Order parameter in the quasicrystal-crystal transformation

Some aspects of the relationship between quasicrystal and crystal structures not considered earlier are discussed. It is shown that the atomic positions in a quasicrystal lattice are intermediate between the positions of periodic incommensurate crystal lattice. For the octagonal symmetry, two such generating lattices can be square and equal to one another. Then any quasicrystal position lies exactly between two crystal positions in different lattices. The classical (phason) mechanism of the quasicrystal-crystal phase transition is interpreted as a relative homogeneous deformation of generating crystal lattices leading to the commensurability of these lattices. The order parameter of such a transition is defined.