Vacancy defects in ${\text{PbTiO}}_3$ and lanthanide-ion-doped ${\text{PbTiO}}_3$: A study of positron lifetimes

Positron lifetime measurements were performed on lanthanide- (Ln) ion-doped ${\text{PbTiO}}_3$ and identified the presence of both Pb vacancy, $V_{\text{Pb}}$, and Ti vacancy, $V_{\text{Ti}}$, related point defects. Increasing the concentration of Ln ions La to Eu resulted in an increase in the dominant contribution to the positron lifetime spectrum from $V_{\text{Pb}}$-related defects, consistent with donor ion substitution at the Pb site. By contrast, increasing the concentration of Dy ions decreased the ratio of $V_{\text{Pb}}$- to $V_{\text{Ti}}$-related defects. The behavior is attributed to the incorporation of ${\text{Dy}}^{3+}$ ions as acceptors at Ti sites. Density-functional theory calculations of positron lifetimes for vacancy complexes, and relaxed structure monovacancy defects, in ${\text{PbTiO}}_3$ are reported and support the vacancy-defect assignments.

Figure 1

(Color online) Unit-cell volume against Ln ion obtained from lattice parameters measured by x-ray diffraction. It should be noted that weak x-ray peaks attributed to a secondary phase of ${\text{SmTi}}_2{\text{O}}_7$ were observed for the $2\text{at}\text{.}\mathrm{\%}$ Sm-doped sample.

Figure 2

(Color online) Positron lifetime measurements for the series of Ln-ion-doped ceramic ${\text{PbTiO}}_3$ samples, both $2\text{at}\text{.}\mathrm{\%}$ (triangle-up) and $8\text{at}\text{.}\mathrm{\%}$ doped (circle) samples shown. Measurements made using both a Kapton foil supported positron source (closed symbols) and a Ni foil supported source (open symbols). The lifetime values 181 and 290 ps are shown using dashed lines.