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.
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