On a Realistic Growth Mechanism for Quasicrystals

Simple rules are discussed that can guide under realistic conditions the growth of quasicrystals. We propose a two-step mechanism where the well-known overlap rules for the fundamental atomic clusters are complemented by the new layer-continuation rule. This rule demands that the sets of atomic layers, crisscrossing each atomic cluster according to its eigensymmetry, have to be continued across all other clusters formed during the growth process. On one hand, this combined growth rule is local because each fundamental cluster already defines the overlap rules as well as the basic set of atomic layers. On the other hand, it is global because the framework of atomic layers originating locally from each cluster extends infinitely. The layer-continuation rule guides the attachment of atoms to the growing quasicrystal and assists the overlap rules, which are at the high temperatures, where crystal growth takes place, only weakly supported by specific atomic arrangements in the shared cluster volumes.