When 10:00 AM - 12:00 PM Jun 23, 2016
Where 1670 Beyster Building
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Analysis of Coarsening of Complex Structures


Chal Park
Thesis Defense

Katsuyo Thornton, Advisor.

 

Coarsening is an ubiquitous phenomenon that alters the microstructure of the material and its properties. While coarsening of spherical particles has been extensively studied over the last half century, the understanding of coarsening of complex microstructures is still at an early stage. The complex morphology and topology pose difficulty in establishing a theory of coarsening of such microstructures. In an effort to elucidate the dynamics of coarsening, we examine the morphological evolution of bicontinuous structures simulated using the phase-field method. To improve the accuracy of the calculation of interfacial characteristics of the simulated structures, we develop a numerically efficient smoothing algorithm termed ``level-set smoothing.'' We employ statistical analyses to uncover correlations between interfacial characteristics, such as curvatures, and their rate of changes, such as interfacial velocities and rate of change of curvatures. As the framework for the coarsening theory development, we propose to consider the evolution as a consequence of (i) the interfacial velocity induced by diffusion and (ii) the resulting evolution of the interfacial curvatures. As a first step, we examine the evolution of a bicontinuous structure simulated via nonconserved dynamics, in which the interfacial velocity is proportional to the local mean curvature, in order to focus on the second aspect of the evolution (ii). We find that, while the interfacial velocity is locally determined, the evolution of mean curvature is nonlocal and depends on the curvatures of the nearby interfaces. As a second step, we examine the evolution of bicontinuous structures simulated via conserved dynamics to investigate both aspects of the evolution, (i) and (ii). Here, we find that the interfacial velocity is correlated with both the mean curvature and the surface Laplacian of mean curvature. Based on these correlations, we employ a semi-analytical approach to predict the average rate of change of mean curvature, which is found to be consistent with the simulation results. Lastly, in an effort to develop a theory of coarsening of complex microstructures, we derive a general continuity equation of interfacial area to predict the evolution ofthe overall morphology of a microstructure undergoing coarsening. Simulation of rods undergoing pinching is also conducted to provide insights into the source term arising from topological singularity.