Length-extensional Vibration Research Articles

Leakage electric field in longitudinal vibration from piezoelectric bars

The edge effects due to leakage electric fields in piezoelectric bar specimens cause non-uniform charge densities, distort electric field lines, and increase capacitance. This increase in capacitance was simulated using finite-element-method-based electric field simulation software. The two-dimensional and three-dimensional simulation results showed that the rate of increase in capacitance decreased when the aspect ratio or dielectric constant increased. To increase measurement accuracy of the dielectric, piezoelectric, and elastic constants of piezoelectric single crystals, the rate of increase in capacitance should be maintained below 0.5%. Actual measurements and theoretical analysis of the transverse- and longitudinal-effect length-extensional vibration in specimens with a small dielectric permittivity were performed. The results indicated that can be obtained directly from the fr of a transverse-effect length-extensional vibration, but kij and dij must be compensated for if the rate of increase in capacitance is greater than 0.5%. After compensation, it is possible to measure kii from longitudinal-effect length-extensional vibration in specimens with a reasonable dielectric permittivity, but one must avoid using it to measure and

Evaluation of a silicon 5 MHz p–n diode actuator with a laterally vibrating extensional mode

In this paper, we describe p–n diode actuators that are laterally driven by the force induced in a depletion layer. The previously reported p–n diode actuators have been vertically driven. Because the resonant frequency depends on the thickness of the vibrating plate, the integration of resonators with different frequencies on a chip has been difficult. The resonators in this work are driven laterally by using length-extensional vibration. We have developed a compact model based on an analytical expression, in which p–n diode actuators are driven by the forces induced by the spread of the depletion layer. The deflection generated by the p–n diode actuators was proportional to the ratio of the depletion layer width to the resonator thickness as well as the position of the p–n junction. Good agreement of experimental results with the theory was confirmed by comparing the measured values for silicon p–n diode rectangular-plate actuators fabricated using a silicon-on-insulator (SOI) substrate. The displacement amplitude of the actuators was proportional to the DC bias, while the resonant frequency was independent of the DC bias. The latter characteristic is very different from that of widely used electrostatic actuators. Although the amplitude of the actuator measured in this work was very small, it is expected that the amplitude will increase greatly by increasing the doping of the p–n diode actuators.

Wireless Power Transmission Based on Sandwiched Composite Piezoelectric Transducers in Length Extensional Vibration

A new type of wireless power transmission system is proposed. It is composed of two sandwiched composite piezoelectric transducers in length extensional vibration, which are connected together by an intermediate metal transmission cylinder. When the dielectric and mechanical losses are considered, the resonance/antiresonance frequency equations are obtained. The effect of the mechanical and the dielectric loss, the geometrical dimension and the load electric impedance on the effective electromechanical coupling coefficient, the voltage gain, and the power ratio is analyzed. It is shown that the mechanical and the dielectric losses almost have no effect on the resonance/antiresonance frequency. The geometrical dimension has obvious effect on the resonance/antiresonance frequency, the voltage gain, the effective electromechanical coupling coefficient and the power ratio. Corresponding to definite geometrical dimensions, the effective electromechanical coupling coefficient and the voltage gain have maximum values. There is optimum load electric impedance at which the power ratio reaches the maximum value. Two wireless power transmission systems are designed and manufactured; the resonance/antiresonance frequencies, the voltage gain, and the power ratio are measured. It is shown the measured frequencies are in good agreement with the theoretical results.

Electrical Properties of Lead-free Niobium Rich Piezoelectric (K0.95Li0.05) (Ta1-x Nb x ) O3 Single Crystals

The high quality (K0.95Li0.05) (Ta1-x Nb x ) O3 (KLTN), x = 0.60, single crystals have been successfully grown by the Top-seeded melt growth method (TSSG). Its structure, dielectric, pyroelectric and piezoelectric properties have been investigated. Based on the dielectric and pyroelectric properties measurements, rhombohedral to orthorhombic and orthorhombic to tetragonal transition temperatures are found to be 88 K, 195 K, respectively, and the Curie temperature was 445 K. From the pyroelectric curves, the integrated spontaneous polarization, ∼16 μC/cm2 and the figure of merits (FOMs) are calculated at room temperature. Resonance and anti-resonance method is used to measure the piezoelectric coefficients; thickness vibration mode (k t) 60.4% and the length-extensional vibration mode (k 31) 56.2%, for the KLTN single crystals are attractive for the piezoelectric and pyroelectric applications.

High-frequency extensional vibrations of piezoelectric ceramic bars polarized in the longitudinal direction

The approximate 1-D governing equations for coupled length-extensional, width-stretch, and symmetric width-shear vibration modes in rectangular finite piezoelectric bars with 6 mm hexagonal symmetry are presented. The bars polarized in the longitudinal direction with electrodes on the faces perpendicular to the length are considered. The system of equations is used to study the frequency spectrum of piezoelectrically forced vibrations of bars made of hard ceramics. The influence of the width-to-thickness ratio on the resonance frequency is discussed. The computed values are compared with experimental data. The material constants used for numerical simulations of resonant frequencies were obtained from the measurements on APC 841 PZT ceramics samples.

Piezoelectric Resonators with Engineered Domain Structures

Domain engineered structures prepared in PZT ceramics are studied for the possible application for piezoelectric resonators. Bar shaped resonators segmented into several domain volumes with antiparallel polarization show multiplication of the fundamental resonant frequency for the length extensional vibration mode. Radial vibration mode for thin disc with two radial domain segments poled in antiparallel direction is further studied theoretically and experimentally. Results reveal that the fundamental resonance could not be shifted by the domain volumes distribution in the resonator, on the contrary to bar resonators. Temperature coefficients for the fundamental resonant frequency of twin domain disc are calculated and measured as a function of domain segment distribution. They were found to be independent on the domain size. Higher overtones might change their frequencies as a function of domain distribution.

Equivalent Network Representation for Length-Extensional Vibration Modes in Side-Plated Piezoelectric Bar with Varying Parameter Operating through Transverse Piezoelectric Effect

Equivalent network representation is derived for length-extensional vibration modes in a side-plated piezoelectric bar with a varying parameter along it. In contrast to the findings of a previous study, which dealt with the longitudinal piezoelectric effect, the bar in this study is presumed to be excited through a transverse piezoelectric effect. The network comprises an electrical transmission line of length corresponding to the bar length and an electrical port with a capacitor that is linked to the line at both its ends via two ideal transformers. The frequency characteristics of the input electric admittance of the bar with a linearly or sinusoidally varying piezoelectric parameter, which shows the unique feature of the vibrator, are demonstrated using equivalent network analysis. The possibility of applying this network to the modeling of the interdigital transducer for the excitation and detection of surface acoustic waves (SAWs) is discussed.

P1-20 Equivalent Network Representation for Length-Extensional Vibration Modes in a Side-Plated Piezoelectric Bar with a Varying Parameter Operating through the Transverse Piezoelectric Effect(Poster session 1)

P1-20 Equivalent Network Representation for Length-Extensional Vibration Modes in a Side-Plated Piezoelectric Bar with a Varying Parameter Operating through the Transverse Piezoelectric Effect(Poster session 1)

Anisotropy of Mono-Domain Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 Single Crystal with Giant Electromechanical Coupling Factor of k31 Mode

The processes to realize giant k 31 over 80% were investigated. The giant k 31 in Pb[(Zn 1/3 Nb 2/3 ) 0.91 Ti 0.09 ]O 3 (PZNT91/09) single-crystal plates was obtained by controlling the process combination of the DC poling and the thermal treatment. Frequency responses of impedance up to 500 kHz in various plate samples were analyzed on the length extensional vibration modes of k 31 and k 32 . It was found that there were two frequency constants of 520 kHz-m and 830 kHz-m on these modes. The anisotropy on k 31 and k 32 modes can be explained by the reorientation for their frequency constants. Furthermore, the appearance of the giant k 31 needed the low frequency constant in k 32 mode, and finally, the PZNT91/09 single crystals changed into a new phase with the low frequency constant in k 31 mode.

Nonlinear Piezoelectric Coefficients in Compositions near Morphotropic Phase Boundary of PbZrO3-PbTiO3-Pb(Mg1/3Nb2/3)O3 Piezoelectric Ceramics

Linear and nonlinear piezoelectric coefficients of second- and third-higher terms in length-extensional vibration were experimentally investigated in the compositions near the morphotropic phase boundary (MPB) of PbZrO3-PbTiO3-Pb(Mg1/3Nb2/3)O3 ternary piezoelectric ceramics. The Zr/Ti ratio showing the maximum value of the piezoelectric constant d31 disagreed with that showing the maximum value of the electromechanical coefficient k31 in the transverse vibration. The disagreement increased with Pb(Mg1/3Nb2/3)O3 (PMN) content. The nonlinear piezoelectric coefficients of the second- and third-higher terms showed their minimum values at the Zr/Ti ratios showing the maximum values of d31. Hence, the Zr/Ti ratio showing the maximum value of d31 was regarded as the MPB composition. The nonlinear coefficients of the second- and third-higher terms on the MPB compositions showed different dependences on PMN content. The nonlinear coefficient of the second-higher term showed a grain size dependence in its change, and that of the third-higher term showed a mechanical quality factor dependence in its change. The difference in the dependences was discussed from the viewpoint of the difference in the occurrence mechanism of nonlinear phenomena dominating the two nonlinear coefficients.

Piezoelectric Properties of Vanadium-Substituted Strontium Bismuth Niobate

Vanadium-substituted strontium bismuth niobate, SrBi2Nb1.95V0.05O9 (SBNV), ceramics were synthesized by a low-temperature process, and the detailed piezoelectric properties of the SBNV ceramics were characterized. Dense SBNV ceramics were obtained at a sintering temperature of 950°C, which is 200°C lower than that for nonsubstituted (SBN) ceramics. With the substitution of vanadium cations for niobium the ferroelectric D–E hysteresis loops were observed at room temperature and the remanent polarization, Pr, and coercive field, Ec, obtained were 5.4 µC/cm2 and 105 kV/cm, respectively. The independent electromechanical coupling factors obtained, which were characterized by the resonance-antiresonance method, were as follows: kp=0.074, k31=0.045, k33=0.175, k15=0.106, and kt=0.140. The mechanical quality factor, Qm, of the SBNV ceramics in the (33)-mode was 5500, which was about three times that of SBN. The temperature dependences of the resonance frequency (TCF) in the length extensional vibration mode of the SBNV and SBN ceramics were 42.1 ppm/°C and 34.6 ppm/°C, respectively.

열에이징에 의한 PZT세라믹스의 내열특성 개선

Temperature stabilities of resonance frequencies of the substrates are very important in piezoelectric ceramics oscillators and fitters. In this study, it was investigated thermal resisting property of the length-extensional vibration mode of PZT ceramics. The mode can be utilized in fabricating ultra-small 55 kHz IF devices. We fabricated the ceramic specimens with x = 0.51, 0.52, 0.53, 0.54, and 0.55 in the Pb(Zr<TEX>$\sub$</TEX>x/Ti<TEX>$\sub$</TEX>1-x/)O<TEX>$_3$</TEX> system. And their resonance frequencies were measured before 1st thermal aging, after 1st and 2nd thermal aging. In order to investigate the influence of thermal aging on thermal resisting properties, thermally aged specimens were once mote thermally aged. Before 1st thermal aging, the specimens of the compositions with morphotropic phase, x = 0.53 and rhombohedral phase, x = 0.54 have weak thermal resisting property of resonance frequency, while tetragonal phase, x = 0.51 has robust thermal resisting property of resonance frequency. 1st thermal aging improved thermal resisting property of resonance frequency in all specimens.

Effect of DC bias field on the complex materials coefficients of piezoelectric resonators

Abstract In many practical applications, piezoelectric devices are driven under strong electric field or under DC bias field. To evaluate the performance of the piezoelectric devices under these strong field conditions, the materials constants measured under weak field are usually not applicable. In this paper, we report our measurement results on the effect of DC bias field on the complex piezoelectric, dielectric and elastic coefficients of piezoelectric lead zirconate titanate ceramic resonator. A thin plate soft PZT resonator (transverse mode) is used in this study. A recently developed accurate method is used to directly characterize the complex materials coefficients, in which for a thin plate PZT resonator with length extensional vibration mode, normalized electric admittance, Y (=Y/ω) instead of admittance Y spectrum is used to determine the materials coefficients under various DC bias fields applied along the polarization direction. It has been found that with DC bias field increasing, elastic compliance, piezoelectric coefficient and dielectric permittivity decrease with approximately linear relationships. Second-order electromechanical coefficients can be estimated through the measurement of materials coefficients under DC bias conditions. Based on the observation of frequency increasing with DC bias field, it is suggested that the DC bias field can be used for frequency tuning or frequency–temperature compensation.

PZT 세라믹스에 있어서 길이진동모드의 경시변화

PZT 세라믹스에 있어서 길이진동모드의 경시변화

A Study on the Rectangular-Bar-Shaped Multilayer Piezoelectric Transformer Using Length Extensional Vibration Mode

The rectangular-bar-shaped multilayer piezoelectric transformer, which employs the length extensional vibration mode and interdigital internal electrodes, has been suggested and developed by us for the application to AC adapters. First, the methods of increasing the power-to-volume ratio of the transformer are investigated experimentally. As a result, it is found that using a high driving frequency and optimizing the positions of input and output parts increase the power-to-volume ratio. Second, to prevent characteristic degradation resulting from spurious vibrations in its driving frequency range, the methods of controlling such spurious vibrations are studied theoretically and experimentally. It is found that controlling the size of the transformer can widen the driving frequency range without spurious vibrations, and that using a low order length extensional vibration mode can decrease the number of spurious vibrations in its driving frequency range. Also, it is found that spurious vibrations can be eliminated or weakened by properly arranging the positions of input and output parts according to the mode pattern of the spurious vibrations.

Analysis of Nonlinear Phenomena in Piezoelectric Ceramics under High-Power Vibration

Generation of higher harmonic voltages in piezoelectric ceramics driven at high-power resonance frequency levels was investigated. Rectangular bar samples with a high mechanical quality factor were prepared for this study. The samples were driven at a fundamental resonance frequency of the length extensional vibration mode by a constant current method, and their current, voltage and displacement were simultaneously measured. When the samples were driven at a constant current higher than the threshold level, distinct distortion in voltage waveform was observed while current waveform and displacement were exactly sinusoidal. By analyzing the distorted voltage waves with a spectrum analyzer, the distortion of the voltage wave was found to be due to the generation of higher harmonic voltages. The 2nd and 3rd harmonic voltages were measured as a function of current, and their magnitudes satisfied the power laws of square and cubic of the current, respectively. These experimental results can be explained by nonlinear piezoelectric equations derived from the ferroelectric theory.

Nonlinear Equivalent Circuit Model Analysis of Acoustic Devices and Propagation of Surface Acoustic Wave

The generation of acoustic phase conjugate waves is demonstrated using our previously reported nonlinear equivalent circuit of thin bar with length-extensional vibration. Next, a new nonlinear equivalent circuit for propagating nonlinear surface acoustic wave (SAW) is proposed. Using this new circuit, it is shown that the metallic grating wave guide of SAW is equivalent to the nonlinear lattice in which the SAW soliton propagates. Finally, the experimental study about this waveguide is successfully performed.