On the structure and optical properties ofquasicrystals
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Quasicrystals are aperiodic structures with long range orientational order. They often posses higher rotational symmetries than is allowed for crystals. Quasicrystals have been both created in a lab and found in nature. Colloidal systems also have been observed to self assemble into quasicrystals. As colloidal systems can be created with length scales that interact with visible light, colloidal quasicrystals have been proposed as materials which might have interesting photonic properties. In this thesis, we make some first steps to addressing how colloidal quasicrystals interact with light. We do this by exploring the structure and defects of a quasicrystal and examining how we can adapt a finite element method, which can be used to solve Maxwell's equations, to the structure of quasicrystals. With respect to the structure of quasicrystals, we use a Monte Carlo method in order to study the self assembly of two-dimensional core corona particles into a quasicrystal. We study the formation of defects through the colloidal quasicrystals and develop a method in order to identify defects in the quasicrystal. Using this method we follow defects moving through the quasicrystal and calculate the diffusion coefficient for different temperatures and packing fractions. With respect to the optical properties of quasicrystals, we propose a finite element method that is adapted to the structure of a one dimensional photonic quasicrystal. We apply this method to a simplification of Maxwell's equations and study the convergence of this method.