Phase-field simulation of solidification and coarsening in dendritic microstructures

Phase-field models are used to simulate dendritic microstructures during solidification and coarsening of metallic alloys. Equiaxed dendrites in a Cu-Ni alloy are simulated during rapid solidification and coarsening. The morphology of the solid-liquid interface is characterized using Interface Shape Distributions. The interface's topology is quantified using genus and number of handles and voids. The system is found to evolve non-self-similarly during solidification and the early stages of coarsening.;A method is developed to calculate the time rate of change of interfacial curvatures for a diffuse interface representation of a microstructure, and an algorithm to calculate the rate of change numerically is implemented. Accurate results are obtained, but relatively large interface widths (> 10 points) are required.;A phase-field model to simulate isothermal coarsening in a binary alloy is implemented and tested against the predictions of a linear stability analysis. Solid-liquid interfacial velocities are calculated from experimental data for isothermal coarsening of an Al-Cu alloy. The experimental data is used in the phase-field model, and interfacial velocities are calculated from simulations and compared to experiment. Qualitative agreement between the velocity distributions is good, while quantitative agreement differs by a factor of 2.9. The possible causes of disagreement are investigated, and the diffusion coefficient of solute in the liquid, DL, is believed to be the greatest source of the disagreement. This suggests the use of phase-field models as a means of determining DL when other physical parameters are well known.;The shape of a liquid tube undergoing pinching by interfacial-energy driven bulk diffusion is determined near the point of pinching. The characteristic length scale of the process varies as t1/3. The shape is found in similarity variables using a boundary-integral method in 2D after pinching, and in 3D before and after pinching. The shape of a solid cylinder in a liquid matrix is also determined in 3D before pinching. The theory is compared to experimental data for isothermal coarsening of an Al-Cu alloy. The agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal, and that the dynamics is well described by the theory well before pinch-off.