A-Site Cation Bulk and Surface Diffusion in A-Site-Deficient BaZrO₃ and SrZrO₃ Perovskites

Diffusion of A-site cations in A-site-deficient BaZrO₃ and SrZrO₃ perovskite oxides was investigated by first-principles nudged elastic band calculations. We found an energy barrier for surface diffusion that was significantly lower than that for bulk diffusion (3.41 eV vs 2.41 eV for Ba diffusion in Ba-deficient BaZrO₃ and 3.07 eV vs 1.44 eV for Sr diffusion in Sr-deficient SrZrO₃), which suggests unusually rapid cation diffusion at low temperatures in nanomaterials with a large proportion of surface-exposed atoms. The lower mobility of Ba in BaZrO₃ compared to that of Sr in SrZrO₃ explains why the proportion of A-site vacancies in BaZrO₃ nanoparticles is much greater than that in SrZrO₃ nanoparticles, as previously observed during nanoparticle formation in which an A-site-deficient nucleus gradually incorporated A-site cations. Finally, thermal and nanoscale effects on the lattice parameter were studied by carrying out high-temperature X-ray diffraction measurements on BaZrO₃ nanoparticles synthesized in supercritical water. The data derived from this experimental investigation and subsequent Rietveld analyses were included in our calculations. We showed that lattice expansion lowered the calculated energy barrier for Ba bulk diffusion from 3.41 to 3.28 eV.