The physical properties of entropic quasicrystals

A review, with 26 references, is given. This paper summarizes recent work on the physical properties of quasicrystals-dislocations, grain boundary structure, and structural phase transitions-in the context of random tiling or entropic models of quasicrystals. Several testable predictions are made on the basis of these models. These should provide decisive tests to settle the question whether the quasicrystal state is the decoration of a single perfect tiling or a statistical superposition stabilized by the large configurational entropy associated with phasons