中文摘要：

在二元合金相场模型研究的基础上，进行扩展获得了多元合金相场模型．以Al-Si-Mg三元合金为例，采用该相场模型实现了逼真地模拟多元合金凝固过程的等轴枝晶生长，得到了二次或更高次晶臂生长等复杂的枝晶形貌．随着第三组元Mg含量的减少，枝晶的二次枝晶越发达，枝晶中溶质的偏析越严重，枝晶尖端的生长速率和半径越大，与丁二腈．丙酮体系中枝晶尖端生长速率、半径随溶质浓度变化关系的理论计算和实验结果相符合．另外，枝晶初生晶臂中心的溶质浓度最低，在被二次晶臂包围的界面区域的溶质浓度最高；固液界面区域具有较大的浓度梯度，其中枝晶尖端前沿的梯度最大．

英文摘要：

A phase-field model for muhicomponent alloys based on the binary phase-field model has been developed. The isothermal dendritic growth of Al-Si-Mg alloys is presented as a numerical example, accordingly, the dendrite growing morphology of multicomponent alloys solidification could be simulated realistically using the phase-field model. As the result, the intricate figures such as secondary and tertiary dendrite arms are revealed. The decrease of solute Mg can trigger the growth of the secondary arms and increase the solute microsegregation rate, the tip speed and radius of dendrite. The variation of the speed and the radius in the dendrite tip agrees well with theoretical and experimental results in succinonitrile-acetone system. In addition, the spines of the primary arms have lowest concentration, and the mushy regions between the dendrite secondary arms have the highest concentration; the solute gradients are higher in the vicinity of the S/L interface regions, and highest in the tip.