1. Polarization Direction and Piezoelectric Response
The polarization direction of piezoelectric materials such as PZT (Lead Zirconate Titanate) determines their electromechanical coupling characteristics.
When the direction of the applied electric field is aligned with the polarization direction, the material undergoes direct mode deformation (longitudinal strain) along the polarization axis, manifested as axial expansion (d33 effect). At the same time, due to the Poisson effect, contraction occurs in the transverse directions while the overall volume remains approximately constant.
If the electric field is applied perpendicular to the polarization direction, it induces shear mode deformation (transverse strain). In this case, the rotation of dipoles dominates the motion, resulting in pure shear deformation (d31/d15 effects).
2. Physical Mechanism of Direct Mode
Electric field parallel to the polarization direction:
The electric field drives dipoles to align along the polarization direction, causing lattice distortion (such as the displacement of Pb²⁺ ions), which produces axial strain (ε33).
Volume conservation:
Transverse contraction (ε11 = ε22) balances axial expansion, resulting in minimal macroscopic volume change.
Application scenarios:
Devices requiring axial deformation, such as:
- Ultrasonic transducers
- Precision displacement actuators
3. Physical Mechanism of Shear Mode
Electric field perpendicular to the polarization direction:
Dipoles rotate under the influence of the transverse electric field (90° domain wall motion), generating shear strain (γ15).
Domain wall motion:
Non-intrinsic effects (domain wall movement) dominate the response. This significantly increases the dielectric constant but introduces noticeable hysteresis effects.
Application scenarios:
Devices requiring transverse deformation, such as:
- Shear wave sensors
- Vibration energy harvesters
4. Mode Comparison and Optimization Directions
| Feature | Direct Mode (d33) | Shear Mode (d31/d15) |
| Strain Direction | Parallel to polarization direction | Perpendicular to polarization direction |
| Energy Efficiency | High (direct domain switching) | Lower (domain wall friction losses) |
| Measurement Conditions | Requires three-axis constraint (to prevent bending) | Requires biaxial stress control |
Optimization Recommendation:
By adjusting the domain structure through polarization processes (such as zoned polarization) or doping (e.g., Nb⁵⁺ doping), the response sensitivity of the shear mode can be improved.
5. Experimental Verification and Challenges
Direct mode measurement:
It is necessary to distinguish between longitudinal strain and bending deformation, as thin samples may easily produce bending errors.
Shear mode control:
Precise control of the angle between the electric field direction and the polarization direction is required (for example, using 45° oblique-cut PZT single crystals).