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.

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.

Homogeneous crystal nucleation in binary hard sphere mixtures is an active area of research for last two decades. Although Classical nucleation theory (CNT) gives a qualitative picture, it fails at high super saturations because of the following reasons. CNT assumes that the cluster formed is spherical in shape, its properties can be modeled using the bulk properties of the stable solid phase and the interfacial free energy γ between the nucleus and the surrounding metastable fluid is equal to the planar surface tension between two phases at coexistence. These assumptions get increasingly tenuous at higher degrees of super saturations where the critical nucleus formed is microscopic in size leading to breakdown in the predictions of CNT. In addition direct experimental observation of critical nucleus is very difficult because, 1. Critical nucleus is microscopic in size, consisting of few hundreds of particles. 2. Formation of critical cluster is very rare (typically of the order of 101– 106nuclei/cm3/s) 3. Its life time is very short (it either rapidly grows to form a solid phase or melts back to fluid) In these circumstances molecular simulations are an attractive tool to study the crystal nucleation, because in these simulations microscopic size critical nucleus properties can be calculated. However, brute force molecular dynamic (MD) simulation techniques to study the homogeneous crystal nucleation is currently not feasible due to long times involved. Hence, an indirect approach is needed. In this work, Monte Carlo Abstract v (MC) molecular simulation techniques are used to calculate free energy barrier height during the crystal nucleation. Phase behavior of Binary hard sphere mixtures with varying ratios of smaller diameter to larger diameter (α) is very similar to that of binary organic liquids. By studying the crystal nucleation in hard sphere system, the physics behind the nucleation for binary organic liquids can be understood. This is the key motivation to study the homogeneous crystal nucleation in binary hard sphere mixtures using MC simulations. Simulations were done using umbrella sampling in combination with local bond order analysis for the identification of crystal nuclei and to compute shape and height of nucleation barrier. Parallel tempering scheme of Geyer and Thomson was utilized to sample phase space more efficiently. Parallel tempering technique was implemented using Message passing interface (MPI) libraries. By using all the above Monte-Carlo simulation techniques, nucleation barrier was calculated during crystallization of binary hard sphere mixtures under the moderate degrees of super cooling in Isothermal-Isobaric semi grand ensembles. Crystal nucleation in binary hard sphere mixtures has been studied for size ratios α = 0.85, 0.42 and 0.43. For α=0.85, phase diagram contains eutectic point. In this system, the effect of eutectic composition on the nucleation barrier height was observed, by calculating nucleation barriers at various fluid mixture compositions keeping Laplace pressure constant. It is observed that as the fluid mixture composition move towards the eutectic point, free energy barrier height, surface tension and critical cluster sizes are increased and the nucleation rate is drastically decreased by a factor of 10-31. Thus the difficulty of homogenous crystal nucleation increases near the eutectic point. For α=0.42 and 0.43 in the hard sphere system, compound solids such as AB and AB2 solids are stable respectively. In these systems crystal nucleation study was done to observe the compound solid formation. It is observed that in these systems crystallization kinetics are very slow and more advanced simulation techniques need to be developed in order to study crystal nucleation.