Crossover in directional solidification and carbon-60 island morphology

We simulate directional solidification using a phase field model solved with an adaptive finite element method. For small surface tension anisotropy directed at 45° relative to the pulling direction, we have observed three types of morphology: Dendritic, seaweed, and cellular. The seaweed pattern is characterized by alternating tip splitting and the branches have no orientation preference. A crossover from the seaweed to dendritic morphology was noticed when lowering the thermal gradient, consistent with previous experimental findings. We also investigate the influence of anisotropy on the morphology. We find that the thermal gradient, pulling velocity, and anisotropy can determine the crystal morphology. We show that the morphology of crystal structures can be unambiguously characterized through the local interface velocity distribution. As the thermal gradient is lowered, large-velocity shoulders begin to appeal in both transverse and growth directions, becoming progressively broader as clearly defined dendrites emerge. We derive semi-empirically an estimate for the crossover from seaweed to dendrite as a function of thermal gradient and pulling velocity, which agrees with our simulation results. The ratio of thermal length to diffusion length has a sharp transition at the crossover region.;In the second part of the thesis, a single variable dynamic model(Model B) is proposed to study C60 ultra-thin film growth on the alkali halide substrate. A triple-well free energy is proposed to explain the coexistence of three layers. The middle well is metastable representing a single layer. We successfully recover "branched and "compact' patterns for both deposition and evolution stage. The influence of fluctuations at the boundary is investigated and shown to be helpful to the formation of complex island morphologies. A diagram showing how the parameters affect the morphologies is given and a reliable criterion is found demonstrating how the well depth and barrier height determine the morphologies. The island morphology depends on substrate temperature. Increasing substrate temperature during deposition makes the "compact" pattern preferred.