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The Diffusive Instability in Growth: DLA, Dendritic Growth, and Solidification

Published online by Cambridge University Press:  03 September 2012

Leonard M. Sander
Leonard M. Sander*
Affiliation:
H.M. Randall Laboratory of Physics, The University of Michigan, Ann Arbor, MI 48109-1120
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Abstract

We give an overview of the influence of the diffusive instability in forming various growth morphologies. We review dendritic growth of crystals, and discuss the DLA model as an approach to the disordered, fractal case. We consider various systems which are reasonably well described by DLA including island shapes in surface growth.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 3
Copyright
Copyright © Materials Research Society 1995

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References

1. Radnoczi, G., Vicsek, T., Sander, L.M. and Grier, D., Phys. Rev. A 35 Rapid Communications,4012 (1987)Google Scholar
2. Grier, D., Ben-Jacob, E., Clarke, R. and Sander, L.M., Phys. Rev. Lett. 56, 1264 (1986).Google Scholar
3. Solids Far From Equilibrium: Growth, Morphology and Defects, Godereche, C., ed. (Cambridge University Press, 1991), articles by Caroli, Caroli, and Roulet, Pomeau and Ben-Amar, and Sander.Google Scholar
4. Kessler, D., Koplik, J., and Levine, H., Adv. in Phys., 37, 255 (1988)Google Scholar
5. Langer, J.S., Rev. Mod. Phys. 52, 1 (1980).Google Scholar
6. Sander, L.M., Nature 322, 789 (1986).Google Scholar
7. Adams, F., Freese, K., and Langer, J., Phys. Rev. D 47, 4303–8 (1993)Google Scholar
8. Ben-Jacob, E., Shochet, O., Tenenbaum, A., Cohen, I, Czirok, A., and Vicsek, T., Fractals 2, 15 (1994).Google Scholar
9. Mullins, W.W. and Sekerka, R., J. Appl. Phys. 28, 333 (1957); J. Appl. Phys. 33, 323 (1963)Google Scholar
10. See Glicksman, M. and Marsh, S. in Handbook of Crystal Growth, Hurle, D., ed. (Elsevier, 1993) 1, p 1077.Google Scholar
11. Ivantsov, G., Dokl. Acad. Nauk. SSSR 58, 56 (1947).Google Scholar
12. Glicksman, M., Koss, M., Winsa, E. A., Phys. Rev. Lett. 73, 573 (1994)Google Scholar
13. Witten, T. A., and Sander, L. M., Phys. Rev. Lett. 47, 1400 (1981); Phys. Rev. B 27, 5686 (1983).Google Scholar
14. Meakin, P., in Phase Transitions and Critical Phenomena, 12, Domb, C. and Lebowitz, J., eds, (Academic, 1988).Google Scholar
15. Mandelbrot, B., Physica A 191, 95 (1992)Google Scholar
16. Meakin, P. and Vicsek, T., Phys. Rev. A 32, 685 (1985)Google Scholar
17. Hegger, R. and Grassberger, P. Phys. Rev. Lett. 73, 1672 (1994)Google Scholar
18. Halsey, T., Phys. Rev. Lett. 72, 1228 (1994)Google Scholar
19. Pietronero, L., Erzan, A., and Evertsz, C., Phys. Rev. Lett. 61, 861 (1988)Google Scholar
20. Barker, R., and Ball, R.C., Phys. Rev. A 42, 6289 (1990)Google Scholar
21. Brady, R., R., and Ball, R. C., Nature 309, 225 (1984)Google Scholar
22. Matsushita, M., Sano, M., M., , Hayakawa, Y., Honjo, H., H., , and Sawada, Y., Phys. Rev.Lett. 52, 286 (1984).Google Scholar
23. Grier, D., Ben-Jacob, E., Clarke, R. and Sander, L.M. Phys. Rev. Lett. 56, 1264 (1986).Google Scholar
24. Sawada, Y., Dougherty, A., Gollub, J., Phys. Rev. Lett. 56, 1260 (1986)Google Scholar
25. Kaufman, J., Baker, C., Nazzal, A., A., , Flickner, M., Melroy, O., and Kapitulnik, A., Phys. Rev. Lett. 56, 1932 (1986)Google Scholar
26. Kuhn, A., Argoul, F., Phys. Rev. E 49, 4298 (1994); A. Kuhn, A and F. Argoul, Fractals; 1, 451-9; (1993)Google Scholar
27. Fleury, V., Chazalviel, J.-N., and Rosso, M., Phys. Rev.E 48, 1279 (1993); V. Fleury, J.-N. Chazalviel, M. Rosso, and B.Sapoval, J. Electroan. Chem. and Interfac. Electrochem. 290, 249 (1990)Google Scholar
28. Hwang, R.Q., Schroder, J., Gunther, C., and Behm, R. J., Phys. Rev. Lett. 67, 3279 (1991)Google Scholar
29. Bales, G. S. and Zangwill, A., Phys. Rev. B 41, 5500 (1991)Google Scholar
30. Ehrlich, G. and Hudda, F.G., J. Chem. Phys., 44, 1039 (1966)Google Scholar
31. Schwoebel, R. L. R.L., and Shipsey, E. J. J. Appl. Phys., 37, 3682 (1966)Google Scholar
32. Amar, J.G., Family, F. and Lam, P-M in Mechanisms of Thin Film Evolution, MRS Proceedings 317, 167 (1994)Google Scholar
33. Bartelt, M.C. and Evans, J. W., Phys. Rev. B 46, 12675 (1992)Google Scholar
34. Tang, L-H, J. de Physique I3, 935 (1993)Google Scholar
35. Ratsch, C., Zangwill, A., Smilauer, P., and Vvedensky, D.D., Phys. Rev. Lett. 72, 3194 (1994)Google Scholar
36. Johnson, M.D., Orme, C., Hunt, A. W., Graff, D., Sudijono, J., Sander, L. M., and Orr, B. G., Phys. Rev. Lett. 72, 116 (1994)Google Scholar
37. Hunt, A. W., Orme, C., Williams, D. R. M., Orr, B. G., and Sander, L. M. to appear in Scale invariance, interfaces and non-equilbrium dynamics, Proceedings of NATO ASI, Cambridge UK June 20-30, 1994 Google Scholar
38. Hunt, A.W., Orme, C., Williams, D.R.M., Orr, B.G. and Sander, L.M.. Europhys. Lett. 27, 611 (1994)Google Scholar
39. Ernst, H-J, Fabre, F., Folkerts, R., R., , and Lapujoulade, J., Phys. Rev. Lett., 72, 112, (1994)Google Scholar