Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-06T15:16:33.020Z Has data issue: false hasContentIssue false

Fractal Coefficients of An Icosahedral Structure of Quasi-Crystals and Amorphous Alloys

Published online by Cambridge University Press:  25 February 2011

J.C.S. Levy
Affiliation:
Laboratoire de Magnétisme des Surfaces Université Paris 7 - 75251 Paris Cédex 05 -, France
D. Mercier
Affiliation:
Laboratoire de Magnétisme des Surfaces Université Paris 7 - 75251 Paris Cédex 05 -, France
Get access

Abstract

Different extended icosahedral structures are obtained from energy minimization and local symmetry Yh. The quasi fractal character of one of these is demonstrated from the quasi algorithm of definition, the gamma density of holes and the measured Hausdorff number ∂. The spectral dimension ∂ is measured and dimensions corresponding to higher derivatives are defined.

Type
Research Article
Copyright
Copyright © Materials Research Society 1986

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.Shechtman, D.S., Blech, I., Gratias, D. and Cahn, J.W., Phys. Rev. Lett. 53, 1951 (1984)Google Scholar
2.Review by Nelson, D.R. and Halperin, B.I., Science, 229, 223 (1985)Google Scholar
3.Levine, D. and Steinhardt, P.J., Phys. Rev. Lett. 53, 2477 (1984)Google Scholar
4.Franck, F.C. and Kasper, J.S., Acta Crystallogr. 11, 184 (1958)Google Scholar
5.Levy, J.C.S., Surf. Sci. 104, 1 (1981)Google Scholar
6.Mercier, D. and Levy, J.C.S., Phys. Rev. B27, 1292 (1983)Google Scholar
7.Levy, J.C.S., J. Phys. 46, 215 (1985)Google Scholar
8.Levine, D., Lubensky, T.C., Ostlund, S., Ramaswamy, S. and Steinhardt, P.J., Phys. Rev. Lett. 54, 1520 (1985)Google Scholar
9.Bak, P., Phys. Rev. Lett. 54, 1517 (1985)Google Scholar
10.Jaric, M.V., Michel, L. and Sharp, R.T., J. Phys. 45, 1 (1984)Google Scholar
11.Benderski, L., Phys. Rev. Lett. 55, 1461 (1985)Google Scholar
12.Turnbull, D. and Cohen, M.H., J. Chem. Phys. 34, 120 (1961)Google Scholar
13.Landau, L. and Lifschitz, E., Mécanique Quantique, Ed. MIR (1967)Google Scholar
14.Feller, W., An Introduction to Probability Theory and its Applications, vol. II, p. 59, 2nd Ed., Edited by Whiey, J. (1971)Google Scholar
15.Mandelbrot, B., The fractal geometry of nature, San Francisco Freeman editor (1982)Google Scholar
16.Levy, J.C.S. and Mercier, D., J. Appl. Phys. 53, 7709 (1982)Google Scholar
17.Finney, J.L. and Wallace, J., J. Non crystalline Solids, 28, 293 (1978)Google Scholar
18.Alexander, S. and Orbach, R., J. Phys. (Paris) Lett. 43, L625 (1982)Google Scholar
19.Handbook of Mathematical Functions, p. 885, edited by Abramoitz, M. and Stegun, I.A., Washington (1964)Google Scholar