Abstract
The branched fractal structures formed by non-equilibrium electrodeposition of metals1 have for several years been considered as model systems for the study of branching and fractal growth processes generally2,3,4,5,6. Most studies have focused on the large-scale structure of the deposits, but the question of how the branching pattern emerges from the nucleation and growth of thepolycrystalline metal at the microscopic scale remains unclear. Here I present experimental and theoretical results which suggest that branched electrodeposits may arise from an oscillatory character in the nucleation kinetics. For this kind of deposition, nucleation is probabilistic but biased towards higher electric fields. I suggest that a given nucleation event is followed by a recovery phase before a subsequent event is possible. This oscillatory nature generates a polycrystalline deposit, the grain size of which determines the level of ‘noise’ which is amplified by the familiar laplacian (‘fingering’) instabilities of non-equilibrium growth2,3,4,5,6 into a macroscopically fractal structure.
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References
Matsushita, M., Sano, M., Hayakawa, Y., Honjo, H. & Sawada, Y. Fractal structures of zinc metal leaves grown by elecctrodeposition. Phys. Rev. Lett. 53, 286–289 (1984).
Stanley, G. & Ostrowsky, N. (eds On Growth and Form NATO ASI Series Vol. 100(Martinus Nijhoff, Kluwer Academic, Boston, (1996)).
Vicsek, T. Fractal Growth Phenomena, 2nd edn (World Scientific, Singapore, (1992)).
Meakin, P. in Phase Transitions and Critical Phenomena Vol. 12, (eds Domb, C. & Leibowitz, J. L.) (Academic, New York, (1988)).
Ben-Jacob, E. & Garik, P. The formation of patterns in non-equilibrium growth. Nature 343, 523–530 (1990).
Witten, T. A. & Sander, L. M. Diffusion limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403 (1981).
Niemeyer, L., Pietronero, L. & Wiesmann, H. J. Phys. Rev. Lett. 52, 1033 (1984).
Chazalviel, J.-N. Electrochemical aspects of the generation of ramified metallic deposits. Phys. Rev. A42, 7355–7367 (1990).
Fleury, V., Chazalviel, J.-N., Rosso, M. & Sapoval, B. Role of the anions in the growth speed of fractal electrodeposits. J. Electroanal. Chem. 290, 249–255 (1990).
Fleury, V., Kaufman, J. & Hibbert, D. B. Mechanism of a morphology transition in ramified electrochemical growth. Nature 367, 435–438 (1994).
Melrose, J. R., Hibbert, D. B. & Ball, R. C. Interfacial velocity in electrochemical deposition and the Hecker effect. Phys. Rev. Lett. 65, 3009–3012 (1990).
Fleury, V. & Barkey, D. Runaway growth in two-dimensional electrodeposition. Europhys. Lett. 36(4) 253–258 (1996).
Despic, A. R. & Popov, K. I. in Modern Aspects of Electrochemistry Vol. 7(eds Conway, B. E. & Bockris, J.O'M.) 199–213 (1972)
Dini, J. Electrodeposition (Noyes, New Jersey, (1992))
Ramasany, P. Handbook of Crystal Growth 1a (ed. Hurle, C. J.) (North Holland, Amsterdam, (1993)).
Bergstrasser, T. R. & Merchant, H. D. in Defect Structure, Morphology and Properties of Deposits (ed. Merchant, H. D.) Proceedings of the Materials Week, Rosemont, 115–168 (TMS publications, Warrendale, PA, USA).
Vetter, K. J. Electrochemical Kinetics — Theoretical AspectsCh. 2, section D, 282–327 (Academic, New York, (1967)).
Budevski, E., Staikov, G. & Lorenz, W. J. Electrochemical Phase Formation and Growth, an Introduction to the Initial Stages of Metal DepositionChs 4, 5 (VCH, New York, (1996)).
Acknowledgements
I am grateful for discussions with D. Barkey; the cell design was in part elaborated in collaboration with him. One series of experiments was prepared with N. Lidgi. I thank A. Chauvineau for lending the AFM. I also shared many stimulating discussions with J.-F. Gouyet, M. Plapp, B. Sapoval, J.-N. Chazalviel, M. Rosso and C. Brissot of the Laboratoire PMC. I acknowledge the help of L.-A. Couturié with image processing.
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Fleury, V. Branched fractal patterns in non-equilibrium electrochemical deposition from oscillatory nucleation and growth. Nature 390, 145–148 (1997). https://doi.org/10.1038/36522
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DOI: https://doi.org/10.1038/36522
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