D0I:10.13374/i.issn1001-053x.1991.03.03M 第13卷第3期 北京科技大学学报 Vol.13 No.3 1991年5月 Journal of University of Science and Technology Beijing May 1991 Atomic Model for 3-Dimensional Periodic Structure and 12-fold Rotational Symmetry in Lequan·Vu Yuzhen· ABSTRACT:A VNi atomic model for 3D periodic structure is posed based on T polyhedrons which are introduced.The fourier transform patterns of the ato- mic model may explain the 12-fold symmetry in electron diffraction patterns of V60Ni40 alloy.This is the first satisfactory explaination since the V60Ni40 alloy has been reported.. KEY WORDS:3D periodicity,VNi alloy,12-fold rotational symmetry,quasi- crystal. In April of 1988,H.Chen et al.reported a VNi alloy with twelvefold rotational symmctry.They have pointed out that the VNi alloy is a new type of 2D quasicrystal.Following the discovery,K.H.Kuo et al.2 has proposed. growth models to explain their observations(11.However these models can not explain all the electron diffraction patterns(EDPs)of the V60Ni40 alloy.In this paper,a 3D atomic model with periodicity has been proposed based on so-called T polyhedrons.The Fourier transform patterns (FTPs)of the ato- mic model are remarkable in agreement with all EDPst of V60Ni40 alloy. The atomic composition of the atomic model is also similar to that of the V60Ni40 alloy. The elementary building unit in the model presented here is so-called T polyhedron shown in Fig.1.Distribution of atoms v and Ni in T polyhe- drons has two different ways which are shown in Fig.1.(a)and (b)respe- ctively.In a unite primitive cell (See Fig.2.(a)and (b))of the model, 1990一07-20收篇 ·数力系(Department of Mathematics and Mechanics) 291第 卷第 期 年 月 北 京 科 技 大 学 学 报 。 班 二二二二二二二二二二二二二二三二二二二二二二二二 一 一 牙 “ 犷 之 ‘ 扭 ， 住 。 一 义 ， ， 一 ， 卜 ， ， 〔 〕 丁 了 · 乏 ， ， 。 〔 ’ 见 〔 。 五 。 ， 卜 ， 一 五 五 扭 观 主 呈 五 五 。 五 卜 ， 一 · ， ， 五 。 · 。 。 ， 一 一 收 稿 数 力系 厂 么 王 DOI ：10．13374／j ．issn1001－053x．1991．03．034