Unconventional Landau theory of quasicrystalline structure formation

We propose an unconventional theory which unifies the description of quasicrystal thermodynamics and quasicrystal structure formation by combining the Landau theory of crystallization and the cluster approach to quasicrystals. The theory is illustrated on the example of pentagonal Penrose quasilattice. It employs the notion of non-linear order parameter dependent on the atomic coordinates which was developed in the theory of reconstructive phase transitions. The coordinates of the quasilattice nodes are calculated by minimizing the Landau free energy with the constraint imposed by internal organization of clusters. The correspondence is shown between the theory proposed and the conventional projection method.