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

• Applicants: Professor Carl Emil Krill III, Ph.D.; Professor Dr. Volker Schmidt
• Subject Area: Computer-Aided Design of Materials and Simulation of Materials Behaviour from Atomic to Microscopic Scale ; Mathematics ; Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 453092613

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.

• DFG Programme: Research Grants