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Structures grown via self-assembly are a unique field in nanotechnology. The morphology of self-assembled structures is affected by the balance between kinetics and thermodynamics during growth. Hence structures with tailored morphologies and properties can be created with adjustments in growth conditions. In this thesis we study crystal nucleation and equilibration, for both real and model systems. The growth of thin bismuth films is investigated on three atomically flat surfaces; Mica, Molybdenum di Sulphide, and highly oriented pyrolitic graphite (HOPG). Films are grown under UHV conditions, and characterised using scanning electron microscopy and atomic force microscopy. For coverages of only a few monolayers, bismuth particles are found to aggregate into flat, isolated islands. Islands have characteristic heights and morphologies for each substrate. By altering the deposition flux and coverage, the island density and morphology can be manipulated. On HOPG substrates, planar islands grown at low flux are replaced by 1D structures at high temperature. These anisotopic structures result from an anisotropy in bond strengths at the crystal-vapour interface. Depositing Bi on HOPG substrates at low flux or high temperature conditions produces nanorods aligned (roughly) perpendicular to step edges on the graphite. The aspect ratios (ARs) of these 1D structures are found to increase as the deposition flux is lowered, or the substrate temperature is increased. The Arrhenius dependence of the AR is determined from experiment. A Kinetic Monte Carlo (KMC) model for high AR step-edge aggregates was developed, determining the likely growth mechanism for the nanorods. A scaling regime devised from the KMC results predicts the dependence of nanorod ARs on flux and temperature, and allows an estimation of the energy binding Bi dimers to the sides of nanorods. Thin films can also be grown via the self-assembly of atomic clusters. After deposition coalescence of clusters has implications for the film morphology, and properties. We use KMC simulations to investigate the coalescence of pairs of 3D atomic clusters (15000 to 130000 atoms in size) via lattice based surface diffusion. For early coalescence stages, the radius of the neck region connecting the two clusters is found to develop with a different powerlaw to classical theory. For later coalescence stages, when the nucleation of new atomic layers on facets of the cluster is required for further coalescence the temperature, cluster size, and cluster orientation all influence the coalescence. Equilibration times for clusters coalescing at high temperature are found to be limited by the dissociation of atomic layers.

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