Direct Energy, 2018a

32 2.3 Piezoelectric Devices
Piezoelectric, pyroelectric, and electro-optic devices all involve this type
of energy conversion, and they are all currently available as sensors and
as other products. In piezoelectric devices, discussed in this section, a
mechanical stress causes a material polarization.
If a large enough strain is exerted on a material, the crystal structure
will change. For example, at high enough temperature and pressure, coal
will crystallize into diamond, and when the pressure is removed, the material
stays in diamond form. Steel can be hardened by repeatedly hitting it
in a process called shot peening. A signicant amount of energy is needed
to permanently change the crystal structure of a material. In this section,
we are not discussing this eect. Instead, we are discussing an eect that
typically requires little energy. When a mechanical strain is exerted on
a piezoelectric device, a material polarization is established. The valence
electrons are displaced, but the nuclei of the material and other electrons
do not move. When we release the stress, the material polarization goes
away.
2.3.1 Piezoelectric Strain Constant
We can describe the material polarization of a piezoelectric insulating material
by incorporating a term which depends on the applied mechanical
stress, [25].
−→ P =
−→ D − ɛ0
−→ E + d
−→ ς (2.14)
In this equation, −→ P is material polarization in m C , −→ D is displacement ux
2
density in m C , ɛ 2 0 is the permittivity of free space in m F , −→ E is the applied
electric eld intensity in m V , d is the piezoelectric strain constant in m −→
V , and
ς is the stress in pascals. Stress can also be given in other units.
1 Pa =1 J m 3 =1 N m 2 (2.15)
For many materials, the piezoelectric strain constant d is zero, and for
many other materials, d is quite small. Barium titanate is used to make
piezoelectric sensors because it has a relatively large piezoelectric strain
coecient, d ≈ 3 · 10 −10 m V
[25, p. 408]. Additional example coecients
are given in the next chapter in Table 3.1.
Mechanical strain is a unitless measure of deection or deformation
while stress has units pascals. Without an external electric eld, these
quantities are related by Young's elastic modulus which has units m N . 2
(
strain =
1
Young's elastic modulus
)
· stress (2.16)