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A higher dimensional description of the structure of β-Mn

Lidin, Sven LU and Fredrickson, Daniel (2012) In Symmetry 4(3). p.537-544
Abstract

The structure of β-Mn crystallizes in space group P4 132. The pseudo 8-fold nature of the 4 1 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 P4 132 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.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Approximant, Octagonal quasicrystal, Six-dimensional space
in
Symmetry
volume
4
issue
3
pages
8 pages
publisher
MDPI AG
external identifiers
  • scopus:84867136560
DOI
10.3390/sym4030537
language
English
LU publication?
yes
id
0ec74e75-d8d8-45d3-95ba-ac24dc5715bf
date added to LUP
2019-04-08 14:55:35
date last changed
2022-01-31 18:46:43
@article{0ec74e75-d8d8-45d3-95ba-ac24dc5715bf,
  abstract     = {{<p>The structure of β-Mn crystallizes in space group P4 <sub>1</sub>32. The pseudo 8-fold nature of the 4 <sub>1</sub> 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 P4 <sub>1</sub>32 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.</p>}},
  author       = {{Lidin, Sven and Fredrickson, Daniel}},
  keywords     = {{Approximant; Octagonal quasicrystal; Six-dimensional space}},
  language     = {{eng}},
  month        = {{09}},
  number       = {{3}},
  pages        = {{537--544}},
  publisher    = {{MDPI AG}},
  series       = {{Symmetry}},
  title        = {{A higher dimensional description of the structure of β-Mn}},
  url          = {{http://dx.doi.org/10.3390/sym4030537}},
  doi          = {{10.3390/sym4030537}},
  volume       = {{4}},
  year         = {{2012}},
}