Covering Clusters in Icosahedral Quasicrystals

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• 作者：Michel Duneau ; Denis Gratias
• 刊名：Springer Tracts in Modern Physics
• 出版年：2002
• 出版时间：2002
• 年：2002
• 卷：180
• 期：1
• 页码：pp.23-62
• 全文大小：1,190 KB
• 刊物类别：Springer Berlin / Heidelberg
• 刊物主题：Physics
  Solid State Physics and Spectroscopy
  Condensed Matter
  Nuclear Physics, Heavy Ions and Hadrons
  Elementary Particles and Nuclei
  Astronomy, Astrophysics and Cosmology
  Optical and Electronic Materials
  Complexity
  
• 出版者：Springer Berlin / Heidelberg

文摘

The structural analysis of various approximant phases of icosahedral quasicrystals shows local environments with icosahedral symmetry: icosahedra, Mackay clusters, and Bergman clusters. For the icosahedral phases i-AlCuFe and i-AlPdMn, these clusters have been proposed as complementary building blocks centered on particular nodes. However, computations have shown that these 2-shell or 3-shell clusters do not cover all atomic positions given by 6D models. On the other hand, the recent concept of a unique covering cluster has been shown to apply to 2D Penrose tilings and Ammann-Beenker tilings. In this chapter we examine the local environments in i-AlCuFe and i-AlPdMn models about Wyckoff positions of the 6D lattice. We consider extended Bergman clusters of 6 shells that appear naturally in the Katz-Gratias model. We discuss the cell decomposition of the atomic surfaces and the variable occupation number of some of the shells. We show that a fixed extended Bergman cluster of 6 shells and 106 atoms covers about 98% of atomic positions. We also prove that a variable extended Bergman cluster of 6 shells, which contains the previous fixed cluster, covers all atomic positions of the theoretical model.