Defects and Diffusion in Colloidal Crystals

Colloids are microscopic particles whose size ranges from a nanometer to several micrometers, that are dispersed in a solvent. One striking characteristic of colloidal systems is that their constituent particles are in a constant state of random motion due to incessant collisions with the fast-moving molecules of the solvent. This allows colloids to spontaneously explore all space available to them, and self-assemble, i.e. organize themselves, into a wide range of phases, such as gases, liquids, crystals, and even quasicrystals - just like atoms and molecules. Hence, to some extent colloids behave like “big atoms”. In this thesis we focus on crystalline phases formed by colloids, often referred to as “colloidal crystals”, and in particular on their crystallographic defects. Even when the concentrations of these defects are low, they can significantly alter the mechanical and transport properties of the crystal. For example, even though particles in a crystal phase are typically orders of magnitude less mobile than those in a fluid, diffusion is still possible via the diffusion of defects. Therefore, understanding the motion of these defects is key to understanding transport processes in crystals. We examine crystal defects in a wide variety of systems, ranging from the archetypical model system of hard spheres to hard cubes, to mixtures of active and passive particles. The chapters in this thesis are organized as follows. We start off in Chapter 2 by looking into the diffusion and interactions of the simplest of defects, namely vacancies and interstitials, in arguably the simplest model system: monodisperse hard spheres. In Chapters 3 and 4 we study binary mixtures of hard spheres. Specifically, in Chapter 3, we investigate the diffusion and interactions of small interstitial particles in a hard-sphere interstitial solid solution. We show how transition state theory can be used to accurately predict diffusion rates in these systems. In Chapter 4, we investigate the role of defects in the colloidal Laves phase. We find a high equilibrium concentration of antisite defects to be present in the Laves phase, thus shedding new light on its self-assembly. In Chapter 5, we study vacancies in a variety of repulsive systems forming simple cubic crystals. In particular, we show that for all these systems the vacancies are “delocalized” along a row of particles, suggesting this to be an inherent feature of simple cubic crystals of repulsive particles. In Chapters 6-8, we study mixtures of passive and active colloids. In Chapters 6 and 7, we show that active particles can provide an elegant new route to removing grain boundaries in polycrystals, in two and three dimensions, respectively. Chapter 8 focusses on a fundamental question: is it possible to predict quantitatively whether two phases of active particles coexist? We show that for a torque-free active system the phase diagram can be predicted by measuring the pressure and a chemical potential-like variable