Nonlinear Piezoelectric Properties

Piezoelectric solids are characterized by constitutive relations among the stress t, strain rj, entropy s, electric field E, and electric displacement D. When uncoupled solutions are sought, it is convenient to express t and D as functions of t], E, and s. The formulation of nonlinear piezoelectric constitutive relations has been considered by numerous authors (see the list cited in [77G06]), but there is no generally accepted form or notation. With some modification in notation, we adopt the definitions of thermodynamic potentials developed by Thurston [74T01]. This leads to the following constitutive relations  

For many problems it is convenient to separate the piezoelectric (i.e., strain induced) polarization P from electric-field-induced polarizations by defining D = P + fi , where s is the permittivity tensor. For uniaxial strain and electric field along the 1 axis, when the material is described by Eq. (4.1) with the E term omitted. 

Mechanical wave-propagation problems are analyzed on the basis of quasistatic electromagnetic conditions. This is an excellent approximation since the electromagnetic wavespeed greatly exceeds the mechanical wavespeed and the particle velocity is typically only about one-tenth of the mechanical wavespeed. (See the discussion by Thurston [74T01].) 

Configurations of interest are those using disk-shaped samples cut from crystals in orientations that permit plane waves of uniaxial strain to propagate through their thickness when a uniform load is applied to their face. When the diameter of the disk is sufficiently large in comparison to its thick- 

74 Chapter 4. Physical Properties Under Elastic Shock Compression 

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Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

In this chapter nonlinear piezoelectric and dielectric behavior shock-induced electrical conductance semiconductors elastic physical properties. 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

It has been known that alternating LB films consisting of two different amphiphiles have noncentrosymmetric structures, and therefore, are expected to provide piezoelectric, pyroelectric and nonlinear optical properties. Therefore, we prepared alternating LB films consisting of 5-(p-dodecyloxyphenyl)pyrazine-2-carboxylic acid (DOPC)... 

The major trends in ferroelectric photonic and electronic devices are based on development of materials with nanoscale features. Piezoelectric, electrooptic, nonlinear optical properties of fe are largely determined by the arrangement of ferroelectric domains. A promising way is a modification of these basic properties by means of tailoring nanodomain and refractive index superlattices. 

UV Raman studies of ferroelectricity in strain-free non-stoichiometric and nominally stoichiometric SrTiOs films, in combination with dielectric, ferroelectric, nonlinear optical and nanoscale piezoelectric property measurements highlighted the sensitive role of stoichiometry when exploring strain and epitaxy-induced electronic phenomena in oxide films, heterostmctures, and interfaces. 

The scanner controlling the tip position and tip scanning is made from piezoelectric materials. The intrinsic physical and mechanical properties of piezoelectric materials, such as nonlinear piezoelectricity, hysteretic piezoelectricity and creep deformation affect the performance of the scanner. Such properties can generate distortion of SPM imaging during scanning. 

A number of other polymeric solids have also been the subject of much interest because of their special properties, such as polymers with high photoconductive efficiencies, polymers having nonlinear optical properties, and polymers with piezoelectric, pyroelectric and ferroelectric properties. Many of these polymeric materials offer significant potential advantages over the traditional materials used for the same application, and in some cases applications not possible by other means have been achieved. 

Thus it appears that amplification in the cochlea resides in the gating of the outer hair cell cflia, while the motility is due to passive piezoelectric properties of the cell wall. The flow through the gate has significant nonlinearity at small amplitudes of displacement of the cilia (10 nm). Sufficiently high amplitudes of displacement of the cilia will cause the tip links to buckle. We estimate that this will occur at around 70 dB sound pressure level, thereby turning off the active process for higher sound intensity. 

Cross-linked polymeric liquid crystals offer a wide variety of unique and in-tere.sting properties. Because of the interaction between the mesogens and the network backbone in liquid crystal elastomers, mechanical deformations can align the director, and these materials are piezoelectric. Industrial applications of liquid crystalline thermosets are driven by additional properties such as toughness, a tunable coefficient of thermal expansion, ferroelectricity, and nonlinear optical properties. Reviews on this topic are given by Barclay and Ober [4] and by Warner and Terentjev [5]. 

Like solid ferroelectrics, the ferroelectric liquid crystals, particularly the FLCPs, show a pyroelectric effect and a piezoelectric effect and are capable of switching polarization direction (dielectric hysteresis). Moreover, they can switch propagating or reflected polarized light. Finally, the polar symmetry of the phase leads to nonlinear optical properties of the FLCPs such as second-harmonic generation, the Pockels effect, and the Kerr effect. These physical properties of the ferroelectric LC polymers are discussed in the following sections. 

Some LC elastomers are ferroelectric that possess spontaneous electric polarization, or piezoelectric that become electrically polarized when mechanically strained, and become mechanically strained when exposed to an electric field. " Some LC elastomers exhibit interesting photonic effects such as nonlinear optical properties " which involve interactions of light such that phase or frequency (including frequency doubling or frequency mixing) characteristics of the incident light change. ... 

The particular choice of the authors was rather to put emphasis on experimental techniques that are either specifically relevant or powerfiil with respect to ferroelectric polymers and fenoelectrets or represent recent experimental developments and trends. In this sense, room was given to nonlinear dielectric properties that can be probed by nonlinear dielectric spectroscopy and various types of hysteresis experiments. Besides a systematic description of piezoelectric and inverse piezoelectric techniques, we have added dielectric resonance spectroscopy as an all-round approach yielding elastic, piezoelectric, and dielectric properties of polymer electrets in a single dielectric measurement. 

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