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Stoichiometry Variation in Materials with Three Mobile Carriers—Thermodynamics and Transport Kinetics Exemplified for Protons, Oxygen Vacancies, and Holes
Author(s) -
Poetzsch D.,
Merkle R.,
Maier J.
Publication year - 2015
Publication title -
advanced functional materials
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.069
H-Index - 322
eISSN - 1616-3028
pISSN - 1616-301X
DOI - 10.1002/adfm.201402212
Subject(s) - thermodynamics , materials science , kinetics , proton , stoichiometry , diffusion , relaxation (psychology) , chemical physics , conductivity , electrolyte , oxide , oxygen transport , oxygen , chemistry , physics , nuclear physics , social psychology , organic chemistry , electrode , psychology , quantum mechanics , metallurgy
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 ap H 2 Oincrease 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 onefold relaxation onp H 2 Ochange, 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.