Third-order Dielectric Constants Research Articles

Third-order elastic, piezoelectric, and dielectric constants

The definitions of the third-order elastic, piezoelectric, and dielectric constants and the properties of the associated tensors are discussed. Based on the energy conservation and coordinate transformation, the relations among the third-order constants are obtained. Furthermore, the relations among the third-order elastic, piezoelectric, and dielectric constants of the seven crystal systems and isotropic materials are listed in detail. These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials. It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups, while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material. The reason is that some of the point groups are centrally symmetric, and the other point groups are high symmetry. These results provide the foundation to measure these constants, to choose material, and to research nonlinear problems. Moreover, these results are helpful not only for the study of nonlinear elastic and piezoelectric problems, but also for the research on flexoelectric effects and size effects.

Analysis of contributions of nonlinear material constants to temperature-induced velocity shifts of quartz surface acoustic wave resonators

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.

NONLINEAR DIELECTRIC MEASUREMENTS IN THE SMECTIC-A-SMECTIC-Cα* PHASE TRANSITION

We have performed precise measurements of the third-order dielectric constant in an antifer-roelectric crystal MHPOCBC. In the vicinity of the SmA- SmCα* phase transition point an anomalous increase of it was observed. We have developed a Landau theory taking into account the pretransitional fluctuations and shown that the fluctuation can contribute to the third-order response. The anomalous behavior near the transition point was discussed on the basis of the theoretical results.

Determination of Electrostrictive and Third-Order Dielectric Constants of Piezoelectric Ceramic

In this study, all six electrostrictive constants and all two third-order dielectric constants of lead zirconate titanate (PZT) ceramic are measured. To measure electrostrictive constants, new dynamic measuring methods to obtain capacitance variation with alternating stress and alternating electric field were used. These new methods enable us to obtain the electrostrictive constants and the third-order dielectric constants in the state of fixed polarization without an aging effect. These measured constants, defined in the d-form basic piezoelectric equation in which the electric field and stress are chosen to be independent field variables, are transformed into the constants defined in the g-form where electric displacement and stress are independent field variables for the reader's convenience.

Nonlinear Dielectric Measurements of Antiferroelectric Liquid Crystals

We have measured the linear and the third-order dielectric constants of an antiferroelectric liquid crystal MHPOBC and mixtures of R and S-enantiomers. In the optically pure and nearly pure samples with the SmCα* phase, the third-order dielectric constant discontinuously increases at the transition point from SmA to SmCα*, while the linear dielectric constant is continuous with a small change of the slope in its temperature dependence. These behaviors were well explained by the Landau theory. The optical purity dependence of the Curie constant was also investigated. The Curie constant slightly decreases as the optical purity is reduced, as predicted by the Landau theory.

Nonlinear dielectric constant in relaxor ferroelectrics

We have measured the linear and the third-order nonlinear dielectric constants in (1 – x)Pb (Mg1/2W1/2)O3–xPbTiO3 with concentrations x from 0·075 to 0·6. The third-order nonlinear constant shows a broad maximum in the temperature dependence and the maximum value steeply increases as x is increased. The third-order dielectric constant is positive for all the concentrations measured. The experimental results are discussed on the basis of a few models proposed to explain the linear dielectric properties.

Electro-Optic Effect and Third-Order Nonlinear Dielectric Response in Antiferroelectric Liquid Crystals

We have theoretically studied the electro-optic effect and third-order nonlinear dielectric response in antiferroelectric liquid crystals on the basis of phenomenological equations of motion. It has been found that the antiferroelectric soft and Goldstone modes can be excited by an electric field, though they respond to the square of the field but not to the field itself, and they modulate the dielectric constant both for the visible light and low frequencies, contributing to the electro-optic effect and the third-order nonlinear dielectric response, respectively. The transmitted intensity and the third-order dielectric constant were theoretically derived, and the former was compared with experimental results.

Nonlinear Dielectric Spectroscopy of the Goldstone Mode in an Antiferroelectric Liquid Crystal

The nonlinear dielectric spectroscopy of the Goldstone mode has been performed in a ferroelectric liquid crystal. The third-order dielectric constant obtained from the experiments was analyzed in terms of a formula derived from a phenomenological equation of motion by Orihara and Ishibashi [J. Phys. Soc. Jpn. 62 (1993) 489]. The dispersion and the Cole-Cole plot of the third-order dielectric constant were well reproduced by the theory, and the relaxation times obtained from the linear and the third-order dielectric constants were the same, indicating that the equation of motion is still valid in obtaining the nonlinear dielectric constants as well as the linear one. On the basis of the experimental results we discuss dynamic equations described in terms of fractional derivatives.

Nonlinear Dielectric Spectroscopy of the Goldstone Mode in a Ferroelectric Liquid Crystal

The nonlinear dielectric spectroscopy of the Goldstone mode has been performed in a ferroelectric liquid crystal. The third-order dielectric constant obtained from the experiments was analyzed in terms of a formula derived from a phenomenological equation of motion by Orihara and Ishibashi [J. Phys. Soc. Jpn. 62 (1993) 489]. The dispersion and the Cole-Cole plot of the third-order dielectric constant were well reproduced by the theory, and the relaxation times obtained from the linear and the third-order dielectric constants were the same, indicating that the equation of motion is still valid in obtaining the nonlinear dielectric constants as well as the linear one. On the basis of the experimental results we discuss dynamic equations described in terms of fractional derivatives.

A Phenomenological Theory of Nonlinear Dielectric Response in a Ferroelectric Liquid Crystal

We have derived expressions for the nonlinear dielectric susceptibility of a ferroelectric liquid crystal and a uniaxial ferroelectric crystal on the basis of equations of motion. Our results are different from a formula proposed by Nakada [O. Nakada: J. Phys. Soc. Jpn. 15 (1960) 2280], which was obtained from a tentative assumption. The temperature and frequency dependences of the third-order dielectric constant of a ferroelectric liquid crystal will be presented.

Nonlinear, elastic, piezoelectric, electrostrictive, and dielectric constants of lithium niobate

All eight electrostrictive, all three third-order dielectric, all thirteen third-order piezoelectric, and all fourteen third-order elastic constants of lithium niobate have been determined. Measurements for the electrostrictive constants have been made by measuring the electric capacity in selected directions when the directed static stresses were applied to the crystal. The third-order dielectric constants have been calculated from these measured electrostrictive constants and the measured capacitance as functions of the applied static electric field. The third-order piezoelectric and elastic constants have both been determined from the above-mentioned two kinds of measured constants and the measured velocities for small-amplitude ultrasonic waves as functions of several applied stresses and static electric fields.

Electrostrictive and Third-Order Dielectric Constants of Lithium Niobate

All 8 electrostrictive and all 3 third-order dielectric constants of lithium niobate have been determined. Measurements for the electrostrictive constants have been made by measuring electric capacity in selected direction when the directed static stresses were applied to the crystal. And the third-order dielectric constants have been calculated from these measured electrostrictive constants and the measured capacitance as a function of the applied static electric field. All of these measurements have been done at 15°C.

Electromechanical resonances for investigating linear and nonlinear properties of dielectrics

Abstract Methods are described for improving the accuracy and sensitivity of measurements of the electric response of crystals piezoelectrically or electrostrictively excited to natural modes of vibration. In such way it is feasible to simultaneously determine linear as well as nonlinear electromechanical and elastic properties on the same specimen. This is especially useful for investigating crystals near ferroelectric phase transitions as shown for barium titanate. The temperature dependence of second-and third-order elastic compliance and of third-order dielectric constant can be explained by distortion of centrosymmetry.

Application of ultrasonic standing waves to optical-beam scanning: Journal of the acoustical society of America, 36, No. 10, 1706 (1964)

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.

Ultrasonic atomization-some recent developments: Fuel efficiency, 12, No. 12, 16 (1964)

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.