Probing fractal abnormal grain growth at the nanoscale: a percolation scenario with microstructurally based selection rules

由于其每单位体积的大的晶界面积，纳米晶材料发现它们自身远离热力学平衡，因为储存在晶界中的过量能量为纳米级微结构的粗化提供了巨大的驱动力。所得到的晶粒生长通常以异常的方式进行，其中小部分晶粒以仍然存在于周围基质中的纳米尺寸的晶粒为代价生长到极大的尺寸。这种行为也在常规的粗晶粒多晶金属和陶瓷中观察到，尽管这不是它们通常的粗化模式。令人惊讶的是，无论是在微米尺度还是在纳米尺度上，我们都没有充分掌握使异常生长的颗粒能够建立并保持相对于其邻居的显着生长优势的环境。这个谜团在纳米尺度上更加复杂，最近的研究发现，纳米晶体模型系统（Pd和Pd-Au合金）中异常生长的晶粒会形成高度不规则的，几乎像肿瘤一样的形状！相应的晶粒周长被发现是分形的性质，很像那些通过随机分布的钉扎位点域壁的强制迁移后形成的结构。此外，这些异常生长的晶粒表现出分形维数，密切配合已知的渗流processes. Inspiration所产生的域，我们假设，异常晶粒生长可以理解为在纳米级的表现形式的渗流现象发生在“网络”所定义的纳米晶基体晶粒的初始排列。这一概念将通过结合最先进的电子显微镜和大规模相场模拟微观结构的演变进行审查。逾渗方案的最大优点是，一方面，它可以对加速边界迁移的各种“选择规则”进行探索性测试（评估它们对分形发展的影响），另一方面，为缩小微观因素的实验研究范围提供了一个框架，（如晶界取向差或浓度梯度）可能与控制分形异常晶粒生长的物理机制相关。最终，实验结果将被翻译成一个最小的选择规则集，并插入到一个修改后的相场模型，允许同时异常和曲率驱动的晶粒生长。模拟结果将进行验证，相对于统计平均和本地的生长动力学和晶粒形态的措施。

Thanks to their large grain boundary area per unit volume, nanocrystalline materials find themselves quite far removed from thermodynamic equilibrium, as the excess energy stored in grain boundaries provides a huge driving force for coarsening of the nanoscale microstructure. The resulting grain growth typically proceeds in an abnormal manner, with a small fraction of grains growing to extremely large sizes at the expense of the nanometer-sized grains still present in the surrounding matrix. Such behavior is also observed in conventional, coarser-grained polycrystalline metals and ceramics, although it is not their usual mode of coarsening. Surprisingly, neither at the microscale nor at the nanoscale do we have an adequate grasp of the circumstances enabling abnormally growing grains to establish and maintain a remarkable growth advantage over their neighbors. This mystery is compounded at the nanoscale, where recent studies discovered that abnormally growing grains in nanocrystalline model systems (Pd and Pd-Au alloys) develop highly irregular, almost tumor-like shapes! The corresponding grain perimeters are found to be fractal in nature, much like those of structures formed upon the forced migration of domain walls through a randomly distributed field of pinning sites. Moreover, these abnormally growing grains exhibit fractal dimensionalities that closely match those of domains generated by known percolation processes.Inspired by this observation, we hypothesize that abnormal grain growth can be understood at the nanoscale as a manifestation of a percolation phenomenon occurring on a "network" defined by the initial arrangement of nanocrystalline matrix grains. This concept will be scrutinized by a combination of state-of-the-art electron microscopy and large-scale phase field simulation of microstructural evolution. The great advantage of the percolation scenario is its amenability to, on the one hand, exploratory testing of various "selection rules" for accelerated boundary migration (evaluating their impact on the development of fractality) and, on the other hand, providing a framework for narrowing down the experimental search for microscopic factors (such as grain boundary misorientations or concentration gradients) of possible relevance to the physical mechanism(s) governing fractal abnormal grain growth. Ultimately, the experimental findings will be translated into a minimal set of selection rules and inserted into a modified phase field model allowing for simultaneous abnormal and curvature-driven grain growth. The simulation results will be validated with respect to statistically averaged and local measures for growth kinetics and grain morphologies.