Hopping and clustering of oxygen vacancies in BaTiO3-? and the influence of the dynamically disordered offcentred 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. The only case where a satisfactory picture has been obtained is cubic SrTiO3-?, through fitting of the anelastic spectra at several O deficiencies [1]. In this manner it has been shown that the activation energy of 1 eV, commonly identified with the barrier for VO diffusion, is actually associated with pairs and larger complexes of VO, which are stable also for ? < 0.01 and above 600 K, while the barrier for the hopping of isolated VO is only 0.6 eV. Similar clean results cannot be obtained in highly doped perovskites, as ionic conductors are, or in the presence of structural phase transitions, including the ferroelectric (FE) ones, because the anelastic spectra become very complicated and/or dominated by domain wall relaxations. Fig. 1. Anelastic spectra of two samples of BaTiO3-? with 0 <= ? <= 0.016. We present similar experiments in barium titanate [2], where the 66 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-? but there are also important differences. In BaTiO3-? 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, but with anomalous softening already below 750 K in BaTiO3. [1] F. Cordero, Phys. Rev. B, 76 (2007) 172106. [2] F. Cordero, F. Trequattrini, D. A. B. Quiroga and P. S. Silva Jr., J. Alloys and Compounds 874 (2022) 159753.