Piezoelectric effect general

In a normal dielectric, the observed polarisation of the material is zero in the absence of an electric field, and this does not change if the material is heated or subjected to mechanical deformation. In a piezoelectric solid a surface electric charge develops when the solid is subjected to a mechanical stress such as pressure, even in the absence of an external electric field. This is called the direct piezoelectric effect. The effect is reversible and the inverse (or converse) piezoelectric effect, in which a voltage applied to a crystal causes a change in shape, also occurs in piezoelectric crystals. The piezoelectric effect generally varies from one direction to another in a crystal, and in some directions a crystal may show no piezoelectric effect at aU whereas in other directions it is pronounced. 

In general terms, the pyroelectric coefficient of a free sample consists of three components. The first, called the real coefficient, depends on the derivative of spontaneous polarization with respect to the temperature. The second is derived from the temperature dilatation and can be calculated based on mechanical parameters. The third coefficient is related to the piezoelectric effect and results from the temperature gradient that exists along the polar axis of the ciystal. 

The two main types of electromechanical transducers are based on either the piezoelectric or the magnetostrictive effect. The more commonly used of which are piezoelectric transducers, generally employed to power the bath and probe type sonicator systems. Although more expensive than mechanical transducers, electromechanical transducers are by far the most versatile and widely used. 

As stated in the Introduction, as-cast polymer films in general show a weak piezoelectric effect in both elongation and bending. The results by Furukawa, Uematsu, Asakawa and Wada (1968) for five kinds of polymer films are illustrated in Figs. 18 and 19. The effect is ascribed to space charges embedded in the film. 

The term piezoelectric nonlinearity is used here to describe relationship between mechanical and electrical fields (charge density D vs. stress a, strain x vs. electric field E) in which the proportionality constant d, is dependent on the driving field, Figure 13.1. Thus, for the direct piezoelectric effect one may write D = d(a)a and for the converse effect x = d(E)E. Similar relationships may be defined for other piezoelectric coefficients (g, h, and e) and combination of electro-mechanical variables. The piezoelectric nonlinearity is usually accompanied by the electro-mechanical (D vs. a or x vs. E) hysteresis, as shown in Figure 13.2. By hysteresis we shall simply mean, in the first approximation, that there is a phase lag between the driving field and the response. This phase lag may be accompanied by complex nonlinear processes leading to a more general definition of the hysteresis [2],... 

Pyroelectricity The piezoelectric effect is generally stronger in materials that... 

Piezoelectric effect is of fundamental importance for the piezoelectric measurements technology. General thermodynamic theory of a piezoelectric effect will be described more in details in this paragraph. Temperature or entropy a is held constant in the diagram according to Fig. 4.1. Hence the diagram is reduced just to the relationship between mechanical quantities or (stress or strain) and electrical quantities Ek or Dk (electric field or electric displacement). No special superscript for isothermal or adiabatic option is further used in linear piezoelectric equations of state. Omitting abovementioned thermal quantities, the system of 24 equations of state in Table 4.1 is reduced just to 8 equations - see Fig. 5.1 and Eqs. (5.1), (5.2), (5.3), (5.4), (5.5), (5.6), (5.7), and (5.8). 

Generally, the piezoelectric effect could exist just in non-centrosymmetrical crystallographic symmetry classes. Mechanical stress/strain as a second-rank symmetrical tensors are basically centrosymmetrical external fields. If the materials crystallographic symmetry include cerrtre of symmetry operation, the resulting symmetry of material subjected to such field is also cerrtrosymmetrical (see Neuman s Law in Nye (1985)). Therefore, piezoelectric effect is excluded. Centrosymmetrical crystal stays centrosymmetrical even after the application of the mechanical stress and no polar direction for the polarization vector might exist in such stmcture. 

Crystallographic symmetry results in some constraints to the tensor components of any material property of the crystal. Tensor components transformation, corresponding to any symmetry element, must not resnlt in any change of the material property tensor. Piezoelectric effect is described by third-rank tensor. According to the general transformation mle (see Eq. (2.39)) applied to piezoelectric tensor... 

Many digital applications require that a highly reproducible and accurately known frequency source be used in conjunction with the measurement of time as shown in Figure 4-4b and c. Generally, electronic frequency sources are ba.sed on quartz crystals that exhibit the piezoelectric effect, as described in Section lC-4. The resonant frequency of a quartz crystal depends on the mass and dimensions of the crystal. By varying these parameters, electrical output frequencies that range from 10 kHz lo 50 MHz or greater can be obtained. Typically, these frequencies are constant to 100 ppm. With special precautions, such as precise temperature control, crystal oscillators can be constructed for time standards that are accurate to 1 part in 10 million. 

For sensor applications, use is made of the direct piezoelectric effect and thus the piezoelectric cube described above now has to be subjected to mechanical fields. Strains and stresses are applied via associated surfaces either by prescribed displacements in a clamped configuration or by applied forces in a free configuration. Besides the intended sensor application, this, of corrse, is also relevant to the case of solely passive transmission of loads. Consequently, the subsequent examinations are also important for the general application of electromechanically coupled materials in adaptive structures. For mechanical fields operating opposed or transverse to the polarization direction, the field levels are limited by the risk of repolarization similar to the actuation case. 

---