RightsCopyright (c) 2004 The Electrochemi

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1 Title A study on transient changes of sur and Sb coelectrodeposition Author(s) Saitou, Masatoshi; Fukuoka, Y Citation Journal of the Electrochemical Soci Issue Date 2004 URL RightsCopyright (c) 2004 The Electrochemi

2 Journal of The Electrochemical Society, C627-C /2004/ /C627/6/$7.00 The Electrochemical Society, Inc. A Study on Transient Changes of Surface Morphologies in Ag and Sb Coelectrodeposition M. Saitou*,z and Y. Fukuoka Department of Mechanical Systems Engineering, University of the Ryukyus, Okinawa , Japan C627 We have investigated transient changes in surface morphologies of Ag-Sb electrodeposits. Microscopic images of the Ag-Sb electrodeposits reveal that the surface morphology comprising Sb-poor and Sb-rich Ag deposits are described by a scaling function that is characterized by scaling exponents related to the growth mechanism of the Ag and Sb coelectrodeposition. The values of the scaling exponents indicate that Sb atoms which arrive at electrodes diffuse only in a local area. On the basis of a scenario that perturbations of ion concentrations in the electrolyte caused by Sb electrodeposition develop with time, a condition for the transient changes in the surface morphology is derived using linearized perturbation equations of the rate equations. The experimental results qualitatively support the instability condition The Electrochemical Society. DOI: / All rights reserved. Manuscript submitted August 5, 2003; revised manuscript received March 10, Available electronically September 15, In electrodeposition, a variety of morphologies named arrays of trees, dendrites, and open fractals have been studied and recognized. 1 These experimental investigations into morphologies have been made for single-element electrodeposits such as copper deposits. The morphological phenomena in binary element electrodeposition becomes more complicated but new morphologies different from the patterns stated above may be observed. In fact, Ag-Sb electrodeposits are reported to form spiral patterns 2,3 under specific experimental procedures. Characteristic patterns in the Ag-Sb electrodeposits as well as spiral patterns in the famous chlorite-iodide-malonic acid CIMA 4 and Belousov-Zhabotinsky BZ 5 reactions may become good candidates for the mechanisms of pattern formation in electrodeposition that emerges in nonequilibrium and irreversible systems. In addition, the patterns may allow us to describe the origin of pattern formation with a few factors. However transient changes, in particular, in the surface morphologies have not been studied in detail. Scaling treatments 6 are found to be useful tools for describing morphologies in phase transitions such as surface roughness. Phase transitions generally obey scaling laws, which are appropriate in the case of electrodeposition. 7,8 For example, computer simulations based on the diffusion-limited aggregates DLA 9 find a scaling relation d f (d) d-a for DLA deposits grown in the d dimensional space. The exponent A is usually given by the density-density correlation function C(r) r A. Zinc metal is electrodeposited onto a carbon tip electrode 10 and is shown to satisfy the scaling relation for their experimental values of d f (d) 1.63 and A In the present paper, not only the fractal dimension of the Ag-Sb electrodeposits but also whether or not the surface morphology of the Ag-Sb electrodeposits obeys scaling laws is examined. In this study, the transient changes in the surface morphology of the Ag-Sb electrodeposits comprising Sb-rich and Sb-poor Ag deposits are reported. In Ag-Sb electrodeposition, complexing agents potassium thiocyanate KSCN added in the electrolyte form complex ions that enable a change in the deposition potential of silver. Negative complex ion species such as Ag SCN) 2 ] are transported into cathodes only by diffusion in a potential-current region called diffusion-limited transport. 11 The deposition process of Ag ions is considered to be stable, which will not affect instability in the surface morphology of Ag-Sb electrodeposits. Hence, it is appropriate to presume the deposition process of Sb ions to be the cause of instability in the surface morphology. We attempt to derive a condition for instability of chemical reactions assuming that the electrodeposition of Sb ions perturbs the stable states of ion concentrations in thermal equilibrium. Surface morphologies in atmospheric conditions have usually * Electrochemical Society Active Member. z saitou@tec.u-ryukyu.ac.jp been observed with atomic force microscopy AFM. AFM offers high resolution for surface roughness but is limited to a scanning area, typically m, which is small in comparison with the dimensions of Sb-rich deposits. On the other hand, laser profile microscopy 12,13 also known as confocal laser microscopy is superior to AFM in terms of a broad magnification range and a wide scanning area of m. So laser profile microscopy was chosen in this study as an observation instrument. The purpose of this paper is to clarify the characteristic properties of the surface morphology of the Ag-Sb electrodeposits in terms of scaling laws, fractal relations, and periodical structures, and to explain the transient changes of the surface morphology from the time development of the relative deviations of ion concentrations in the electrolyte from thermal equilibrium caused by Sb electrodeposition. Experimental Experiments were performed using the electrolyte that includes the following components g/l : AgNO ; K 4 Fe CN 6 3H 2 O, 72; KSCN, 146; KNaC 4 H 4 O 6 4H 2 O, 59.3; C 8 H 4 K 2 O 12 Sb 2 3H 2 O APT, 6.7 or 13.3; K 2 CO 3, 31.3 or 0. The concentration of antimony potassium tartrate APT in this study was larger than that in other experiments. 2,3 This makes it easy to observe changes in the surface morphology of Ag-Sb deposits at the initial stage owing to the fast electrochemical reactions. Polycrystalline copper and carbon plates 20 mm long and 10 mm wide were prepared for the working and counter electrodes, respectively. These electrodes cleaned by a wet process were located parallel in a quiescent condition at a temperature of 300 K. Direct current densities applied between the two electrodes during electrodeposition were within a range of ma/cm 2. Ag-Sb deposits were grown on the copper substrates for the deposition time ranging from 60 to 600 s. The surface morphologies were observed with a laser profile microscope that has an accuracy of the order of 0.23 m and analyzed through the digitized microscope surface images with a resolution of pixels. The Sb concentration in the Ag-Sb electrodeposits and the crystallographic structures were determined by electron probe microanalyzer EPMA and X-ray diffraction XRD with Cu K radiation, respectively. Results and Discussion Electrodeposition that is a kind of phase transition should exhibit scaling and self-similar properties, irrespective of specific experimental systems and experimental details such as current densities. We first examine whether or not the Ag-Sb electrodeposits follow the Ag-Sb thermoequilibrium phase diagram. Figure 1 shows typical microscopic surface images of the Ag-Sb electrodeposits at a deposition time of 180 s. The surface morphology comprises bright and dark regions, which correspond to Sb-poor and Sb-rich Ag deposits, 2,3 respectively. According to the Ag-Sb thermoequilibrium

3 C628 Journal of The Electrochemical Society, C627-C Figure 3. Consecutive microscopic surface images of the Ag-Sb electrodeposits grown at a current density of 17 ma/cm 2 and a concentration of 6.7 g/l APT: a 60, b 90, c 120, and d 150 s. Figure 1. Typical microscopic surface images of the Ag-Sb electrodeposits at a deposition time of 180 s. The bright regions correspond the Sb-poor phases. a Ag-Sb electrodeposits at a concentration of 6.7 g/l APT and a current density of 17 ma/cm 2, b Ag-Sb electrodeposits at a concentration of 13.3 g/l APT and a current density of 15 ma/cm 2. phase diagram, 14 phases of silver including wt % Sb are stable at room temperature. At a higher Sb concentration of wt % phases appear in the system. Figure 2 shows a typical XRD pattern of the Ag-Sb electrodeposit grown from the electrolyte of APT 6.7 g/l. Several primary diffraction peaks in Fig. 2 are shifted to smaller angles of scattering. The average lattice constant of Ag determined from Fig. 2 is nm larger than nm in the standard table. 15 This implies that the lattice constant of Ag increases owing to the solid solution of Sb atoms. On the other hand, the EPMA measurements of the Ag-Sb electrodeposits determines the Sb concentration within a range of wt % that allows coexisting of the and phases according to the Ag-Sb phase thermoequilibrium diagram. However, no XRD pattern indicates that there exist and Sb phases in the electrodeposits, which in fact leads to the conclusion that the Ag deposits contain only solutes of Sb, that is the phase. Moreover, the surface morphology shows no lamellar structures comprising and phases. These results indicate deviations from the prediction of the Ag-Sb phase diagram. Next, let us examine the scaling properties of the transient surface morphology. Consecutive images of the Ag-Sb deposits with the same magnification of the laser profile microscope are shown in Fig. 3. It is clear that the distance between the Sb-poor phases bright images increases with the deposition time. Scaling and selfsimilarity are important concepts in modern statistical physics, 16 especially in phase transitions. Scaling is often described by simple power laws consisting of exponents that determine universality classes characterizing the scaling behavior, irrespective of experimental details. In order to understand the transient change quantitatively, we measure the density of the bright pixels in binary images of the digitized microscope images. The number of pixels, N, in units of pixels is defined by, N i x i 1 that behaves as x i 1 if a bright pixel exists at x i 0 if a dark pixel exists at x i where x i indicates the height of the ith pixel in the binary image. Figure 4 shows log-log plots of N vs. the deposit time t for two kinds of APT concentrations, 6.7 and 13.3 g/l. The slopes of Fig. 4a and b best fitted to the data are and , respectively. The number of the bright pixels obeys the following scaling law N t 2 Figure 2. Typical XRD pattern of the Ag-Sb electrodeposit grown from the electrolyte of APT 6.7 g/l at a current density of 17 ma/cm 2 and a growth time of 180 s. Several strong diffraction peaks are due to the diffraction of the copper substrate. where is an exponent that can be related to the growth mechanism of the Ag-Sb deposits. For example, N R 2 yields R t /2 from Eq. 2 where R is the average distance between the Sb-poor phases. If 2/3, the system will obey the Lifshiftz law. 17 We determine the fractal dimension of the Sb-poor deposits using a box-counting method that gives a simple relationship between N and l window size

4 Journal of The Electrochemical Society, C627-C C629 Figure 5. Determination of the fractal dimension using a box-counting method: a a typical binary image of the Ag-Sb electrodeposit grown at a concentration of 13.3 g/l APT, and a current density of 13.5 ma/cm 2, b a plot of log N vs. log l. The slope yields the fractal dimension d f (d) Figure 4. Log-log plots of the number of the bright pixels, N vs. the deposition time, t: a a concentration of 6.7 g/l APT and a current density of 17 ma/cm 2, b a concentration of 13.3 g/l APT and a current density of 15 ma/cm 2. N l d f d) where N is the number of bright pixels including in an area of 1 1 and d f (d) is the fractal dimension in the d dimensional space. Figure 5a shows a binary image of the Ag-Sb microscope image that yields the fractal dimension d f (d) of as shown in Fig. 5b. Figure 6 shows the dependence of the fractal dimension d f (d) on the deposition time, which gives the average fractal dimension , which is almost the same value as in the case of the DLA model in two dimensions. This implies that Sb atoms on the cathode electrode are unable to diffuse sufficiently. Does a scaling relation between d f (d) and exist as well as in the DLA model? The experimental results in Fig. 4 and 5 suggest that there exits a scaling function f (x) defined by N L d f f t d) 4 L z 3 where f x x at x 1 const at x 1 Dynamic scaling is often described by a scaling function, which gives scaling exponents that characterize the university class. 16 Equation 4 means no presence of characteristic scales in the system. The values of d f (d),, and in this study are considered to be related to the growth mechanisms of thin films. For example, in a diffusion-governing field, 18 a system size L is related to the square root of time t 1/2 and a new variable L/t 1/2, which is a kind of spatiotemporal variable, is introduced into the system. If diffusion governs the system in this study, Eq. 4 yields 1/2 and z d f (d) 1. However, the experimental values of in this study are greater than 1/2, which fact means that Sb atoms on the electrode diffuse in a local area. On the other hand, for t L z, if Eq. 4 is equivalent to Eq. 2, we have z d f (d) and. Figure 7 shows that all the data in Fig. 4 collapse on the scaling function proposed in this study and the slope of the straight line in Fig. 7 is approximately consistent with the values of in Fig. 6. Hence, the scaling function proposed in this study well describes the experimental results at the initial stage. Consequently, the values of and d f (d) indicate that Sb atoms deposited on the cathode surface diffuse only in a local area. Hence,

5 C630 Journal of The Electrochemical Society, C627-C Figure 6. Dependence of the fractal dimension d f (d) on the growth time for the Ag-Sb electrodeposits at a concentration of 13.3 g/l APT and a current density of 15 ma/cm 2. the transient surface morphology is due to the Sb concentration changes in the electrolyte during electrodeposition rather than due to the surface diffusion of Sb atoms. A periodical distribution of the Sb-poor deposits is investigated by a Fourier transform technique. Figure 8 shows a typical power spectrum of the pixels that lie on the P-Q line in Fig. 1a. Owing to the presence of a fundamental frequency, we here propose a scenario that ion concentrations in the electrolyte in thermal equilibrium are perturbed by Sb electrodeposition and the perturbations develop with time. Figure 9 shows the potential between the anode and cathode electrodes dependent on time for different current densities. For a current density of 11 ma/cm 2 at which no transient change in the Figure 8. Power spectrum of the pixels that lie on the P-Q line in Fig. 1a. Here f is the frequency and f 0 is a fundamental frequency. surface morphology is observed, the potential increases with time and approaches a saturated value. On the other hand, for a current density of 14.5 ma/cm 2 at which the transient change in the surface morphology is observed, the potential at first does not show the oscillatory behavior and after an increase in the potential the oscil- Figure 7. All the data in Fig. 4 collapse on the scaling function. The slope best fitted to data gives a value of Figure 9. Typical plots of the time dependence of the potential between the cathode and anode electrodes in the electrolyte including the K 2 CO 3.

6 Journal of The Electrochemical Society, C627-C C631 Sb OH) 3 3H Sb 3 3H 2 O 9 k 5 where k i is the rate constant, which is required if the concentrations in the system change. Three rate equations of Sb 3, Sb OH) 3 ], and H can be easily derived for the electrochemical Reactions 5-9 at the cathode electrodes d Sb 3 /dt k 5 Sb OH 3 ] H 3 k 1 SbO H 2 k 3 Sb 3 OH 3 10 d Sb OH 3 ]/dt k 3 Sb 3 OH 3 k 4 Sb OH 3 ] OH k 5 Sb OH 3 ] H 3 11 d H /dt k 1 SbO H 2 2k 2 SbO k 5 Sb OH 3 ] H 3 12 Figure 10. Typical plots of the potential between the cathode and anode electrodes vs. time using the K 2 CO 3 -free electrolyte. lation takes place. This implies that the electrodeposition of Sb ions perturbs the stable states in thermal equilibrium. Hence, we first assume the concentration changes caused by the electrodeposition of Sb ions to be perturbations that develop with time. To analyze the unstable property of Sb electrochemical reactions, we attempt to derive linearized perturbation equations of the rate equations. The electrodeposition of Sb ions will obey SbO 2 2H 2 O 3e Sb 4 OH, which causes the concentration changes in the electrolyte. The following reactions 19 are assumed SbO 2H Sb 3 H 2 O 5 k 1 SbO H 2 O SbO 2 2H 6 k 2 Sb 3 3 OH Sb OH) 3 7 k 3 Sb OH) 3 OH SbO 2 2H 2 O 8 k 4 where... indicates concentrations of chemical species in the electrolyte. We set the concentrations of the following chemical species at the steady state to be Sb 3 0 x 0, Sb OH) 3 ] 0 and H z 0. The concentrations of SbO and OH are so large that the perturbation terms related to them can be ignored. In addition, three constants are defined as a k 1 SbO, b k 3 OH 3, and c k 4 OH. Let the perturbation terms of Sb 3, Sb OH) 3 ], and H to be x, y, and z, respectively. The linearized perturbation equations can be derived from Eq ẋ b x k 5 z 0 3 y 3k 5 y 0 z 0 2 2az 0 z ẏ b x c k 5 z 0 3 y 3k 5 y 0 z 0 2 z ż k 5 z 0 5 y 2az 0 3k 0 y 0 z 0 2 z where ẋ d x/dt. Instead of solving an eigen value problem of a3 3 matrix for Eq , for simplicity, we derive a secondorder differential equation with respect to time. The sum of Eq. 13 and Eq. 15 yields ż b x ẋ 16 Differentiating Eq. 13 and Eq. 14 with respect to t and applying Eq. 16 to the result, we have ẍ 2az 0 ẋ 2abz 0 x const 17 Hence a condition for the oscillatory electrochemical reaction is given by k 1 SbO H 0 2k 3 OH 3 18 Figure 11. Consecutive microscopic images of the Ag-Sb electrodeposits at a concentration of 13.3 g/l APT and a current density of 17 ma/cm 2 for two kinds of electrolyte, electrolyte including K 2 CO 3, a 120, b 150, and c 240 s; K 2 CO 3 -free electrolyte, d 120, e 150, and f 240 s.

7 C632 Journal of The Electrochemical Society, C627-C This condition indicates that a lower concentration of OH will prevent the oscillatory reactions. Potassium carbonate generally dissolves in water and produces OH ions K 2 CO 3 H 2 O K OH HCO 3 19 To ascertain whether or not Eq. 18 is valid, we have made experiments using the Ag-Sb deposits grown from the K 2 CO 3 -free electrolyte. Figure 10 shows the dependence of the potential between the cathode and anode electrodes on time for the K 2 CO 3 -free electrolyte. In comparison with Fig. 9 the potential oscillation at a current density of 14.5 ma/cm 2 is inhibited and occurs at about 270 s. The microscopic surface images are shown in Fig. 11d-f. No Sb-poor Ag deposit is observed in Fig. 11d and e. These results qualitatively seem to support Eq. 18. Conclusions We have investigated the surface morphologies of Ag and Sb coelectrodeposits and the effect of instability in electrodeposition on the surface morphology, which gives rise to the patterns comprising Sb-rich and Sb-poor Ag deposits. Spatiotemporal images of the Sbpoor phases observed by the laser probe microscope are analyzed on the basis of the scaling properties and the instability condition of the rate equations in perturbed states. The transient development of the Sb-poor Ag deposits is shown to obey a scaling law described by N t at the initial stage where N is the number of pixels of the Sb-poor deposits and t is the deposition time, and also to have a distribution in space with a fundamental frequency. The fractal relation between the fractal dimension d f (d) and the scaling exponent is discussed. In addition, the condition for instability in the electrochemical reactions that cause a distribution of the Sb-rich and Sb-poor deposits is derived using the linearized perturbation equations. The instability condition qualitatively supports the experimental result. Acknowledgments Hideki Higa at the University of the Ryukyus is thanked for the experimental preparations. University of Ryukus assisted in meeting the publication costs of this article. References 1. F. Sagués, M. Q. L-Salvans, and J. Claret, Phys. Rep., 337, I. Kristev, M. Nikolova, and I. Nakada, Electrochim. Acta, 8, I. Krastev and M. T. M. Kopper, Physica A, 213, P. DeKepper, I. R. Epstein, K. Kustin, and M. Orbán, J. Phys. Chem., 86, K. Kapral and K. Showalter, Chemical Waves and Patterns, pp , Kluwer Academic Press, Dordrecht J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. J. Newman, The Theory of Critical Phenomena, Oxford Press, London M. Saitou, K. Hamaguchi, and W. Oshikawa, J. Electrochem. Soc., 150, C D. G. Foster, Y. Shapir, and J. Jorne, J. Electrochem. Soc., 150, C T. A. Witten and L. M. Sander, Phys. Rev. Lett., 19, M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo, and Y. Sawada, Phys. Rev. Lett., 53, P. K. Pandey, S. N. Sahu, and S. Chandra, Handbook of Semiconductor Electrodeposition, pp , Marcel Dekker Inc., New York M. Nopharatana, D. A. Mitchell, and T. Howes, Biotechnol. Bioeng., 81, M. Alschinger, M. Maniak, F. Stietz, T. Vartanyan, and F. Träger, Appl. Phys. B: Lasers Opt., 76, T. B. Massalski, Binary Alloy Phase Diagrams, Vol. 1, pp , ASM International, Metals Park, OH CRC Handbook of Chemistry and Physics, 79th ed., D. R. Linde, Editor, CRC Press, Boca Raton, FL A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge I. M. Lifshiftz and V. V. Slyozov, J. Phys. Chem. Solids, 19, G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Press, London M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, pp , National Association of Corrosion Engineering, Houston, TX 1974.