Lord E A, Ranganathan S
Department of Metallurgy, Indian Institute of Science, Bangalore 560012, India.
Acta Crystallogr A. 2001 Sep;57(Pt 5):531-9. doi: 10.1107/s0108767301007504. Epub 2001 Sep 1.
Steinhardt, Jeong, Saitoh, Tanaka, Abe & Tsai [Nature (London) (1998), 396, 55-57] have demonstrated that the structure of decagonal Al-Ni-Co can be built from overlapping clusters of a single type. The structure arises from a decoration of the decagons of a Gummelt covering. The unit (essentially a decagonal prism) was called by Steinhardt et al. a 'quasi unit cell'. In this work, a classification scheme is proposed for 'G patterns'--quasiperiodic patterns obtained by decorating a decagonal quasi unit cell. The classification makes use of the fact that G patterns can also be derived from decoration of a tiling. The tiles are analogues, for decagonal quasiperiodic patterns, of the 'asymmetric units' of a periodic pattern; they provide a simple mode of description and classification of the 'Gummelt-type structures'. Four existing models for decagonal phases are considered from this viewpoint.
施泰因哈特、郑、斋藤、田中、阿部和蔡[《自然》（伦敦）（1998年），396卷，55 - 57页]已经证明，十边形Al - Ni - Co的结构可以由单一类型的重叠团簇构建而成。该结构源自对古默尔特覆盖层十边形的修饰。施泰因哈特等人将这个单元（本质上是一个十棱柱）称为“准晶胞”。在这项工作中，针对“G模式”——通过修饰十边形准晶胞得到的准周期模式，提出了一种分类方案。该分类利用了这样一个事实，即G模式也可以从平铺的修饰中推导出来。对于十边形准周期模式，这些平铺类似于周期模式的“不对称单元”；它们为“古默尔特型结构”提供了一种简单的描述和分类方式。从这个角度考虑了现有的四种十边形相模型。
