Applications of the Phase-Field Method for the Solidification of Microstructures in Multi-Component Systems

The solidification of multicomponent alloys is of high technical and scientific importance. In this review, we describe the ongoing research of the phase-field method for the solidification of dendritic and eutectic structures. Therefore, the corresponding experimental and theoretical investigations are presented. First, an overview of the historical development in solidification research is given. Thereafter, the ongoing progress of the phase-field models is reviewed. Then, we address the experimental and simulative investigations of different forms of dendritic and eutectic solidification. We distinguish between thermal and solutal dendritic growth as well as thin-sample and Bridgman furnace experiments of eutectic growth. Impurity-driven Mullins-Sekerka instabilities like cell structures, eutectic colonies and spiral dendritic growth are presented. Then, validation methods for the comparison between simulations, experiments and theoretical approaches are addressed. Subsequently, related aspects to simulate solidification are introduced. Especially, further physical aspects and computational optimizations are considered. Concluding, possible future research in the context of the phase-field method for solidification is discussed.