Time dependent Phase Diagram

时间相关相图是一种假设相图，它除了具有普通组成轴外还具有时间轴。因此，在无限的时间限制下，它出现一个平衡相图。为了处理时间相关的现象，这是时间相关相图的基础，我们使用了两种理论工具。一种是聚类变分法（和路径概率法），另一种是相场法。除了这两种方法外，电子结构计算也尝试进行第一性原理计算。相场法由Cahn-Hilliard扩散方程和随时间变化的Ginzubrug - Landau方程组成。通常采用相场法来处理微观结构的演化过程，很少尝试进行原子计算。而聚类变分法是原子理论，处理离散晶格上的统计力学问题。为了能够一致地描述从原子尺度到微观尺度的多尺度现象，引入适当的粗粒化过程是必不可少的。重整化群论是一种严谨的数学工具，但将其应用于具体问题却不是一件容易的事。本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，可以提供合理的结果，并且足够有效，可以在合理的时间尺度内进行计算。该方法使我们能够尝试对Fe-Pd和Fe-Pt体系无序l10跃迁相关的反相边界时间演化过程进行第一性原理计算。这个过程是相当强大的，但是时间尺度的粗粒度仍然是未来的主题。这将通过扩展路径概率法来解决，并且已经尝试了初步的计算。

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.