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

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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.