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Abstract Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the smoothed boundary method to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method’s capability. 

Data associated with the article "Simulating Hindered Grain Boundary Diffusion Using the Smoothed Boundary Method" [1]. 1. Hanson, E., Andrews, W. B., Powers, M., Jenkins, K. G., & Thornton, K. (2024). Simulating hindered grain boundary diffusion using the smoothed boundary method. Modelling and Simulation in Materials Science and Engineering, 32(5), 055027. 

Electrochemical impedance spectroscopy (EIS) is a powerful technique for material characterization and diagnosis of the solid oxide fuel cells (SOFC) as it enables separation of different phenomena such as bulk diffusion and surface reaction that occur simultaneously in the SOFC. In this work, we simulate the electrochemical impedance in an experimentally determined, three-dimensional (3D) microstructure of a mixed ion-electron conducting (MIEC) SOFC cathode. We determine the impedance response by solving the mass conservation equation in the cathode under the conditions of an AC load across the cathode’s thickness and surface reaction at the pore/solid interface. Our simulation results reveal a need for modifying the Adler-Lane-Steele model, which is widely used for fitting the impedance behavior of a MIEC cathode, to account for the difference in the oscillation amplitudes of the oxygen vacancy concentration at the pore/solid interface and within the solid bulk. Moreover, our results demonstrate that the effective tortuosity is dependent on the frequency of the applied AC load as well as the material properties, and thus the prevalent practice of treating tortuosity as a constant for a given cathode should be revised. Finally, we propose a method of determining the aforementioned dependence of tortuosity on material properties and frequency by using the EIS data. 

The dataset associated with the article: Goel, V., Cox, D., Barnett, S. A., & Thornton, K. (2021). Simulation of the electrochemical impedance in a three-dimensional, complex microstructure of solid oxide fuel cell cathode and its application in the microstructure characterization. Frontiers in Chemistry, 9, 627699.