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On the indexing and reciprocal space of icosahedral quasicrystal

Published online by Cambridge University Press:  31 January 2011

Alok Singh  and
S. Ranganathan
Alok Singh
Affiliation:
Centre for Advanced Study, Department of Metallurgy, Indian Institute of Science, Bangalore, 560 012, India
S. Ranganathan
Affiliation:
Centre for Advanced Study, Department of Metallurgy, Indian Institute of Science, Bangalore, 560 012, India
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Abstract

Important features of the icosahedral reciprocal space have been brought out. All reciprocal vectors up to sixth generation (by addition of icosahedral vectors) have been considered. Some more relationships for indexing the icosahedral phase are derived, and it is shown that the zone law using Cahn indices is also analogous to that valid for crystals. All important vectors, i.e., up to fourth generation and sixth generation, have been identified. Poles of all these vectors have been determined and shown to be one of the zone axes formed by these vectors. The types of indices that the planes and axes will have in three-dimensional and six-dimensional coordinates is discussed.

Type
Articles
Information
Journal of Materials Research , Volume 14 , Issue 11 , November 1999 , pp. 4182 - 4187
Copyright
Copyright © Materials Research Society 1999

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References

REFERENCES

1.Shechtman, D., Blech, I., Gratias, D., and Cahn, J.W., Phys. Rev. Lett. 53, 1951 (1984).CrossRefGoogle Scholar
2.Elser, V., Phys. Rev. B 32, 4892 (1985).CrossRefGoogle Scholar
3.Bancel, P.A., Heiney, P.A., Stephens, P.W., Goldman, A.I., and Horn, P.M., Phys. Rev. Lett. 54, 2422 (1985).CrossRefGoogle Scholar
4.Cahn, J.W., Shechtman, D., and Gratias, D., J. Mater. Res. 1, 13 (1986).CrossRefGoogle Scholar
5.Chattopadhyay, K., Lele, S., Prasad, R., Ranganathan, S., Subbanna, G.N., and Thangaraj, N., Scripta Metall. 19, 1331 (1985).CrossRefGoogle Scholar
6.Singh, A. and Ranganathan, S., Scripta Metall. Mater. 25, 409 (1991).CrossRefGoogle Scholar
7.Dai, M. and Wang, R., Solid State Comm. 73, 77 (1990).CrossRefGoogle Scholar
8.Weber, S., J. Appl. Cryst. 30, 85 (1997).Google Scholar
9.Nelson, D.R. and Sachdev, S., Phys. Rev. B: Solid State Condens. Mater. 32, 689 (1985).CrossRefGoogle Scholar
10.Field, R.D. (unpublished).Google Scholar