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]   |  

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 (CC BY 3.0).
SciFeed

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
RIS
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

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