Pyroelectricity

Pyroelectricity (from the two Greek words "pyr" meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the ability of certain materials to generate a temporary voltage when they are heated or cooled. The change in temperature modifies the positions of the atoms slightly within the crystal structure, such that the polarization of the material changes. This polarization change gives rise to a voltage across the crystal. If the temperature stays constant at its new value, the pyroelectric voltage gradually disappears due to leakage current. The leakage can be due to electrons moving through the crystal, ions moving through the air, or current leaking through a voltmeter attached across the crystal.
Explanation.
Pyroelectricity can be visualized as one side of a triangle, where each corner represents energy states in the crystal: kinetic, electrical and thermal energies. The side between electrical and thermal corners represents the pyroelectric effect and produces no kinetic energy. The side between kinetic and electrical corners represents the piezoelectric effect and produces no heat.
Pyroelectric charge in minerals 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 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, 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 electrets. 
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 dipole moment. As a consequence there are no 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:
where "pi" (Cm−2K−1)
is the vector for the pyroelectric coefficient.
History.
The first reference to the pyroelectric effect is found in writings by Theophrastus (c. 314 BC), who noted that "lyngourion", tourmaline, could attract sawdust or bits of straw when heated. Tourmaline's properties were rediscovered in 1707 by Johann Georg Schmidt, who noted that the stone attracted only hot ashes, not cold ones. In 1717 Louis Lemery noticed, as Schmidt had, that small scraps of non-conducting material were first attracted to tourmaline, but then repelled by it once they contacted the stone. In 1747 Linnaeus first related the phenomenon to electricity (he called tourmaline "Lapidem Electricum", "the electric stone"), although this was not proven until 1756 by Franz Ulrich Theodor Aepinus.
Research into pyroelectricity became more sophisticated in the 19th century. In 1824 Sir David Brewster gave the effect the name it has today. Both William Thomson in 1878 and Woldemar Voigt in 1897 helped develop a theory for the processes behind pyroelectricity. Pierre Curie and his brother, Jacques Curie, studied pyroelectricity in the 1880s, leading to their discovery of some of the mechanisms behind piezoelectricity.
Crystal classes.
All crystal structures belong to one of thirty-two crystal classes based on the number of rotational axes and reflection planes they possess that leave the crystal structure unchanged (point groups). Of the thirty-two crystal classes, twenty-one are non-centrosymmetric (not having a centre of symmetry). Of these twenty-one, twenty exhibit direct piezoelectricity, the remaining one being the cubic class 432. Ten of these twenty piezoelectric classes are polar, i.e., they possess a spontaneous polarization, having a dipole in their unit cell, and exhibit pyroelectricity. If this dipole can be reversed by the application of an electric field, the material is said to be ferroelectric. Any dielectric material develops a dielectric polarization (electrostatics) when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material. Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar. All polar crystals are pyroelectric, so the ten polar crystal classes are sometimes referred to as the pyroelectric classes.
Piezoelectric crystal classes: 1, 2, m, 222, mm2, 4, -4, 422, 4mm, -42m, 3, 32, 3m, 6, -6, 622, 6mm, -62m, 23, -43m
Pyroelectric: 1, 2, m, mm2, 3, 3m, 4, 4mm, 6, 6mm
Related effects.
Two effects which are closely related to pyroelectricity are ferroelectricity and piezoelectricity. Normally materials are very nearly electrically neutral on the macroscopic level. However, the positive and negative charges which make up the material are not necessarily distributed in a symmetric manner. If the sum of charge times distance for all elements of the basic cell does not equal zero the cell will have an electric dipole moment (a vector quantity). The dipole moment per unit volume is defined as the dielectric polarization. If this dipole moment changes with the effect of applied temperature changes, applied electric field, or applied pressure, the material is pyroelectric, ferroelectric, or piezoelectric, respectively. 
The ferroelectric effect is exhibited by materials which possess an electric polarization in the absence of an externally applied electric field such that the polarization can be reversed if the electric field is reversed. Since all ferroelectric materials exhibit a spontaneous polarization, all ferroelectric materials are also pyroelectric (but not all pyroelectric materials are ferroelectric).
The piezoelectric effect is exhibited by crystals (such as quartz or ceramic) for which an electric voltage across the material appears when pressure is applied. Similar to pyroelectric effect, the phenomenon is due to the asymmetric structure of the crystals that allows ions to move more easily along one axis than the others. As pressure is applied, each side of the crystal takes on an opposite charge, resulting in a voltage drop across the crystal. 
Pyroelectricity should not be confused with thermoelectricity: In a typical demonstration of pyroelectricity, the whole crystal is changed from one temperature to another, and the result is a temporary voltage across the crystal. In a typical demonstration of thermoelectricity, one part of the device is kept at one temperature and the other part at a different temperature, and the result is a "permanent" voltage across the device as long as there is a temperature difference. Both effects convert temperature change to electrical potential, but the pyroelectric effect converts temperature change over "time" into electrical potential, while the thermoelectric effect converts temperature change with "position" into electrical potential.
Pyroelectric materials.
Although artificial pyroelectric materials have been engineered, the effect was first discovered in minerals such as tourmaline. The pyroelectric effect is also present in bone and tendon.
The most important example is gallium nitride, a semiconductor. The large electric fields in this material are detrimental in light emitting diodes (LEDs), but useful for the production of power transistors. 
Progress has been made in creating artificial pyroelectric materials, usually in the form of a thin film, using gallium nitride (GaN), caesium nitrate (CsNO3), polyvinyl fluorides, derivatives of phenylpyridine, and cobalt phthalocyanine. Lithium tantalate (LiTaO3) is a crystal exhibiting both piezoelectric and pyroelectric properties, which has been used to create small-scale nuclear fusion ("pyroelectric fusion"). Recently, pyroelectric and piezoelectric properties have been discovered in doped hafnium oxide (HfO2), which is a standard material in CMOS manufacturing.
Applications.
Heat sensors.
Very small changes in temperature can produce a pyroelectric potential. Passive infrared sensors are often designed around pyroelectric materials, as the heat of a human or animal from several feet away is enough to generate a voltage. 
Power generation.
A pyroelectric can be repeatedly heated and cooled (analogously to a heat engine) to generate usable electrical power. One group calculated that a pyroelectric in an Ericsson cycle could reach 50% of Carnot efficiency, while a different study found a material that could, in theory, reach 84-92% of Carnot efficiency (these efficiency values are for the pyroelectric itself, ignoring losses from heating and cooling the substrate, other heat-transfer losses, and all other losses elsewhere in the system). Possible advantages of pyroelectric generators for generating electricity (as compared to the conventional heat engine plus electrical generator) include: potentially lower operating temperatures, less bulky equipment, and fewer moving parts. Although a few patents have been filed for such a device, such generators do not appear to be anywhere close to commercialization.
Nuclear fusion.
Pyroelectric materials have been used to generate large electric fields necessary to steer deuterium ions in a nuclear fusion process. This is known as pyroelectric fusion.