From Online Dictionary of Crystallography

Revision as of 06:18, 6 March 2006 by AndreAuthier (talk | contribs)

Piezoélectricité (Fr). Piezoelectrizität (Ge). Piezoelectricidad (Sp).


Piezoelectricity is the property presented by certain materials that exhibit an electric polarization when submitted to an applied mechanical stress such as a uniaxial compression. Conversely, their shape changes when they are submitted to an external electric field; this is the connverse piezoelectric effect. The piezoelectric effect and the converse efect are described by third-rank tensors:

  • For a small stress, represented by a second-rank tensor, Tij, the resulting polarization, of components Pk , is given by:
Pk = dkijTij

where dkij is a third-rank tensor representing the direct piezoelectric effect.

  • For a small applied electric field, of components Ek, the resulting strain, represented by a second-rank tensor, Sij, is given by:
Sij = dijkEk + QijklEkEl

where the first-order term, dijk, represents the inverse piezoelectric effect and the second-orer term, Qijkl, a symmetric fourth-rank tensor, the electrostriction effect. The sense of the strain due to the piezoelectric effect changes when the sign of the applied electric field changes , while that due to electrostriction, a quadratic effect, does not.

The matrices associated to the coefficients dkij and dkij of the direct and converse piezoelectric effects, respectively, are transpose of one another.

Piezoelectric point groups

The appearance of piezelectricity is compatible with the symmetry properties of the non-centrosymmetric point groups, with the exception of 432. The 20 piezoelectric point groups are therefore:

1, 2, m, 222, 2mm,

3, 32, 3m, 4, [math]{\bar 4}[/math],422, 4mm, [math]{\bar 4}[/math]2m, 6, [math]{\bar 6}[/math],622, 6mm, [math]{\bar 6}[/math]2m

23, [math]{\bar 4}[/math]3m

Quartz, of point group 32, is the most widely used piezoelectric crystal.


It is considerations of symmetry that led the brothers Jacques (1855-1941) and Pierre Curie (1859-1906) to the discovery of piezoelectricity on materials such as tourmaline, quartz, boracite, sodium chlorate, Rochelle salt (Curie J. and Curie P., 1880, C. R. Acad. Sci. Paris, 91, 294-295, Développement, par pression, de l'électricité polaire dans les cristaux hémièdres à faces inclinées. The inverse piezoelectric effect was predicted by Lippmann G., 1881, Ann. Chim. Phy. 24, 145-178, Principe de conservation de l'électricité and discovered by Curie J. and P., 1881, C. R. Acad. Sci. Paris, 93, 1137-1140 , Contractions et dilatations produites par des tensions électriques dans les cristaux hémièdres à faces inclinées.

See also

Section 10.2 of International Tables of Crystallography, Volume A
Section 1.1.4 of International Tables of Crystallography, Volume D