Polarization contributions to the vacancy binding energy in doped oxides

An effective medium theory due to Onsager is generalized to yield the macroscopic dielectric constant of a random assembly of associated vacancy-dopant bound pairs embedded in a dielectric host. The model is then further developed to give the vacancy-dopant binding energy, employing concepts long-established in electrolyte theory. The results of this analysis are used to compute the activation enthalpy for electrical conduction in the ionic conduction regime. The values so found are in reasonable accord with experimental data from various sources on Ce_1?xCa_xO_2?x, with x?0.02, assuming a vacancy migration enthalpy of 0.71 eV. The latter is the only adjustable parameter in the theory here developed. With this same value, the predicted variation of the low-temperature conduction activation enthalpy in Ce_1?2xY_2xO_2?x and Ce_1?2xGd_2xO_2?x (again at small x) are acceptably reproduced, although more experimental data would be desirable. The dielectric constant of the yttria-doped material is also described by the present model, again with no adjustable parameters. Several different features of the theory lead to its loss of validity in more concentrated mixtures. These are examined in detail.