十二边形准晶的高维投影结构

THE PROJECTION STRUCTURE OF DODECAGONAL QUASICRYSTAL PHASE

本文研究 V_3Ni_2、V_(15)Ni_(10)Si 及 NiCr 合金十二边形相在高维空间中的对称性。十二边形相是四纬空间在二维空间的投影相;四维点隈满足1mm 的点群对称;十二边形相的电子衍射图是这个四维空间点阵在二维空间的投影,因而,衍射斑可用四指数标定;十二边形相的稳定条件是其自由能展式的三次项系数 B<0。

The symmetry of the dodecagonal phase which is a kind of 2 dimmensional quasicrystal in V_3 Ni_2、V_(15)Ni_(10)Si and NiCr alloys is studied.The periodicity of dodecagonal phase is restored in 4-dimensional super space.The point symme- try of the 4-dimensional lattice is 12 mm.Projecting the lattice to 2 dimensi- onal space give rise to the diffraction pattern of this phase which is of self- similar.The self simmilar transformation matrices are given and the diffrac- tion spots are indexed with four indices.In the end,the stability of the dode- cagonal quasicrystal phase is discussed.