A classification of the periodic directions in the rational approximants of icosahedral quasicrystals

Ovidiu Radulescu

This paper shows that there are three types of periodic directions in the rational approximants of an icosahedral quasicrystal : weakly, planar and strongly periodic directions. The classifying criteria take into account the periodicity properties of these directions in the direct and the reciprocal space, as well as the existence of atomic planes and atomic rows, orthogonal, respectively parallel to these directions. The set of periodic directions of all the possible rational approximants are module directions in the icosahedral Z-module which is the “ Bravais ” lattice of the icosahedral quasicrystal. These module directions belong to some compatibility classes, which are indexed by the series of square-free numbers of the form 5 x2 -y2, x, $y\in \mathbb{Z}$.

Domaines: Articles anciens

Ovidiu Radulescu. A classification of the periodic directions in the rational approximants of icosahedral quasicrystals. Journal de Physique I, 1993, 3 (10), pp.2099-2113. ⟨10.1051/jp1:1993234⟩. ⟨jpa-00246854⟩