Indexing of icosahedral quasiperiodic crystals
Indexing of icosahedral quasiperiodic crystals
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DOI：
10.1557/jmr.1986.0013
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发表时间：
1986-01
影响因子：
2.7
通讯作者：
J. Cahn;D. Shechtman;D. Gratias
中科院分区：
文献类型：
--
作者：
J. Cahn;D. Shechtman;D. Gratias
由于准周期性的定义与傅里叶变换的索引密切相关，因此对于二十面体固体的情况，描述了使用衍射证明物体是准周期性的必要步骤。讨论了各种坐标系，并给出了选择与一组三个正交二折轴对齐的坐标系的原因。基于该坐标系，提出了主要的晶体学投影，并演示了几种分析的单晶电子衍射图案。比较了五个二十面体布拉维准晶格中的三个的消光规则，并导出了与六维切割和投影晶体学的一些简单关系。该分析产生了用于索引粉末衍射图案的简单应用。
Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.