Low artificial anisotropy cellular automaton model and its applications to the cell-to-dendrite transition in directional solidification

Abstract

A low artificial anisotropy cellular automaton (CA) model is developed for the simulation of microstructure evolution in directional solidification. The CA model's capture rule was modified by a limited neighbor solid fraction (LNSF) method. Various interface curvature calculation methods have been compared. The simulated equilibrium shapes agree with the theoretical shapes, when the interface energy anisotropy coefficient is {\epsilon}=0.01, {\epsilon}=0.03 and {\epsilon}=0.05, respectively.The low artificial anisotropy CA model is used in the numerical simulation of the cell-to-dendrite transition (CDT) in directional solidification. The influence of physical parameters ({\Gamma}, Dl, k0, ml) on CDT has been investigated. The main finding in this paper is the discovery of the changing behavior of the Vcd when the solute partition coefficient k0 is larger than a critical value. When k0 is less than 0.125, the Vcd follows the Kurz and Fisher criterion Vc/k0; while when k0>0.125, the Vcd equals to 8Vc. The experimental data of succinonitrile-acetone (SCN-ace, k0=0.1) and SCN-camphor (k0=0.33) support the conclusion from CA simulations.