Hopping and clustering of oxygen vacancies in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ by anelastic relaxation

The complex elastic compliance $s_{11}(\omega ,T)$ of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ has been measured as a function of the O deficiency $\delta <0.01$. The two main relaxation peaks in the absorption are identified with hopping of isolated O vacancies over a barrier of $0.60\mathrm{eV}$ and reorientation of pairs of vacancies involving a barrier of $1\mathrm{eV}$. The pair binding energy is $\simeq 0.2\mathrm{eV}$, and indications for additional clustering, possibly into chains, is found already at $\delta \sim 0.004$. The anisotropic component of the elastic dipole of an O vacancy is $\Delta \lambda =0.026$. The possible role of electrostatic repulsion between vacancies in slowing the kinetics for their aggregation is discussed.

Figure 1

Elastic energy loss coefficient of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ measured at $5.4\mathrm{kHz}$ at various concentrations of $V_{\mathrm{O}}$. The sequence is according to $\delta$ and not chronological.

Figure 2

Anelastic spectra corresponding to curves 1, 2, and 5 of Fig. 1, measured on the first (circles) and fifth (lines) modes.

Figure 3

(a) possible configurations of two or three $V_{\mathrm{O}}$ (empty circles) with the respective energies. The Ti atoms are at the cell centers and Sr at the vertices. (b) Potential energy profile for various jumps of $V_{\mathrm{O}}$; below each minimum is shown the corresponding configuration.

Figure 4

(Color online) Fit of the experimental curves for $\delta =0.007$ measured at 5.5 and $73\mathrm{kHz}$ with $E_p=0.183\mathrm{eV}$ and $E_c=0.267\mathrm{eV}$; also shown are the components P1, P2, and P3 at $5.5\mathrm{kHz}$.