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We propose the theory which unifies the description of quasicrystal assemblythermodynamics and quasicrystal structure formation by combining the Landautheory of crystallization and the cluster approach to quasicrystals. The theoryis illustrated on the example of pentagonal Penrose quasilattice. Thecoordinates of the quasilattice nodes are calculated by minimizing the Landaufree energy with the constraint imposed by internal organization of atomicclusters, without explicit use of high-dimensional crystallography. Theprocedure proposed establishes direct relations between the clusterorganization, quasicrystalline structure and thermodynamic properties of thequasicrystalline state. The correspondence is shown between the basic featuresof the proposed algorithm for quasilattice construction, on the one hand, andthe conventional projection method, on the other hand. It provides a newphysical justification for high-dimensional crystallography methodsapplication.

Bridging the Landau theory of crystallization and the cluster approach to quasicrystals