The quasicrystal-to-crystal transformation. II. Landau theory

A phenomenological description of the quasicrystal-to-crystal transformation is presented in terms of Landau theory. The basic idea is to describe the structures of quasicrystals as incommensurately modulated structures and to use the tools developed for phase transitions of this kind. The usefulness of this description is demonstrated on quasiperiodic model structures: the one-dimensional (1D) Fibonacci sequence and the 2D Penrose tiling. The transformation to periodic structures is discussed generally for rational approximants.