TOPOLOGICAL CONSTRAINTS FOR QUASICRYSTALS

1 June 1989

journal article
Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics B

Vol. 3 (6) , 877-896
https://doi.org/10.1142/s0217979289000658

Abstract

Topological constraints necessary for the existence of icosahedral quasicrystals having continuous phasons are found. As a result of application of these constraints a model of a new type for icosahedral quasicrystals is constructed. The “atomic surfaces” in R⁶ in this model are free of discontinuities, i.e. the displacements of atoms are continuous as functions of a phason shift. The positions of atoms in the physical space R³ from 60 interpenetrating rhombohedral lattices. The model exhibits diffraction properties of an ideal quasiperiodic structure and has perfect icosahedral symmetry.

Keywords

TOPOLOGICAL CONSTRAINTS
MODEL
PHASONS
INTERPENETRATING
CONSTRAINTS NECESSARY
QUASICRYSTALS TOPOLOGICAL
ICOSAHEDRAL QUASICRYSTALS
CONTINUOUS

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