Ferroelectricity and piezoelectricity with examples

Ferroelectricity

Ferroelectricity is the property of some crystals to show spontaneous polarization (even without an applied field) that can be reversed by an external electric field. It is the electrical analogue of ferromagnetism.

Main features:

• P–E hysteresis loop, with remanent polarization $P_r$ and coercive field $E_c$.
• Domains: regions with the same direction of polarization.
• Curie temperature $T_c$: above it the material becomes paraelectric, and $\varepsilon_r = \dfrac{C}{T - T_c}$ (Curie–Weiss law).
• Very high permittivity near $T_c$ ($\varepsilon_r$ of thousands).

          P
          ^    ____
          |   /   /
     -Ec  |  /   /   Pr
    ------+-/---/------> E
         / /  | +Ec
     ___/ /   |

Example: Barium titanate (BaTiO₃). Above 120 °C it is cubic, with Ti⁴⁺ at the centre of the O²⁻ octahedron (no dipole). Below 120 °C the cell becomes tetragonal and Ti⁴⁺ shifts off centre, giving each cell a permanent dipole. Neighbouring cells align, forming domains. Other examples: PZT, Rochelle salt, KH₂PO₄.

Uses: high-value ceramic capacitors (MLCC), FeRAM non-volatile memory, thermistors (PTC).

Piezoelectricity

Piezoelectricity is the generation of electric polarization (voltage) when a crystal is mechanically stressed (direct effect), and the change of its dimensions when an electric field is applied (converse effect). It occurs only in crystals without a centre of symmetry.

• Stress shifts the positive and negative ion centres unequally, creating a net dipole moment: $P = d\,T$ (d = piezoelectric coefficient, T = stress).
• Converse: strain $S = d\,E$.

   force
     |
   +---+         + + + +
   |   |  --->   crystal   ---> voltage V
   +---+         - - - -
     |
   force

Example: Quartz (SiO₂). Squeezing a quartz plate gives a voltage across its faces; applying AC voltage makes it vibrate at a very stable natural frequency. Other examples: PZT, Rochelle salt, ZnO, PVDF.

Uses: quartz crystal oscillators in watches and microprocessors, gas lighters, microphones, ultrasonic transducers, pressure sensors, piezo buzzers.

Relation

All ferroelectrics are piezoelectric (they lack a centre of symmetry), but not all piezoelectrics are ferroelectric; quartz is piezoelectric but not ferroelectric.