Editing Pyroelectricity (section)

== Explanation ==
Pyroelectric charge in [[mineral]]s develops on the opposite faces of asymmetric crystals. The direction in which the propagation of the charge tends is usually constant throughout a pyroelectric material, but, in some materials, this direction can be changed by a nearby electric field. These materials are said to exhibit [[ferroelectricity]].

All known pyroelectric materials are also [[piezoelectricity|piezoelectric]]. Despite being pyroelectric, novel materials such as boron aluminum nitride (BAlN) and boron gallium nitride (BGaN) have zero piezoelectric response for strain along the c-axis at certain compositions,<ref>{{Cite journal|title=Wurtzite BAlN and BGaN alloys for heterointerface polarization engineering|journal = Applied Physics Letters|volume = 111|issue = 22|pages = 222106|last=Liu|first=Kaikai|doi=10.1063/1.5008451|year = 2017|bibcode = 2017ApPhL.111v2106L|url = http://repository.kaust.edu.sa/kaust/handle/10754/626289|hdl = 10754/626289|hdl-access = free}}</ref> the two properties being closely related. However, note that some piezoelectric materials have a crystal symmetry that does not allow pyroelectricity.

Pyroelectric materials are mostly hard and crystals; however, soft pyroelectricity can be achieved by using [[electret]]s.<ref>{{cite journal|date=2018|journal=Soft Matter|title=Designing Soft Pyroelectric and Electrocaloric Materials Using Electrets|last1=Darbaniyan|first1=F.|last2=Sharma|first2=P.|volume=15|issue=2|pages=262–277|doi=10.1039/C8SM02003E|pmid=30543261|bibcode=2019SMat...15..262D|s2cid=56145736}}</ref>

Pyroelectricity is measured as the change in net polarization (a vector) proportional to a change in temperature. The total pyroelectric coefficient measured at constant stress is the sum of the pyroelectric coefficients at constant strain (primary pyroelectric effect) and the piezoelectric contribution from thermal expansion (secondary pyroelectric effect). Under normal circumstances, even polar materials do not display a net [[electric dipole moment|dipole moment]]. As a consequence, there are no [[Electric Dipole|electric dipole]] equivalents of bar magnets because the intrinsic dipole moment is neutralized by "free" electric charge that builds up on the surface by internal conduction or from the ambient atmosphere. Polar crystals only reveal their nature when perturbed in some fashion that momentarily upsets the balance with the compensating surface charge.

Spontaneous polarization is temperature dependent, so a good perturbation probe is a change in temperature which induces a flow of charge to and from the surfaces.  This is the pyroelectric effect.  All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes. Pyroelectric materials can be used as infrared and millimeter wavelength radiation detectors.

An [[electret]] is the electrical equivalent of a permanent magnet.

=== Mathematical description ===
The pyroelectric coefficient may be described as the change in the spontaneous polarization vector with temperature:<ref>{{cite journal|last1=Damjanovic|first1=Dragan|year=1998|title=Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics|journal=Rep. Prog. Phys.|volume=61|issue=9|pages=1267–1324|doi=10.1088/0034-4885/61/9/002 | bibcode=1998RPPh...61.1267D|s2cid=250873563 }}</ref>
<math display="block">
p_i = \frac{\partial P_{S,i}} {\partial T}  
</math>
where ''p<sub>i</sub>'' (Cm<sup>−2</sup>K<sup>−1</sup>) is the vector for the pyroelectric coefficient.