# Pyroelectricity

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

If the crystal is also piezoelectric, the polarization due to an applied temperature variation is also partly due to the piezoelectric effect. The *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

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 *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

- Section 10.2 of
*International Tables of Crystallography, Volume A* - Section 1.1.4 and part 3 of
*International Tables of Crystallography, Volume D*