Periodic diffraction patterns for 1D quasicrystals

TL;DR

This paper introduces a model for 1D quasicrystals based on Fibonacci sequences with variable spacings, demonstrating a transition between periodic and non-periodic diffraction patterns through analytical calculations.

Contribution

It presents a new analytical approach to study diffraction patterns in 1D quasicrystals with variable spacings, bridging periodic and aperiodic structures.

Findings

Demonstrates continuous transition between periodic and non-periodic diffraction patterns

Provides analytical calculations using 'cut and project' and 'average unit cell' methods

Highlights the physical space properties of 1D quasicrystal structures

Abstract

A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction patterns are calculated analytically both using ``cut and project'' and ``average unit cell'' methods, taking advantage of the physical space properties of the structure.