# Difference between revisions of "Pyroelectricity"

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− | < | + | <font color="blue">Pyroélectricité</font> (''Fr''). <font color="red">Pyroelektrizität</font> (''Ge''). <font color="black">Piroelettricità</font> (''It''). <font color="purple">焦電効果</font> (''Ja''). <font color="green">Piroelectricidad</font> (''Sp''). |

+ | |||

== Definition == | == Definition == | ||

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</center> | </center> | ||

− | where ''p<sub>i</sub><sup>T</sup>'' is the pyroelectric coefficient at constant stress. Pyroelectric crystals actually have a spontaneous polarization, but the pyroelectric effect can only be observed during a temperature change. If the | + | where ''p<sub>i</sub><sup>T</sup>'' is the pyroelectric coefficient at constant stress. Pyroelectric crystals actually have a spontaneous polarization, but the pyroelectric effect can only be observed during a temperature change. If the polarization can be reversed by the application of an electric field, the crystal is ferroelectric. |

If the crystal is also piezoelectric, the polarization due to an applied temperature variation is also partly due to the piezoelectric effect. The coefficient describing the pure pyroelectric effect is the pyroelectric coefficient at constant strain, ''p<sub>i</sub>''<sup>''S''</sup>. The two coefficients are related by: | If the crystal is also piezoelectric, the polarization due to an applied temperature variation is also partly due to the piezoelectric effect. The coefficient describing the pure pyroelectric effect is the pyroelectric coefficient at constant strain, ''p<sub>i</sub>''<sup>''S''</sup>. The two coefficients are related by: | ||

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where the ''c<sub>ijkl</sub>'' are the elastic stiffnesses, the ''d<sub>kln</sub>'' the [[piezoelectricity| piezoelectric]] coefficients and the α''<sub>jn</sub>'' the linear [[thermal expansion]] coefficients. | where the ''c<sub>ijkl</sub>'' are the elastic stiffnesses, the ''d<sub>kln</sub>'' the [[piezoelectricity| piezoelectric]] coefficients and the α''<sub>jn</sub>'' the linear [[thermal expansion]] coefficients. | ||

− | The converse effect is the | + | The converse effect is the [[electrocaloric effect]]. If a pyroelectric crystal is submitted to an electric field, it will undergo a change of entropy Δσ: |

<center> | <center> | ||

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</center> | </center> | ||

− | and will release or absorb a quantity of heat | + | and will release or absorb a quantity of heat given by Θ'' V'' Δσ where Θ is the temperature of the specimen and ''V'' its volume. |

== Pyroelectric point groups == | == Pyroelectric point groups == | ||

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== History == | == History == | ||

− | The appearance of electrostatic charges upon changes of temperature has been observed since ancient times, in particular on tourmaline. It | + | The appearance of electrostatic charges upon changes of temperature has been observed since ancient times, in particular on tourmaline and was described, among others, by Steno, Aepinus and Haüy. It was Sir David Brewster (1781-1788) who coined the term 'pyroelectricity' [Brewster, D. (1824). ''Edinburgh. J. Sci.'', '''1''', 208-215, ''Observations on the pyroelectricity of minerals'', translated into German, ''Poggendorf Ann. Phys.'' (1824). '''2''', 297-307, ''Beobachtungen über die, in den Mineralien, durch Wärme erregte Electrizität'']. |

== See also == | == See also == | ||

− | [http://www.iucr.org/ | + | *[http://www.iucr.org/education/pamphlets/18/ ''An introduction to crystal physics''] (Teaching Pamphlet No. 18 of the International Union of Crystallography) |

− | + | *Chapter 3.2.2.5 of ''International Tables for Crystallography, Volume A'', 6th edition | |

− | + | *Chapter 1.1.4 and Part 3 of ''International Tables for Crystallography, Volume D'' | |

− | |||

− | [[Category:Physical properties of crystals]] | + | [[Category:Physical properties of crystals]] |

## Latest revision as of 10:13, 17 November 2017

Pyroélectricité (*Fr*). Pyroelektrizität (*Ge*). Piroelettricità (*It*). 焦電効果 (*Ja*). Piroelectricidad (*Sp*).

## Definition

Pyroelectricity is the property presented by certain materials that exhibit an electric polarization *P _{i} * when a temperature variation δΘ is applied uniformly:

*P _{i} * =

*p*δΘ

_{i}^{T}where *p _{i}^{T}* is the pyroelectric coefficient at constant stress. Pyroelectric crystals actually have a spontaneous polarization, but the pyroelectric effect can only be observed during a temperature change. If the polarization can be reversed by the application of an electric field, the crystal is ferroelectric.

If the crystal is also piezoelectric, the polarization due to an applied temperature variation is also partly due to the piezoelectric effect. The coefficient describing the pure pyroelectric effect is the pyroelectric coefficient at constant strain, *p _{i}*

^{S}. The two coefficients are related by:

*p _{i}^{T} * =

*c*α

_{ijkl}d_{kln}*+*

_{jn}*p*

_{i}^{S}

where the *c _{ijkl}* are the elastic stiffnesses, the

*d*the piezoelectric coefficients and the α

_{kln}*the linear thermal expansion coefficients.*

_{jn}The converse effect is the electrocaloric effect. If a pyroelectric crystal is submitted to an electric field, it will undergo a change of entropy Δσ:

Δσ = *p _{i} E^{i} *

and will release or absorb a quantity of heat given by Θ* V* Δσ where Θ is the temperature of the specimen and *V* its volume.

## Pyroelectric point groups

The geometric crystal classes for which the piezoelectric effect is possible are determined by symmetry considerations (see Curie laws). They are the classes of which the symmetry is a subgroup of the symmetry associated with that of the electric field, *A*_{∞} ∞*M*:

1, 2, 3, 4, 6, *m*, 2*mm*, 3*m*, 4*mm*, 6*mm*

## History

The appearance of electrostatic charges upon changes of temperature has been observed since ancient times, in particular on tourmaline and was described, among others, by Steno, Aepinus and Haüy. It was Sir David Brewster (1781-1788) who coined the term 'pyroelectricity' [Brewster, D. (1824). *Edinburgh. J. Sci.*, **1**, 208-215, *Observations on the pyroelectricity of minerals*, translated into German, *Poggendorf Ann. Phys.* (1824). **2**, 297-307, *Beobachtungen über die, in den Mineralien, durch Wärme erregte Electrizität*].

## See also

*An introduction to crystal physics*(Teaching Pamphlet No. 18 of the International Union of Crystallography)- Chapter 3.2.2.5 of
*International Tables for Crystallography, Volume A*, 6th edition - Chapter 1.1.4 and Part 3 of
*International Tables for Crystallography, Volume D*