Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Post Office Box 49, H-1525 Budapest, Hungary.
Laboratoire Physique de la Matière Condensée, École Polytechnique, Centre National de la Recherche Scientifique, Université Paris-Saclay, 91128 Palaiseau Cedex, France.
Phys Rev E. 2017 May;95(5-1):053303. doi: 10.1103/PhysRevE.95.053303. Epub 2017 May 9.
In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a log-normal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [R. Kobayashi, J. A. Warren, and W. C. Carter, Physica D 140, 141 (2000)PDNPDT0167-278910.1016/S0167-2789(00)00023-3; H. Henry, J. Mellenthin, and M. Plapp, Phys. Rev. B 86, 054117 (2012)PRBMDO1098-012110.1103/PhysRevB.86.054117] that an insufficient resolution of the small angle grain boundaries leads to a log-normal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our paper indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.
在文献中，关于二维和准二维多晶系统中晚期晶粒长大特征的极限（长时间）晶粒尺寸分布（LGSD）的形式，已经发表了相互矛盾的结果。虽然实验和相场晶体（PFC）模型（一种简单的动力密度泛函理论）表明存在对数正态分布，但其他工作，包括基于依赖粗粒场的常规相场模拟的理论研究，如多相场（MPF）和取向场（OF）模型，得出了明显不同的分布。在最近的一项工作中，我们已经表明，粗粒相场模型（无论是 MPF 还是 OF）产生的极限尺寸分布非常相似，这些分布似乎与理论预测不同。在此，我们重新研究了这个问题，并在 OF 模型的情况下进行了演示[R. Kobayashi, J. A. Warren, and W. C. Carter, Physica D 140, 141 (2000)PDNPDT0167-278910.1016/S0167-2789(00)00023-3; H. Henry, J. Mellenthin, and M. Plapp, Phys. Rev. B 86, 054117 (2012)PRBMDO1098-012110.1103/PhysRevB.86.054117]，即小角度晶界分辨率不足会导致接近实验和分子尺度 PFC 模拟中观察到的对数正态分布。我们的论文进一步表明，LGSD 对评估过程的细节非常敏感，并提出了 LGSD 结果之间的差异可能源于小角度晶界检测差异的可能性。
