Reverse engineering the kinetics of grain growth by time-resolved 3D microstructural mapping combined with tessellation-based modeling

尽管在多晶材料中晶粒生长已经研究了几十年，但我们对其潜在机制的理解仍然不完整。这一现象的某些方面——比如大晶粒以牺牲小晶粒为代价而生长的趋势——可以归因于弯曲晶界（GBs）受到指向其曲率中心的净力。其他方面，比如单个颗粒大小和形状的变化，就不容易解释了；在这方面，即使是大规模的计算机模拟也不能产生令人满意的结果，特别是当应用于显示异常晶粒生长的实际系统时。在竞争激烈的工业世界中，公司有时试图通过观察内部部件的相互作用来推断其工作原理，从而对竞争对手的产品进行“逆向工程”。我们建议将类似的策略应用于晶粒生长，假设上述差异可以追溯到GB的“降低迁移率”，这是一个鲜为人知的特征，等于GB速度除以平均曲率。传统的测量迁移率降低的方法可以得到一个特定的GB取向偏差和倾角组合的值，但是为了建立真实的晶粒生长模型，我们需要知道在五维GB参数空间中所有位置的迁移率降低情况。逆向工程通过并行而不是顺序地确定数以万计的降低迁移率值来应对这一挑战！这是可行的，这要归功于基于同步加速器的x射线显微镜的绘图能力，我们将应用于表现正常生长的铝合金和另一种生长异常的铝合金。在等温退火步骤之间记录的三维微观结构快照中，我们将跟踪数千gb随时间的形貌和取向错误。利用扭曲镶嵌的新概念拟合GB网络，我们将得到解析的GB参数化，从而得到局部的GB曲率和倾角。单个GB区域的新颖“轨迹分析”将提供局部GB位移和速度。这些量加在一起，降低了迁移率。后一个量对GB错取向和倾斜度的依赖将使用copulas数学建模，并且神经网络Ansatz将对基于镶嵌的方法进行基准测试，作为该方法常规应用的潜在途径。最后，将结果输入到相场模型中，以评估真实降低的GB迁移率在多大程度上提高了计算机模拟与实验的一致性。如果这样的输入也能使模拟产生异常的晶粒生长，那么我们就证明了异常GB迁移的根本原因是迁移率降低对GB错取向和倾斜的依赖。

Although grain growth has been studied in polycrystalline materials for decades, our understanding of its underlying mechanisms remains incomplete. Some aspects of the phenomenon—such as the tendency of larger grains to grow at the expense of their smaller neighbors—can be attributed to curved grain boundaries (GBs) experiencing a net force directed toward their center of curvature. Other aspects, like the change in size and shape of individual grains, do not lend themselves to such easy explanation; in this regard, not even large-scale computer simulations yield satisfactory results, particularly when applied to real systems exhibiting abnormal grain growth.In the cutthroat world of industry, companies sometimes try to “reverse engineer” a competitor’s product by extrapolating from the observed interplay of internal parts to the working principle. We propose applying a similar strategy to grain growth, presuming that the aforementioned discrepancies can be traced to the “reduced mobility” of GBs, a poorly understood characteristic equal to the GB velocity divided by mean curvature. Conventional methods for measuring reduced mobility yield a value for a particular combination of GB misorientation and inclination, but to develop realistic models of grain growth we need to know the reduced mobility at all locations in the five-dimensional GB parameter space.Reverse engineering meets this challenge by determining tens of thousands of reduced mobility values in parallel rather than sequentially! This is feasible thanks to the mapping capability of synchrotron-based x-ray microscopies, which we will apply to an Al alloy manifesting normal growth and another one that grows abnormally. In 3D microstructural snapshots recorded between isothermal annealing steps, we will track the morphology and misorientation of thousands of GBs over time. Fitting the network of GBs using the new concept of warped tessellations, we will obtain analytic GB parameterizations, from which the local GB curvature and inclination follow. A novel “trajectory analysis” of individual GB regions will deliver local GB displacements and velocities. Together, these quantities give the reduced mobility.The latter quantity’s dependence on GB misorientation and inclination will be modeled using the mathematics of copulas, and a neural network Ansatz will be benchmarked against the tessellation-based approach as a potential avenue toward routine application of the method. Finally, the results will be input into a phase field model to assess the degree to which true reduced GB mobilities improve the agreement of computer simulations with experiment. If such input also enables simulations to generate abnormal grain growth, then we will have demonstrated that the underlying cause of abnormal GB migration is encoded in the reduced mobility’s dependence on GB misorientation and inclination.