Structural crossover from nonmodulated to long-period modulated tetragonal phase and anomalous change in ferroelectric properties in the lead-free piezoelectric $\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2}\mathrm{Ti}{\mathrm{O}}_3\text{−}\mathrm{BaTi}{\mathrm{O}}_3$

The highly complex structure-property interrelationship in the lead-free piezoelectric $\left(x\right)\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2}\mathrm{Ti}{\mathrm{O}}_3\text{−}(1-x)\mathrm{BaTi}{\mathrm{O}}_3$ is a subject of considerable contemporary debate. Using comprehensive x-ray, neutron diffraction, dielectric, and ferroelectric studies, we have shown the existence of a new criticality in this system at $x=0.80$, i.e., well within the conventional tetragonal phase field. This criticality manifests as a nonmonotonic variation of the tetragonality and coercivity and is shown to be associated with a crossover from a nonmodulated tetragonal phase (for $x<0.8$) to a long-period modulated tetragonal phase (for $x>0.80$). It is shown that the stabilization of long-period modulation introduces a characteristic depolarization temperature in the system. While differing qualitatively from the two-phase model often suggested for the critical compositions of this system, our results support the view with regard to the tendency in perovskites to stabilize long-period modulated structures as a result of complex interplay of antiferrodistortive modes [Bellaiche and Iniguez, Phys. Rev. B 88, 014104 (2013); Prosandeev, Wang, Ren, Iniguez, ands Bellaiche, Adv. Funct. Mater. 23, 234 (2013)].

Figure 1

Temperature dependence of dielectric permittivity of $(1-x\left)\mathrm{BT}\text{−}\right(x)\mathrm{NBT}$ measured at $10\mathrm{kHz}$.

Figure 2

Frequency dispersion in temperature dependence of the imaginary part of the dielectric permittivity for three representative compositions of $(1-x\left)\mathrm{BT}\text{−}\right(x)\mathrm{NBT}$: $x=0.2$, 0.3, and 0.4.

Figure 3

Temperature difference between the dielectric anomaly of the imaginary part at $10\mathrm{kHz}$ and $100\mathrm{kHz}$ as a function of composition in $(1-x\left)\mathrm{BT}\text{−}\right(x)\mathrm{NBT}$.

Figure 4

Graphical view of the temperature dependence of the $\left(200\right)/\left(002\right)$ tetragonal Bragg profile of $(1-x)\mathrm{BT}\text{−}\left(x\right)\mathrm{NBT}$. The arrows mark the tetragonal-cubic transition.

Figure 5

Composition dependence of (a) tetragonality $c/a$ and (b) coercive field of $(1-x\left)\mathrm{BT}\text{−}\right(x)\mathrm{NBT}$.

Figure 6

Part of the neutron powder diffraction pattern of $(1-x\left)\mathrm{BT}\text{−}\right(x)\mathrm{NBT}$. The small reflections marked with asterisks are superlattice reflections.

Figure 7

Rietveld fitted neutron powder diffraction pattern of 0.90NBT-0.10BT shown in a limited 2θ region near the observed superlattice reflections. The observed pattern is shown by open circles. The fitted patterns are shown by continuous lines. The unaccounted observed peaks are shown with arrows. Bragg peak positions are marked by vertical bars. Fitting was carried out by structural refinement using the $P4bm$ model (a), Le Bail fitting by a $2a_t\times 2b_t\times 2c_t$ cell (b). (c)–(f) Patterns are Le Bail fitted with a $\surd 2a_t\times \surd 2b_t\times n{c}_t$ type cell with $n=4$ (c), $n=6$ (d), $n=8$ (e), and $n=10$ (f).

Figure 8

Temperature dependence of relative permittivity of $(1-x\left)\mathrm{BT}\text{−}\right(x)\mathrm{NBT}$ for (a) $x=0.90$ and (b) $x=0.80$.