Direct Energy, 2018a

54 3.2 Pyroelectricity
Material
Chemical
composition
Piezoelectric
strain const.
d in m V from
[38] [39]
Pyroelectric
coe. | −→ b | in
C
m 2 K from
[38] [39]
Pockels
electro-optic
coe. γ in m V
from [27]
Sphalerite ZnS 1.60 · 10 −12 4.34 · 10 −7 1.6 · 10 −12
Quartz SiO 2 2.3 · 10 −12 1.67 · 10 −6 0.23 · 10 −12
Barium
Titanate
BaTiO 3 2.6 · 10 −10 12 · 10 −6 19 · 10 −12
Table 3.1: Example piezoelectric strain constants, pyroelectric coecients,
and Pockels electro-optic coecients. Values for sphalerite assume the 43m
crystal structure. Pockels coecients assume a wavelength of λ = 633
nm. Average values specied in the references are given. See the cited
references for additional assumptions. The Pockels electro-optic coecient
γ is dened in Sec. 3.3.1.
Rontgen in 1914 [3] [40]. This eect occurs in insulators, so it is dierent
from the thermoelectric eect. The thermoelectric eect, to be discussed in
Chapter 8, is a process that converts between energy of a temperature difference
and electricity and occurs because heat and charges ow at dierent
rates through junctions.
If an insulating crystal is placed in an external electric eld, the material
will polarize. The electrons will displace slightly forming electric dipoles,
and energy can be stored in this material polarization. In some pyroelectric
materials, heating or cooling will also cause the material to polarize. We
can model the material polarization by adding a term to Eq. 2.14 to account
for the temperature dependence [3, p. 327].
−→ P =
−→ D − ɛ0
−→ E +
−→ b ΔT. (3.1)
As in Eq. 2.14 , −→ P represents material polarization in m C , −→ D represents
2
displacement ux density in m C , −→ E represents electric eld intensity in V 2 m ,
and ɛ 0 is the permittivity of free space in m F . The pyroelectric coecient
−→ b has units C
m2·K , and ΔT represents the change in temperature. The
coecient −→ b is a vector because the material polarization may be dierent
along dierent crystal directions. Table 3.1 lists example values for the
pyroelectric coecient as well as for other coecients. (Note that this
denition of −→ b is similar but not identical to the denition in [3].) In some
materials, the material polarization depends linearly on the temperature