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Indexing of icosahedral quasiperiodic crystals

Published online by Cambridge University Press:  03 March 2011

John W. Cahn ,
Dan Shechtman  and
Denis Gratias
John W. Cahn
Affiliation:
Institute for Materials Science and Engineering, National Bureau of Standards, Gaithersburg, Maryland, 20899
Dan Shechtman
Affiliation:
Department of Materials Engineering, Israel Institute of Technology, Technion, 32000 Haifa, Israel
Denis Gratias
Affiliation:
C.E.C.M./C.N.R.S., 15 rue Georges Urbain, 94400 Vitry-sur-Seine, France
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Abstract

Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

Type
Articles
Information
Journal of Materials Research , Volume 1 , Issue 1 , February 1986 , pp. 13 - 26
Copyright
Copyright © Materials Research Society 1986

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References

REFERENCES

1Shechtman, D., Blech, I., Gratias, D., and Cahn, J. W., Phys. Rev. Lett. 53, 1951 (1984).CrossRefGoogle Scholar
2Shechtman, D. and Blech, I., Met. Trans. 16A, 1005 (1985).CrossRefGoogle Scholar
3Bendersky, L., Phys. Rev. Lett. 55, 1461 (1985).CrossRefGoogle Scholar
4Ishimasa, T., Nissen, H. U., and Fukano, Y., Phys. Rev. Lett. 55, 511 (1985).CrossRefGoogle Scholar
5Bohr, H. A., Almost Periodic Functions (Chelsea, New York, 1947).Google Scholar
6Besicovitch, A. S., Almost Periodic Functions (Cambridge U. P., London, 1932).Google Scholar
7Kramer, P. and Neri, R., Acta Cryst. A 40, 580 (1984).CrossRefGoogle Scholar
8Duneau, M. and Katz, A., Phys. Rev. Lett. 54, 2688 (1985).CrossRefGoogle Scholar
9Elser, V., Phys. Rev. Lett. 54, 1730 (1985); Acta Cryst. A (to be published).CrossRefGoogle Scholar
10Kalugin, P. A., Yu Kitayev, A., and Levitov, L. S., J. Phys. Lett. 46, L601 (1985).CrossRefGoogle Scholar
11Bancel, P. A., Heiney, P. A., Stephens, P. W., Goldman, A. I., and Horn, P. M., Phys. Rev. Lett. 54, 2422 (1985).CrossRefGoogle Scholar
12Elser, V., “Introduction to Quasicrystals,” Acta Cryst. A (to be published).Google Scholar
13Nelson, D. B. and Sachdev, S., Phys. Rev. B 32, 689, 1480 (1985).Google Scholar
14Levine, D. and Steinhardt, P., Phys. Rev. Lett. 53, 2477 (1984).CrossRefGoogle Scholar
15Schaefer, R. J., Bendersky, L. A., Shechtman, D., Boettinger, W. J., and Biancaniello, F. S., submitted to Met. Trans.Google Scholar
16Kuriyama, M., Long, G. G., and Bendersky, L., Phys. Rev. Lett. 55, 849 (1985).CrossRefGoogle Scholar
17Pauling, L., Nature 317, 512 (1985).CrossRefGoogle Scholar
18Cahn, J. W., Gralias, D., and Shechtman, D., Nature 319, 102 (1986).CrossRefGoogle Scholar