Coordination and cluster packing in quasicrystals

Abstract

We discuss some local and global characteristics of quasicrystalline structures. Firstly, we present an analysis of the coordination numbers in the Cd_5.7Yb binary quasicrystal. A majority of the Cd and Yb atoms occupy 12- and 16-fold coordinated sites, respectively. It is argued that the coordination properties are closely related to the local stability of the quasicrystals. Secondly, a simple inflation algorithm is presented for generating an icosahedral quasilattice which has a dense packing of a given structural motif or cluster. The atomic surface of a P-type icosahedral quasilattice generated in this way has a fractal boundary.

Keywords:

• coordination number
• icosahedral quasilattice
• inflation method
• atomic structure
• clusters

Acknowledgements

The authors would like to thank A. Yamamoto for providing the structural data of the Cd_5.7Yb QC, H. Takakura, C. P. Gómez and M. de Boissieu for helpful comments and discussions. They are grateful to one of the referees for pointing out 10,11.

Notes

Notes

1. The structural data was provided by the courtesy of A. Yamamoto, who is one of the authors of 2.

2. A rough estimate reveals that the innermost tetrahedral shell does not affect the coordinations of the third and the fourth (the outermost) shells. While sites in the second shell are mainly 11-fold coordinated, the innermost tetrahedral sites can have 9 to 13-fold coordinations depending on its configuration.

3. We use the same indexing scheme as in 17.

4. The shells 0 to 5 form an extended Mackay type cluster which has been reported as one of the covering clusters of Katz–Gratias model of Al-Pd-Mn QC 18.