R. Zohourian, R. Merkle
Proton-conducting acceptor-doped perovskites have three carriers: oxygen vacancies , protons , and electron holes . Their concentrations are determined by two reactions describing water and oxygen uptake:
Alternatively, proton uptake can occur by a redox reaction as expense of holes:
(this reaction is a linear combination of reactions (1) and (2), i.e. not independent). Under conditions leading to a high and low concentration (high pO2, and/or redox-active perovskites), this is the dominating mode of proton uptake.
Because in the three carrier system only all three carriers together have to fulfil the electroneutrality conditions, an increase of pH2O can lead to complex stoichiometry relaxation phenomena. At sufficiently high hole concentration, "two-fold" relaxation is observed, which also comprises a characteristic non-monotonic change of the hole concentration.
Qualitatively, in first approximation this can be viewed as fast uptake of protons at expense of holes, followed by a slower uptake of oxygen again compensated by hole migration. The overall reaction is essentially water uptake, but it proceeds via an over-reduced intermediate state of the sample. A derivation of exact analytical expressions and numerical examples are given on the publication below.