Theoretical analysis of surface waves in piezoelectric medium with periodic shunting circuits

The investigations of surface waves in the piezoelectric medium bring out great possibility in designing smart surface acoustic wave(SAW)devices.It is important to study the dispersion properties and manipulation mechanism of surface waves in the semi-infinite piezoelectric medium connected with periodic arrangement of shunting circuits.In this study,the extended Stroh formalism is developed to theoretically analyze the dispersion relations of surface waves under different external circuits.The band structures of both the Rayleigh wave and the Bleustein-Gulyaev(BG)wave can be determined and manipulated with proper electrical boundary conditions.Furthermore,the electromechanical coupling effects on the band structures of surface waves are discussed to figure out the manipulation mechanism of adjusting electric circuit.The results indicate that the proposed method can explain the propagation behaviors of surface waves under the periodic electrical boundary conditions,and can provide an important theoretical guidance for designing novel SAW devices and exploring extensive applications in practice.

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.

WAVE PROPAGATION IN TWO-DIMENSIONAL DISORDERED PIEZOELECTRIC PHONONIC CRYSTALS

The wave propagation is studied in two-dimensional disordered piezoelectric phononic crystals using the finite-difference time-domain （FDTD） method. For different cases of disorder, the transmission coefficients are calculated. The influences of disorders on band gaps are investigated. The results show that the disorder in the piezoelectric phononic crystals has more significant influences on the band gap in the low frequency regions than in the high frequency ones. The relation between the width of band gap and the direction of position disorder is also discussed. When the position disorder is along the direction perpendicular to the wave transmission, the piezoelectric phononic crystals have wider band gaps at low frequency regions than the case of position disorder being along the wave transmission direction. It can also be found that the effect of. size disorder on band gaps is analogous to that of location disorder. When the perturbation coefficient is big, it has more pronounced effects on the pass bands in the piezoelectric phononic crystals with both size and location disorders than in the piezoelectric phononic crystals with single disorder. In higher frequency regions the piezoelectric effect reduces the transmission coefficients. But for larger disorder degree, the effects of the piezoelectricity will be reduced.

Vibration analysis of a new polymer quartz piezoelectric crystal sensor for detecting characteristic materials of volatility liquid

We present a new polymer quartz piezoelectric crystal sensor that takes a quartz piezoelectric crystal as the basal material and a nanometer nonmetallic polymer thin film as the surface coating based on the principle of quartz crystal microbalance(QCM). The new sensor can be used to detect the characteristic materials of a volatile liquid. A mechanical model of the new sensor was built, whose structure was a thin circle plate composing of polytef/quartz piezoelectric/polytef. The mechanical model had a diameter of 8 mm and a thickness of 170 μm. The vibration state of the model was simulated by software ANSYS after the physical parameters and the boundary condition of the new sensor were set. According to the results of experiments, we set up a frequency range from 9.995850 MHz to 9.997225 MHz, 17 kinds of frequencies and modes of vibration were obtained within this range. We found a special frequency fspof 9.996358 MHz. When the resonant frequency of the new sensor's mechanical model reached the special frequency, a special phenomenon occurred. In this case, the amplitude of the center point O on the mechanical model reached the maximum value. At the same time, the minimum absolute difference between the simulated frequency based on the ANSYS software and the experimental measured stable frequency was reached. The research showed that the design of the new polymer quartz piezoelectric crystal sensor perfectly conforms to the principle of QCM. A special frequency value fspwas found and subsequently became one of the most important parameters in the new sensor design.

Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.

Influence of temperature on the properties of one-dimensional piezoelectric phononic crystals

The current study investigates the influence of temperature on a one-dimensional piezoelectric phononic crystal using tunable resonant frequencies. Analytical and numerical examples are introduced to emphasize the influence of temperature on the piezoelectric phononic crystals. It was observed that the transmission spectrum of a one-dimensional phononic crystal containing a piezoelectric material（0.7 PMN-0.3 PT） can be changed drastically by an increase in temperature.The resonant peak can be shifted toward high or low frequencies by an increase or decrease in temperature, respectively.Therefore, we deduced that temperature can exhibit a large tuning in the phononic band gaps and in the local resonant frequencies depending on the presence of a piezoelectric material. Such result can enhance the harvesting energy from piezoelectric materials, especially those that are confined in a phononic crystal.

High sensitive piezoelectric quartz crystal liquid density sensor

We report for the first time a cleavage phenomenon in the resonant peak of a piezoelectric quartz crystal(PQC) in liquid phase.In the presence of a strong longitudinal wave effect,an additional resonant peak appears in the conductance-frequency curve.With gradually increasing liquid density,the additional peak moves from low to high frequency region then disappears.The frequency of the additional resonant peak is sensitive to the change in liquid density.The frequency shift of the additional peak is linear with the liquid density in a given range.For a 5 MHz PQC with a reflection distance of 16 mm for longitudinal wave,the sensitivity to liquid density is 2.61×10^6 Hz g^-1 cm^3.The overlap between the primary resonant peak and the additional resonant peak causes a decrease in the intensity of the former and an increase in the intensity of the latter.In a combined impedance analysis method,the changes in surface mass loading,density and viscosity of the liquid were monitored simultaneously by a PQC sensor.

Propagation behavior of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with line defects

Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.

Exact thickness-shear resonance frequency of electroded piezoelectric crystal plates

The determination of the precise thickness-shear frequency of electroded crystal plates has practical importance in quartz crystal resonator design and fabricatiom especially when the high fundamental thickness-shear frequency has reduced the crystal plate thickness to such a degree that proper consideration of the effect of electrodes is very important. The electrodes effect as mass loading in the estimation of the resonance frequency has to be modified to consider the stiffness of electrodes, as the relative strength is increasingly noticeable. By following a known procedure in the determination of the thickness-shear frequency of an infinite AT-cut crystal plate, frequency equations of crystal plate without and with piezoelectric effect are obtained in terms of elastic constants and the electrode material density. After solving these equations for the usual design parameters of crystal resonators, the design process can be optimized to pinpoint the precise configuration to avoid time-consuming trial and reduction steps. Since these equations and solutions are presented for widely used materials and parameters, they can be easily integrated into the existing crystal resonator design and manufacturing processes.

A Piezoelectric Friction-Inertial Linear Motor Based on Piezoelectric Single-Crystal Cymbal Displacement Amplification Mechanism

Piezoelectric friction-inertial motor is known for its promise for a long-range and high-resolution motion.The movement of the slider/rotor of the motor is achieved by stick-slip effect.We report a relaxor-based-ferroelectric-single-crystal cymbal actuator and a miniature piezoelectric friction-inertial linear motor(abbreviated as PFILM)fabricated with the cymbal actuator.The cymbal actuator is fabricated with a 10 mm diameter disk of 0.70Pb(Mg_(1/3)Nb_(2/3))O_3-0.30PbTiO_3 single crystal.The displacement of the cymbal actuator increases almost proportionally from 0to 23μm with driving voltage up to 500 V,and the minimal hysteresis is observed.The cymbalPFILM with 20 mm motion range works under driving voltage frequency of ca.100 Hz to ca.5kHz,the fastest speed is obtained with 3.5kHz and the no-load speed is 14mm/s and the maximum thrust force is 98 mN.Compared with a PFILM based on multilayer piezoelectric ceramic,the proposed motor has a larger stroke under DC/quasistatic input voltage in fine motion mode,but a smaller driving force in long-travel mode due to lower resonance frequency.

Effect of KNbO_3 content on the crystal structure and electrical properties of(1-x)PbZr_(0.54)Ti_(0.46)O_3-xKNbO_3 piezoelectric ceramics

（1 - x）PbZr0.54Tio.4603-xKNbO3 （0 〈 x 〈 25mo1%） （abbreviated as PZT-xKN） piezoelectric ceramics were successfully fabricated by a traditional sintering technique at 1225℃ for 30 min. The influence of KNbO3 content on the crystal structure and electrical properties of the PZT-xKN piezoelectric ceramics was studied. Samples with 0 〈 x 0.20 show a pure peroskite structure, indicating that ul KNbOdiffused ito the crystal lattice of PZT to form a single solid solution in this compositional range. A second Pb3Nb4013 phase is observed in the PZT-0.25KN sample, showing that the maximum solid solubility of KNbO3 in PZT matrix ceramic is less than 25mo1%. Compared with pure PZT piezoelectric ceramics, samples containing KNbO3 have smaller crystal grains. PZT-0.15KN exhibits excellent piezoelectric properties with d33 ： 209 pC/N.

The First-Principle Calculation of La-doping Effect on Piezoelectricity in Tetragonal KNN Crystal

The La-dopping effect on the piezoelectricity in the K0.5Na0.5NbO3 （KNN） crystal with a tetragonal phase is investigated for the first time using the first-principle calculation based on density functional theory. The full potentiallinearized augumented plane wave plus local orbitals （APW-LO） method and the supercell method are used in the calculation for the KNN crystal with and without the La doping. The results show that the piezoelectricity originates from the strong hybridization between the Nb atom and the O atom, and the substitution of the K or Na atom by the La impurity atom introduces the anisotropic relaxation and enhances the piezoelectricity at first and then restrains the hybridization of the Nb-O atoms when the La doping content further increases.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Alkaline treatment kinetics of calcium phosphate by piezoelectric quartz crystal impedance

Calcium phosphate film was prepared by electrochemical deposition technology. Subsequently, the alkaline treatment process of calcium phosphate film in 0.1 mol/L NaOH solution was monitored on real time by the piezoelectric quartz crystal impedance （PQCI） technique. The variations of morphology and composition for the alkaline treatment products were characterized by scanning electron microscopy （SEM）, Fourier transform infrared （FT-IR） and X-ray diffraction （XRD）, respectively. The dynamic variations of calcium phosphate can be characterized by the change of equivalent circuit parameters. The results show that the forming process of hydroxyapatite （HA） is composed of three stages： （1） acidic calcium phosphate dissolution; （2） phase transformation; and （3） HA formation. Furthermore, the correlative kinetic equations and parameters are obtained by fitting the static capacitance （C8）-time curves.

A Series Piezoelectric Quartz Crystal Response Kinetics for T.ferrooxidans Growth in the Presence of Cu(Ⅱ)

The kinetics on the growth of T.ferrooxidans in the presence of Cu(Ⅱ) was studied using of series piezoelectric quartz crystal (SPQC). Arsenic ion inhibits the growth of T.ferrooxidans , which is consistent with the previous results by other measuring methods. This further demonstrates that the SPQC can monitor the chemical activity of T.ferrooxidans growth. Cupric ion accelerates the growth of T.ferrooxidans . The mechanism was discussed, i. e., copper promotes the protein enzyme of T.ferrooxidans , rusticyanin, to form over the range of cupric ion concentration studied. The reaction order of cupric ion in accelerating the bacterial growth is 0.067. The growth of T.ferrooxidans is dependent on temperature, the apparent reaction activation energy decreases from 25.56 kJ/mol to 18.32 kJ/mol because of the addition of 10 mg/L Cu(Ⅱ) to the bacterial growth solution of pH 2.0 at initial inoculum of 10%.

An Unexpected Frequency Response of A Piezoelectric Quartz Crystal Sensor to the Density and Viscosity of the Liquid

An unexpected frequency response for a piezoelectric quartz crystal (PQC) sensor to liquid density and viscosity was reported. For a PQC oscillating in a liquid phase, the frequency shifts (?f ) show a wave-shape response to liquid density (ρ) and viscosity (η) in fine structure, if the longitudinal wave effect was not eliminated. This result is different from the well-known linear relationship between of ?f and (ρη)1/2. An oscillating frequency-temperature curve of the sensor was observed and explained.

Intrinsic Orientation Effect on the Piezoelectric Response of Multi-domain 0.26Pb(In1/2Nb1/2)O3–0.46Pb(Mg1/3Nb2/3)O3–0.28PbTiO3 Crystals

The crystal intrinsic orientation effect on the piezoelectric response of multi-domain 0.26Pb（Inl/2Nbm）O3-0.46Pb（Mg1/3Nb2/3）O3-0.28PbTiO3 （PIN-PMN-0.28PT） crystals was investigated by coordinate transformation method. The results indicate that crystal intrinsic orientation effect plays a crucial role in determining the piezoelectric properties of multi-domain crystals. Almost 58% and 69% of the transverse piezoelectric coefficients d31 and d32, respectively, and 67% longitudinal piezoelectric coefficient d33 of multi- domain PIN-PMN-0.28PT crystals poled along [011 ]c originate from crystal intrinsic orientation effect. For [001 ]c poled multi-domain PIN-PMN-0.28PT crystals, intrinsic orientation effect contributes to the transverse and longitudinal piezoelectric coefficient at least 79% and 74%, respectively.

The effects of point defects on transmission coefficients in two-dimensional piezoelectric phononic crystals

Based on finite-difference time-domain(FDTD) method,the wave propagation and localization in two-dimensional defect-containing piezoelectric phononic crystals are investigated when the mechanical-electrical coupling is taken into account.The characteristics of localized defect modes are studied,and the effects of the number and direction of defects on the defect modes and transmission coefficients are discussed.Numerical results of defect modes and transmission coefficients are presented for BaTiO3/polymer piezocomposite,and from which we can see that the number and direction of defects have pronounced effects on the defect modes and transmission coefficients.The results also show the existence of elastic wave localization in piezoelectric phononic crystals containing defects.

Determination of elastic,piezoelectric,and dielectric constants of an R:BaTiO_3 single crystal by Brillouin scattering

From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh：BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromeehanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh：BaTiO3 in the （010） plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.

Temperature dependence of mode coupling effect in piezoelectric vibrator made of[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT ternary single crystals with high electromechanical coupling factor

The influence of temperature on mode coupling effect in piezoelectric vibrators remains unclear.In this work,we discuss the influence of temperature on two-dimensional(2D)mode coupling effect and electromechanical coupling coefficient of cylindrical[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT piezoelectric single-crystal vibrator with an arbitrary configuration ratio.The electromechanical coupling coefficient kt decreases with temperature increasing,whereas k33 is largely invariant in a temperature range of 25℃-55℃.With the increase of temperature,the shift in the‘mode dividing point’increases the scale of the poling direction of the piezoelectric vibrator.The temperature has little effect on coupling constantΓ.At a given temperature,the coupling constantΓof the cylindrical vibrator is slightly greater than that of the rectangular vibrator.When the temperature changes,the applicability index(M)values of the two piezoelectric vibrators are close to 1,indicating that the coupling theory can be applied to piezoelectric vibrators made of late-model piezoelectric single crystals.