Interdiffusion in Sc-doped and Ta-doped BaTiO 3 -BaZrO 3 perovskites was examined, both theoretically and experimentally. Analytical expressions for the lattice velocity, v, and the interdiffusion coefficient, D , were obtained. The v and the D were numerically evaluated as a function of dopant type (trivalent-acceptor or pentavalent-donor) and concentration using literature values of oxygen vacancy diffusivity, D V O , the A-site vacancy diffusivity, D V A , and assumed values for the B-site vacancy diffusivities, D V B and D V B . Regardless of the chosen values of D V B and D V B , the calculated D increased with the Ta concentration and decreased with the Sc concentration. The dependence (shape) of the calculated v vs dopant type and concentration, however, was a function of the magnitudes of D V A and D V B . For D V A < (D V B , D V B ) < D V O , the calculated v exhibited a maximum at ∼0.8% acceptor dopant.
Diffusion couples in the BaTiO 3 -BaZrO 3 system doped with either Sc (acceptor) or Ta (donor) were annealed in air over a temperature range between 1300°and 1500°C. Extensive Kirkendall porosity was observed in several samples. The measured porosity vs dopant concentration (acceptor/donor) trace was similar to that of calculated v vs dopant concentration (acceptor/ donor). However, the measured D vs dopant concentration (acceptor/donor) was not in accord with the calculations.This difference is attributed to a nonequilibrium vacancy supersaturation and the accompanying porosity formation. To obtain further evidence of the deviation from equilibrium, experiments were also conducted on both coarsegrained and fine-grained samples. The coarse-grained samples, which are expected to have fewer vacancy sinks and sources, exhibited greater Kirkendall porosity and greater D values compared to the fine-grained samples, consistent with a greater deviation from equilibrium.