Abstract
THE similarity of many patterns formed in non-equilibrium growth processes in physics, chemistry and biology is conspicuous, and many attempts have been made to discover common mechanisms underlying their formation1. A central question is what causes some patterns to be dendritic (symmetrically branched, like snowflakes) and others fractal (randomly ramified). In general, the transition from fractal to dendritic growth is regarded as a manifestation of the predominance of anisotropy over random noise in the growth process. In electrochemical deposition, this transition is observed as the growth speed is varied2,3. Here we report a crossover from fractal to dendritic growth in two dimensions on the microscopic scale. We use the scanning tunnelling microscope to study diffusion-limited aggregation of silver atoms on a Pt(lll) surface. The transition occurs as the deposition flux is increased, and our observations suggest that the increasing importance of anisotropy of edge diffusion at higher flux is responsible for this crossover. We anticipate that a similar phenomenon may operate in three-dimensional crystal growth.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Takayasu, H. Fractals in the Physical Sciences (Manchester Univ. Press, New York, 1990).
Sawada, Y., Dougherty, A. & Gollub, J. P. Phys. Rev. Lett. 56, 1260–1263 (1986).
Grier, D., Ben-Jacob, E., Clarke, R. & Sander, L. M. Phys. Rev. Lett. 56, 1264–1267 (1986).
Witten, T. A. & Sander, L. M. Phys. Rev. Lett. 47, 1400–1403 (1981).
Meakin, P. Phys. Rev. A27, 1495–1507 (1983).
Hwang, R. Q., Schröder, J., Günther, C. & Behm, R. J. Phys. Rev. Lett. 67, 3279–3282 (1991).
Röder, H., Hahn, E., Brune, H., Bucher, J. P. & Kern, K. Nature 366, 141–143 (1993).
Eckmann, J. P., Meakin, P., Procaccia, I. & Zeitak, R. Phys. Rev. Lett. 65, 52–55 (1990).
Meakin, P. Phys. Rev. A33, 3371–3382 (1986).
Ben-Jacob, E., et al. Phys. Rev. Lett. 55, 1315–1318 (1985).
Buka, A., Kertész, J. & Vicsek, T. Nature 323, 424–425 (1986).
Horváth, V., Vicsek, T. & Kertész, J. Phys. Rev. A35, 2353–2356 (1987).
Couder, Y., Cardoso, O., Dupuy, D., Tavernier, P. & Thom, W. Europhys. Lett. 2, 437–443 (1986).
Nittmann, J. & Stanley, H. E. Nature 321, 663–668 (1986).
Nittmann, J. & Stanley, H. E. J. Phys. A 20, L1185–L1191 (1987).
Meakin, P. Phys. Rev. A36, 332–339 (1987).
Vicsek, T. Fractal Growth Phenomena (World Scientific, Singapore, 1989).
Eckmann, J. P., Meakin, P., Procaccia, I. & Zeitak, R. Phys. Rev. A39, 3185–3195 (1989).
Brune, H., Röder, H., Boragno, C. & Kern, K. Phys. Rev. B49, 2997 (1994).
Michely, T., Hohage, M., Bott, M. & Comsa, G. Phys. Rev. Lett. 70, 3943–3946 (1993).
Ehrlich, G. Surf. Set. 246, 1–12 (1991).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brune, H., Romainczyk, C., Röder, H. et al. Mechanism of the transition from fractal to dendritic growth of surface aggregates. Nature 369, 469–471 (1994). https://doi.org/10.1038/369469a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/369469a0
This article is cited by
-
A fractional diffusion equation with sink term
Indian Journal of Physics (2020)
-
Two-dimensional growth of germanium under a diffusion limited aggregation environment
Electronic Materials Letters (2017)
-
Electrochemical deposition of layered copper thin films based on the diffusion limited aggregation
Scientific Reports (2016)
-
Assembling molecular Sierpiński triangle fractals
Nature Chemistry (2015)
-
Buckling and Delamination of Ti/Cu/Si Thin Film During Annealing
Journal of Electronic Materials (2014)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.