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Fractal Models and the Structure of Materials

Published online by Cambridge University Press:  29 November 2013

Dale W. Schaefer
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Extract

Science often advances through the introdction of new ideas which simplify the understanding of complex problems. Materials science is no exception to this rule. Concepts such as nucleation in crystal growth and spinodal decomposition, for example, have played essential roles in the modern understanding of the structure of materials. More recently, fractal geometry has emerged as an essential idea for understanding the kinetic growth of disordered materials. This review will introduce the concept of fractal geometry and demonstrate its application to the understanding of the structure of materials.

Fractal geometry is a natural concept used to describe random or disordered objects ranging from branched polymers to the earth's surface. Disordered materials seldom display translational or rotational symmetry so conventional crystallographic classification is of no value. These materials, however, often display “dilation symmetry,” which means they look geometrically self-similar under transformation of scale such as changing the magnification of a microscope. Surprisingly, most kinetic growth processes produce objects with self-similar fractal properties. It is now becoming clear that the origin of dilation symmetry is found in disorderly kinetic growth processes present in the formation of these materials.

Type
Technical Feature
Information
MRS Bulletin , Volume 13 , Issue 2 , February 1988 , pp. 22 - 27
Copyright
Copyright © Materials Research Society 1988

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References

1.Mandelbrot, B.B., The Fractal Geometry of Nature (Freeman, San Francisco, 1982).Google Scholar
2.Meakin, P., in On Growth and Form, edited by Stanley, E. and Ostrowsky, N. (Martinus-Nijhoff, Dordrocht, Netherlands, 1986) p. 111.CrossRefGoogle Scholar
3.Hurd, A.J. and Schaefer, D.W., Phys. Rev. Lett. 54 (1985) p. 1043.CrossRefGoogle Scholar
4.Martin, J.E. and Hurd, A.J., J. Appl. Cryst. 20 (1987) p. 61.CrossRefGoogle Scholar
5.Schaefer, D.W., Martin, J.E., Hurd, A.J., and Keefer, K.D., in Physics of Finely Divided Matter, edited by Boccara, M. and Daoud, M. (Springer-Verlag, New York, 1985) p. 31.CrossRefGoogle Scholar
6.Schaefer, D.W., in Better Ceramics Through Chemistry II, edited by Brinker, C.J., Clark, D.E., and Ulrich, D.R. (Mat. Res. Soc. Symp. Proc. 79, Pittsburgh, PA, 1987) p. 47.Google Scholar
7.Schaefer, D.W. and Keefer, K.D., in Fractals in Physics, edited by Pietronero, L. and Tosatti, E. (North-Holland, New York, 1986) p. 39.CrossRefGoogle Scholar
8.Witten, T.A. and Sander, L.M., Phys. Rev. Lett. 47 (1981) p. 1400.CrossRefGoogle Scholar
9.Forrest, S.R. and Witten, T.A., J. Phys. A 12 (1979) p. L109.Google Scholar
10.Hurd, A.J., in Physics of Complex and Supermolecular Fluids, edited by Safran, S.A. and Clark, N.A. (Wiley Interscience, New York, 1987) p. 493.Google Scholar
11.Martin, J.E. and Schaefer, D.W. (to be published).Google Scholar
12.Hurd, A.J. and Flower, W.F., J. Colloid Int. Sci. (in press), also Sandia Laboratories Report SAND87-2372 (available from National Technical Information Service, U.S. Dept. of Commerce, 5285 Port Royal Road, Springfield, VA 22161).Google Scholar
13.Hurd, A.J., Schaefer, D.W., and Martin, J.E., Phys. Rev. A 35 (1987) p. 2361.CrossRefGoogle Scholar
14.Schaefer, D.W., Martin, J.E., Wiltzius, P., and Cannell, D., Phys. Rev. Lett. 52 (1984) p. 2371.CrossRefGoogle Scholar
15.Schaefer, D.W. and Keefer, K.D., Scattering, Deformation and Fracture in Polymers, edited by Wignall, G.D., Crist, B., Russell, T.P., and Thomas, E.L. (Mat. Res. Symp. Proc. 73, Pittsburgh, PA, (1986) p. 277.Google Scholar
16.Schaefer, D.W., Shelleman, R.A., Keefer, K.D., and Martin, J.E., Physica 140A (1986) p. 105.CrossRefGoogle Scholar
17.Keefer, K.D. and Schaefer, D.W., Phys. Rev. Lett. 56 (1986) p. 2376.CrossRefGoogle Scholar
18.Brinker, C.S., Keefer, K.D., Schaefer, D.W., and Ashley, C.S., J. Non-Cryst. Solids 48 (1982) p. 47.CrossRefGoogle Scholar