Brunini Victor E, Schuh Christopher A, Carter W Craig
Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Feb;83(2 Pt 1):021119. doi: 10.1103/PhysRevE.83.021119. Epub 2011 Feb 28.
Percolation thresholds and critical exponents for universal scaling laws are computed for microstructures that derive from phase-transformation processes in two dimensions. The computed percolation threshold for nucleation and growth processes, p(c)≈0.6612, is similar to those obtained by random placement of disks and greater than that of spinodal decomposition, p(c)≈0.4987. Three critical exponents for scaling behavior were computed and do not differ significantly from universal values. The time evolution of a characteristic microstructural length was also computed: For spinodal decomposition, this length grows according to a power law after a short incubation period; for nucleation and growth, there are several transitions in the nature of the growth law. We speculate that the transitions in nucleation and growth derive from competing effects of coalescence at short times and then subsequent coarsening. Short-range order is present, but different, for both classes of microstructural evolution.
针对源自二维相变过程的微观结构，计算了通用标度律的渗流阈值和临界指数。通过成核与生长过程计算得到的渗流阈值(p(c)≈0.6612)，与通过随机放置圆盘得到的结果相似，且大于旋节线分解的渗流阈值(p(c)≈0.4987)。计算了标度行为的三个临界指数，其与通用值并无显著差异。还计算了特征微观结构长度的时间演化：对于旋节线分解，在短暂的孕育期后，该长度按照幂律增长；对于成核与生长，生长规律的性质存在若干转变。我们推测，成核与生长过程中的转变源于短时间内聚结以及随后粗化的竞争效应。对于这两类微观结构演化，均存在短程有序，但有所不同。
