Oxygen incorporation in acceptor-doped perovskites

Oxygen is experimentally known to be incorporated in acceptor-doped perovskites at high temperatures, leading to a hole conductivity proportional to pO21/4 and increasing with temperature [$1/2{O}₂+{V}O^{•{}•{}}{→}{O}OX+2{h}^{•{}}$]. Either this high-temperature incorporation is thermodynamically favored by temperature, suggesting an endothermic process (${Δ}{H}⁰$ > 0), or it is exothermic. In the latter case, since it is obviously associated with a ${Δ}{S}⁰$ 0, the process should be favorable only at low temperatures, except if kinetically blocked. To examine this phenomenon, the reaction of ${O}₂$ incorporation into the acceptor-doped perovskites BaSnO${}₃$ and BaZrO${}₃$, doped by trivalent dopants (Ga, Sc, In, Y), according to $BaSn/{Zr}_{1{-}x}{M}ₓ{O}_{3{-}x/2}+x/4{O}₂{→}BaSn/{Zr}_{1{-}x}M{}ₓ{O}₃$, is studied by density-functional calculations for a high dopant concentration ($x=0.25$). In this process, the charged vacancies ${V}O^{•{}•{}}$ resulting from the charge compensation produced by doping, are filled with oxygen atoms, yielding a metallic compound with holes. It is found to be exothermic in all cases, showing that these acceptor-doped perovskites are able to incorporate oxygen at low temperatures, whereas the reaction is unfavorable above a given temperature, whose value is discussed. At any rate, it is suggested that the process is kinetically blocked at low temperatures due to very slow thermally activated vacancy diffusion. A thermochemical approach is presented that tentatively explains why the hole conductivity increases with temperature at high temperatures, although the hole concentration decreases, yielding a model compatible with experimental observations and theoretical calculations.