An extinction rule for a class of 1D quasicrystals

TL;DR

This paper investigates a specific class of one-dimensional quasicrystals derived from a two-dimensional lattice, analyzing how the relative positioning of decorated sites affects their structure factor and extinction properties.

Contribution

It introduces a general expression for the structure factor of these quasicrystals and explores an example of an extinction rule based on site positioning.

Findings

Derived a general formula for the structure factor.

Identified conditions for extinction in the structure factor.

Analyzed the effect of site positioning on diffraction patterns.

Abstract

We study decorated one-dimensional quasicrystal obtained by a non-standard projection of a part of two-dimensional lattice. We focus on the impact of varying relative positions of decorated sites. First, we give general expression for the structure factor. Subsequently we analyze an example of extinction rule.