Stoichiometry Variation in Materials with Three Mobile Carriers-Thermodynamics and Transport Kinetics Exemplified for Protons, Oxygen Vacancies, and Holes

Materials with three independent mobile charge carriers, in the sense of not being in local defect-chemical equilibrium though naturally coupled through electroneutrality, are encountered in various cases of scientific and technological relevance. Examples are proton conducting perovskites under conditions at which hole and also oxygen vacancy conductivity may become significant, and mixed conducting cathode materials suited for fuel cells using proton conducting oxide electrolytes. Already the thermodynamics of the equilibrium situation is complex as a pH(2)O increase can lead to proton incorporation by water uptake (pure acid-base reaction) or by hydrogenation (redox reaction). As far as the even more complex transport kinetics are concerned, diffusion equations are derived which are exact for the interaction-free (ideally dilute) situation. Kinetic implications are discussed and checked by exemplary numerical simulations. The treatment includes simple sub-cases such as one-fold relaxation on pH(2)O change, as well as complex patterns characterized by the appearance of more than one characteristic time scales (twofold relaxation) or apparent moving boundary kinetics. Implications for stability and functionality of ceramic materials are discussed.