# Pyroelectricity

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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 electic field, it will undergo a change of entropy Δσ: |

<center> | <center> |

## Revision as of 08:51, 12 January 2007

Pyroélectricité (*Fr*). Pyroelectrizität (*Ge*). Pyroelectricidad (*Sp*). Piroelettricità (*It*)

## Contents |

## 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 polarisation 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 electic field, it will undergo a change of entropy Δσ:

Δσ = *p _{i} E^{i} *

and will release or absorb a quantity of heat gien 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. It is 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 Electricität*).

## See also

An introduction to crystal physics (Teaching Pamphlet of the *International Union of Crystallography*)

Section 10.2 of *International Tables of Crystallography, Volume A*

Section 1.1.4 and part 3 of *International Tables of Crystallography, Volume D*