# Stacking Sequences and Symmetry Properties of Trigonal Vacancy-ordered Phases ($\tau$ phases)

Lord, Eric A and Ranganathan, S and Subramaniam, Anandh (2002) Stacking Sequences and Symmetry Properties of Trigonal Vacancy-ordered Phases ($\tau$ phases). In: Philosophical Magazine A, 82 (2). pp. 255-268.

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## Abstract

The vacancy-ordered phases known as tau phases are described and the literature dealing with the observed stacking sequences is reviewed. It is shown that the stacking sequences along the threefold axis can be derived from a projection method involving projection on to an axis of type [rrq]. The structure has alternating filled and empty lamellae parallel to planes of type (rrq). The particular cases in which r and q are consecutive numbers of the Fibonacci sequence can be regarded as rational approximants to a one-dimensional quasiperiodic structure. Some mathematical properties of the sequences, and their relationship with the three-dimensional structures, are presented.

Item Type: Journal Article Copyright of this article belongs to Taylor and Francis. Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy) Kujur Pawan 02 Jun 2006 27 Aug 2008 12:08 http://eprints.iisc.ac.in/id/eprint/7413