Analysis of dislocations in quasicrystals composed of self-assembled nanoparticles

TL;DR

This paper presents an automated method to analyze dislocations in self-assembled quasicrystals using TEM images, decomposing the structure into Fourier modes to identify topological features and Burgers vectors.

Contribution

It introduces a novel automated approach to identify and characterize dislocations and their topological properties in quasicrystals from TEM images.

Findings

All observed Burgers vectors are of lowest order, with components 0 or 1.

The density of different Burgers vector types depends on their energetic cost.

The method effectively links topological analysis to experimental TEM data.

Abstract

We analyze transmission electron microscopy (TEM) images of self-assembled quasicrystals, composed of binary systems of nanoparticles. We use an automated procedure that identifies the positions of dislocations and determines their topological character. To achieve this we decompose the quasicrystal into its individual density modes, or Fourier components, and identify their topological winding numbers for every dislocation. This procedure associates a Burgers function with each dislocation, from which we extract the components of the Burgers vector after choosing a basis. The Burgers vectors that we see in the experimental images are all of lowest order, containing only 0's and 1's as their components. We argue that the density of the different types of Burgers vectors depends on their energetic cost.