Next Article in Journal
Barrel Pseudotilings
Next Article in Special Issue
On the Notions of Symmetry and Aperiodicity for Delone Sets
Previous Article in Journal
Supersymmetric Extensions of Non-Relativistic Scaling Algebras
Previous Article in Special Issue
Symmetry-Adapted Fourier Series for the Wallpaper Groups
Symmetry 2012, 4(3), 537-544; doi:10.3390/sym4030537
Article

A Higher Dimensional Description of the Structure of β-Mn

1,*  and 2
1 CAS, Lund University, P.O. Box 124, Lund 22100, Sweden 2 Department of Chemistry, University of Wisconsin, 1101 University Avenue, Madison, WI 53706, USA
* Author to whom correspondence should be addressed.
Received: 3 July 2012 / Revised: 22 August 2012 / Accepted: 22 August 2012 / Published: 27 August 2012
(This article belongs to the Special Issue Crystal Symmetry and Structure)
View Full-Text   |   Download PDF [306 KB, uploaded 27 August 2012]   |   Browse Figure

Abstract

The structure of β-Mn crystallizes in space group P4132. The pseudo 8-fold nature of the 41 axes makes it constitute an approximant to the octagonal quasicrystals. In this paper we analyze why a five-dimensional super space group containing mutually perpendicular 8-fold axes cannot generate P4132 on projection to 3-d space and how this may instead be accomplished from a six-dimensional model. A procedure for generating the actual structure of β-Mn lifted to six-dimensional space is given.
Keywords: octagonal quasicrystal; approximant; six-dimensional space octagonal quasicrystal; approximant; six-dimensional space
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Lidin, S.; Fredrickson, D. A Higher Dimensional Description of the Structure of β-Mn. Symmetry 2012, 4, 537-544.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert