Hopping and clustering of oxygen vacancies in BaTiO3− and the influence of the off-centred Ti atoms

The diffusion and aggregation of oxygen vacancies (VO) in perovskites are still poorly understood, even though they are involved in a wide range of applications and phenomena, from solid-state electrolytes for fuel cells to ferroelectric fatigue. In strontium titanate it has been possible, by measuring the complex elastic modulus, to identify peaks in the elastic energy loss versus temperature due to hopping of isolated and paired VO and evaluate all the relevant kinetic and thermodynamic parameters. We present similar experiments in barium titanate, where the ferroelectric transition at TC = 400 K partially hides the anelastic relaxation processes due to VO. The introduction of VO, however, depresses TC, and it has been possible to lower it enough to reveal all the relaxation processes due to free and clustered VO. The resulting anelastic spectra are similar to those of SrTiO3−δ but there are also important differences. In BaTiO3−δ the anisotropy of the elastic dipole of the isolated VO is about three times larger, the anelastic relaxation peaks markedly shift to lower temperature with doping, the activation energy for the diffusion of the isolated VO is 0.72 eV, larger than 0.60 eV in SrTiO3, while that for the pair reorientation is smaller, 0.86 eV compared to 0.97 eV. All these observations are explained by taking into account that, unlike in SrTiO3, Ti is dynamically disordered over eight off-centre positions. A strong indication in this sense comes from the temperature dependence of Young’s modulus, with anharmonic stiffening perfectly linear in temperature down to 200 K in SrTiO3, and with anomalous softening already below 750 K in BaTiO3