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arXiv 0802.0732cond-mat.mtrl-sci
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相场模型中均匀形核与生长的胞元动力学直接数值模拟

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Masao Iwamatsu

摘要:

采用胞元动力学方法对最简单的二维相场模型中的均匀形核和生长过程进行了数值研究。从成核到生长的整个过程进行了模拟,并显示密切遵循Kolmogorov-Johnson-Mehl-Avrami(KJMA)的相变的情况。新稳定相的体积分数随时间的变化符合KJMA公式。通过拟合KJMA公式直接模拟数据,不仅Avrami指数,但成核速率的大小,特别是,孵化时间的定量研究。修正的Avrami图也被用来验证导出的KJMA参数。发现Avrami指数接近理想理论值m=3。成核速率的温度依赖性遵循经典成核理论所预期的激活型行为。另一方面,孵育时间的温度依赖性不遵循指数激活型行为。相反,温育时间与根据Shneidman和Weinberg的理论[J. Non-Cryst. Solids { \bf 160},89(1993)]预测的温度成反比。此外,还讨论了在仿真中限制热噪声以推导正确的Avrami指数的必要性.

英文摘要:

Homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. Whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m=3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.

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