Correlation model of mixed ionic–electronic conductivity in solid oxide lattices in the presence of point and line defects for solid oxides fuel cells

This paper concerns a 3D mathematical model about the mixed ionic–electronic conductivity in solid oxides in the presence of point and line lattice defects. It is known that the presence of vacancies increases the ionic conductivity; moreover, there is experimental evidence that samples with large compression strains exhibit higher conductivity, which supports the idea that the ion mobility inside the solid oxide is enhanced by a high density of dislocations. The present model aims to show that the diffusion rate of ions is enhanced by the lattice stress field of dislocations properly oriented with respect to the electric potential gradient. Simple considerations quantify the interaction of the ions with the stress field and demonstrate that the presence of dislocations in the crystal lattice causes a drift force additional to that due to the concentration and electric potential gradients; thus, explaining the increase of conductivity experimentally evidenced. Although the model concerns for simplicity a homogeneous and isotropic single crystal of solid oxide, the information provided is of direct interest also for the case of polycrystalline solid oxides with grain boundaries. Copyright © 2011 John Wiley & Sons, Ltd.