Geometric Characterization of the SOFC Electrodes Microporosity Using Fractal and Multifractal Analysis

Nowadays, fractal geometry is suitable for characterizing complex geometric shapes such as porous microstructures. For this purpose, the main objective of this work is to analyze images of the porous microstructures of a Lanthanum Strontium Manganite (LSM) electrode, belonging to a fuel cell, in order to describe its complex geometry. For this, it is necessary to establish consistent relationships between (multi-)fractal parameters and the microporosity of the cell microstructure. The box-counting method and the method of moments were used on the analysis of these images to extract the main fractal and multifractal parameters, respectively, as they are, the fractal Dimension, Df, and the generalized dimensions function, D(q), which allow study the microstructure. The results obtained show the robustness of the methods used in its application to the study of the porous microstructure of these ceramic materials. The main conclusions of the work are that small scales, δ = [1, 32], exhibit a monofractal behavior, characterized by a Df = 1,804 ± 0,042. Although, as the scale observation increases, a remarkable complexity in the microstructure of LSM stacks emerges, characterized by a degree of multifractality of ΔD(q) = 0,421.