中文摘要：

在二元合金元胞自动机模型的基础上，通过耦合多元合金热力学相平衡求解器PanEngine，建立了三元合金改进的元胞自动机模型，可模拟初生相枝晶的生长过程．模型考虑了曲率过冷和成分过冷对界面平衡溶质成分的影响，通过不同组元的无量纲溶质过饱和度方程和界面溶质守恒方程之间的耦合来求解界面生长速率，并通过PanEngine计算界面处的液相线温度．采用本模型模拟了A1—7％Si-χMg三元合金自由枝晶的生长形态，结果表明Mg含量的增加会抑制枝晶一次臂的生长和二次臂的产生．同时模拟了不同抽拉速度下A1-7％Si-0．5％Mg合金柱状枝晶的竞争生长过程，随着抽拉速度的增大，柱状枝晶一次枝晶臂间距逐渐减小，与Hunt理论模型符合较好．

英文摘要：

Based on the binary cellular automaton method, a modified cellular automaton model for temary alloys is developed to simulate dendrite growth controlled by solutal effects and microsegregation in the low Peclet number regime by coupling PanEngine, which is a multicomponent thermodynamic and equilibrium calculation engine. The model can be used to calculate the interfacial equilibrium composition by considering the influence of Gibbs-Thomson effect induced curvature undercooling, and multicomponents contributed constitutional undercooling. Meanwhile, the growth velocity of interface is determined by solving the solute conservation equation simultaneously with dimensionless solute supersaturation equation for each alloying element. Moreover, equilibrium liquidus temper- ature and equilibrium solid concentration at the interface are derived by PanEngine. Free dendrite growth of A1-7%Si-χMg temary alloys is simulated by the present model, which shows that the increase of solute Mg can suppress the growths of both primary and secondary dendrite arms. Meanwhile, constrained columnar dendrite growth of A1-7%Si-0.5%Mg with the increases of pulling veloc- ity and constant thermal gradient during directional solidification is calculated. The results reveal the competitive growth of columnar dendrites, and demonstrate that the primary dendrite arm spacing would decrease as the pulling velocity increases, which accords well with the Hunt model.