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Time dependent Phase Diagram

时间相关相图

基本信息

批准号：
17560580
负责人：
MOHRI Tetsuo
金额：
$ 2.05万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17560580/
关键词：
Phase Diagram Cluster Variation Method Phase Field Method Path Probability Method Coarse graining 自己触媒反応時空粗視化スケーリング則

项目摘要

Time dependent phase diagram is a hypothetical phase diagram which posses a time axis in addition to an ordinary composition axis. Hence, in the infinite time limit, it emerges to an equilibrium phase diagram. In order to deal with time dependent phenomena which is the basis of the time dependent phase diagram, we employed two theoretical tools. One is the Cluster Variation Method (and Path Probability Method) and the other is the Phase Field Method. In addition to these two methods, electronic structure calculation is also attempted to perform first-principles calculations. The Phase Field Method consists of Cahn-Hilliard diffusion equation and Time dependent Ginzubrug Landau equation. In general, Phase filed Method is employed to deal with microstructure evolution process and not much attempt has been performed for atomistic calculations. While Cluster Variation Method is the atomistic theory and deal with the statistical mechanics on the discrete lattice. In order to describe the multiscale phenomena from atomistic to microstructural scale in a consistent manner, it is indispensable to introduce a proper coarse graining procedure. The renormalization group theory is a rigorous mathematical tool, however it is not an easy task to apply the theory to individual problems. The body of this project has been devoted to establish and introduce coarse graining procedure which is proper enough to provide a reasonable result and efficient enough to perform calculations within a reasonable time scale. The developed method enables us to attempt first principles calculation of time evolution process of Anti Phase Boundary associated with the disorder-L10 transition for Fe-Pd and Fe-Pt systems. The procedure is quite powerful, however the coarse graining of the time scale remains as the future subject. This will be settled by extending Path Probability Method, and preliminary calculations are already attempted.

含时相图是一种假想的相图，它除了包含一个通常的成分轴外，还包含一个时间轴。因此，在无限的时间限制下，它会出现一个平衡相图。为了处理作为含时相图基础的含时现象，我们采用了两种理论工具。一种是簇变分法（和路径概率法），另一种是相场法。除了这两种方法，电子结构计算也尝试进行第一性原理计算。相场法由Cahn-Hilliard扩散方程和含时的Ginzubrug朗道方程组成。相场法一般用于处理微观结构的演化过程，对原子级计算的尝试不多。而集团变分法是原子论的理论，处理的是离散格点上的统计力学。为了以一致的方式描述从原子尺度到微观结构尺度的多尺度现象，引入适当的粗粒化过程是必不可少的。重整化群理论是一种严格的数学工具，然而将其应用于具体问题却不是一件容易的事情。该项目的主体致力于建立和引入粗粒化程序，该程序足够适当以提供合理的结果，并且足够有效以在合理的时间范围内执行计算。该方法使我们能够尝试用第一性原理计算Fe-Pd和Fe-Pt体系的无序-L10相变反相边界的时间演化过程。该过程是相当强大的，但是时间尺度的粗粒化仍然是未来的主题。这将通过扩展路径概率方法来解决，并且已经尝试了初步的计算。