A self-similar ordered structure with a non-crystallographic point symmetry

TL;DR

This paper introduces superquasicrystals, a new class of self-similar ordered structures with non-crystallographic symmetries, characterized as limit-quasiperiodic and derived from higher-dimensional recursive superlattices.

Contribution

It presents the theoretical concept of superquasicrystals, expanding the understanding of ordered structures beyond traditional quasicrystals with a novel recursive superlattice framework.

Findings

Superquasicrystals are limit-quasiperiodic structures.

They exhibit non-crystallographic point symmetries.

Potential real materials may be candidates for superquasicrystals.

Abstract

A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice structures. Such structures turn out to be limit-quasiperiodic, distinguishing themselves from quasicrystals which are quasiperiodic. There exist a few real materials that seem to be promising candidates for superquasicrystals.