Hostname: page-component-6bf8c574d5-2jptb Total loading time: 0 Render date: 2025-02-22T23:42:42.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractal and Dendritic Growth of Surface Aggregates

Published online by Cambridge University Press:  10 February 2011

H. Brune ,
K. Bromann ,
K. Kern ,
J. Jacobsen ,
P. Stoltze ,
K. Jacobsen  and
J. Nørskov
H. Brune
Affiliation:
Institut de Physique Expérimentale, EPFL, CH- 1015 Lausanne, Switzerland
K. Bromann
Affiliation:
Institut de Physique Expérimentale, EPFL, CH- 1015 Lausanne, Switzerland
K. Kern
Affiliation:
Institut de Physique Expérimentale, EPFL, CH- 1015 Lausanne, Switzerland
J. Jacobsen
Affiliation:
Center for Atomic-scale Materials Physics and Physics Department Technical University of Denmark, DK-2800 Lyngby, Denmark
P. Stoltze
Affiliation:
Center for Atomic-scale Materials Physics and Physics Department Technical University of Denmark, DK-2800 Lyngby, Denmark
K. Jacobsen
Affiliation:
Center for Atomic-scale Materials Physics and Physics Department Technical University of Denmark, DK-2800 Lyngby, Denmark
J. Nørskov
Affiliation:
Center for Atomic-scale Materials Physics and Physics Department Technical University of Denmark, DK-2800 Lyngby, Denmark
Get access

Abstract

The similarity of 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 growth. The central question in this context is what causes some patterns to be dendritic, as e.g. snowflakes, while others grow fractal (randomly ramified). Here we report a crossover from fractal to dendritic patterns for growth in two dimensions: the diffusion limited aggregation of Ag atoms on a Pt(111) surface as observed by means of variable temperature STM. The microscopic mechanism of dendritic growth can be analyzed for the present system. It originates from the anisotropy of the diffusion of adatoms at corner sites which is linked to the trigonal symmetry of the substrate. This corner diffusion is observed to be active as soon as islands form, therefore, the classical DLA clusters with the hit and stick mechanism do not form. The ideas on the mechanism for dendritic growth have been verified by kinetic Monte-Carlo simulations which are in excellent agreement with experiment.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 407: Symposium M – Disordered Materials and Interfaces-Fractals, structure and Dynamics , 1995 , 379
Copyright
Copyright © Materials Research Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Witten, T. A. and Sander, L. M., Phys. Rev. Lett. 47, 1400 (1981).Google Scholar
[2] Witten, T. A. and Sander, L. M., Phys. Rev. B 27, 5686 (1983).Google Scholar
[3] Meakin, P., Phys. Rev. A 27, 1495 (1983).Google Scholar
[4] Eckmann, J. P., Meakin, P., Procaccia, I. and Zeitak, R., Phys. Rev. Lett. 65, 52 (1990).Google Scholar
[5] Grier, D., Ben-Jacob, E., Clarke, R. and Sander, L. M., Phys. Rev. Lett. 56, 1264 (1986).Google Scholar
[6] Sawada, Y., Dougherty, A. and Gollub, J. P., Phys. Rev. Lett. 56, 1260 (1986).Google Scholar
[7] Langer, J. S., Rev. Mod. Phys. 52, 1 (1980).Google Scholar
[8] Amer, M. B., Pelcé, P. and Tabeling, P., Growth and Form: nonlinear aspects (Plenum Press, New York, 1991).Google Scholar
[9] Takayasu, H., Fractals in the physical sciences (Manchester University Press, Manchester, New York, 1990).Google Scholar
[10] Meakin, P., Phys. Rev. A 33, 3371 (1986).Google Scholar
[11] Brune, H., Romainczyk, C., Röder, H. and Kern, K., Nature 369, 469 (1994).Google Scholar
[12] Nittmann, J. and Stanley, H. E., J. Phys. Math. Gen. 20, L981 (1997).Google Scholar
[13] Buka, A., Kertész, J. and Vicsek, T., Nature 323, 424 (1986).Google Scholar
[14] Ben-Jacob, E., Godbey, R., Goldenfeld, N. D., Koplik, J., Levine, H., Mueller, T. and Sander, L. M., Phys. Rev. Lett. 55, 1315 (1985).Google Scholar
[15] Horváth, V., Vicsek, T. and Kertész, J., Phys. Rev. A 35, 2353 (1987).Google Scholar
[16] Nittmann, J. and Stanley, H. E., Nature 321, 663 (1986).Google Scholar
[17] Vicsek, T., Fractal Growth Phenomena (World Scientific, Signapore, 1989).Google Scholar
[18] Meakin, P., Phys. Rev. A 36, 332 (1987).Google Scholar
[19] Chambliss, D. D. and Wilson, R. J., J. Vac. Sci. Technol. B 9, 928 (1991).Google Scholar
[20] Brodde, A., Wilhelmi, G., Badt, D., Wengelnik, H. and Neddermeyer, H., J. Vac. Sci. Technol. B 9, 920 (1991).Google Scholar
[21] Hwang, R. Q., Schroöer, J., Günther, C. and Behm, R. J., Phys. Rev. Lett. 67, 3279 (1991).Google Scholar
[22] Bartelt, M. C. and Evans, J. W., Surf. Sci. 314, L829 (1994).Google Scholar
[23] Bales, G. S. and Chrzan, D. C., Phys. Rev. Lett. 74, 4879 (1995).Google Scholar
[24] Pimpinelli, A., Villain, J. and Wolf, D. E., J. Phys. (Paris) 3, 447 (1993).Google Scholar
[25] Röder, H., Bromann, K., Brune, H. and Kern, K., Phys. Rev. Lett. 74, 3217 (1995).Google Scholar
[26] Michely, T., Hohage, M., Bott, M. and Comsa, G., Phys. Rev. Lett. 70, 3943 (1993).Google Scholar
[27] Röder, H., Brune, H., Bucher, J. P. and Kern, K., Surf. Sci. 298, 121 (1993).Google Scholar
[28] Brune, H., Röder, H., Romainczyk, C., Boragno, C. and Kern, K., Appl. Phys. A 60, 167 (1995).Google Scholar
[29] Jensen, P., Barabási, A. L., Larralde, H., Halvin, S. and Stanley, H. E., Nature 368, 22 (1994).Google Scholar
[30] Jensen, P., Barabási, A. L., Larralde, H., Halvin, S. and Stanley, H. E., Phys. Rev. B 50, 15316 (1994).Google Scholar
[31] Bardotti, L., Jensen, P., Hoareau, A., Treilleux, M. and Cabaud, B., Phys. Rev. Lett. 74, 4694 (1995).Google Scholar
[32] Bartelt, M. C. and Evans, J. W., Phys. Rev. B 46, 12675 (1992).Google Scholar
[33] Bales, G. S. and Chrzan, D. C., Phys. Rev. B 50, 6057 (1994).Google Scholar
[34] Amar, J. G. and Family, F., Phys. Rev. Lett. 74, 2066 (1995).Google Scholar
[35] Liu, S., Zhang, Z., Comsa, G. and Metiu, H., Phys. Rev. Lett. 71, 2967 (1993).Google Scholar
[36] Jacobsen, J., Jacobsen, K. W., Stoltze, P. and Norskov, J. K., Phys. Rev. Lett. 74, 2295 (1995).Google Scholar
[37] Zhang, Z., Chen, X. and Lagally, M. G., Phys. Rev. Lett. 73, 1829 (1994).Google Scholar
[38] Wang, S. C. and Ehrlich, G., Phys. Rev. Lett. 67, 2509 (1991).Google Scholar
[39] Brune, H., Röder, H., Boragno, C. and Kern, K., Phys. Rev. B 49, 2997 (1994).Google Scholar
[40] Kertész, J. and Vicsek, T., J. Phys. A: Math. Gen. 19, L257 (1986).Google Scholar
[41] During preparation of this manuscript it came to our attention that also Michely et al. interpret their islands as dendritic. They suggest a similar explanation based on anisotropic corner diffusion.Google Scholar
[42] This important difference has first been realized by Zhang et al. in ref. 37Google Scholar
[43] In a former publication (ref. 11) we have suggested that anisotropy in edge diffusion might be responsible for dendritic growth.Google Scholar
[44] Michely, T. and Comsa, G., Surface Science 256, 217 (1991).Google Scholar
[45] Jacobsen, K. W., Nørskov, J. K. and Puska, M. J., Phys. Rev. B 35, 7423 (1987).Google Scholar
[46] Stoltze, P., J. Phys. Condens. Matter 6, 9495 (1994).Google Scholar
[47] Mullins, W. W. and Sekerka, R. F., J. Appl. Phys. A 34, 323 (1963).Google Scholar
[48] Brune, H., Röder, H., Boragno, C. and Kern, K., Phys. Rev. Lett. 73, 1955 (1994).Google Scholar
[49] Brune, H., Bromann, K., Röder, H., Kern, K., Jacobsen, J., Stolze, P., Jacobsen, K. and Nørskov, J., Phys. Rev. B rapid communications in press (1995).Google Scholar