Dodecagonal spherical quasicrystals

TL;DR

This paper predicts the imminent discovery of 2D dodecagonal spherical quasicrystals and explores how planar quasicrystal order adapts to spherical geometry through defect formation and energy minimization.

Contribution

It introduces a theoretical framework for understanding the formation of spherical quasicrystals from planar dodecagonal quasicrystals, emphasizing defect arrangements and energy considerations.

Findings

Curvature induces topological defects in spherical QCs.

Defect locations depend on initial planar order and shape.

Energy minimization guides defect placement and structure stability.

Abstract

We argue that 2D dodecagonal spherical quasicrystalls (QCs) will be discovered in the nearest future and investigate how the planar QC order becomes compatible with the spherical geometry. We show that the appearance of curvature-induced topological defects and low-energy structural rearrangements are sufficient to obtain the regular spherical QC structures. Minimization of total energy required for the order reconstruction determines the number of topological defects, which are located near the vertices of snub cub or icosahedron in dependence on type of the initial dodecagonal order.