent and nearly independent of the applied voltage. The weak voltagedependent variation ofB in Figure 7 is in the range 0.891.00. The weaknature ofthis variation justifies the earlier

=:m 1.0

0.5

-pbC.

----

1

---

1.D

4

t

0.5

0.0

CI

1.o

0.5

0.5

0.0

-0.6

V-03(vs. -0.4 SCE)

-0.3

I

V (vs. SCE)

Figure 6. Plot of the optical parameters(v)/s(Vm).The circles in A and B represent experimental points in terms of eq 34, obtained from the SHG data of parts B and C of Figure 2,

7

-0.5

0.0

Figure 6. Electrochemicalparameters j3 (circles)and a = 1 j3 (triangles)obtained from the numerical fits of electrochemical and optical data in Figure 5. The open circles and triangles in A and the solid circles and triangles in B represent results using the experiments involving 1064-and 532-nmincident wavelengths, respectively. The straight lines in A and B correspond t o the average values of /3 (0.187 and 0.197, respectively)and a (0.813and 0.803,respectively).

/3 to vary over a relatively small range as the value of V is changed. The results of these analyses are shown in Figures 5 and 6. The circles in parts A and B of Figure 5 represent experimental values of [s(V)Is(VhlJ,obtained by applying eq 34 to the SdV) data of parts B and C of Figure 1,respectively. The dashed lines in Figure 5 show numerical fits of eq 35 to these experimental data points. These values of/3(triangles) and a(circ1es)used in the fits of Figure 5A and 5B are shown in Figure 6A and 6B, respectively. The averaged (over the used voltage range) values of a andp are indicated by the solid lines in Figure 6. As seen in Figures 5 and 6,all experimental data points are fully accounted for with /3 = 0.187 f 0.005 (a= 0.813 fO.O05)forkw= 1.17eVand/3=0.197f0.005(a=0.803 f0.005) for fiw = 2.34 eV. These results imply essentially a single voltage- and wavelength-independent value (-0.2) for /3 in the normally expected domain of charge-transfer coefficients for Faradaic reactions. At low voltages, the points in Figure 6 display relatively large deviations for their average values. This is also an expected observation in terms of the discussion of section 3.iv where we noted that the validity of eq 17 becomes questionable for V < V a . Thus, we find that the LLR description of the electrochemical data for SD from brass is consistent with

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(51) Osbom, J. A. Phys. Rev. 1945, 67, 351

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3466 Langmuir, Vol.11, No.9, 1995

-0.6

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-0.3

I

V (vs. SCE)

Figure 8. Voltage-dependent surface degradation, as a result of the Zn dissolution process, measured in terms of lateral (9) and inward (H) damage spreadingparameters. Fractiong (from eq 7) of the initially flat electrode and fraction g' (from eq 21) of the total electrode surface covered by the Cu islands are shown in A and B, respectively. The total height H (from eq 3)ofthe islands,representingthe depth ofdamageto the surface is shown in C. The open and solid symbols correspond to results for the 1064- and 532-nm incident wavelengths, respectively.

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made assumption of B l.52 The results of Figure 7 explicitly show how the surface roughness features generated in the SD reaction of our present study cannot support EM enhancements in SHG. (iii)Growth of Surface Damage. In sections 2.ii and 3.i of this paper, we have noted that the growth of surface degradation due to SD can be measured in terms of the lateral growth parameter, g(V), and the inward growth parameter, H(V).These parameters for the present system can be calculated with the results presented in Figures 2-6. We use eqs 7 and 8, with I(V)from Figure 2a and from Figure 5, to calculate g(V). From this g(V), we also calculateg'(V) using eq 21. These results forg(V), g'(V), and H(V) are plotted in parts A, B, and C of Figure 8, respectively. Since all three parameters examined here (52) Zhang, J. Y.;Shen, Y.R.J . Appl. Phys. 1992,71,2665.

are strictly geometric, they do not show any wavelength dependencies. In addition, g ' ( n does show some detectable deviations fromg(lr). The latter observation further emphasizes an earlier mentioned point that the coverage of surface structures should be appropriately recalibrated for optical considerations. While the results of Figures 4-7 examine the mechanism of SD, those of Figure 8 provide time(voltage1resolved information about surface damage. Both aspects of these results are commonly considered as the central issues of studying alloy degradati0n.l SHG, as an accompanying technique of electrochemistry in this work, has allowed us to simultaneously address these issues in a single theoretical framework. 7. Conclusions

In this report, we have demonstrated how SHG from brass can be utilized to probe the mechanism of SD of this alloy. Focusing on the corrosion-free voltage region, we have tested a previously proposed theoretical (LLR)model of SD. We have shown that the surface optical response is dominated by the lateral spreading of SD-generated islands, while the roughness of these islands is a rather irrelevant factor. Both of these observations are consistent with the SD mechanism in the LLR model and support this model as a reasonable description of the experimental system used in this work. On the basis of this description, we have also demonstrated that the propagation of surface damage during SD can be characterized with SHG. Several other models of SD, both similar and dissimilar to the LLR model, are found in the literature.' Many of them are considered to be system-specific and cannot be tested readily with electrochemical experiments alone. With further studies, the analyses presented here can be extended to test such models for both corrosion-free and corrosion-affected SD reactions on other binary alloys. Such efforts can lead to a valuable expansion of surface SHG techniques in the area of alloy electrochemistry. LA950397Y