Atomistic origin of huge response functions at the morphotropic phase boundary of $\left(1-x\right){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_3\text{−}x{\mathrm{BaTiO}}_3$

The ferroelectric solid solution $\left(1-x\right){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_3\text{−}{\mathrm{BaTiO}}_3 \left(\mathrm{NBT}\text{−}x\mathrm{BT}\right)$ is a promising material to substitute for the environmentally undesired Pb-based ferroelectrics. The strong enhancement of the dielectric permittivity and piezoelectric coefficients near the morphotropic phase boundary (MPB) in ferroelectric $AB{\mathrm{O}}_3$-type solid solutions is commonly related to the existence of a single or several long-range-ordered phases resulting in a complex nanodomain pattern. Here, $\mathrm{NBT}\text{−}x\mathrm{BT}$ is studied by Raman scattering and complementary synchrotron x-ray total elastic scattering to follow the temperature evolution of the mesoscopic-scale structural transformations for $x$ below, at, and slightly above $x_{\mathrm{MPB}}$. The most remarkable result is that at $x\sim x_{\mathrm{MPB}}$ the phonon mode involving vibrations of both off-centered A-site Bi and B-site Ti experiences strong softening and damping near the triple-point temperature in the phase diagram, in strong contrast to the compounds with $x<x_{\mathrm{MPB}}$ or $x>x_{\mathrm{MPB}}$. The chemically enhanced coupling between the Bi and Ti subsystems at $x_{\mathrm{MPB}}$ is facilitated by the subtle disturbance of the coupling processes within the Bi subsystem induced by Ba at $x_{\mathrm{MPB}}$. These mesoscopic-scale structural and dynamic phenomena seem to be significant for the enhanced response functions at the MPB in $\mathrm{NBT}\text{−}x\mathrm{BT}$.

Figure 1

Raman spectra of $\mathrm{NBT}\text{−}x\mathrm{BT}$ with $x$ = 0, 0.06, and 0.08 measured at 80 and 870 K (solid black lines), the fitting pseudo-Voigt peak functions (thin lines), and the resultant spectrum profiles (dashed red lines). The blue thin lines mark the Raman peaks for which the temperature evolution is further discussed. Note that the Gaussian contribution to the shape of peaks 3, 4, and 5 was negligibly small within the entire temperature range 80–870 K.

Figure 2

Temperature evolution of the wave number ω and FWHM of Bi-localized mode in $\mathrm{NBT}\text{−}x\mathrm{BT}$ for $x$ = 0, 0.06, and 0.08; gray and black symbols represent the higher energy and lower energy component, respectively. The dashed lines in the bottom plots are polynomial baselines of the datasets, representing the conventional decrease of phonon mode widths on cooling in the absence of phase transition.

Figure 3

Temperature evolution of the wave number ω, FWHM, and intensity of Ti-localized mode in $\mathrm{NBT}\text{−}x\mathrm{BT}$ for $x$ = 0, 0.06, and 0.08; gray and black symbols represent the higher energy and lower energy component, respectively.

Figure 4

Temperature evolution of the wave number, FWHM, and intensity of Bi-${\mathrm{TiO}}_3$ mode comprising vibrations of both Bi and Ti atoms.

Figure 5

Temperature-dependent x-ray PDF patterns of $\mathrm{NBT}\text{−}x\mathrm{BT}$ for $x$ = 0, 0.06, and 0.08. The short-dashed lines (3.3 Å) mark the feature corresponding to A-B distances; the dashed (3.7 Å) and dotted lines (3.9 Å) mark the two components in the feature related to A-A and B-B distances.

Figure 6

Temperature evolution of x-ray PDF intensities for $\mathrm{NBT}\text{−}x\mathrm{BT}$ for $x$ = 0, 0.06, and 0.08; the dashed rectangles mark the temperature ranges of the most pronounced changes in PDFs.