Physical space description of decorated 1D aperiodic sequences

Abstract

In this paper, a systematic method of dealing with the arbitrary decorations of quasicrystals is presented. The method is founded on the average unit cell formalism and operates in the physical space only, where each decorating atom manifests itself just as an additional component of the displacement density function in the average unit cell. This approach allows us to use almost all classical crystallography algorithms for structure refining based on experimental data and may meaningly decrease the number of parameters which have to be fit. Further help for structure analysis may be the use of proposed recently average Patterson function, here applied to decorated sets. As an example we present a description of class of decorated quasicrystals based on Sturmian sequence of two interatomic spacings: we calculate explicitly structure factor, the shape of average Patterson function and give an algorithm for pattern analysis.

Notes

†Current address: Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany.

Additional information

Notes on contributors

P. Buczek†

†Current address: Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany.