A seed-based structural model for constructing rhombic quasilattice with 7-fold symmetry

Abstract

A seed-based theoretical model with built-in local degree of freedom for constructing rhombic quasilattice with 7-fold symmetry is presented. This new approach mitigates a key limitation with existing structural models for describing quasicrystals, which do not incorporate atomic fluctuations or phasonic flips in their approaches. Here, we propose a structural model that works in concert with the seed-initiated nucleation growth models of quasicrystals and incorporates a degree of flexibility that allows the lattice to rearrange locally without affecting the global long-range order. This approach suggests that the position of high-symmetry motifs locally and globally is defined by one long-range framework and not based on local rules (i.e., inflation, deflation, substitution, matching, overlapping, etc.). The proposed model is based on building a hierarchical network that allows the self-similar quasilattice to expand infinitely without any gaps, overlaps, or mismatches. The use of a global relational logic provides scientists, artists, and teachers with a simple method for creating a wide variety of complicated hierarchical quasilattice formations without the need for any specialized software or complicated mathematics and could possibly provide a deeper understanding of how the atoms interact to form their complicated long-range quasicrystalline formations.