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Nonlinear piezoelectric constant

The measured relationships between piezoelectric polarization and strain for x-cut quartz and z-cut lithium niobate are found to be well fit by a quadratic relation as shown in Fig. 4.4. In both materials a significant nonlinear piezoelectric effect is indicated. The effect in lithium niobate is particularly notable because the measurements are limited to much smaller strains than those to which quartz can be subjected. The quadratic polynomial fits are used to determine the second- and third-order piezoelectric constants and are summarized in Table 4.1. Elastic constants determined in these investigations were shown in Chap. 2. [Pg.79]

The determination of piezoelectric constants from current pulses is based on interpretation of wave shapes in the weak-coupling approximation. It is of interest to use the wave shapes to evaluate the degree of approximation involved in the various models of piezoelectric response. Such an evaluation is shown in Fig. 4.5, in which normalized current-time wave forms calculated from various models are shown for x-cut quartz and z-cut lithium niobate. In both cases the differences between the fully coupled and weakly coupled solutions are observed to be about 1%, which is within the accuracy limits of the calculations. Hence, for both quartz and lithium niobate, weakly coupled solutions appear adequate for interpretation of observed current-time waveforms. On the other hand, the adequacy of the uncoupled solution is significantly different for the two materials. For x-cut quartz the maximum error of about 1%-1.5% for the nonlinear-uncoupled solution is suitable for all but the most precise interpretation. For z-cut lithium niobate the maximum error of about 8% for the nonlinear-uncoupled solution is greater than that considered acceptable for most cases. The linear-uncoupled solution is seriously in error in each case as it neglects both strain and coupling. [Pg.81]

Several structural theories of piezoelectricity [72M01, 72M02, 72A05, 74H03] have been proposed but apparently none have been found entirely satisfactory, and nonlinear piezoelectricity is not explicitly treated. With such limited second-order theories, physical interpretations of higher-order piezoelectric constants are speculative, but such speculations may help to place some constraints on an acceptable piezoelectric theory. [Pg.82]

The bending piezoelectricity in drawn and polarized polymer films was studied in detail by Kawai (1) (1970). Kitayama and Nakayama (1971) reported a very high piezoelectricity in composite films of polymer (PVDF, nylon 11, PVC) and powdered ceramics (barium titanate, PZT) after poling. In the case of PVDF and nylon, the piezoelectric constant increase by a factor of 102 when the ceramics make up 50% of the volume. The pyroelectricity and optical nonlinearity of polarized PVDF films have been studied by Bergmann, McFee, and Crane (1971). [Pg.47]

With this background, we have proposed and developed a new purely electrical method for imaging the state of the polarizations in ferroelectric and piezoelectric material and their crystal anisotropy. It involves the measurement of point-to-point variations of the nonlinear dielectric constant of a specimen and is termed scanning nonlinear dielectric microscopy (sndm) [1-7]. This is the first successful purely electrical method for observing the ferroelectric polarization distribution without the influence of the screening effect from free charges. To date, the resolution of this microscope has been improved down to the subnanometer order. [Pg.303]

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],... [Pg.251]

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... [Pg.589]

Landolt-Bomstein Numerical Data and Functional Relationships in Science and Technology, III/ll, Elastic, Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals, Springer-Verlag, Berlin, 1979. [Pg.1714]

Landolt-Bomstein Tables, Neue Serie Vol. lll/30b. Springer Verlag. Gurzadyan GG, Charra F (2000) High Fiequeney Properties of Dielectrie Crystals. Nonlinear Dieleetric Susceptibilities. Lee S-H, Roh Y (2007) Characterization of all the elastic, piezoelectric, and dielectric constants of tetragonal PMN-PT single crystals, Jpn J Appl Phys 46, 7B 4462 465 Levinson LM (1988) Electronic ceramics - Properties, Devices and Applications. Marcel Dekker, New York, NY... [Pg.182]

Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constant, and Nonlinear Dielectric Susceptibilities 4.607... [Pg.900]


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