Interaction of oxygen with oxides: How to interpret measured effective rate constants?

Taking oxygen incorporation as an example into oxides, it is shown how effective interfacial rate constants measured under various experimental conditions have to be interpreted. The treatment in terms of chemical kinetics allows us to correlate them with microscopic rate constants and carrier concentrations. Close to equilibrium the situation is also considered from the standpoint of linear irreversible thermodynamics. After a brief discussion of bulk transport, interfacial steps are treated. As in the bulk different effective interfacial rate constants have to be considered depending on whether one performs a chemical experiment ((k) over bar (delta), stoichiometric change), a tracer experiment ((k) over bar*, change in the tracer distribution) or a (stationary) conductivity experiment ((k) over bar (Q)). Besides the fact that the three rate constants may differ due to different experimental conditions (presence of electrodes etc.), they may be characterised by different mechanisms (different chemical resistances due to the different roles of the electrons) and are finally conceptually different (different chemical capacitance). Owing to the special role of the electrons, it proves worthwhile to distinguish between electron-rich and electron-poor compounds. As far as the first category is concerned, the mechanism, i.e. the rate determining step, is expected to be the same and the rate constants are then shown to scale in a manner analogous to the bulk diffusion coefficients ((k) over bar (-delta)/w(O) = (k) over bar* and (k) over bar* similar or equal to (k) over bar (Q) provided that the experimental conditions are comparable). This is no longer true in the case of an electron-poor material, in which mechanistic differences appear. In the case of free surfaces, ionisation steps are difficult in the chemical experiment, while in the tracer experiment this step can be by-passed by a direct tracer exchange mechanism ((k) over bar (delta)/w(O) not equal (k) over bar*). A metal coating enhances the electron transfer rate for the chemical experiment; in addition anomalous surface Haven ratios are possible ((k) over bar (Q) not equal (k) over bar*). The treatment shows that the (k) over bars are determined by the product of the exchange rate of the rate determining step (inverse effective resistance) and the bulk chemical capacitance. The scaling term reduces to the inverse ionic defect concentration in the case of electron-rich materials. It is also shown that the latter result is valid even far from equilibrium for a variety of mechanisms (though not for all) while proximity to equilibrium must be assumed if changes in the electron concentration become important. Processes at internal interfaces are also considered with special emphasis on space charge effects. Finally, the fact is stressed that, similarly as in the conductivity experiment, in the case of tracer and chemical experiments fur constriction phenomena lend to effective surface resistances which could be erroneously interpreted as a proper blocking mechanism. The interfacial treatment is applied to experimental examples, in particular to acceptor-doped SrTiO3. (C) 2000 Elsevier Science BN. All rights reserved.