Abstract
We numerically simulate the dynamics of atomic clusters aggregation deposited on a surface interacting with the growing island. We make use of the well-known DLA model but replace the underlying diffusion equation by the Smoluchowski equation which results in a drifted DLA model and anisotropic jump probabilities. The shape of the structures resulting from their aggregation-limited random walk is affected by the presence of a Laplacian potential due to, for instance, the surface stress field. We characterize the morphologies we obtain by their Hausdorff fractal dimension as well as the so-called external fractal dimension. We compare our results to previously published experimental results for antimony and silver clusters deposited onto graphite surface.
Similar content being viewed by others
References
R. Tokita, T. Katoh, Y. Maeda, J. Wakita, M. Sano, T. Matsuyama, M. Matsushita, J. Phys. Soc. Jpn 78, 074005 (2009)
L. Niemeyer, L. Pietronero, H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)
D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, C. Tang, Rev. Mod. Phys. 58, 977 (1986)
F. Ciuchi, L. Sorriso-Valvo, A. Mazzulla, J.M. Redondo, Eur. Phys. J. E 29, 139 (2009)
T.R. NíMhíocháin, G. Hinds, A. Martin, Z.Y.E. Chang, A. Lai, L. Costiner, J.M.D. Coey, Electrochim. Acta 49, 4813 (2004)
R.Q. Hwang, J. Schröder, C. Günther, R.J. Behm, Phys. Rev. Lett. 67, 3279 (1991)
A.R. Howells, L. Hung, G.S. Chottiner, D.A. Scherson, Solid State Ion. 150, 53 (2002)
B. Yoon et al., Surf. Sci. 443, 76 (1999)
L. Bardotti, P. Jensen, A. Hoareau, M. Treilleux, B. Cabaud, Phys. Rev. Lett. 74, 4694 (1995)
L. Bardotti, P. Jensen, A. Hoareau, M. Treilleux, B. Cabaud, A. Perez, F. Cadete Santos Aires, Surf. Sci. 367, 276 (1996)
C. Brechignac et al., Surf. Sci. 518, 192 (2002)
P. Jensen, Rev. Mod. Phys. 71, 1695 (1999)
B.B. Mandelbrot, B. Kol, A. Aharony, Phys. Rev. Lett. 88, 055501 (2002)
M.T. Batchelor, C.I. Henry, A.P. Roberts, Phys. Rev. E 51, 807 (1995)
B. Schraiman, D. Bensimon, Phys. Rev. A 30, R2840 (1986)
T.A. Witten, L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)
L.P. Kadanoff, J. Stat. Phys. 39, 267 (1985)
M.B. Hastings, L.S. Levitov, Physica D 116, 244 (1998)
M.G. Stepanov, L.S. Levitov, Phys. Rev. E 63, 061102 (2001)
F. Barra, B. Davidovitch, I. Procaccia, Phys. Rev. E 65, 046144 (2002)
T.A. Witten, P. Meakin, Phys. Rev. B 28, 5632 (1983)
R. Jullien, M. Kolb, R. Botet, J. Phys. 45, 395 (1984)
T.R. NíMhíocháin, J.M.D. Coey, Phys. Rev. E 69, 061404 (2004)
S.C. Ferreira, S.G. Alves, A. Faissal Brito, J.G. Moreira, Phys. Rev. E 71, 051402 (2005)
P. Ramanlal, L.M. Sander, Phys. Rev. Lett. 54, 1828 (1985)
P. Meakin, R.C. Ball, P. Ramanlal, L.M. Sander, Phys. Rev. A 35, 5233 (1987)
L.D. Landau, E.M. Lifshitz, Theory of Elasticity, 3rd edn. (Butterworth-Heinemann Ltd, 1984)
T. Aukrust, M.A. Novotny, D.A. Browne, K. Kaski, Phys. Rev. A 39, 2587 (1989)
A.Yu. Menshutin, L.N. Shchur, V.M. Vinokur, Phys. Rev. E 75, 010401R (2007)
A. Lando, N. Kébaïli, P. Cahuzac, A. Masson, C. Bréchignac, Phys. Rev. Lett. 93, 133402 (2006)
A.Yu. Menshutin, L.N. Shchur, Phys. Rev. E 73, 011407 (2006)
W.G. Hanan, D.M. Heffernan, Chaos Solitons Fractals 12, 193 (2001)
P. Garik, Phys Rev. A 32, 1276 (1985)
M. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (W.H. Freeman, New York, 1991), pp. 41–42
A.Yu. Menshutin, L.N. Shchur, Comput. Phys. Commun. 182, 1819 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carlier, F., Brion, E. & Akulin, V.M. Fractal growth in the presence of a surface force field. Eur. Phys. J. B 85, 152 (2012). https://doi.org/10.1140/epjb/e2012-20756-4
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-20756-4