Analysis of Dislocations in Quasicrystals Composed of Self-assembled Nanoparticles

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 0s and 1s as their components. We argue that the density of the different types of Burgers vectors depends on their energetic cost.