Modeling the generation, distribution and transport of point defects in oxide mixed ionic-electronic conductors

Point defect equilibria were used to develop analytical expressions for the dependence of defect concentration on oxygen partial pressure ($PO2$) in mixed ionic-electronic conductors (MIECs) with the fluorite and perovskite structures. This thermodynamic model was able to reproduce the results of the conventional Brouwer approach in the Brouwer regimes but unlike that approach the models were continuous across two Brouwer regimes. To verify the model, a case study was effected for samaria-doped ceria (SDC) in which (a) the model was compared to numerical solutions of SDC defect equilibria, (b) the model was used to obtain values for the external equilibrium constant, K_r, (c) the model was fitted to experimental data for total (ionic plus electronic) conductivity as a function of $PO2$ and (d) the impact of defect associates on defect concentration and total conductivity was evaluated. In addition K_r was correlated to the ratio of the diffusivities of the electronic and ionic species, Θ (= D_e/4D_V), and K_r(3+4Θ)2 constitutes a material constant.; Fundamental transport laws were then used to derive transport models for the spatial distribution and transport of defects in an MIEC in a $PO2$ gradient with and without assuming a linear potential gradient across the MIEC. The former was found to be applicable to true electrolytes (i.e., electrolytes with negligible electronic conductivity) while the latter had general application to all MIECs. As an advance over present models, the use of potential dependent rather than fixed boundary conditions was investigated. It was found that using fixed boundary conditions often caused misleading results. The transport model for open-circuit conditions was applied to experimental data consisting of OCV measurements for various values of $PO2$ (on the reducing side) and at temperatures from 500°C to 800°C. Excellent fits of this model to the experimental data were obtained, thereby demonstrating its accuracy.; Finally, both thermodynamic and transport models were used to determine the optimal thickness ratio of a bilayered electrolyte consisting of SDC and erbia-stabilized bismuth oxide. The optimal (giving the lowest total resistance) thickness ratio of the layers was shown to depend on which layer was more resistive to the transported species, which were charged in closed-circuit conditions and were neutral in open-circuit conditions.