On the correlation of macroscopic and microscopic rate constants in solid state chemistry

The relationships between the effective surface rate constants ((k) over bar) derived from chemical diffusion experiments ((k) over bar(delta)), tracer experiments ((k) over bar*) and electrical conductance experiments ((k) over bar(Q)), between each other and with regard to the microscopic rate constants are investigated. In addition to the possibility of referring to different rate limiting steps (and apart from experimental modifications), the three (k) over bar-values are conceptionally different, similar to the corresponding diffusion coefficients. The latter point is analysed by considering the case that the same (ionic) steps are rate limiting. The convenient master example considered is the electron-rich electron conductor (more precisely a mixed conductor with overwhelming electronic conductivity and electronic carrier concentration). The considerations offer an interpretation of the experimental findings: that (k) over bar(delta) may be much larger than (k) over bar*, that often (k) over bar*similar or equal to (k) over bar(Q) and that there exists, at least in some cases, a clear correlation between (k) over bar* and the tracer diffusion coefficient (D*). Three prototype situations are treated, (a) surface kinetics limited by a poorly conductive surface layer, (b) phase transfer determined and (c) adsorption determined surface kinetics. We restrict our investigations to a dilute defect chemistry and excluded space charge and trapping effects for simplicity. It is shown that the defect concentrations relate (k) over bar* and (k) over bar(delta) to each other. If no charging occurs (transient case), the scaling factor is analogous to the factor between the corresponding diffusion coefficients (ambipolar concentration; boundary resistances if mechanisms are different). The (k) over bar*- and (k) over bar(Q) values are formally identical (up to correlation and other minor correction factors) in the cases considered. Again for the master example the resulting relationships for the (k) over bar-values are discussed with respect to the dependencies on the controlling parameters (oxygen partial pressure, temperature, doping content) and their dependence on the bulk defect concentration, and thus on D*, is analysed. Since only prototype situations and materials are treated, the specific situation has to be considered in individual cases. In particular the different role of the electrons has to be paid attention to. Nevertheless the analysis shows how to tackle related problems and how to get useful information on the mechanism by such an analysis. (C) 1998 Elsevier Science B.V. All rights reserved.