Interdiffusion and Kirkendall effect in doped BaTiO3-BaZrO3 perovskites: Effect of vacancy supersaturation

Interdiffusion in Sc-doped and Ta-doped BaTiO3-BaZrO3 perovskites was exami ned, both theoretically and experimentally. Analytical expressions for the lattice velocity, v, and the interdiffusion coefficient, (D) over tilde, we re obtained. The v and the (D) over tilde were numerically evaluated as a f unction of dopant type (trivalent-acceptor or pentavalent-donor) and concen tration using literature values of oxygen vacancy diffusivity, Dt;, the A-s ite vacancy diffusivity, DX, and assumed values for the B-site vacancy diff usivities, D-B(V) and D-B(V). Regardless of the chosen values of D-B(V) and D-B(V), the calculated D increased with the Ta concentration and decreased with the Sc concentration. The dependence (shape) of the calculated v vs d opant type and concentration, however, was a function of the magnitudes of D-A(V) and D-B(V). For D-A(V) < (D-B(V), D-B(V)) < Da, the calculated v exh ibited a maximum at similar to 0.8% acceptor dopant, Diffusion couples in t he BaTiO3-BaZrO3 system doped with either Sc (acceptor) or Ta (donor) were annealed in air over a temperature range between 1300 degrees and 1500 degr ees C, Extensive Kirkendall porosity was observed in several samples. The m easured 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 v acancy supersaturation and the accompanying porosity formation. To obtain f urther evidence of the deviation from equilibrium, experiments were also co nducted on both coarse-grained and fine-grained samples. The coarse-grained samples, which are expected to have fewer vacancy sinks and sources, exhib ited greater Kirkendall porosity and greater (D) over tilde values compared to the fine-grained samples, consistent with a greater deviation from equi librium.