A model for the spatial distribution and transport properties of defects in mixed ionic-electronic conductors part I: Defect concentration — Pressure relationships and the spatial distribution of defects

Abstract

The spatial distribution and transport of defect species in a mixed ionic-electronic conductor (MIEC) depend on the activity of the external gas phase at either side of the MIEC, the defect equilibria and mobility of the species within the MIEC. Previous researchers [1, 2] developed models for defect distribution and transport based on various assumptions, the most prevalent of which is that the concentration of the ionic defect species is constant through the range of activities of the external gas phase in which the MIEC finds application. However, the defect equilibria for many MIECs do not support this assumption. It is desirable, therefore, to have explicit, analytical expressions for the spatial distribution of the defects as a function of position and the flux as a function of the activity gradient of the defect species and the gas phase. Towards the development of such a model, the defect concentration-oxygen partial pressure dependence in an oxide MIEC, such as Ce0.8Sm0.2O2−δ, is considered. From the defect equilibria, equations are developed for the dependence of the defect species on the oxygen activity in the oxide MIEC. Then, to relate the defect equilibria to the spatial parameters of the MIEC, an analytic expression for the variation of oxygen activity as a function of position in an electrolyte is derived. Equations relating oxygen activity to position and defect concentration to oxygen activity are then combined to obtain a defect concentration-position relation. All the relations are derived without the assumption of constant vacancy concentration. Finally, the results are compared with those of previous models.