Probing fractal abnormal grain growth at the nanoscale: a percolation scenario with microstructurally based selection rules
Final Report Abstract
Thanks to their large grain boundary (GB) area per unit volume, nanocrystalline materials find themselves quite far removed from thermodynamic equilibrium, as the excess energy stored in GBs 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 much-smaller grains remaining in the surrounding matrix. Such behavior is sometimes observed in conventional, microcrystalline metals and ceramics, as well, but it is not their usual mode of coarsening. Surprisingly, neither at micrometer length scales nor at the nanoscale do we have an adequate grasp of the circumstances enabling abnormally growing grains to establish and maintain a growth advantage over their neighbors. This mystery is compounded in nanocrystalline Pd-Au alloys by the fact that abnormally growing grains quickly develop highly irregular, almost tumor-like shapes. In fact, the resulting grain perimeters are so convoluted that they resemble fractal objects! Needless to say, our usual notion of curvature-driven GB migration fails to explain the persistence of these boundary fluctuations, as the conventional mechanism should smoothen out any such fluctuations instead of accentuating them. Inspired by this apparent contradiction, we hypothesized in the F RACTAL AGG project that, at the nanoscale, abnormal grain growth may be governed by a GB migration mechanism quite different from that active in conventional polycrystals. Instead of each point along a GB moving at a rate proportional to the boundary’s local mean curvature (i.e., curvature-driven growth), a grain might grow “fractally” by a process similar to percolation, in which some kind of selection rule—based presumably on the microstructure in and around a given segment of a GB—determines the optimal direction of boundary migration (e.g., the direction that lowers the specimen’s excess free energy as quickly as possible). We scrutinized this concept using a combination of state-of-the-art electron microscopy techniques and phase field-based computational simulations of microstructural evolution. Assuming a coalescence model mediated by nanograin rotations, we were able to generate boundary morphologies having a similar fractal dimension to that observed in electron backscatter diffraction (EBSD) mappings. However, a more sophisticated box-counting analysis of higher-resolution EBSD images revealed spatial boundary fluctuations to be largely absent in the submicrometer regime. Initially, we attributed this finding to GB smoothing that had occurred after impingement of the abnormally growing grains, but an automated crystal orientation mapping (ACOM) performed on the interface between an abnormal grain and its neighboring nanograins confirmed that abnormal grain perimeters are smooth at the nanoscale, even when they are moving through the matrix. This discovery rules out the rotation-based mechanism as well as any other concept that relies on local differences at the level of individual matrix grains. Consequently, we had to abandon our original percolation hypothesis. Although puzzling at first, the “crossover” from locally smooth GB migration at the nanoscale to spatial fluctuations growing in amplitude over micrometer distances appears to be a natural consequence of a competition between, on the one hand, the usual curvature-based driving force for GB migration and, on the other hand, drag forces that impede this migration. The strength of the latter—which can be attributed to phenomena like Zener pinning and/or the segregation of solute and impurity atoms to GBs—determines a critical length scale above which curvature-based forces no longer are able to suppress the development of boundary fluctuations. In conventional polycrystals, we do not observe fractal boundaries because the high temperatures needed to induce grain growth lower the strength of the drag terms and raise the critical length scale for crossover to distances well above the grain size. In nanocrystalline materials, however, GBs migrate at much lower temperatures, which permits abnormal grains to grow beyond the critical size for crossover—a fact that is reflected in the morphology of the resulting grain perimeters. The generality of this explanation implies that it should apply to any material that manifests abnormal grain growth out of an initially nanocrystalline state.
Publications
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“Abnormal grain growth mediated by fractal boundary migration at the nanoscale.” Scientific Reports 8 (2018) 1592
Christian Braun, Jules M. Dake, Carl E. Krill III, and Rainer Birringer
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“Influence of rapid annealing on the evolution of fractal abnormal grains in nanocrystalline Pd–10 at% Au.” IOP Conference Series: Materials Science and Engineering 580 (2019) 012055
Raphael A. Zeller, Harms J. Fey, Christian Braun, Rainer Birringer, and Carl E. Krill III
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“Orientation mapping linked to fractal analysis: A method for studying abnormal grain growth in nanocrystalline PdAu.” Journal of Applied Physics 128 (2020) 185109
Christian Braun, Raphael A. Zeller, Hanadi Menzel, Jörg Schmauch, Carl E. Krill III, and Rainer Birringer
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“Structural relaxation of nanocrystalline PdAu alloy: Mapping pathways through the potential energy landscape.” Journal of Applied Physics 127 (2020) 125115
Michael J. Deckarm, Nils Boussard, Christian Braun, and Rainer Birringer
