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

Abstract

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 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 onefold relaxation on 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.

Gd- and Pr-based double perovskite cobaltites as oxygen electrodes for proton ceramic fuel cells and electrolyser cells

“…12). It may be noted that protonation of BGLC -depending on its dominating defect structure -can also partly be accompanied by reduction and hence correspond to hydrogenation, as shown by Poetzsch et al for a mixed oxide ion, proton and electron hole conductor [29]. This would mean that the weight gain observed reflects higher concentrations of protons than calculated here, and that the thermodynamics would need to be interpreted differently, but we will for the sake of simplicity not dwell with this possibility here.…”

Mixed‐Conducting Perovskites as Cathode Materials for Protonic Ceramic Fuel Cells: Understanding the Trends in Proton Uptake

“…The combination of reactions and yieldswhich describes proton uptake at expense of holes in the form of a redox reaction (which is, however, not an independent reaction). It has been shown theoretically as well as experimentally that depending on the conditions, the predominant proton uptake reaction can switch from hydration to redox reaction . In the case of ideally dilute conditions, the border is given by the condition ; for higher the hydration reaction prevails.…”

“…Proton concentrations have only been reported for a few perovskite cathode materials. In thermogravimetry (TG) measurements, complications arise from the fact that the proton uptake can either occur by H 2 O or H incorporation, depending on the concentrations of the other point defects . Ex situ measurements of thermally desorbed water from hydrated samples can solve this issue, but are very time‐consuming .…”

Proton uptake in the H+-SOFC cathode material Ba0.5Sr0.5Fe0.8Zn0.2O3−δ: transition from hydration to hydrogenation with increasing oxygen partial pressure

“…Reproduced with permission from ref 17 ,. Right: Materials with perceptible concentration of mobile holes show two-fold relaxation of fast hydrogen uptake followed by slower re-oxidation.…”

“…This behavior will now be illustrated by numerical simulations.In ref 17 ,. 12 , the solid grey line the O V •• diffusivity calculated from O permeation measurements on BSFZ.…”