Piezoelectricity
- Page ID
- 17640
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, 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-order 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.