On the dependence of the ionic conductivity on dopant concentration in the cubic zirconium oxide doped with oxides of trivalent metals

It is theoretically shown that formation of complexes of oxygen vacancies and dopant ions, which have opposite electric charges, leads to the existence of a maximum in the dependence of conductivity on dopant concentration. By comparison with the published experimental data on this dependence in doped cubic zirconium oxide doped with oxides of trivalent metals, the corresponding equilibrium constants are calculated in the reaction of formation of the complexes, as well as the diffusion coefficients of oxygen anions in zirconia. Temperature dependence of these quantities is established, from which certain useful consequences follow for the dopant concentration providing a maximal conductivity in this solid electrolyte used in solid oxide fuel cells. The change in maximal number of oxygen vacancies and in conductivity caused by the temperature is discussed.