The phase field technique for modeling multiphase materials
The phase field technique for modeling multiphase materials
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DOI：
10.1088/0034-4885/71/10/106501
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发表时间：
2008-10
影响因子：
18.1
通讯作者：
I. Singer-Loginova;H. Singer
中科院分区：
文献类型：
--
作者：
I. Singer-Loginova;H. Singer
本文综述了计算材料科学中发展最快的领域之一相场技术的方法和应用。相场法是一种理论和计算工具，用于预测材料中任意形状形态和复杂微观结构的演变。在该方法中，两相（例如固体和液体）之间的界面被处理为具有不同物理量的逐渐变化的有限宽度的区域，即它是扩散界面模型。引入了一个辅助变量，即相场或序参量，它将一个相与另一个相区分开来。通过相场的变化来识别界面。我们开始介绍了相场法的物理背景，并给出了详细的相场方程的数学推导。我们演示了如何在相界面的平衡和非平衡物理现象被纳入相场方法。然后，我们详细地解决纯合金和多元合金的枝晶和定向凝固，自然对流和强制流动的影响，晶粒生长，形核，固-固相变和突出相场方法的其他应用。特别是，我们回顾了新的相场晶体模型，它结合了原子的长度尺度与扩散的时间尺度。我们还讨论了定量相场建模方面，如薄界面渐近分析和耦合到热力学数据库。相场法求解偏微分方程组需要进行大量的计算，因而限制了相场法的应用范围。随后，我们回顾了数值方法来解决相场方程，并提出了各向异性拉普拉斯算子的有限差分离散。
This paper reviews methods and applications of the phase field technique, one of the fastest growing areas in computational materials science. The phase field method is used as a theory and computational tool for predictions of the evolution of arbitrarily shaped morphologies and complex microstructures in materials. In this method, the interface between two phases (e.g. solid and liquid) is treated as a region of finite width having a gradual variation of different physical quantities, i.e. it is a diffuse interface model. An auxiliary variable, the phase field or order parameter , is introduced, which distinguishes one phase from the other. Interfaces are identified by the variation of the phase field. We begin with presenting the physical background of the phase field method and give a detailed thermodynamical derivation of the phase field equations. We demonstrate how equilibrium and non-equilibrium physical phenomena at the phase interface are incorporated into the phase field methods. Then we address in detail dendritic and directional solidification of pure and multicomponent alloys, effects of natural convection and forced flow, grain growth, nucleation, solid–solid phase transformation and highlight other applications of the phase field methods. In particular, we review the novel phase field crystal model, which combines atomistic length scales with diffusive time scales. We also discuss aspects of quantitative phase field modeling such as thin interface asymptotic analysis and coupling to thermodynamic databases. The phase field methods result in a set of partial differential equations, whose solutions require time-consuming large-scale computations and often limit the applicability of the method. Subsequently, we review numerical approaches to solve the phase field equations and present a finite difference discretization of the anisotropic Laplacian operator.