Landau theory of crystallization and self-assembly of octagonal quasicrystals

The theory of crystallization of quasicrystal structures that does not use the concept of multidimensional crystallography for describing the quasicrystal order has been proposed. It has been shown using the structure of the MnSiAl octagonal quasicrystal as an example that the coordinates of the sites in the corresponding quasicrystal lattice can be calculated by conditional minimization of the Landau free energy. The abandonment of the unconditional minimization of the free energy has been justified by special features of the local atomic order in the considered structure. The proposed theory gives a new physical meaning to the traditional concepts of multidimensional crystallography and can also be used for explaining the formation of quasicrystal structures with other quasicrystal lattices.