Piezoelectric materials and piezoelectric effect

Piezoelectric materials are crystals that become electrically polarized when mechanically stressed, and change dimensions when an electric field is applied. The crystal must lack a centre of symmetry. Examples: quartz (SiO₂), Rochelle salt, barium titanate, PZT (lead zirconate titanate), ZnO.

Piezoelectric effect in terms of polarization

In an unstressed piezoelectric crystal, the positive and negative ions are arranged so that the centres of positive and negative charge in each unit cell coincide. The dipole moments cancel and the net polarization is zero.

When a stress $T$ is applied, the ions are displaced unequally. Because the cell has no centre of symmetry, the centre of positive charge moves away from the centre of negative charge. Each cell then has a net dipole moment, and the crystal acquires a polarization $P$. Bound charges appear on opposite faces and a voltage can be measured between electrodes.

 Unstressed         Compressed (force down)
     +                  +
   -   -              -   -
     +    P=0         -+-     P != 0
   +   +             + . +   (+ centre moves)
     -                  -

For small stresses the induced polarization is proportional to stress:

$$P = d\,T$$

where $d$ is the piezoelectric coefficient (C/N). Reversing the stress (tension instead of compression) reverses $P$.

Converse effect: an applied field $E$ shifts the ions and produces a strain $S = dE$; the crystal expands or contracts.

Applications

• Direct effect: gas lighters and spark igniters, microphones, pressure and vibration sensors, accelerometers.
• Converse effect: quartz crystal oscillators (in watches and computers), ultrasonic transducers, buzzers, precision actuators.