Models for quasicrystal-crystal epitaxy

Not long after the discovery of quasicrystals, a specific orientation relationship between crystalline and quasicrystalline structures was observed. The specific orientational relationships were discovered in many systems, for instance surface alterations of bulk quasicrystals, the growth of atomic overlayers on quasicrystalline substrates and quasicrystalline thin films on crystalline substrates. In this paper, we review various models described in the literature in explaining such quasicrystal-crystal epitaxy.