Piezoelectric effect direct

In many microelectromechanical systems (mems) based on piezoelectric thin films, flexure is deliberately used to amplify the available displacements (or alternatively to increase the sensitivity of a sensor). For simplicity (and to keep poling and actuation voltages low), films are often poled and driven by electrodes at the top and bottom surfaces. As a result, the critical piezoelectric coefficient is often e31 j, rather than d33j [24], For the direct effect, the effective film coefficient, e3ij can be defined by... 

Figure 13.1 Examples of the field dependence of piezoelectric coefficients (a) direct effect in ferroelectric ceramics, measured with a dynamic press (b) converse effect in rhombohedral 60/40 pzt thin films with different orientations, measured with an optical interferometer [1], correspond to pseudocubic axes.

Piezoelectric properties are described in terms of the parameters D, E, X and x, where X is stress. The electrical response due to the direct effect can be expressed in terms of strain by... 

Piezoelectric effect The generation of a small potential difference across certain crystals when they are subjected to stress (direct effect), or the change in shape of a crystal that accompanies the application of a potential difference across a crystal (inverse effect). The piezoelectric effect is only shown by noncentrosymmetric crystals. 

Piezoelectricity is a reversible property possessed by a select group of materials that does not have a center of symmetry. When a dimensional change is imposed on the dielectric, polarization occurs and a voltage or field is created. This is the direct effect. When an electric field is applied to a dielectric, polarization may change its dimensions. This is the inverse effect, also called electrostric-tion. Dielectric materials that display this reversible behavior are piezoelectric. 

The piezoelectric effect (Fig. 4) was discovered by Pierre and Jacques Curie in 1880. The direct piezoelectric effect consists of the ability of crystalline materials (ceramics) to generate an electrical charge in proportion to an externally applied force. The direct effect is used in force transducers. According to the inverse piezoelectric effect, an electric field parallel to the direction of polarizatitMi induces an expansion of the ceramic (Preumont 1997). 

As in the piezoelectricity of solids, flexoelectricity also manifests as a direct effect [f, Eq. (6.4)] and a converse effect [f, Eq. (6.5)], with an electric field-induced curvature ... 

Polarization associated with a given strain is always the same, whether the strain is due to mechanical forces (direct effect) or to an impressed electric field (corrverse effect). Later on, in Chap. 4, we will prove the equality of the piezoelectric constants used to describe both effects. 

The direct effect coefficients are defined by the derivatives (5D/SX) = d (piezoelectric strain coefficient), (5D/5x) = e, -(5E/5X) = g (piezoelectric voltage constant) and -(5E/5x) = h. The converse-effect coefficients are defined by the derivatives (8x/5E) = d, (5x/5D) = g, -(5X/5E) = e, and -(5X/5D) = h. As the piezoelectric coefficients are higher-rank tensors, their mathematical treatment is rather tedious. Fortunately, in higher symmetric crystals the number of tensorial components will be drastically reduced due to symmetry constraints. An example is shown below. 

Direct effect Direct piezoelectricity d, e, g, h) Dieiectrostriction/stress birefringence... 

The piezoelectric phenomena also occur as both the direct and converse effect. With the direct effect, an external stress, crjk, results in a change in polarisation, P . The direct effect is mathematically described... 

We now consider the converse of the above, namely the distortion suffered by an anisotropic crystal as a response to an externally applied electric field , which is known as the converse piezoelectric effect. Here the imposition of an electric field creates a unique alignment direction for the dipoles that eliminates the cancellation effect described earlier. As a result, the crystal deforms. The coefficients relating the strain to the electric field are the same as those that connect the polarization to the stress in the direct effect. The proof will be provided later by noncircular arguments. We thus characterize the present linear dependence by the relation... 

Pyroelectrics. Pyroelectric ceramics are materials that possess a uoique polar axis and are spontaneously polarized ia the abseace of an electric field. Pyroelectrics are also a subset of piezoelectric materials. Ten of the 20 crystal classes of materials that display the piezoelectric effect also possess a unique polar axis, and thus exhibit pyroelectricity. In addition to the iaduced charge resultiag from the direct pyroelectric effect, a change ia temperature also iaduces a surface charge (polarizatioa) from the piezoelectric aature of the material, and the strain resultiag from thermal expansioa. 

For mechanical wave measurements, notice should be taken of the advances in technology. It is particularly notable that the major advances in materials description have not resulted so much from improved resolution in measurement of displacement and/or time, but in direct measurements of the derivative functions of acceleration, stress rate, and density rate as called for in the theory of structured wave propagation. Future developments, such as can be anticipated with piezoelectric polymers, in which direct measurements are made of rate-of-change of stress or particle velocity should lead to the observation of recognized mechanical effects in more detail, and perhaps the identification of new mechanical phenomena. 

The piezoelectric response investigation also provides direct evidence that significant inelastic deformation and defect generation can occur well within the elastic range as determined by the Hugoniot elastic limit. In quartz, the Hugoniot elastic limit is 6 GPa, but there is clear evidence for strong nonideal mechanical and electrical effects between 2.5 and 6 GPa. The unusual dielectric breakdown phenomenon that occurs at 800 MPa under certain... 

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