Abstract
We summarize the results of studies on quasicrystals (QCs) at extreme conditions over the last 4 decades with particular emphasis for compositions falling in the Al-based ternary system as the closest to those of quasicrystals discovered in nature, such as icosahedrite and decagonite. We show that, in contrast with what thought in the past, both pressure and temperature act to stabilize QCs, for which a clear phase transition to either crystalline approximants or amorphous material has been limited to very few compositions only. Such stabilization is proved by the compressibility behavior of QCs that resembles that of the pure constituent metals. Additional remarks come from the experimental observation of QC formation at high pressure and temperature in both static and dynamic experiments. These results seem, in conclusion, to suggest that the occurrence of QCs in nature might be more a rule rather than an exception.