Indexing schemes for quasilattices

Abstract

Various schemes have been proposed and employed, which extend the method of indexing lattice vectors and reciprocal-lattice vectors, so that it can be used in the context of quasicrystals. The concept of the generalized inverse of a matrix provides an elegant unified approach to the vectors and reciprocal vectors of quasilattices, and their associated zone laws and inflation rules. We present a survey, from the viewpoint provided by the concept of the Moore–Penrose inverse, of the indexing problem for quasicrystals.

Acknowledgements

I thank Professor S. Ranganathan, for his interest in my work and for making the facilities of the Department of Metallurgy, Indian Institute of Science, available to me. Financial support from the Department of Science and Technology, New Delhi, the Office of Naval Research and the Defence, Research and Development Organisation, Ministry of Defence, Government of India is gratefully acknowledged.