A Higher Dimensional Description of the Structure of β-Mn

doi:10.3390/sym4030537

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Symmetry 2012, 4(3), 537-544; doi:10.3390/sym4030537

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A Higher Dimensional Description of the Structure of β-Mn

Sven Lidin^1,* and Daniel Fredrickson²

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; in revised form: 22 August 2012 / Accepted: 22 August 2012 / Published: 27 August 2012

(This article belongs to the Special Issue Crystal Symmetry and Structure)

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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

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MDPI and ACS Style

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

AMA Style

Lidin S, Fredrickson D. A Higher Dimensional Description of the Structure of β-Mn. Symmetry. 2012; 4(3):537-544.

Chicago/Turabian Style

Lidin, Sven; Fredrickson, Daniel. 2012. "A Higher Dimensional Description of the Structure of β-Mn." Symmetry 4, no. 3: 537-544.

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