A Higher Dimensional Description of the Structure of β-Mn

Symmetry

Sven Lidin¹ 

[1] CAS, Lund University, P.O. Box 124, Lund 22100, Sweden

关键词: octagonal quasicrystal;    approximant;    six-dimensional space;   

DOI  :  10.3390/sym4030537

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.