Kim Seong Gyoon, Kim Dong Ik, Kim Won Tae, Park Yong Bum
Department of Materials Science and Engineering, Kunsan National University, Kunsan 573-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Dec;74(6 Pt 1):061605. doi: 10.1103/PhysRevE.74.061605. Epub 2006 Dec 27.
We developed an efficient computation scheme for the phase-field simulation of grain growth, which allows unlimited number of the orientation variables and high computational efficiency independent of them. Large-scale phase-field simulations of the ideal grain growth in two-dimensions (2D) and three-dimensions (3D) were carried out with holding the coalescence-free condition, where a few tens of thousands grains evolved into a few thousand grains. By checking the validity of the von Neumann-Mullins law for individual grains, it could be shown that the present simulations were correctly carried out under the conditions of the ideal grain growth. The steady-state grain size distribution in 2D appeared as a symmetrical shape with a plateau slightly inclined to the small grain side, which was quite different from the Hillert 2D distribution. The existence of the plateau stems from the wide separation of the peaks in the size distributions of the grains with five, six, and seven sides. The steady-state grain size distribution in 3D simulation of the ideal grain growth appeared to be very close to the Hillert 3D distribution, independent of the initial average grain size and size distribution. The mean-field assumption, the Lifshitz-Slyozov stability condition, and all resulting predictions in the Hillert 3D theory were in excellent agreement with the present 3D simulation. Thus the Hillert theory can be regarded as an accurate description for the 3D ideal grain growth. The dependence of the growth rate in 3D simulations on the grain topology were discussed. The large-scale phase-field simulation confirms the 3D growth law obtained from the Surface Evolver simulations in smaller scales.
我们开发了一种用于晶粒生长相场模拟的高效计算方案，该方案允许无限数量的取向变量，并且与它们无关的情况下具有高计算效率。在保持无聚结条件下，对二维（2D）和三维（3D）理想晶粒生长进行了大规模相场模拟，其中数万个晶粒演变成数千个晶粒。通过检查单个晶粒的冯·诺依曼-穆林斯定律的有效性，可以表明当前模拟是在理想晶粒生长条件下正确进行的。二维中的稳态晶粒尺寸分布呈现出对称形状，有一个向小晶粒侧略微倾斜的平台，这与希勒特二维分布有很大不同。该平台的存在源于具有五、六和七条边的晶粒尺寸分布中峰值的广泛分离。理想晶粒生长的三维模拟中的稳态晶粒尺寸分布似乎非常接近希勒特三维分布，与初始平均晶粒尺寸和尺寸分布无关。希勒特三维理论中的平均场假设、利夫希茨-斯廖佐夫稳定性条件以及所有由此得出的预测与当前的三维模拟非常吻合。因此，希勒特理论可以被视为对三维理想晶粒生长的准确描述。讨论了三维模拟中生长速率对晶粒拓扑结构的依赖性。大规模相场模拟证实了从小尺度表面演化器模拟中获得的三维生长定律。
