Hsun Yi Chen

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

In this paper, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against numerical solutions of the corresponding sharp-interface equations. The potential of the approach is demonstrated with five applications: surface-reaction?diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces and relaxation of a droplet on irregular surfaces.

Three Dimensional Reconstruction of Solid Oxide Fuel Cell Electrodes Using Focused Ion Beam - Scanning Electron Microscopy

Solid oxide fuel cell (SOFC) electrodes typically consist of contiguous electronically and ionically conducting solid phases in an interconnected porous structure. Quantitatively analyzing this microstructure remains a key challenge in connecting materials processing with electrode performance. This paper will describe the application of dual-beam focused ion beam – scanning electron microscopy for three-dimensional reconstruction of Ni-YSZ cermet anodes, LSM-YSZ cathodes, and (La,Sr)CoO3 cathodes. Different methods for segmentation, i.e. converting images to 3D data sets, are compared and the tradeoff between calculation accuracy and analysis time is discussed.