Three-Phase Solid Oxide Fuel Cell Anode Microstructure Realization Using Two-Point Correlation Functions

Abstract

A Monte Carlo methodology is developed as a means for three-dimensional (3D) reconstruction of the microstructure of a three-phase anode used in solid oxide fuel cells, based on two-point statistical functions. The salient feature of the presented reconstruction methodology is the ability to realize the 3D microstructure from its 2D SEM image for a three-phase medium extendable to n-phase media. In the realization procedure, different phases of the heterogeneous medium are represented by different cells which are allowed to grow. The growth of cells, however, are controlled via several optimization parameters related to rotation, shrinkage, translation, distribution and growth rates of the cells. Indeed, the proposed realization algorithm can be categorized as a member of dynamic programming methods and is designed so comprehensive that can realize any desired microstructure. To be more specific, at first the initial 2D image is successfully reconstructed and then the final optimization parameters are used as the initial values for the initiation of the 3D reconstruction algorithm. This paper presents a novel hybrid stochastic methodology based on the colony and kinetic algorithm for the simulation of the virtual microstructure. The simulation procedure involves repeated realizations where each realization in turn consists of nucleation and growth of cells. For each of the subsequent realizations, the controlling parameters get updated by minimization of an objective function at the end of the preceding realization. Here, the objective function is defined based on the two-point correlation functions from the simulated and real microstructures. The kinetic growth algorithm is established on the cellular automata approach which facilitates the simulation procedure. Comparison of the two-point correlation functions from different sections of the final 3D reconstructed microstructure with the initial real microstructure shows a satisfactory agreement which confirms the proposed methodology.