Octahedral tilt-suppression of ferroelectric domain wall dynamics and the associated piezoelectric activity in $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3$

The $R3m\text{−}R3c$ transition is in a limited phase field in the $\mathrm{Pb}({\mathrm{Zr}}_{1-x},{\mathrm{Ti}}_x){\mathrm{O}}_3$ (PZT) phase diagram and is a ferroelectric-ferroelectric phase transition that involves the coupling of a secondary displacive ferroelastic phase transition, associated with a structural rotation of the octahedra about the polar threefold axis. Through systematic temperature-dependent piezoelectric characterization under resonance conditions and high-field unipolar ac drive the influence of the aforementioned transition on piezoelectric and electromechanical properties is noted for two compositions $x=0.30$ and $x=0.40\mathrm{mol}$ fraction lead titanate. Applying Rayleigh law analysis to access the relative extrinsic domain wall contributions to the nonlinear permittivity and converse piezoelectric properties, we observe significant differences in the nonlinear response between the $R3m$ and $R3c$ phases and note a discontinuity at the transition for both PZT compositions. A complementary study was conducted through diffraction contrast transmission electron microscopy to access structure property relations. Diffraction contrast imaging reveals that antiphase boundaries (APB’s) associated with octahedral tilt may coincide with non-180° ferroelectric domain walls. This microstructural evidence suggests that APB’s suppress the motion of non-180° ferroelectric domain walls, leading to reduced extrinsic contributions to the piezoelectric and dielectric response in the low-temperature phase $\left(R3c\right)$. The implications of these observations are discussed in relation to both the PZT system and other perovskite-based systems such as $\mathrm{Bi}\mathrm{M}{\mathrm{O}}_3\text{−}\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ systems.

Figure 1

The unit cell of the $R3c$ tilted perovskite phase consisting of four perovskite formula units. The lead ions are indicated at the cube corners while the (Ti and Zr) cations (not visible) would be found at the center of the octahedra; the octahedra are drawn with the oxygen anions removed for clarity.

Figure 2

The schematic illustration of the dielectric and piezoelectric response in ferroelectric materials. The intrinsic response is shown to be associated with the single domain response arising from the polarizability of the crystal lattice, leading to both a linear dielectric displacement and net strain response. The extrinsic contribution is associated with the motion of ferroelectric domain walls preferentially enhancing the fraction of domains most nearly aligned with the applied field. Note that there is no net strain contribution due to 180° inversion domains.

Figure 3

Low-field electromechanical resonance response for $\mathrm{Pb}({\mathrm{Zr}}_x,{\mathrm{Ti}}_{1-x}){\mathrm{O}}_3$ with 30 (a), (c) and 40 (b), (d) mol % titanium content.

Figure 4

Temperature dependence of high field unipolar piezoelectric response $d_{33}$ for PZT $60∕40$. Error bars indicate 95% confidence bands from linear regression analysis.

Figure 5

Nonlinear dielectric response indicates increased field dependence in the untilted phase (dotted lines) for PZT compositions with $x=30$ (a) and 40 (b) mol % Zr content.

Figure 6

(Color online) The temperature dependence of Rayleigh slope parameters for PZT compositions, with $x=30$ (a) and 40 (b) mol % Zr content, shows a clear enhancement in field dependence of both the dielectric response above the tilt transition temperature. Error bars indicate 95% confidence bands from linear regression analysis.

Figure 7

The low-field or initial permittivity values $\left({\epsilon }_{\mathrm{init}}^{*}\right)$ indicate a change in slope at the tilt transition temperature, as shown for the $30\mathrm{mol}\%$ Zr PZT composition. Error bars indicate 95% confidence bands from linear regression analysis.

Figure 8

(Color online) Diffraction contrast image of $\mathrm{Pb}({\mathrm{Zr}}_{0.30},{\mathrm{Ti}}_{0.70}){\mathrm{O}}_3$ taken using transmitted and $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ superstructure reflections in the [211] zone axes (lower right, calculated CaRIne). The locations of the antiphase boundaries (APB’s) are indicated as are regions in which the APB’s are pinned at ferroelectric domain boundaries. A possible variance across the APB’s is illustrated in the inset (upper right).

Figure 9

A self-consistent $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3\text{−}\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ phase diagram has been compiled from a number of sources to include complete space group details (Refs. 10, 11, 12, 13, 14, 15, 55, 56). Open squares indicate revised data points for the position of the $R3m\text{−}R3c$ transition (current work) and $Cm\text{−}Cc$ transition (after Hatch et al.) confirming the tilt boundary (dashed line) is continuous across the rhombohedral-monoclinic phase boundary (Ref. 14).