Stochastic 3D modeling of complex three-phase microstructures in SOFC-electrodes with completely connected phases

•Development of a 3D stochastic model for three-phase microstructures.•Stochastic model is based on tools from stochastic geometry and graph theory.•Virtual Ni–YSZ structures with completely connected phases can be generated.•Model is fit to experimental image data for Ni–YSZ structures before degradation.•Model validation by numerical simulation of effective properties. A parametric stochastic 3D model for the description of complex three-phase microstructures is developed. Such materials occur for example in anodes of solid oxide fuel cells (SOFC) which consist of pores, nickel (Ni) and yttria-stabilized zirconia (YSZ). The model is constructed using tools from stochastic geometry. More precisely, we model the backbones of the three phases by a certain class of random geometric graphs called beta-skeletons. This allows us to reproduce complete connectivity of all three phases as observed in experimental image data of a pristine Ni–YSZ anode as well as the prediction of volume fractions by model parameters. Finally a slightly generalized version of this model enables a good fit to experimental image data with respect to transport relevant microstructure characteristics and the length of triple phase boundary. Model validation is performed by comparing effective transport properties from finite element (FE) simulations based on 3D-data from the stochastic model and from tomography of real Ni–YSZ anodes. Moreover, the virtual, but realistic Ni–YSZ microstructures can be used for investigating the quantitative influence of microstructure characteristics on various physical properties and consequently on the performance of the anode material.