Extension of the Johnson-Mehl-Avrami-Kolmogorov theory incorporating anisotropic growth studied by Monte Carlo simulations
Extension of the Johnson-Mehl-Avrami-Kolmogorov theory incorporating anisotropic growth studied by Monte Carlo simulations
复制标题
DOI：
10.1103/physrevb.73.054103
复制
发表时间：
2006-02
影响因子：
3.7
通讯作者：
B. Kooi
中科院分区：
文献类型：
--
作者：
B. Kooi
基于Monte Carlo（MC）模拟，建立了一个描述d-1维生长在d维空间（d为2或3）中的成核和随后的生长等温相变动力学的解析理论。这种类型的增长是感兴趣的，因为它通常是各向异性的，导致硬碰撞，并获得从传统的Johnson-Mehl-Avrami-Kolmogorov（JMAK）理论的强烈偏差。在MC模拟中，一维生长可以在二维空间中的两个或三个不同的非平行方向上以相等的概率发生。在3D空间中，2D生长可以在三个（或两个）不同的正交方向上以相等的概率发生。MC模拟表明，最初总是一个政权是存在的JMAK理论占上风，但经过一个明确的临界时间过渡到阻塞制度发生。这两个制度的特点是明显不同的，但几乎恒定的值的Avrami指数，这取决于生长和空间的维数和时间依赖性的成核。的临界时间和扩展分数内的阻塞制度（基于扩展体积的JMAK理论的概念）的成核和生长参数的依赖性已被广泛分析和MC模拟的所有结果已被捕获内的分析理论。
An analytical theory has been developed, based on Monte Carlo (MC) simulations, describing the kinetics of isothermal phase transformations proceeding by nucleation and subsequent growth for d-1 dimensional growth in d dimensional space (with d 2 or 3). This type of growth is of interest since it is generally anisotropic, leads to hard impingement, and obtains strong deviations from the traditional Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. Within the MC simulations 1D growth can occur with equal probability in two or three different nonparallel orientations in 2D space. In 3D space 2D growth can occur with equal probability in three (or two) different orthogonal orientations. The MC simulations show that initially always a regime is present where JMAK theory prevails, but that after a well-defined critical time a transition to a blocking regime occurs. Both regimes are characterized by clearly different, but nearly constant values of the Avrami exponent which depend on the dimensionality of growth and space and on the time dependence of nucleation. The dependence of the critical time and of the extended fraction within the blocking regime (based on the concept of the extended volume of the JMAK theory) on the nucleation and growth parameters has been extensively analyzed and all results of the MC simulations have been captured within the analytical theory.