Phase-Field Modeling of Solidification

Abstract

Pattern formation in solidification is one of the most well known freeboundary problems [1, 2]. During solidification, solute partitioning and release of the latent heat take place at the moving solid/liquid interface, resulting in a build-up of solute atoms and heat ahead of the interface. The diffusion field ahead of the interface tends to destabilize the plane-front interface. Conversely, the role of the solid/liquid interface energy, which tends to decrease by reducing the total interface area, is to stabilize the plane solid/liquid interface. Therefore the solidification pattern is determined by a balance between the destabilizing diffusion field effect and the stabilizing capillary effect. Anisotropy of interfacial energy or interface kinetics in a crystalline phase contributes to form an ordered pattern with a unique characteristic length scale rather than a fractal pattern. The key ingredients in pattern formation during solidification thus are contributions of diffusion field, interfacial energy and crystalline anisotropy [2].