A Higher Dimensional Description of the Structure of β-Mn
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 spac...
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| Language: | English |
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MDPI AG
2012-08-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/4/3/537 |
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doaj-6c02409af88b47158db463f19504cee72020-11-24T21:53:24ZengMDPI AGSymmetry2073-89942012-08-014353754410.3390/sym4030537A Higher Dimensional Description of the Structure of β-MnDaniel FredricksonSven LidinThe 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.http://www.mdpi.com/2073-8994/4/3/537octagonal quasicrystalapproximantsix-dimensional space |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Daniel Fredrickson Sven Lidin |
| spellingShingle |
Daniel Fredrickson Sven Lidin A Higher Dimensional Description of the Structure of β-Mn Symmetry octagonal quasicrystal approximant six-dimensional space |
| author_facet |
Daniel Fredrickson Sven Lidin |
| author_sort |
Daniel Fredrickson |
| title |
A Higher Dimensional Description of the Structure of β-Mn |
| title_short |
A Higher Dimensional Description of the Structure of β-Mn |
| title_full |
A Higher Dimensional Description of the Structure of β-Mn |
| title_fullStr |
A Higher Dimensional Description of the Structure of β-Mn |
| title_full_unstemmed |
A Higher Dimensional Description of the Structure of β-Mn |
| title_sort |
higher dimensional description of the structure of β-mn |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2012-08-01 |
| description |
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. |
| topic |
octagonal quasicrystal approximant six-dimensional space |
| url |
http://www.mdpi.com/2073-8994/4/3/537 |
| work_keys_str_mv |
AT danielfredrickson ahigherdimensionaldescriptionofthestructureofbmn AT svenlidin ahigherdimensionaldescriptionofthestructureofbmn AT danielfredrickson higherdimensionaldescriptionofthestructureofbmn AT svenlidin higherdimensionaldescriptionofthestructureofbmn |
| _version_ |
1725872561257971712 |