# Coincidence-site lattices as rational approximants to irrational twins

Ranganathan, S and Srivastava, AK and Lord, EA (2006) Coincidence-site lattices as rational approximants to irrational twins. In: Journal of Materials Science, 41 (23). pp. 7696-7703.

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## Abstract

It is well known that sequences of crystals with Mackay icosahedral motif and increasing lattice parameters exist converging to the icosahedral quasicrystal in the limit. They are known as rational approximants. It has also been demonstrated that it is possible to create icosahedral symmetry by irrational twins involving five variants by $72^o$ rotations around an irrational axis [\tau 1 0] or an irrational angle of $44.48^o$ around a rotation axis [1 1 1]. These twinned crystals do not share a coincidence site lattice. In this paper, it is demonstrated that the above twinning relationship arises in the limit of a sequence of coincidence site lattices starting with the cubic twins with $\sum=3$ and extending through \sum=7, 19, 49, 129, 337, …,\infty created by rotation around [1 1 1] axis. It is also noted that the boundaries of higher CSL values $(\sum > 7)$ are composed of a combination of structural units from $\sum=3$ and $\sum=7$ boundaries.

Item Type: Journal Article Copyright of this article belongs to Springer. Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy) 28 Feb 2007 19 Sep 2010 04:34 http://eprints.iisc.ernet.in/id/eprint/9523