A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

Sasisekharan, V (1986) A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds. In: Pramana, 26 (3). L283-L293.

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Abstract

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.

Item Type:	Journal Article
Publication:	Pramana
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian Academy of Sciences.
Keywords:	Quasi;aperiodic 2D lattices;seven;fold axes;five-fold axes.
Department/Centre:	Division of Biological Sciences > Molecular Biophysics Unit
Date Deposited:	27 Jan 2010 07:28
Last Modified:	19 Sep 2010 05:42
URI:	http://eprints.iisc.ac.in/id/eprint/22539

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