6.8: Piezoelectricity
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 ij , the resulting polarization, of components 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 k , the resulting strain, represented by a second-rank tensor, S ij , is given by:
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 ijkl , 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 d kij and d kij of the direct and converse piezoelectric effects, respectively, are transpose of one another.