Complex Surface Dynamics during Anodic Dissolution of Ni

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Complex Surface Dynamics during Anodic Dissolution of Ni A. G. Munõz,*,† M. E. Vela,‡ and R. C. Salvarezza‡ Institute of Thin Films and Interfaces (ISG 3), Research Centre Juelich, D-52425 Juelich, Germany, and Instituto de Investigaciones Fisicoquı´micas Teo´ ricas y Aplicadas (INIFTA), Universidad Nacional de La Plata-CONICET, Sucursal 4 Casilla de Correo 16, 1900 La Plata, Argentina Received March 9, 2005. In Final Form: June 25, 2005 The evolution of the surface roughness during the anodic dissolution of polycrystalline Ni was investigated by means of ex situ AFM in acid phosphate solutions. To characterize the time and spatial scaling behavior of surface roughness, the interface width and the power spectral density of the surface at different dissolution stages were analyzed in terms of dynamic scaling theories. The time dependence of global surface roughness, W(L,t), shows an unstable behavior characterized by a continuous increase without saturation following the relation W ∼ tβ, where β > 0.5. The unstable behavior results from the development of wide grooves that originates a surface consisting of mounds. Two scaling regimes at scales shorter and larger than the mound dimensions (lc) were observed. For l < lc, we found R ∼ 1 consistent with mounds exhibiting smooth (faceted) walls, whereas an anomalous scaling behavior with a proper local roughness exponents (Rloc < 1) dominates at l > lc. The introduction of nitrite in the solution, a common additive used in phosphating baths, leads to some changes in the scaling behavior as a consequence of different generated chemical surface conditions during dissolution. The different dissolution rates of the exposed crystal orientations and surface diffusion of adatoms were identified as the physical processes that govern the interface dynamic for this system.

1. Introduction The competition among different processes occurring during the anodic dissolution of a metal surface, such as dissolution and passivation, conducts to the development of a particular topography closely related with the kinetics of the interface under the generated near surface conditions.1-3 These processes are generally related with the participation of adsorbed intermediate species that can influence the rate of each individual step in the reaction scheme.4 This may lead to a different distribution of active sites, generating different types of roughness evolution. Therefore, the characterization of the dynamic evolution of irregular surfaces by a quantitative approach under non-steady and stationary regimes seems to be of great utility to understand the mechanisms of dissolution and corrosion processes. Numerous studies were devoted to study the growth of interfaces by means of vapor deposition,5 beam molecular epitaxy,6-8 or electrodeposition.9 In some cases, models were proposed to describe these processes on the basis of different stochastic aggregation rules. Then, the validity of each model was determined by comparison of the * To whom correspondence should be addressed. E-mail: [email protected]. Tel: +49-2461-61-1452. Fax: +49-246161-3907. † Research Centre Juelich. ‡ Universidad Nacional de La Plata-CONICET. (1) Wayne Suggs, D.; Bard, A. J. J. Am. Chem. Soc. 1994, 116, 10725. (2) Fernandes, M. G.; Latanison, R. M.; Searson, P. C. Phys. Rev. B 1993, 47, 11749. (3) Vela, M. E.; Andreasen, G.; Salvarezza, R. C.; Hernańdez-Creus, A.; Arvia, A. J. Phys. Rev. B 1996, 53, 10217. (4) Co´rdoba-Torres, P.; Nogueira, R. P.; Fairen, V. J. Electroanal. Chem. 2002, 529, 109. (5) Meakin, P.; Ramanlal, P.; Sander, M. L.; Ball, R. C. Phys. Rev. A 1986, 34, 509. (6) Family, F. Physica A 1990, 168, 561 and reference therein. (7) Villain, J. J. Phys. I 1991, 1, 19. (8) Das Sarma, S.; Tamborenea, P. Phys. Rev. Lett. 1991, 66, 325. (9) Meakin, P. In The Fractal Approach to the Heterogeneous Chemistry; Avnir, D., Ed.; J. Wiley & Sons: New York, 1989; p 131.

experimental and predicted dynamic scaling behaviors through the roughness (R) and growth (β) exponents for a determined scaling form. In contrast to this, only a few models were proposed for describing the evolution of surface topography under dissolution.4,10,11 Due to the stochastic nature of the dynamics of metal dissolution, the roughness of the surface is expected to change with time.2 Then, the characteristics of this evolution will depend on the surface structure and composition since the presence of defects and impurities will have an important contribution in the number of active sites with different reactivity. The influence of potential, on the other hand, is directly related with the detachment probabilities of the different types of surface sites. Thus, the change of potential may lead to a kinetic-roughening transition. Accordingly, it is expected that the adsorption of inhibitors will also have an important influence on the atomic scale processes conducting to different roughness evolutions. The influence of nitrite and the related adsorbed N-species generated during its reduction on the dissolution of Ni was studied in detail in previous papers.12,13 There, it was determined that the reduction of nitrite gives rise to various adsorbed N-species which competes with the adsorption of hydroxyl ions and consequently producing the inhibition of the dissolution process on exceeding anodically the potential of zero charge.13 Thus, the presence of nitrite causes not only a displacement the active dissolution region to more positive potentials but also an increase of surface roughness. This effect may be related with pronounced differences in the local dissolution rate as a consequence of local pinning promoted by passivating adsorbates as were addressed by others on studying the active dissolution of Ni(111).14 (10) Sieradzki, K. J. Electrochem. Soc. 1983, 140, 2868. (11) Benjamin, J. D.; Uren, M. J.; Chew, G.; Cullis, A. J. J. Cryst. Growth 1986, 75, 408. (12) Munõz, A. G.; Schultze, J. W. Electrochim. Acta 2004, 49, 293. (13) Munõz, A. G.; Benı´tez, G.; Vela, M. E.; Salvarezza, R. C. Langmuir 2004, 20, 2361.

10.1021/la050636+ CCC: $30.25 © 2005 American Chemical Society Published on Web 08/26/2005

Dynamics during Anodic Dissolution of Ni

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In this paper, we have further studied these effects in terms of the Ni surface dynamics during its dissolution by analyzing the scaling behavior in the images obtained by contact atomic force microscopy. We have found that this system exhibits a complex interface dynamics with two well-defined regimes irrespective of the presence of nitrite in the electrolyte. The first one is observed at length scales smaller than the size of mounds generated by the growth of grooves into the Ni surface. The second one is related to the roughness arising from height differences among the mounds growing at different rates. The difference in dissolution rates of the exposed crystal orientations and surface diffusion of adatoms were identified as the physical processes that govern the interface dynamic for this system. Nitrite affects the interface dynamics more markedly at length scales smaller than the mound size. 2. Experimental Details Polycrystalline Ni 99.98% with an exposed area of 0.502 cm2 was used as the working electrode. It was polished with 1000 emery paper and 0.3 µm alumina and finally sonicated in pure water. Electrochemical experiments were performed in a conventional cell, using a Pt sheet and a saturated sulfate electrode (sse; E0 ) 0.64 V versus a standard hydrogen electrode) as the counter and reference electrodes, respectively. Solutions were prepared from analytical-grade chemicals and pure water (Millipore-Q). A 1M NaH2PO4 solution of pH 3 was used as the base electrolyte. Potentials are referred to the sse. The concentration of NO2- was maintained in 1.5 × 10-3 M. All experiments were carried out under a saturated N2 atmosphere and at room temperature. Sweep voltammetries were performed using a linear-voltage sweep generator EG&G PAR model 175. Morphology studies were performed by using ex situ AFM imaging with a Nanoscope III equipment (Digital Instrument, Santa Barbara, CA). Silicon-nitride tips were used under the contact mode by applying different forces in the range 70 nN < f < 250 nN. The scaling analysis was carried out with images of 256 × 256 pixels resolution.

3. Results and Discussion 3.1. Dissolution Mechanism. Before discussing the dynamics of surface evolution, we must analyze some features concerned with the dissolution mechanism of Ni. Figure 1a shows the corrosion curves of Ni in phosphate solution with and without the presence of nitrite. As can be observed, the presence of nitrite not only increases the reduction current but also brings about a displacement of the active dissolution region ca. 100 mV toward more positive potentials. This effect is related to the preferential adsorption of NO2- and the related reduction products, impeding the adsorption of OH-, an intermediate step in the mechanism of Ni dissolution:15,16

Ni + H2O T NiOHads + H+ + e

(1)

NiOHads f NiOH+ + e (f Ni(OH)2,ads )

(2)

This mechanism is also in agreement with an anodic slope of aprox. 40 mV dec-1 observed with and without the presence of nitrite. However, in the presence of nitrite, it deviates to higher values on exceeding anodically E ) -0.6 V. In fact, an adsorption competition between N-species and passivating Ni(OH)2 is expected in this (14) Scherer, J.; Ocko, B. M.; Magnussen, O. M. Electrochim. Acta 2003, 48, 1169. (15) Plieth, W. F. In Encyclopedia of Electrochemistry of the Elements; Bard, A. J., Ed.; Marcel Dekker: New York, 1978; p 321. (16) Itagaki, M.; Nakazawa, H.; Watanabe, K.; Noda, K. Corros. Sci. 1997, 39, 901.

Figure 1. (a) Polarization curves of Ni in phosphate solutions, v ) 5 × 10-4 V s-1; (b) Time dependence of potential of Ni after applying a constant current density i ) 300 µA cm-2 in phosphate solutions.

potential region. This was also confirmed by the beginning of a marked decay of the relation N/O, obtained from ex situ Auger experiments, on exceeding anodically this potential.13 To analyze the evolution of the surface morphology, we applied a constant anodic current i ) 300 µA cm-2 (galvanostatic mode) within the active dissolution region in solutions with and without the presence of nitrite. Figure 1b shows the time dependence of the potential in both cases. As can be observed, a relatively stable potential is maintained in the absence of nitrite. On the contrary, a potential increase of 50 mV toward more positive values is observed after 20 min in its presence. This result reflects a certain type of dissolution inhibition. It is probably caused by an increase of the coverage fraction of adsorbed N-species as a consequence of the reduction of nitrite after long polarization times. 3.2. Dynamic Scaling Forms. To analyze the evolution of surface morphology, it is helpful to review briefly the theories of dynamic scaling. Generally, the presence of a self-affine surface is expected when dissolution is dominated by surface processes, whereas an unstable interface arises when they are coupled with either electrical or concentration gradients.17 In the first case, it is possible to analyze the evolution of the surface roughness by applying the Family-Vicsek dynamic scaling theory18,19

W (L,t) ) tR/z f (L/ξ(t)) f (L/ξ(t)) ∼ [L/ξ(t)]R ∼ const

(3)

if (L/ξ(t)) , 1 if (L/ξ(t)) . 1

(4)

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Figure 2. 10 µm × 10 µm AFM images of Ni surface obtained after different dissolution times at i ) 300 µA cm-2 in phosphate solutions. Time in seconds.

where the surface width W (L,t) is given by the root-mean square (rms) of interface height fluctuations

W(L,t) )

[

1

]

∑(hi - 〈h〉)2 N i

1/2

(5)

R is the roughness exponent and characterizes the stationary regime, that is, when the horizontal correlation length ξ(t) ∼ t1/z has reached a value larger than L, the system size. The ratio β ) R/z is the growth exponent and characterizes the short time behavior of the surface. A convenient function for the analysis of the roughness evolution is the power spectral density (PSD), obtained by applying a two-dimensional fast Fourier transform algorithm to the interface height.20-22 This function provides valuable information not only on the height deviation of the roughness profile but also on the lateral distribution, so giving a more general description of the surface roughness than the rms-roughness. Then, the Family-Vicsek scaling can be expressed in terms of the PSD as follows:

S(k,t) ) k-(2R+D) s (k t1/z) s (u) ∼ const

if u . 1

2R+D

if u , 1

∼u

(6)

(7)

where D is the Euclidean dimension. The existence of a Family-Vicsek scaling and the assumption of the selfaffine character of the interface implies that the local width w(l,t), which measures the surface height fluctuations over a window of size l , L, scales in the same manner as eq 3-4 with a local roughness exponent Rloc ) R. However, in some cases, the scaling behavior of the global width differs substantially from that of the local interface fluctuations. This different type of scaling was termed (17) Baraba´si, A. L.; Stanley, H. E. Fractal Concepts in Surface Growth; Cambridge University Press: New York, 1995; p 45. (18) Family, F.; Vicsek, T. J. Phys. A 1985, 18, L75. (19) Va´zquez, L.; Salvarezza, R. C.; Herrasti, P.; Ocoń, P.; Vara, J. M.; Arvıá, A. J. Phys. Rev. B 1995, 52, 2032. (20) Ruppe, C.; Duparre´, A. Thin Solid Films 1996, 288, 8. (21) Lo´pez, J. M.; Rodriguez, M. A.; Cuerno, R. Physica A 1997, 246, 329. (22) Tong, W. M.; Williams, S. R. Annu. Rev. Phys. Chem. 1994, 45, 401.

“anomalous”.23-25 In this case, two exponents, namely Rloc and R, must be considered to give a complete description of the scaling behavior of the surface. The anomalous scaling may be either associated with a super-roughening, where the global scaling exponent R > 1 and Rloc ) 1, or with an intrinsic anomalous roughening, where the PSD scales according to

s(u) ∼ u2(R-Rloc) ∼ u2R+D

if u . 1

(8)

if u , 1

(9)

The physical origin of this type of scaling has not been clearly resolved yet. However, on the basis of the existent experimental evidence, focused mainly on electrodeposited films, it was suggested that nonlocal effects arising from Laplacian fields such as bulk diffusion are responsible for such behavior.17 Then, this case can be identified by a growth exponent β > 0.5, when applying the Family-Vicsek scaling form. 3.3. Scaling Analysis. Figure 2 shows a sequence of AFM images obtained after different dissolution times with and without the presence of nitrite. As can be observed, the initial surface presents regular distributed linear scratches that are characteristic after the mechanical polishing. These discontinuities act as preferential sites for the attack as can be inferred from the linear patterned distribution of grains at the first stages of dissolution (t < 180 s). At first glance, it can be noted that the initial granulated morphology evolves in both cases toward mounds of increasing width. The surface cross sections of these images (Figure 3) show more clearly this effect. Here, grains with a relative constant size around 100-200 nm seem to be superimposed on the contour of widening cavities. These grains may originate in different dissolution rates for the different crystallographic orientations. At advanced dissolution stages, the mounds exhibit crystallographic facets as shown in Figure 2. Note that in the presence of nitrite a lower number density of grains of lower heights arises although it is evident that the interface profile evolves faster. Therefore, (23) Lo´pez, J. M.; Rodriguez, M. A.; Cuerno, R. Phys. Rev. E 1997, 56, 3993. (24) Castro, M.; Cuerno, R.; Sańchez, A.; Domıńguez-Adame, F. Phys. Rev. E 1998, 57, R2491. (25) Huo, S.; Schwarzacher, W. Phys. Rev. Lett. 2001, 86, 256.


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Figure 3. Cross-section profiles corresponding to the Ni surface after different dissolution times at i ) 300 µA cm-2 in phosphate solution. Circles indicate the grains generated by preferential attack in the scratches.

Figure 4. High-pass filtered 5 µm × 5 µm AFM images highlighting the grain size distribution of crystallographic attack after different dissolution times in the presence of nitrite (Z ) 200 nm, left). Right: corresponding nonfiltered images.

a comparison between both profiles at the same time is not strictly valid. The comparison of a high-pass filtered AFM image of the initial substrate with those corresponding to different dissolution times (Figure 4) allows some conclusions to be obtained about the influence of the initial polishing grooves on further evolution of the surface roughness. As can be clearly observed from the filtered images, the initial striped pattern transforms into a grain like one after few minutes of dissolution (180 s). This points out the crystallographic nature of the dissolution control. Also, the grain size distribution seems not to vary so much during dissolution, showing a mean grain size of about 100 nm. After comparing the filtered images (Figure 4 left) with the nonfiltered ones (right), it is evident that the initial grooves act as preferential points of attack leading to the

development of mounds (Figure 4, 180s). In this way, facets are formed that grow until they reach the grain boundaries (Figure 4, 5400 s). As we will discuss later, this fact brings important consequences for the evolution of morphology, where two roughening mechanisms can be distinguished. As a first approach to the analysis of the system, we analyzed the dependence of the surface width w(l,t) with the length scale for different dissolution times (Figure 5a) in the absence of nitrite, although a similar scheme was also observed in its presence. As can be seen, saturation is attained in all cases for l > 20 µm. This means that the roughness becomes independent of the scale length or [l/(t)] . 1. This fact makes it then possible to know the time dependence of the global surface width W from images equal or larger than this size. Figure 5b shows the plot of log W (L ) 20 µm) vs log t, where a continuous linear increase without saturation is observed in all cases, but with slightly higher values in the presence of nitrite. After analyzing these data according to the Family-Vicsek scaling form (eq 3), a growth exponent β ≈ 0.6 could be estimated in both cases. In principle, this type of dependence might be associated with an unstable growth characterized by a random detachment without relaxation processes, that is, with the absence of a correlation length.17,26 However, this is not the case here if we regard the corresponding power spectra, as it will be shown in the following, since a frequency independent spectrum is expected for a stochastic roughening.22 Figure 6 shows the PSD of the interface taken at short and long dissolution times in the absence of nitrite. Two straight lines with different slopes and a crossover point at kcrossover are observed irrespective of the dissolution time and electrolyte composition (with and without nitrite). This suggests that different roughening regimes are being operative at both sides of the crossover (regions I and II). As expected, a saturation region is also observed at large scale lengths (l > 10-20 µm, k < 0.05 µm-1) for all samples, introducing a new crossover that limits region II. This fact, which is consistent with the saturation of w(l,t) observed in Figure 5a, was specially pointed out by expanding the scale in the low-frequency region (see detail inserted in Figure 6). First, we discuss some aspects related to the crossover point that itself defines a typical length scale lc ) (kcrossover)-1. It is interesting to note that the kcrossover value (26) Kardar, M. Physica B 1996, 221, 60.

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Figure 7. Two-dimensional power spectral density obtained on Ni surface after different dissolution times in the presence of nitrite. Additionally, the corresponding top-view 2 µm × 2 µm AFM images of the surface with corresponding cross sections are also shown. (O) Initial substrate. Figure 5. (a) Spatial dependence of the surface width w(l, t) obtained from 100 µm × 100 µm images after dissolution without nitrite. (b) Time dependence of the global surface width obtained from 20 µm × 20 µm AFM images.

Figure 8. Time dependence of the characteristic length (lc) at which the changes of the slope occurs in the power spectra.

Figure 6. (a) Two-dimensional power spectral density obtained on Ni surface after different dissolution times in the absence of nitrite; (O) Initial substrate. Dotted lines indicate the value of lc for 600 and 10 800 s. Double arrows indicate the transition from region I to II.

shifts to smaller frequencies, i.e., increasing lc, with the dissolution time (t). A careful analysis of the PSD plots and the AFM images reveals that lc is closely related to the mound size resulting from the groove formation (Figure 3). Therefore, the increase in lc with t reflects the coarsening of the mounds during the electrodissolution process. Now we analyze the scaling behavior observed in region I. For l < lc the slope of the straight line in the PSD plots is -4 (RI ) 1), a figure consistent with the development

of mounds with relatively smooth surfaces. In fact, the slope of -4 appears at larger scales than the size of the grains (≈200 nm) but at smaller lengths than lc suggesting that the mound surface is Euclidean at these scales. In fact, detailed inspection of the mounds in the AFM images, taken at long electrodissolution times, reveals that their walls consist of facets (Figure 2). The presence of nitrite seems not to affect the general roughening mechanisms (Figure 7) and a similar analysis can then be made. In the AFM images inserted in Figure 7, we can observe how the displacement of the linear part of power spectra toward higher values is correlated with the growth of mounds. The increase of lc with time (Figure 8) presents a figure that is consistent with an electrodissolution process under surface reaction control (lc ∝ tn) as expected from eqs 1-2.


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Otherwise, a leveling effect should arise from a mass transport control.27 According to these results, one could regard the wall of mounds as expanding crystallographic (faceted) domains with a particular roughening mechanism operating upon them. Then, their mean size lc can be associated with the corresponding correlation length and consequently with a time dependence given by an expression of the type lc ∝ t1/z with zI ) 1. Accepting that it is true, we are able to estimate a generic β ) R/z, which can be used to characterize the dynamic behavior. When this is done, a value of β ) 1 can be estimated in the absence of nitrite. On the other hand, in the presence of nitrite (Figure 8, open circles), the growth of the mounds resulting from the electrodissolution process is accelerated. In this case, the faster increase observed for lc at t > 2000 s may be a consequence of a modulation effect brought about by adsorption of the N-species on the dissolution rate. In this case, we have lc ∝ t1.7 a figure that leads to zI ) 0.6. Moreover, considering RI ) 1 and zI ) 0.6, we obtain βI ) 1.7; that is, the interface becomes rougher more rapidly in the presence of nitrite (see also Figure 5). Therefore, the influence of nitrite is mainly focused in the expansion rate of the mounds that is much faster (1/z ) 1.7) than in the absence of the additive in the solution (1/z ) 1). This effect is probably related with the blockage of dissolution sites by the adsorption of hydroxide, which limits the growth of the smooth zones. In fact, nitrite reduces the surface coverage by OH species due to competitive adsorption and then could accelerate mound coarsening and roughening. Finally, we discuss the interface dynamics observed for region II. In this case, scaling data are related to the fluctuations of mound heights as they correspond to l > lc. The continuous displacement of the PSD spectra toward larger values with time in this region also indicates that we are in the case of an anomalous scaling (eqs 8 and 9). As already discussed, a third independent exponent is needed in the case of anomalous scaling to collapse these portions in a single line (eqs 8 and 9). Thus, the power spectrum for (k t1/z) . 1 must be given by

S(k,t) ) k-(2Rloc+D) t2(R-Rloc)/z

(10)

where Rloc is the spectral or local roughness exponent. To adjust the power spectra to the anomalous roughness form (eqs 8 and 9), they were represented as [S(k,t) k2R+D] vs (k t1/z) (Figure 9). The parameters R and z were varied up to find the collapse of the spectra obtained at different dissolution times. This was assessed by imposing values of RII ) 1.0 and zII ) 1.7 and 2 without and with the presence of nitrite, respectively. Accordingly, a local roughness exponent Rloc of 0.3 and 0.23 could be calculated from the corresponding slopes of the ascending part of the curves (eq 8). The global growth exponent βII for the second region can be calculated from eq 11

βII ) RII/zII

(11)

leading to 0.52 and 0.58 with and without the presence of nitrite, respectively. Both figures are in excellent agreement with β ) 0.58 derived from the log W vs log t plot (Figure 5) for 20 µm × 20 µm AFM images. On the other hand, the local β* value estimated from

β* ) (RII - Rloc)/zII

(12)

adopts a value of ∼0.4 with and without the presence of nitrite.

Figure 9. Collapse of the PSD data obtained from AFM images after different dissolution times in solutions without (a) and with (b) the presence of nitrite.

The global roughness exponent RII ) 1.0 may indicate that at larger scales the surface resulting from the electrodissoltion process is not fractal. From this point on, the whole surface behaves as smooth, and the revealing of grains can be clearly observed (Figure 10). On the other hand, despite the lack of a defined physical meaning of the local roughness exponent, this seems to reflect the noise generated by the development of mounds that grow at different rates. The decrease in Rloc caused by the introduction of nitrite indicates some small changes in the roughening kinetics. In this case, the depassivation generated by adsorption of N-species conducts to a more marked differentiation in the dissolution rate of the different crystal orientations, which in turn conducts to a rougher surface. At this point, it should be remarked that the behavior of the power spectra for the case of anomalous scaling does not affect the behavior of the global width, which preserves its Family-Vicsek form: W(L,t) ) tβ for t , Lz. The interface dynamics observed in region I for Ni electrodissolution (RI ) 1, βI > 0.5) resembles that generated by the model described in ref 28 at long dissolution times when a site dependence atom detachment and particle surface diffusion was considered. This model is based on random removal of particles with a site dependent probability given by

Pd (N) ) 6 - N/5

(13)

where Pd is the detachment probability and N is the coordination number of the site. Then, after atom detachment from a site i, the remaining particles around the vacancy can diffuse a length l to find sites with higher coordination numbers with an equal direction probability. In the absence of step-edge energy barriers, the model (27) Saunier, J.; Chausse´, A.; Stafiej, J.; Badiali, J. P. J. Electroanal. Chem. 2004, 563, 239.

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Figure 10. Top-view 50 µm × 50 µm AFM images of the Ni surface after dissolution: (a) without nitrite, t ) 10 800 s; (b) with nitrite, t ) 5400 s. Z ) 1.5 µm.

predicts R ≈ 1, whereas the growth exponent changes from an initial regime with β ) 0.25 to β f 1 for advanced stages of dissolution. In fact, after an initial stable growth consistent with the linear (surface) diffusion equation (R ) 1, β ) 0.25), groove formation takes place, and the dissolving surface evolves toward mounds with smooth surfaces. As a consequence of the groove development, the interface becomes unstable without reaching saturation (β > 0.5). Therefore, this model captures some aspects of our experimental system, in particular the groove development and the formation of mounds with smooth

Mun˜ oz et al.

surfaces. The absence of the initial growth regime with β ) 0.25 in our experimental data could be explained considering the nonnegligible surface roughness of the substrate that could mask the initial portion of the log W vs log t plots (Figure 5). Therefore, dissolution coupled with surface diffusion of adatoms can account for the interface dynamics for l < lc in the presence and in the absence of nitrite. On the other hand, for region II, we observed an anomalous scaling with RII ∼ 1 and βII ∼ 0.6 and Rloc ∼ 0.3 (without nitrite), Rloc ∼ 0.23 (with nitrite), and β* ∼ 0.4. Anomalous scaling has also been reported by Schwarzacher et al.25 for electrodeposition of Cu and Au, where values of R ∼ 0.8 and β ∼ 0.4 were found, independently of the electrodeposition conditions. On the other hand, these authors also suggested certain link between anomalous scaling and bulk diffusion after observing a variation of β* with deposition current. The contribution of diffusional or electric fields has frequently been assigned as being responsible of the anomalous scaling.29,30 However, in our case, the onset of a diffusion field in the electrolyte can be disregarded as a possible cause, since it is not observed from electrochemical results. Evermore, if it were the case, dissolution under diffusion control would lead to a surface leveling rather (by preferentially dissolving of protrusions) than to roughening. On the other hand, no ohmic contributions are observed in the electrochemical data. Therefore, we propose that the anisotropy resulting from differences in the electrodissolution rate of the different crystal faces exposed to the electrolyte can account for the observed anomalous behavior of the interface dynamics. As were formulated by others on studying the anodic dissolution of Cu,31 the origin of instabilities can be mainly related to the different dissolution rates of the exposed crystallographic planes. Similarly, different potentials will be established on the Ni surface depending on the crystal orientation for a galvanostatic experiment. As a consequence, dissimilar extents of passivation arise on the dissolving surface. As were pointed out in the discussion of Figure 4, the presence of preferential points of attack at the initiation of dissolution constitutes also a reliable explanation for the unstable roughness evolution and the consequent appearance of an anoumalous scaling. Then, the similarity of the global scaling coefficients with those obtained during deposition suggests a possible link between the two processes related to the precense of preferential acitve sites. From our analysis, there is some evidence that the influence of the initial polishing grooves on the evolution of surface roughness is linked with the origin of mounds. However, this point remains still obscure and needs

Figure 11. Schematic representation of the surface processes taking place during dissolution at short and large scales.


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Table 1. Summary of Scaling Exponents in the Electrodissolution of Ni in Phosphate Solutions of pH 3 region I nonfractal

region II anomalous scaling

RI ∼ 1 βI ∼ 1 (without NO2-) βI ∼ 1.7(with NO2-) zI ∼ 1 (without NO2-) zI ∼ 1.7 (with NO2-) RII ∼ 1 (∼ 0.8 electrodeposition25) βII ∼ 0.6 (∼0.4 electrodeposition25) zII ∼ 1.7 (without NO2-) zII ∼ 2 (with NO2-)

additional work concerning different starting surfaces in order to be resolved. The schematic representation of the surface evolution depicted in Figure 11 helps to give a better understanding of the discussion exposed above. Here, it can be seen how the different displacement rates of faceted walls by dissolution conduct to the formation of mounds with a particular scaling behavior. This later can be divided in two scaling regions characterized by different parameters, obtained from the analysis of the PSD, which are summarized in Table 1. According to this scheme, it is evident that both scaling regimes have the same origin, which is the expansion of nonfractal crystallographic facets. Therefore, the presence of an anomalous scaling may be physically interpreted in terms of a roughness dynamics governed by the development non fractal domains at shorter scales. In this way, the coefficient Rloc in the region II reflects the height fluctuations introduced by differenciated rates of the local advancing fronts. Accordingly, it is not surprinsing that the global roughness coefficient RII ∼ 1, since the whole surface behaves as nonfractal. The use of the PSD as a tool of analysis makes it possible to describe this type of behavior that would be impossible to be carried out by applying the scaling laws in the real space, since the roughening dynamics does not maintain at l , lc. In other words, the anomalous scaling behavior is not valid in the whole scale range, as usual in the (28) Hernańdez-Creus, A.; Carro, P.; Salvarezza, R. C.; Arvıá, A. J. Langmuir 1997, 13, 833. (29) Vazquez, L.; Abella, J. M.; Salvarezza, R. C.; Arvıá, A. J.; Levy, R. A.; Perese, D. Appl. Phys. Lett. 1996, 68, 1285. (30) Iwamoto, A.; Yoshinobu, T.; Iwasaki, H. Phys. Rev. E 1999, 59, 5133. (31) Aziz, S. G.; Vela, M. E.; Andreasen, G.; Salvarezza, R. C.; Hernandez-Creus, A.; Arvia, A. J. Phys. Rev. B 1997, 56, 4166.

Rloc ∼ 0.23 (with NO2-) Rloc ∼0.3 (without NO2-) β*(local)∼ 0.4 (with and without NO2-)

traditional analyzed systems, where the roughening mechanism lies in continuous models with an atomic basis. 4. Conclusions The evolution of the surface morphology during the corrosion of Ni in the presence of nitrite was analyzed by means of power spectra. It could be observed that the surface roughness evolves following two dynamics regimes at shorter and longer length scales than lc. This behavior arises from the dependence of the dissolution rate on crystal orientation combined with surface mobility and is manifested in the groove formation that leads to mounds with facetted walls. Differences in the rate of crystal dissolution together with the presence of initial irregularities introduced by scratches in the starting surface are the main cause for the unstable growth. The surface evolution can be characterized by an anomalous scaling behavior at scales larger than the mound size lc. On the other hand, the crystallographic texture inside these zones is characterized by a roughness coefficient R ∼ 1 and the consequent loss of fractality. Then, the coarsening and growth of these zones conducts to the progressive revealing of grains. Here, the adsorption of N-species derived from the reduction of nitrite deepens the differences among the dissolution rates on the different crystallographic planes, conducting to a more roughen surface at the first stages of dissolution. Acknowledgment. A.G.M. acknowledges specially The Alexander Von Humboldt Foundation for a research fellowship. The Consejo Nacional de Investigaciones Cientı´ficas y Tećnicas (CONICET) and the ANPCyT (PICT 02-11111) are also acknowledged for financial support. M.E.V. is a member of the research career of CIC. LA050636+

Complex Surface Dynamics during Anodic Dissolution of Ni

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