Direct observation of domain wall motion and lattice strain dynamics in ferroelectrics under high-power resonance

Domain wall motion and lattice strain dynamics of ferroelectrics at resonance were simultaneously measured by combining high-power burst excitation and in situ high-energy x-ray diffraction. The increased loss at high vibration velocity was directly related to the increased domain wall motion, driven by dynamic mechanical stress. A general relationship between the microstructural strain contributions and macroscopic electromechanical behavior was established, allowing the prediction of high-power stability of ferroelectric materials. The results indicate that the materials' stability during high-power drive is predominantly related to the basic chemical composition, while the piezoelectric hardening mechanisms mainly influence the small-signal behavior.

Figure 1

Schematics of the high-power piezoelectric pulse drive measurement with a laser vibrometer combined with a time-resolved in situ synchrotron diffraction measurement. Electric field was applied in the 3 direction ($E_3$), while largest strain was realized in the 1 direction (${\varepsilon }_1$) due to the fundamental transverse resonance vibration mode (31). The inset shows exemplarily a reconstructed 2θ section of a diffractogram between 5.75° and 5.95° including the (002/200) doublet reflection with the scattering vector in the 1 direction perpendicular to the applied electric field. The time scale depicts the intensity evolution over the entire sinusoidal field cycle. The intensity interchange between the two reflections during the positive and negative field states directly evidences the motion of non-180° domain walls during the soft PZT sample's resonance vibration at 1.5 m/s.

Figure 2

(a), (b) Experimentally determined resonance quality factor in transverse length mode ($Q_{31}^R$) as a function of macroscopic vibration velocity ($v_1$) measured at the sample's edge. The maximum electric field amplitudes ($E_3^{\max }$) were 40 V/mm (hard PZT) and 120 V/mm (soft PZT). (c), (d) Vibration velocity ($v_1$) as a function of the driving frequency ($f$) at and around the samples’ resonance frequency ($f^R$, indicated by open symbols) at constant electric field amplitudes ($E_3$) of 6.4 V/mm (hard PZT) and 74 V/mm (soft PZT). Measurements were done with decreasing frequency. Red points mark the conditions at which the diffraction experiments were conducted.

Figure 3

Lattice strain (${\varepsilon }_{1,\mathrm{lattice}}$) and strain contribution from non-180° domain wall motion (${\varepsilon }_{1,\mathrm{non}-{180}^{\circ }}$), determined from the XRD measurement, in comparison to the resonance quality factor ($Q_{31}^R$), determined from the pulse drive measurement, as a function of edge vibration velocity ($v_1$) perpendicular to the applied electric field ($E_3$, 31 vibration mode) for (a) hard and (b) soft PZT. The same analysis for the 33 vibration mode (longitudinal strain ${\varepsilon }_3$) is shown in Fig. S1 [29].

Figure 4

Strain ratio revealing the relative strain contribution from non-180° domain wall motion (${\varepsilon }_{1,\mathrm{non}-{180}^{\circ }}$) to the total strain determined by XRD measurement (${\varepsilon }_{1,\mathrm{XRD}}$, sum of ${\varepsilon }_{1,\mathrm{lattice}}$ and ${\varepsilon }_{1,\mathrm{non}-{180}^{\circ }}$). Continuous lines depict the exponential dependency [Eq. (3)], while dotted lines indicate the determined saturation ratio.

Figure 5

Lattice strain (${\varepsilon }_{1,\mathrm{lattice}}$) and strain contribution from non-180° domain wall motion (${\varepsilon }_{1,\mathrm{non}-{180}^{\circ }}$), determined from the XRD measurement, in comparison to the vibration velocity ($v_1$), determined from pulse drive measurement, as a function of driving frequency ($f$) measured at and near the resonance frequency ($f^R$, marked by open symbols) for (a) hard and (b) soft PZT.

Figure 6

(a) Transversal strain (${\varepsilon }_1$) versus the vibration velocity ($v_1$) of hard PZT obtained from the diffraction measurement (${\varepsilon }_{1,\mathrm{XRD}}$, sample center) and macroscopic measurement with the laser vibrometer (${\varepsilon }_{1,\mathrm{vibro}}$, sample edge), and calculated from the piezoelectric coefficient (${\varepsilon }_{1,\mathrm{el}}$) and from the FEM model (${\varepsilon }_{1,\mathrm{FEM}}$, sample center), as well as the strain ratio (${\varepsilon }_{1,\mathrm{XRD}}/{\varepsilon }_{1,\mathrm{vibro}}$). (b) Piezoelectric charge coefficient ($-d_{31}$) and elastic compliance ($s_{11}^E$) as a function of vibration velocity ($v_1$) for hard PZT. (c) Resonance quality factor ($Q_{31}^R$) determined from the pulse drive measurement, contrasted to the calculated average ($T_{1,\mathrm{average}}$) and maximum ($T_{1.\max }$) stress values in the sample and the FEM-simulated center strain value ($T_{1,\mathrm{FEM}}$). (d) FEM sample model and traces of the transverse strain (${\varepsilon }_1$) and stress ($T_1$) amplitude distributions in the 1 direction over the normalized sample position ($x_1$) at 0.6 m/s vibration velocity.