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Pattern Formation in Materials Science

Published online by Cambridge University Press:  29 November 2013

J.P. Gollub  and
L.M. Sander
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The growth of materials at interfaces frequently leads to patterns with length scales that can be much larger than atomic sizes. Patterns resulting from morphological instabilities occur during crystal growth and are responsible for the intricate shapes of snowflakes, dendritic crystals, and the like. They also occur during the electrochemical deposition of metals on surfaces, and during the growth of thin films by vapor deposition. Our purpose is to point out some particularly interesting connections that have come to be appreciated during the past five years between different types of pattern-forming phenomena, and to summarize some recent theoretical approaches to understanding them.

The phenomenon of dendritic crystal growth, though studied for many years, is still a great challenge. As an example, we show the development of a needle crystal of ammonium bromide (NH4Br) from supersaturated aqueous solution in Figure 1. The contours are cross sections of the interface at 20-second intervals, obtained by digital image analysis. One can see that an approximately parabolic tip translates at constant speed, and that the needle crystal is apparently unstable to the development of a train of sidebranches that propagate outward from the main stem but do not move forward with the tip.

Type
Technical Feature
Information
MRS Bulletin , Volume 12 , Issue 6 , September 1987 , pp. 98 - 100
Copyright
Copyright © Materials Research Society 1987

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References

1.Kessler, D.A., Koplik, J., and Levine, H., Phys. Rev. A 33 (1986) p. 2621 and 2634; and Advances in Physics, to be published.CrossRefGoogle Scholar
2.Langer, J.S., Les Houches Lectures (1986), to be published.Google Scholar
3.Meiron, D., Phys. Rev. A 33 (1986) p. 2704.CrossRefGoogle Scholar
4.Saito, Y., Goldbeck-Wood, G., and Muller-Krumbhaar, H., Phys. Rev. Lett. 58, (1987) p. 1541.CrossRefGoogle Scholar
5.Hobbs, P.V., Ice Physics (Clarendon Press, Oxford, 1974), p. 524.Google Scholar
6.Huang, S-C. and Glicksman, M.E., Acta Met. 29 (1981) p. 701 and 717.CrossRefGoogle Scholar
7.Pieters, R. and Langer, J.S., Phys. Rev. Lett. 56, (1986) p. 1948; D.A. Kessler and H. Levine, Phys. Rev. Lett. 57 (1986) p. 3069; B. Caroli, C. Caroli, and B. Roulet, private communication.CrossRefGoogle Scholar
8.Dougherty, A., Kaplan, P.D., and Gollub, J.P., Phys. Rev. Lett. 58 (1987) p. 1652.CrossRefGoogle Scholar
9.Bensimon, D., Kadanoff, L.P., Liang, S., Shraiman, B.I., and Tang, C., Revs. Mod. Phys. 58 (1986) p. 977; G.M. Homsy, Ann. Rev. Fluid Mech. 19 (1987) p. 271.CrossRefGoogle Scholar
10.Ben-Jacob, E., Godby, R., Goldenfeld, N.D., Koplik, J., Levine, H., Mueller, T., and Sander, L.M., Phys. Rev. Lett. 55 (1985) p. 1315.CrossRefGoogle Scholar
11.Couder, Y., Gerard, N., and Rabaud, M., Phys. Rev. A 34, (1986) p. 5175.CrossRefGoogle Scholar
12.Sawada, Y., Dougherty, A., and Gollub, J.P., Phys. Rev. Lett. 56 (1986) p. 1260.CrossRefGoogle Scholar
13.Grier, D., Ben-Jacob, E., Clarke, R., and Sander, L.M., Phys. Rev. Lett. 56 (1986) p. 1264.CrossRefGoogle Scholar
14.Leamy, H.J., Gilmer, G.H., and Dirks, A.G., in Current Topics in Materials Science, edited by Katdis, E. (North-Holland, 1980).Google Scholar
15.Vold, M.J., J. Colloid Interface Sci. 18, (1963) p. 684.CrossRefGoogle Scholar
16.Kardar, M., Parisi, G., and Zhang, Y-C., Phys. Rev. Lett. 56 (1986) p. 889.CrossRefGoogle Scholar
17.Meakin, P., Ramanlal, P., Sander, L.M., and Ball, R.C., Phys. Rev. A 34 (1986) p. 5091.CrossRefGoogle Scholar
18.Ramanlal, P. and Sander, L.M., Phys. Rev. Lett. 54 (1985) p. 1828.CrossRefGoogle Scholar
19.Mandelbrot, B., The Fractal Geometry of Nature (Freeman, San Francisco, 1982).Google Scholar
20.Witten, T. and Sander, L.M., Phys. Rev. Lett. 47 (1981) p. 1400; Phys. Rev. B 27 (1983) p. 1119.CrossRefGoogle Scholar
21.Radnoczi, G., Viscek, T., Sander, L.M., and Grier, D., Phys. Rev. A 35 (1987) p. 4012.CrossRefGoogle Scholar
22.Niemeyer, L., Pietronero, L., and Wiesmann, H., Phys. Rev. Lett. 52 (1984) p. 1033.CrossRefGoogle Scholar
23.Honjo, H., Ohta, S., and Matsushita, M., J. Phys. Soc. Japan 55 (1986) p. 2487.CrossRefGoogle Scholar