Direct Energy, 2018a

3 PYROELECTRICS AND ELECTRO-OPTICS 55
as described by Eq. 3.1. In other materials, more terms are needed to
describe the dependence of the material polarization on temperature.
−→ P =
−→ D − ɛ0
−→ E +
−→ b ΔT +
−−→
bquad (ΔT ) 2 ... (3.2)
Many materials exhibit pyroelectricity only below a temperature known as
the pyroelectric Curie temperature.
In the last chapter, we saw that we could determine whether or not a
crystalline material was piezoelectric from its crystal structure. To do so,
we identied the symmetries of the crystal structure. Crystal structures are
grouped into 32 classes called crystal point groups based on the symmetries
they contain. Crystal structures in the 21 of the crystal point groups that
do not have a center of symmetry can be piezoelectric. We can use a similar
technique to determine if a crystalline material is or is not pyroelectric.
All pyroelectric crystals are piezoelectric, but not all piezoelectric crystals
are pyroelectric. To determine if a crystalline material can be pyroelectric,
identify its crystal structure and determine the corresponding crystal
point group. Crystals in the 10 crystal point groups listed in Table 2.2 are
pyroelectric [3, p. 366] [26, p. 557].
3.2.2 Pyroelectricity in Amorphous and Polycrystalline Materials
and Ferroelectricity
In the Sec. 2.3.3 we saw that some materials, called ferroelectric piezoelectric
materials, had a material polarization that depended nonlinearly
on the mechanical stress applied. These materials could be crystalline,
amorphous, or polycrystalline. When a charge separation occurred in one
atom, the charges from that electric dipole induce dipoles to form in nearby
atoms, and electrical domains withaligned material polarization form in
the material. This eect depends on the mechanical stress applied to the
material previously, and the dependence on past history is called hysteresis.
Materials can also be ferroelectric pyroelectric, and these materials can
be crystalline, amorphous, or polycrystalline. In these materials, the material
polarization depends nonlinearly on the temperature, as opposed to
the mechanical stress. As with the piezoelectric version of this eect, polarization
of one atom induces a material polarization in nearby atoms.
Such materials can have a material polarization even when no temperature
gradient is applied, and they can exhibit hysteresis.
3.2.3 Materials and Applications of Pyroelectric Devices
Pyroelectricity has been studied in a number of materials including barium
titanate BaTiO 3 , lead titanate PbTiO 3 , and potassium hydrogen phosphate