摘要
在分析正五边形的几何特征和正五边形的周期与准周期排列的基础上,讨论具有五边形单元的二维周期点阵与准周期点阵的异同以及它们之间的转变。在Al-Co二元系中,除了已知的单斜Al_(13)Co_4及正交Al_3Co的五角层状结构,还发现有五边形的边长及单胞参数α,c均为τ~2和τ~3倍的合金相(无理数τ=2 cos 36°=(1+5^(1/2))/2=1.61803…),如此无限膨胀,就会得到单胞参数为无穷大的十次准晶。另一方面,Al_(60)Mn_(11)Ni_4的两种已知正交结构的点阵参数α,c均可用近似的有理数(如1/0及2/1或3/2及2/1)置换十次准晶的两个正交准周期方向的无理数τ得出。高分辨电子显微像证明十次准晶和这两种正交近似晶体相有相同的结构单元。
It is well known that the decagonal quasicrystal and its crystalline approximants have similar composition and local structure. In the Al-rich Al-Co and Al-Mn-Ni cases, both the structure of the crystalline and quasicrys-talline phases is built of layers consisting of pentagons,arranged periodically in the crystalline approximants and quasiperiodically in the decagonal quasicrystal. The Co atoms in the monoclinic Al_(13)Co_4(b=0.81 nm,β≈108°) form pentagons with a side length of 0.47 nm in the flat layers. The structure of the orthorhombic Al_3Co can be derived from Al_(13)Co_4 by a repeated shift of 0.47 nm, i. e., a unit length of a pentagon, in the [001]direction. In addition to these phases, a family of τ-in-flated Al_(13)Co_4 and Al_3Co phases, such as τ~2-Al_(13)CO_4, τ~3-Al_(13)Co_4, τ~2-Al_3Co and τ~3-Al_3Co, with lattice parameters a and c as well as the side length of the Co atom pentagons also inflated by approximately τ~2 and τ~3 times (τ=2 cos 36°=(1+5^(1/2))/2=1.61803…) have been found by transmission electron microscopy. If such a τ-inflation continues infinitely,the pentagons as well as the unit cell will become infinitely large and a decagonal quasicrys-tal with a layer structure will thus form. Two orthorhombic structures of Al_(60)Mn_(11)Ni_4 were known. It is shown that the lattice parameters a and c of both phases can be reproduced by substituting a pair of rational ratios of two successive Fibonacci numbers, F_(n+1)/F_n, as approximants for the irrational τ in the two orthogonal quasiperiodical directions in the decagonal quasicrystal. One is the (1/0,2/1) approximant and the other the (3/2,2/1) approximant, and the pentagonal layer structure of the latter can be derived from that of the former. Moreover, the Al-Mn-Ni decagonal qua-sicrystal is shown to have the same structural subunits, but arranged aperiodically.
出处
《电子显微学报》
CAS
CSCD
1996年第2期240-251,共12页
Journal of Chinese Electron Microscopy Society
