Spontaneous ferroelectric order in lead-free relaxor $\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2}\mathrm{Ti}{\mathrm{O}}_3$-based composites

Short-range ordered polar nanoregions are key to the giant electromechanical properties exhibited by relaxor ferroelectrics. Stabilization of the long-range ferroelectric order in relaxor systems has typically been achieved by applying external fields. In this work, spontaneous (zero-field) ferroelectric order is demonstrated in the composites constituting of nonergodic relaxor matrix phase $0.91\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2}\mathrm{Ti}{\mathrm{O}}_3\text{−}0.09\mathrm{BaTi}{\mathrm{O}}_3$ with ZnO inclusions. Direct structural evidence is provided for the long-range ferroelectric order in the composites using in situ electric-field-dependent synchrotron investigations and ${}^{23}\mathrm{Na}$ nuclear magnetic resonance spectroscopy. Thermodynamic analysis incorporating microelasticity reveals the role of spatial residual stress in stabilizing the ferroelectric order. The work provides a direct correlation between the stabilized ferroelectric order and enhanced thermal stability, which can be utilized to guide the design of spontaneous long-range order in other relaxor systems.

Figure 1

Temperature- and frequency- dependent permittivity (heating cycle) of the composites in comparison to NBT9BT. The dashed arrow indicates the increasing order of frequency of the measurement. The dashed vertical lines denote $T_{\mathrm{F}\text{−}\mathrm{R}}$.

Figure 2

In situ synchrotron investigations on NBT9BT and composite with 0.1 mole ratio of ZnO. (a), (b) depicts the evolution of ${200}_{\mathrm{pc}}$ reflection upon application of electric field from the unpoled state of the material. (c)–(f) compares the $hk{l}_{\mathrm{pc}}$ reflections at critical fields for $\psi =0$.

Figure 3

Azimuthal (ψ) dependence of the ${200}_{\mathrm{pc}}$ diffraction profile of NBT9BT and composite NBT9BT:0.1ZnO at (a), (b) 0 kV/mm (virgin) and (c), (d) 5.5 kV/mm.

Figure 4

(a) Macroscopic strain measured from the bar-shaped synchrotron samples using an optical displacement sensor. Strain (b), rhombohedral phase fraction (c) and tetragonal unit cell distortion (d) evaluated from the in situ electric field-dependent synchrotron data. The dashed lines denote the inflection points corresponding to the start and end of the field-induced phase transformation from the relaxor to the ferroelectric state. $S_{\mathrm{optical}}$ is obtained from the same sample used in the synchrotron measurement at 0.2 mHz. Since the samples used in the synchrotron measurements had already experienced high electric fields, the samples were annealed before performing the strain-field hysteresis.

Figure 5

(a) Cubic phase fraction and the intensity ratio between the satellite (ST) and central (CT) transitions evaluated from the ${}^{23}\mathrm{Na}$ NMR spectra for unpoled samples. The central and satellite transitions are depicted in the figures below (b), (c).

Figure 6

Stress components (dashed curves) ${\sigma }_{\parallel }$ parallel to the matrix/inclusion interface and (solid curves) ${\sigma }_{\perp }$ perpendicular to the matrix/inclusion interface as a function of distance from the interface, in the NBT9BT matrix of the NBT9BT:0.1ZnO and NBT9BT:0.2ZnO composites. The distance adopts a reduced unit, where 0 and 1 indicate the two NBT9BT/ZnO interfaces between the NBT9BT phase and two neighboring ZnO inclusions, respectively.

Figure 7

Free energy density of NBT9BT and NBT9BT regions around the matrix/inclusion interface in the NBT9BT:0.1ZnO composite as a function of polarization for the (a) tetragonal and (b) rhombohedral phases. A more negative free energy density indicates a more stable phase. Free energy density of the (c) tetragonal and (d) rhombohedral phases as a function of distance from the matrix/inclusion interface. The dash-dotted line indicates the free energy $\left(f_0\right)$ required for NBT9BT to stabilize in the ferroelectric state.