Hydration of Acceptor-Doped Perovskites

Practical cases of proton conduction in perovskites almost exclusively involve acceptor-doped systems with charge-compensating oxygen vacancies in the dry state. The doping reaction for an acceptor Mf on the B site of a II-IV perovskite ABO3 in dry atmospheres can in this case be written as follows  

In the presence of water vapor, protons can be incorporated directly as charge-compensating defects during the synthesis according to this equation  

Oxygen vacancies and protons are in equilibrium through the important hydration reaction  

The expression requires that the concentrations are all given in the same units, so that the standard concentrations cancel, and that the partial pressure of water is given in bars. The electroneutrality condition in our case reads  

On the other hand, if protons are in the minority so that 2[vq] [Acc j = constant, the proton concentration becomes  

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