Abstract
The established concept of quasicrystals is described, in which quasicrystals are defined as the structure having (1) a long-range quasiperiodicity and (2) a crystallographically-forbidden rotational symmetry. It is shown that the quasicrystalline structure is regarded as a section of a higher-dimensional crystalline structure. The concepts of phason strain, random tiling model and approximant crystal are introduced according to the higher-dimensional description of the quasicrystalline structure. Experimental investigations made so far on the structure of the quasicrystalline phases are discussed in the light of these concepts. Important roles of approximant crystals in the research of quasicrystals are emphasized.
