相场方法及其在晶体生长中的应用

相场方法已被发掘出用于直接求解时的自由边界问题－著名的斯特藩方程。该方法作为晶体生长过程中模拟复杂图形成图的计算工具，已呈现出强有力的生命力。目前的研究在于努力发展精巧的计算技术，以便于晶体生长和金属凝固过程进行了理论模拟，而这些技术将有可能方法地应用于工业流程。相场方法之所以具有吸引力，基于如下事实：在计算机模拟过程中，即可避免对于边界实时追踪，又不需要反复判别是否满足显式边界条件。在过去的10年中，它已逐步被用于研究晶体生长的基础课题。诸如；热质输运，晶体生长动力学，二维和三维枝晶生长，图形选择，生长形态和显微结构等。本文对相场方法进行评述，同时给出其最新应用结果。

Phase-field Method and Application in Crystal Growth

The phase-field method has been explored to solve directly the full time dependent free boundary problem described as well known Stefan equations and it has recently emerged as a viable computational tool for simulating formation of complex interfacial patterns in crystal growth. Recent research efforts have led to development of sophisticated computational techniques for modeling important dynamical processes in crystal growth and solidification. These techniques are applicable to the wide range of industrial processes. Its attractiveness is from the fact that explicit tracking of the interface and explicitly satisfying interfacial boundary conditions is completely avoided. In the past decade,the phase field method has been used to study the fundamental subjects on crystal growth, such as the transport of heat and /or solute,the kinetics of crystal growth, the two and three dimensional dendritic growth,the pattern selection,the crystal morphology and microscopic structure etc.An overview of the phase field method and somes new results for its application are given in this paper.