The Piezoelectric Effect

The generation of electricity by the bending of certain crystals is known as the piezoelectric effect. Electricity that is created by the piezoelectric effect is called Piezoelectricity. The reverse piezoelectric effect is observed in several crystals when an applied voltage causes bending in the crystal. In Greek “Piezo” means to squeeze or to press.
The piezoelectric property is dictated by the way in which the atoms of the crystal align themselves. The crystal consists of many interlocking domains which have positive and negative charges. The domains within the crystal are symmetrical, with the result that the crystal has a net charge of zero, this symmetry is broken when a stress or load is applied to the crystal , and in order to recover

(1)
Where ε_ij and τ_kl denote the strain and stress tensor, respectively. S_ijkl is the compliance, and it is fourth-rank tensor quantity. The direct consequence of the symmetry in the strain and the stress tensors is that only 36 components of the compliance tensor are independent and distinct terms, instead of 81 components of the compliance tensor. The relation between the stress and the strain can be simplified through applying the Voigt notation as the following: ε_i=S_ij τ_j ………….. (2)
Because of the symmetry in the compliance tensor for the general anisotropic linear elastic solid, there are 21 independent elastic constants. By considering the symmetry conditions found in the wurtzite crystal structure of the ZnO NRs, the stress-strain relations are expressed as (the z-axis is the c-axis for wurtzite crystal): ……………. (3)

The elastic modulus (Young’s modulus) in remarkable crystallographic directions can be extracted from the compliance matrix as the following equations : E_([2(11) ̅0])=τ_1/ε_1=〖(S_11)〗^(-1) ………….. (4) E_([011 ̅0])=τ_2/ε_2=〖(S_11)〗^(-1) ………….. (5) E_([0001])=τ_3/ε_3=〖(S_33)〗^(-1) ………….. (6)

2.3 Theory of Piezoelectricity for Wurtzite