Theoretical Studies of Crystallisation in Hard Sphere Systems

Abstract

The primary focus of this work is to develop an understanding of crystallisation in hard sphere systems. The thesis is presented in two parts. The first section is an investigation of the liquid/crystal interface at equilibrium using molecular dynamical simulations. The objective is to understand how the interface might bridge between the disordered and ordered states in liquid/crystal environments. Topological measures of structure are used to investigate whether any precursor structures are present in the liquid phase, close to the interface, that would allow transition from disorder to order. This differs from other work where simpler measures of structure, classifying phases into either liquid or crystal, are used. The results indicate that the liquid/crystal interface of a hard sphere system is very narrow and no readily observable structures were found that extended past the width of the equilibrium interface. The second section of the thesis is a theoretical study of growth kinetics in hard sphere systems using density functional theory. The kinetics in a fixed volume are examined with a single conserved order parameter. The work is extended incorporating both conserved particle and non-conserved structure dynamics. The kinetics of growth are examined and it is shown that the small initial crystals are quickly isolated from the higher pressure of the surrounding system through the development of a depletion zone.