Phase field model for dendritic growth with impurities

Abstract

A phase field model is used to study dendritic growth in a media with impurities. The model consists of a square lattice where a parameter [Formula: see text] can take values between [Formula: see text] and [Formula: see text] at each site. A site is in the solid phase for [Formula: see text], in the liquid phase for [Formula: see text], and the solid-liquid interface is expressed by [Formula: see text]. A fraction of the sites are considered impurities that cannot be solidified, i.e. [Formula: see text] is fixed and taken as zero. These impurities are distributed randomly. As the probability [Formula: see text] of impure sites in the lattice increases, the growth loses its dendritic characteristic. It is shown that the perimeter of the growing solid goes from quadratic to a linear function with time. It was also found that as the probability of impurities reaches [Formula: see text], the solid undergoes a transition from anisotropic to isotropic growth.