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Branched fractal patterns in non-equilibrium electrochemical deposition from oscillatory nucleation and growth

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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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Figure 1: A typical deposit in a cell 100 µm thick, with copper sulphate 0.
Figure 2: Texture as a function of growth speed.
Figure 3: AFM analysis of the growths at 10 µA (a and b) and 8 µA (c and d), obtained with a P.
Figure 4: Growth of a line of grains deposited by nucleation and growth events.

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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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  1. Laboratoire de Physique de la Matière Condensée, École Polytechnique, 91128 Palaiseau cedex, France

    Vincent Fleury

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  1. Vincent Fleury
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Correspondence to Vincent Fleury.

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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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