Defect Structures of Proton-conducting Oxides

Defect-structure-wise there are two main routes to a mixed proton-electron conducting oxide. The simplest would be to dissolve protons compensated by electrons originating directly from hydrogen gas  

This reaction was reported for ZnO already in the 1950s [7], and it was found that protons and electrons were the dominating defects in hydrogen atmospheres, so that the electroneutrality condition and concentrations are expressed as  

It may be shown that one may only hope to achieve this situation when the material is already dominated by electrons (and some positive point defects, such as oxygen vacancies) under hydrogen-free reducing conditions. By increasing pjj, the native positive defects are replaced by the protonic ones. Protons compensated by electrons are, however, hardly known in systems other than ZnO, and instead one tends to use acceptor-doped oxides in which the concentrations of protons and aU other positive defects are enhanced by the doping. The acceptors are most often substitutionaUy dissolved lower-valent cations, while, in principle, interstitial anions or substitutional higher-valent anions (e.g., N - substituting O ) can also be used. We shall simply refer to the acceptors as A, and, in the ionized state. A/. 

Assuming that the acceptors are compensated by oxygen vacancies in the absence of hydrogen-containing gases, the reaction with water vapor is given by  

The equilibrium constant, K, for the reaction, and the Umiting electroneutrality condition (1.7) 

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