# Difference between revisions of "Piezoelectricity"

### From Online Dictionary of Crystallography

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− | < | + | <font color="blue">Piezoélectricité</font> (''Fr''). <font color="red">Piezoelektrizität</font> (''Ge''). <font color="black">Piezoelettricità</font> (''It''). <font color="purple">圧電効果</font> (''Ja''). <font color="green">Piezoelectricidad</font> (''Sp''). |

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

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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 converse piezoelectric effect. The piezoelectric effect and the converse effect are described by third-rank tensors: | 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 converse piezoelectric effect. The piezoelectric effect and the converse effect are described by third-rank tensors: | ||

− | * For a small stress, represented by a second-rank tensor, ''T<sub>ij</sub>'', the resulting polarization, of components P''<sub>k</sub> | + | * For a small stress, represented by a second-rank tensor, ''T<sub>ij</sub>'', the resulting polarization, of components ''P''<sub>''k''</sub>, is given by |

<center>''P<sub>k</sub>'' = ''d<sub>kij</sub>T<sub>ij</sub>'' | <center>''P<sub>k</sub>'' = ''d<sub>kij</sub>T<sub>ij</sub>'' | ||

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

− | where the first-order term, ''d<sub>ijk</sub>'', represents the inverse piezoelectric effect and the second- | + | where the first-order term, ''d<sub>ijk</sub>'', represents the inverse piezoelectric effect and the second-order term, ''Q<sub>ijkl</sub>'', 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 | + | The matrices associated with the coefficients ''d<sub>kij</sub>'' and ''d<sub>ijk</sub>'' of the direct and converse piezoelectric effects, respectively, are transpose of one another. |

== Piezoelectric point groups == | == Piezoelectric point groups == | ||

− | The [[geometric crystal | + | The [[geometric crystal class]]es for which the piezoelectric effect is possible are determined by symmetry considerations (see [[Curie laws]]). They are the non-centrosymmetric classes, with the exception of 432. The 20 piezoelectric crystal classes are therefore: |

1, 2, ''m'', 222, 2''mm'', | 1, 2, ''m'', 222, 2''mm'', | ||

+ | 3, 32, 3''m'', 4, <math>{\bar 4}</math>,422, 4''mm'', <math>{\bar 4}</math>2''m'', 6, <math>{\bar 6}</math>, 622, 6''mm'', <math>{\bar 6}</math>2''m'', | ||

+ | 23, <math>{\bar 4}</math>3''m''. | ||

− | + | Quartz, belonging to geometric crystal class 32, is the most widely used piezoelectric crystal. | |

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− | Quartz, | ||

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

− | It | + | It was considerations of symmetry that led the brothers Jacques (1855-1941) and Pierre Curie (1859-1906) to the discovery of piezoelectricity in 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 == | == See also == | ||

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

+ | *Chapter 3.2.2.6 of ''International Tables for Crystallography, Volume A'', 6th edition | ||

+ | *Chapter 1.1.4 of ''International Tables for Crystallography, Volume D'' | ||

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

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

## Latest revision as of 09:49, 17 November 2017

Piezoélectricité (*Fr*). Piezoelektrizität (*Ge*). Piezoelettricità (*It*). 圧電効果 (*Ja*). Piezoelectricidad (*Sp*).

## Definition

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 converse piezoelectric effect. The piezoelectric effect and the converse effect are described by third-rank tensors:

- For a small stress, represented by a second-rank tensor,
*T*, the resulting polarization, of components_{ij}*P*_{k}, is given by

*P*=

_{k}*d*

_{kij}T_{ij}where *d _{kij}* is a third-rank tensor representing the direct piezoelectric effect.

- For a small applied electric field, of components
*E*, the resulting strain, represented by a second-rank tensor,_{k}*S*, is given by:_{ij}

*S*=

_{ij}*d*+

_{ijk}E_{k}*Q*

_{ijkl}E_{k}E_{l}where the first-order term, *d _{ijk}*, represents the inverse piezoelectric effect and the second-order term,

*Q*, 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.

_{ijkl}The matrices associated with the coefficients *d _{kij}* and

*d*of the direct and converse piezoelectric effects, respectively, are transpose of one another.

_{ijk}## Piezoelectric point groups

The geometric crystal classes for which the piezoelectric effect is possible are determined by symmetry considerations (see Curie laws). They are the non-centrosymmetric classes, with the exception of 432. The 20 piezoelectric crystal classes are therefore:

1, 2, *m*, 222, 2*mm*,
3, 32, 3*m*, 4, [math]{\bar 4}[/math],422, 4*mm*, [math]{\bar 4}[/math]2*m*, 6, [math]{\bar 6}[/math], 622, 6*mm*, [math]{\bar 6}[/math]2*m*,
23, [math]{\bar 4}[/math]3*m*.

Quartz, belonging to geometric crystal class 32, is the most widely used piezoelectric crystal.

## History

It was considerations of symmetry that led the brothers Jacques (1855-1941) and Pierre Curie (1859-1906) to the discovery of piezoelectricity in 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

- An introduction to crystal physics (Teaching Pamphlet No. 18 of the International Union of Crystallography)
- Chapter 3.2.2.6 of
*International Tables for Crystallography, Volume A*, 6th edition - Chapter 1.1.4 of
*International Tables for Crystallography, Volume D*