Effect of local elastic strain on the structure of Pb-based relaxors: A comparative study of pure and Ba- and Bi-doped ${\text{PbSc}}_{0.5}{\text{Nb}}_{0.5}{\text{O}}_3$

The temperature evolution of the nanoscale structure of ${\text{PbSc}}_{0.5}{\text{Nb}}_{0.5}{\text{O}}_3$ (PSN) and $\left(\text{Pb},A^{″}\right){\text{Sc}}_{0.5}{\text{Nb}}_{0.5}{\text{O}}_3$, $\left(A^{″}=\text{Ba},\text{Bi}\right)$ is analyzed by applying synchrotron single-crystal and high-resolution powder x-ray diffraction as well as polarized Raman spectroscopy. The study compares the effect of incorporation of two-valent cations with isotropic electron structure $\left({\text{Ba}}^{2+}\right)$ and three-valent cations with stereochemically active lone pairs $\left({\text{Bi}}^{3+}\right)$ on the structure of Pb-based perovskite-type relaxor ferroelectrics. The results reveal that the violation of the host system of cations with lone-pair electrons $\left({\text{Pb}}^{2+}\right)$, i.e., the reduction in ferroic species with coherent off-centered Pb atoms, is the major factor for the suppression of long-range ferroelectric ordering at low temperatures. The local charge imbalance associated with $A$ site chemical disorder has negligible impact on the development of ferroelectric order if the second type of $A$-positioned cations also forms lone-pair electrons. The substitution of ${\text{Bi}}^{3+}$ for ${\text{Pb}}^{2+}$ even enhances the cubic-to-ferroelectric transformation processes in PSN and results in a structural state consisting of abundant ferroelectric domains, which are large enough to be identified by polarized Raman spectroscopy as crystalline, but with an average size close to the intrinsic detection limit of synchrotron single-crystal x-ray diffraction.

Figure 1

The $\left(hk0\right)$ and $\left(hk1\right)$ layers of the reciprocal space reconstructed from synchrotron data for PSN, PSN-Ba, and PSN-Bi. The Miller indices are given in a cubic double-perovskite $Fm\overline{3}m$ unit cell. The powder rings are artificial contributions from a quartz capillary used for some of the measurements. The ellipses mark examples of diffuse scattering between pairs of adjacent points with the indices $\left(hk1\right)$ and $\left(h+ik+j1\right)$ with $h=2n$, $k=n$, and $i=+1$ for $h$, $i=-1$ for $\overline{h}$, $j=+1$ for $\overline{k}$, and $j=-1$ for $k$.

Figure 2

(a) Enlarged segments of the $\left(hk0\right)$ layers (see Fig. 1) at 300 and 150 K. The indices of the four strong Bragg reflections are (640), (840), (620), and (820), respectively. (b) Enlarged segments of the $\left(hk1\right)$ layers (see Fig. 1) at 150 K; the peaks in the corners have the indices (531), (551), (331), and (531), respectively.

Figure 3

Raman scattering of PSN, PSN-Ba, and PSN-Bi collected at different temperatures. The black and gray lines represent $Z\left(XX\right)\overline{Z}$ and $Z\left(XY\right)\overline{Z}$ polarized spectra, respectively. The arrows mark the Raman scattering near $53{\text{cm}}^{-1}$, which is related to the Pb-localized vibrations, and near $255{\text{cm}}^{-1}$, which is related to the $B$-cation-localized mode.

Figure 4

Temperature dependence of the depolarization ratio $\eta$ for PSN, PSN-Ba, and PSN-Bi; $\eta =I_{\text{cp}}/\left(I_{\text{pp}}+I_{\text{cp}}\right)$, where $I_{\text{pp}}$ and $I_{\text{cp}}$ denote the integrated intensity of the Raman scattering between 750 and $950{\text{cm}}^{-1}$ measured in $Z\left(XX\right)\overline{Z}$ and $Z\left(XY\right)\overline{Z}$ experimental geometries, respectively (Ref. 28). The line is a guide for the eyes.

Figure 5

Example multiple peak fit of $Z\left(XX\right)\overline{Z}$ and $Z\left(XY\right)\overline{Z}$ polarized Raman spectra of PSN-Bi measured at 300 K. The experimental spectrum is given by black solid line, the fitting Lorentzians by gray thin lines, and the resultant spectrum profile by dashed red line. The symmetry-allowed-Raman-active modes in $Fm\overline{3}m$ are designated in the corresponding plots. Detailed symmetry analysis of the observed peaks and their assignment to definite atomic vibrations are given in Ref. 27.

Figure 6

Temperature dependence of the wave number $\omega$ of the allowed $Z\left(XY\right)\overline{Z}$ ($F_{2\text{g}}$ mode in $Fm\overline{3}m$, open circles) and anomalous $Z\left(XX\right)\overline{Z}$ (filled circles) Raman scattering near $53{\text{cm}}^{-1}$ measured for PSN, PSN-Ba, and PSN-Bi. The experimental uncertainties are within the size of the symbols.

Figure 7

Temperature dependence of the wave number $\omega$ and the FWHM of the Raman scattering near $255{\text{cm}}^{-1}$ measured for PSN, PSN-Ba, and PSN-Bi in $Z\left(XX\right)\overline{Z}$ scattering geometry.

Figure 8

Temperature evolution of the unit-cell parameters of PSN, PSN-Ba, and PSN-Bi. The lines represent linear fits in the ranges $T^{\star }<T<T_B$ and $T_B<T<T_{\text{max}}$; $T_P$ indicates the maximum of the pseudocubic unit-cell parameter of PSN, which coincides with the phase transition to rhombohedral phase found by Perrin et al. (Ref. 16).