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

TL;DR

This paper introduces a unified theory combining Landau crystallization and cluster approaches to better understand quasicrystal formation and structure, exemplified by the Penrose tiling, linking thermodynamics, structure, and atomic organization.

Contribution

It presents a novel framework that directly relates cluster organization to quasicrystal structure and thermodynamics without high-dimensional crystallography, bridging two traditional approaches.

Findings

Calculated quasilattice nodes by minimizing free energy with cluster constraints.

Established direct relations between cluster organization and quasicrystal properties.

Connected the proposed method with the conventional projection approach.

Abstract

We propose the theory which unifies the description of quasicrystal assembly 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. The coordinates of the quasilattice nodes are calculated by minimizing the Landau free energy with the constraint imposed by internal organization of atomic clusters, without explicit use of high-dimensional crystallography. The procedure proposed establishes direct relations between the cluster organization, quasicrystalline structure and thermodynamic properties of the quasicrystalline state. The correspondence is shown between the basic features of the proposed algorithm for quasilattice construction, on the one hand, and the conventional projection method, on the other hand. It provides a new physical justification for high-dimensional crystallography methods application.