This dissertation presents a computational study of microstructure formation and evolution during rapid solidification using phase-field modeling, with a focus on nucleation, morphological transitions, and banded growth in alloy systems relevant to additive manufacturing. Major work was done to investigate rapid solidification in a binary Fe-Cr alloy, used as a surrogate for 316L stainless steel. Using Bayesian-guided simulations, the study mapped transitions between dendritic, cellular, and planar morphologies across a wide range of thermal gradients and solidification velocities. The model captured unstable growth patterns in intermediate regimes, offering insights beyond the scope of traditional kinetic growth theory. The results demonstrated strong consistency with analytical stability thresholds while also revealing conditions where theoretical assumptions begin to fail. Subsequent work investigated banding, an oscillatory microstructural growth mode occurring between dendritic and planar growth, in representative alloys: Al-Cu, and Fe-Cr (surrogate for 316L stainless steel).

Systematic variation of key alloy parameters revealed that increasing the interface kinetic coefficient induces banding in alloys that typically do not exhibit this behavior, while decreasing it can suppress banding in systems that normally do see banding. Increased capillary anisotropy also reduced banding intensity. These trends were quantified through oscillations in tip temperature and microstructural analysis, offering a mechanistic understanding of how kinetic and interfacial properties influence the emergence of banding. The final study used a separate phase-field framework for modeling nucleation and growth. Simulations of thousands of nucleated particles enabled direct comparison with classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. Results confirmed excellent agreement in predicting the critical nucleation radius and incubation times under ideal conditions. However, when nuclei sizes approached the critical threshold, prolonged incubation led to deviations from classical behavior, particularly in continuous nucleation regimes. These findings highlight the need for statistical interpretation of transformation kinetics in phase-field studies.

Collectively, this work advances the predictive capabilities of phase-field modeling for solidification phenomena and provides practical insights into controlling microstructure in rapidly solidified materials, particularly in additive manufacturing contexts. Multiple computational models were developed, including the combination of Bayesian optimization with phase-field modeling which has advanced the state of the art of the field.