Time dependent Phase Diagram

时间相关相图是一种假设的相图，除了普通的成分轴之外，还具有时间轴。因此，在无限的时间限制内，出现平衡相图。为了处理作为时间相关相图基础的时间相关现象，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。除了这两种方法外，还尝试电子结构计算来进行第一性原理计算。相场法由 Cahn-Hilliard 扩散方程和时间相关的 Ginzubrug Landau 方程组成。一般而言，采用相场法来处理微观结构演化过程，对于原子计算的尝试较少。而簇变分法是原子理论，处理离散晶格上的统计力学。为了以一致的方式描述从原子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，但将该理论应用于个别问题并不是一件容易的事。该项目的主体致力于建立和引入粗粒度程序，该程序足够合适以提供合理的结果，并且足够高效以在合理的时间范围内执行计算。所开发的方法使我们能够尝试与 Fe-Pd 和 Fe-Pt 体系的无序-L10 转变相关的反相边界时间演化过程的第一性原理计算。该过程非常强大，但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.