Katsuyo Thornton

L.H. and F.E. Van Vlack Professor


2022 HH Dow
T: (734) 615-1498




Topological Complexity and the Dynamics of Coarsening

Sponsor: Department of Energy
Dendritic microstructures are commonly observed during the solidification of alloys. These topologically complex structures are altered through a coarsening, or Ostwald ripening, process in nearly isothermal conditions. Since the resultant size scale of the dendritic microstructure influences the overall mechanical properties of the solidified alloy, complete characterization of the coarsening process is necessary. To fully capture these complicated structures, three-dimensional reconstructions are created using serial sections. By ensuring that the serial sections are obtained with a high degree of accuracy and resolution, many properties can be measured and used to characterize the coarsening process. Since coarsening is driven by surface curvature, measurement of the mean and Gaussian interfacial curvature can be used as a characterization method by measuring the probability of finding an interfacial patch with a given curvature range. The orientation of the microstructure can be quantified by performing stereographic projections of the interfacial normals of the microstructure. Stereographic projections collapse the three-dimensional spacial orientation of the microstructure into a two-dimensional image that facilitates the detection of any directionality found in the microstructure. Further characterization of the coarsening process can be obtained by examining the topological properties of the microstructure. The three aspects that can be reported through topological characterization within the unit volume analyzed are the number of independent bodies, the genus, and the total number of handles within the microstructure. These measurements may prove beneficial for the study of coarsening in microstructures with dendritic morphologies. Theory and experiment can be coupled by using the experimentally measured three-dimensional microstructure as an initial condition for phase-field calculations. These results can be used to predict the evolution of the microstructure in curvature space and, along with the phase-field calculated interfacial velocity, provide insight into the complex mechanisms involved with the coarsening process. Increased knowledge of the coarsening process ultimately aids in the understanding of solidification as a whole. This understanding will increase the design and predictability of the performance in products that undergo solidification as a manufacturing step.
Highlights (Click an image for more information)
  • Three Dimensional Reconstruction of Interfacial Morphologies

    A small portion of the three-dimensional reconstruction of the experimentally measured interfacial morphology after 90 minutes of coarsening is shown. The solid phase is transparent with the liquid regions intersecting the edges of the reconstruction box being capped. The three-dimensional reconstruction was created by accurately stacking serial sections taken from the sample. The microstructure is primarily composed of undulating walls of liquid and liquid tubes.

  • Curvature Flow Diagram Corresponding to Interfacial Morphologies

    This experimentally measured intensity plot shows the most probable interfacial shapes for a given curvature range found within the 90-minute coarsened sample. The largest peak corresponds to the bends in the liquid walls, while the secondary peak arises from the presence of liquid tubes. The overlaid arrows are predicted flux in curvature space from a phase-field calculation that predicts the evolution of the 10-minute coarsened sample, which point to increasing probability of cylindrical surfaces in agreement with experimental results.