A higher dimensional description of the structure of β-Mn
(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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https://lup.lub.lu.se/record/0ec74e75-d8d8-45d3-95ba-ac24dc5715bf
- author
- Lidin, Sven LU and Fredrickson, Daniel
- organization
- publishing date
- 2012-09-01
- 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}}, }