Cite this article as:

MIN Le-quan, Nonclassical Periodic Models Fourier Transforms and Group, J. Univ. Sci. Technol. Beijing , 1(1994), No. 1-2, pp.104-112.
MIN Le-quan, Nonclassical Periodic Models Fourier Transforms and Group, J. Univ. Sci. Technol. Beijing , 1(1994), No. 1-2, pp.104-112.
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非经典周期模型Fourier变换和群

摘要: 本文提出3类具有局部8、10和12次对称的非经典平面周期格子,它们可被解释为相应的多面体所组成的空间模型在平面的投影,空间模型的Fourier变换图显示出近似的8、10和12次旋转对称,但这些对称很难区别于相应的具有严格数学意义的旋转对称,并定性地相似于对应准晶的电子衍射图中显示的8、10和12次对称.利用传统的平移操作和旋转操作"合成"的新规则可描述非经典周期格,而这些合成操作本身构成了群,从而建立了非经典平晶体群。

 

Nonclassical Periodic Models Fourier Transforms and Group

Abstract: Three kinds of nonclassical periodic plane-lattices with locally 8-, 10-, and 12-fold symmetry are proposed. they can be interpreted as the projections on the plane of space models consisting of different polyhedra.The Fourier-transform patterns of the space models have approximate 8-, 10-, and 12-fold rotational symmetry which is hardly distinguishable from the corresponding symmetry in the strict mathematical sense and qualitatively similar to the electron-diffraction patterns with 8-,10-, and 12-fold symmetry of corresponding quasicrystals. These lattice can be described by a new "composites" of the traditional translation operations and rotation operations. Nonclassical crystallographic groups are set up.

 

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