Heterogeneous nucleation models to predict grain size in solidification

Heterogeneous nucleation models in solidification have been developed to predict grain size over several decades. Up to now, the models are divided into three categories. The first is a well-known spherical cap nucleus model, where the effectiveness of nucleant, i.e. contact angle, is mainly focused on characterising the nucleants. In this model, the kinetics is determined by activation energy of embryos formation and the adsorption rate of atoms into the embryos. The second is a free growth model, in which active nucleants are determined by the size distribution of nucleants, and the heterogeneous nucleation is considered as an athermal process. The third is a constitutional supercooling model in which active nucleants are triggered by the constitutional undercooling at the front of growing crystals. All models remain uncertain to describe constitutionally the kinetics of heterogenous nucleation. In addition, the crystal growth rate affects significantly the heterogeneous nucleation events since growing crystals release solute atoms and heat. Therefore it is very important to approximate a flux of solute at the solid–liquid interface. In practical aspect, how to predict the grain size in the equiaxed zone is of interest. Equiaxed grains in front of growing columnar block the growth when the volume of equiaxed grains reaches a critical value, and eventually equiaxed zones are formed, i.e. columnar to equiaxed transition (CET). It is believed that the grain size in the equiaxed zone can be predicted using the cooling rate of remained melt at the time when CET occurs. In addition, further investigations on the efficiency variation of grain refiner are also required, although it is agreed that the efficiency decreases significantly with increasing amounts of nucleant.