Crystallography of Quasicrystals; Application to Icosahedral Symmetry
Abstract
Crystallographic concepts are extended to quasicrystalline structures. The fact is used that any ddimensional noncrystallographic point group has Ddimensional representations (D > d) which are compatible with periodicity, i.e. can be viewed as point groups of Ddimensional periodic structures. These periodic structures can be classified by conventional crystallographic methods: Bravais lattices, point groups and space groups can be calculated. This program is carried out for icosahedral symmetry, for which the minimal dimension D is 6. There are surprisingly few types of 6dimensional crystals with icosahedral symmetry: 3 Bravais lattice types, 2 point groups and totally 11 space groups can occur. The nonsymmorphic space groups lead to systematic extinctions of Bragg peaks, similar to the case of ordinary crystals. These extinctions, if present, can help to distinguish between quasiperiodic and competing glass models for icosahedral quasicrystals.
 Publication:

Physica Scripta Volume T
 Pub Date:
 January 1989
 DOI:
 10.1088/00318949/1989/T25/067
 Bibcode:
 1989PhST...25..367R
 Keywords:

 Bravais Crystals;
 Crystal Lattices;
 Crystallography;
 Icosahedrons;
 Crystal Structure;
 Crystallinity;
 SolidState Physics