Structural phase transitions from and to the quasicrystalline state

Phase transitions from and to the quasicrystalline state show a typical signature due to some structural peculiarities. Both quasicrystals and most of their translationally periodic transformation products, the approximants, consist of the same basic structural units (`clusters'). This is the cause of low-energy interfaces between the newly forming phase and the parent phase. It is also the origin of the rather high stability of the frequently resulting orientationally twinned nanodomain structures. Owing to topological incompatibilities between quasiperiodic and periodic structures, purely displacive phase transitions are impossible. Diffusion of a significant fraction of atoms, at least on the scale of the cluster diameters, always has to take place. Locally similar icosahedral structural ordering between parent phase and nucleating phase is also responsible for the frequently occurring formation of icosahedral quasicrystals from undercooled liquid alloys or during devitrification of metallic glasses. The different types of experimentally observed phase transitions are discussed, from amorphous to quasicrystalline, quasicrystalline to ordered/disordered quasicrystalline and quasicrystalline to crystalline as a function of temperature, pressure, irradiation and high-energy ball milling, respectively.