Crystallographic Method for Exact Describing Quasicrystal Structures

Details Crystallographic Method for Exact Describing Quasicrystal Structures Crystallographic Method for Exact Describing Quasicrystal Structures

2001-07-10

arxiv.org/abs/cond-mat/0107191v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 5 figures-eps, LaTeX2e, AmS-LaTeX, see also http://www.kirensky.ru/download/tilings.zip, submitted to Acta Crystall

Scientific paper

In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be presented as a particular case of a quasicrystal. The simple and explicit analytical formulas which describe the location of each atom in a quasicrystal are given. The exact solutions for Penrose and Ammann-Beenker quasicrystal structures are given. On the basis of the analytical formulas the routines are created. The routines are inserted directly into graphical files generating the quasiperiodic structures.

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