The phase field model is developed by the effective mobility approach to slow and rapid solidification. The phase field model equations are reduced to the hodograph equation for solid-liquid interface movement which is applied to the problem of solute trapping in a binary alloy. A specific method based on the one-point Cauchy problem is developed for solution of the hodograph equation with the solute diffusion equation. The method is tested in comparison with the rapid solidification of Si–0.1 at.% As alloy previously analyzed experimentally and using phase field modelling.

中文翻译：

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有效迁移率方法中二元系统中的溶质俘获现象和全息图方程

相场模型是通过有效的流动性方法开发的，以实现缓慢而快速的凝固。相场模型方程简化为固液界面运动的全息图方程，该方程适用于二元合金中的溶质俘获问题。提出了一种基于单点柯西问题的具体方法来求解带溶质扩散方程的全息图方程。与先前通过实验和使用相场模型分析的Si–0.1 at。％As合金的快速凝固相比较，对该方法进行了测试。