Thickness Mode Resonance Research Articles

High-frequency and high-temperature electromechanical performances of new PZT–PNN piezoceramics

Ferroelectric ceramics based on a solid solution between a PZT ferroelectric phase and a relaxor phase from the lead–nickel–niobium system are characterised. Two different mixed-oxide routes have been used in order to compare the dielectric, piezoelectric and elastic properties of the two ceramics obtained. The characterisation method is based on measurements of the electrical impedance of samples as a function of frequency and allows the determination of the thickness mode resonance parameters. Results are given as a function of frequency (5 to over 25 MHz) and temperature (ambient to over 230°C). Finally, several simulations, using a K.L.M. model, of medical transducers are performed. The results show that the ceramic is well adapted for medical imaging applications, in particular for array transducer configurations.

Interdigital pair bonding for high frequency (20-50 MHz) ultrasonic composite transducers.

Interdigital pair bonding is a novel methodology that enables the fabrication of high frequency piezoelectric composites with high volume fractions of the ceramic phase. This enhancement in ceramic volume fraction significantly reduces the dimensional scale of the epoxy phase and increases the related effective physical parameters of the composite, such as dielectric constant and the longitudinal sound velocity, which are major concerns in the development of high frequency piezoelectric composites. In this paper, a method called interdigital pair bonding (IPB) is used to prepare 1-3 piezoelectric composite with a pitch of 40 microns, a kerf of 4 microns, and a ceramic volume fraction of 81%. The composites prepared in this fashion exhibited a very pure thickness-mode resonance up to a frequency of 50 MHz. Unlike the 2-2 piezoelectric composites with the same ceramic and epoxy scales developed earlier, the anticipated lateral modes between 50 to 100 MHz were not observed in the current 1-3 composites. The mechanisms for the elimination of the lateral modes at high frequency are discussed. The effective electromechanical coupling coefficient of the composite was 0.72 at a frequency of 50 MHz. The composites showed a high longitudinal sound velocity of 4300 m/s and a high clamped dielectric constant of 1111 epsilon 0, which will benefit the development of high frequency ultrasonic transducers and especially high frequency transducer arrays for medical imaging.

Processing and properties of 15–70 MHz 1–3 PZT fiber/polymer composites

This paper reports on the fabrication and characterization of fine scale piezoelectric composites with 1–3 connectivity using fibers derived from a metal alkoxide sol-gel process. Using this technique, pure thickness mode resonance for this type of composite has been increased from 15 MHz up to 70 MHz by maintaining pillar aspect ratio requirements. Piezoceramic fibers of Nb or La modified lead zirconate titanate (PZT) were produced with final diameters ranging from 15 to 50 μm.Composites having 1–3 connectivity were produced using the fibers as pillars. Composites could be fabricated with volume fractions from 10 to 45% allowing tailoring of both the dielectric constant and acoustic impedance without degrading coupling. Dielectric constant, polarization and coercive field values varied slightly from bulk values due to clamping by the polymer matrix, increasing as the fiber diameter decreased. Composites with resonance frequencies ranging from 15 to 70 MHz were studied. The thickness dependence of the properties gave indications to radial mode/thickness mode interactions at pillar aspect ratios near 1.7 to 1 thickness to diameter. Coupling coefficients (kt) from 58% to 73% with mechanical quality factors <15 were detected.

Comparison of several methods to characterise the high frequency behaviour of piezoelectric ceramics for transducer applications

Thickness mode resonances in commercial piezoelectric ceramics have been characterised as a function of frequency by two methods. The first is based on a fit on the electrical impedance for the fundamental and the overtones. This method has been applied to a large number of PZT ceramic samples and frequency dependence for all the parameters is investigated, in particular for the piezoelectric coefficient e 33. The second is based on the measurement of the mechanical displacement at the centre of the surface of a PZT ceramic disk. With a modified KLM scheme, this displacement is modelled. The dielectric, elastic and piezoelectric parameters are extracted and compared for the fundamental and the third overtone. The results are found to be in good agreement.

Lead zirconate titanate/poly(vinylidene fluoride-trifluoroethylene) 1-3 composites for ultrasonic transducer applications

A new procedure for preparing lead zirconate titanate (PZT)/poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) 1-3 composites with both phases piezoelectrically active is described. Sintered PZT rods are inserted into a prepoled copolymer matrix, and the composite is repoled under a lower electric field. Using this new procedure, the dipoles in the two phases are aligned in either the same or opposite directions. Composite disks, of 12.7-cm diameter and 0.33- to 0.60-mm thicknesses, have been fabricated with PZT rods of 0.8 or 1 mm diameter distributed in a square pattern with 3 mm center-to-center separation. The ceramic volume contents of the composite disks are 3.6 and 5.6%, respectively. The resonance characteristics of the composite disks consist of the resonance modes of the two constituent phases, but they are dominated by the coupled longitudinal thickness mode (H-mode) of the PZT rods. The coupled radial mode (L-mode) resonance of the PZT rods is significant only for thin disks. The observed resonance frequencies of the H- and L-modes agree well with the values calculated from the coupling theory. The thickness mode resonance of the copolymer matrix (T-mode) is present but hardly observable in thick disks. The composite disks have been fabricated into transducers with air-backing and with no front face matching layer, and their performance characteristics have been evaluated in water. The transmitting and receiving voltage responses of a PZT/P(VDF-TrFE) composite transducer are better than those of a PZT/epoxy composite transducer. The transmitting and receiving voltage responses are improved when the PZT rods and copolymer matrix are poled in opposite directions, especially when the resonance frequencies of the H- and T-modes are approximately equal. When the phases are poled in the same direction and the resonance peaks associated with the Hand T-modes just overlap, the bandwidth is improved. Using 0.33-mm thick composite disks, a transducer can be produced with three operating frequencies by poling the constituent phases in the same direction, or with two operating frequencies at equal efficiency by poling the constituent phases in opposite directions. The PZT/P(VDF-TrFE) 1-3 composite transducer, especially the one with multiple operating frequencies, should be very promising in the applications of medical ultrasonic imaging.

Influence of the different loss parameters on piezoelectric material performances

Piezoelectric materials such as polymers (PVDF), copolymers (P(VDF-TrFE)), lead metaniobates or ceramic/polymer composites possess high losses. In this case, the characterisation method described in IEEE Standard on Piezoelectricity (1987) for low-loss materials is not applicable. Several methods have been proposed to determine the losses by introducing complex parameters in the piezoelectric constitutive equations. A number of these methods consider mechanical, dielectric and piezoelectric losses, but others only take into account mechanical and dielectric losses. In this paper, we investigate the influence of these types of losses on the electrical impedance of a thickness mode resonator. This study shows that piezoelectric losses have very little effect and that only dielectric and mechanical losses need to be taken into account for transducer design. Measurements were also performed on three different materials. The results using our method are compared to those of previously published studies.

Acousto-ultrasonic evaluation of adhesively bonded CFRP-aluminum joints

Correlation between the amount of artificial defects in bonded region and the acousto-ultrasonic parameters (AUPs) including the signal amplitude in adhesively bonded joints of carbon-fiber reinforced plastic (CFRP) laminates and Al6061 plates was investigated. The effect of the frequency content and the bandwidth of input signals were studied using 200 kHz, 650 kHz, 1 MHz, 2 MHz pulses and 1 MHz tone-burst signals. With increasing fraction of defects, the signal amplitude and AUP1 were decreased but AUP2 was increased. This result was attributed to the energy transfer characteristics of bonded joints with delamination-type defects and the change of spectral content as a result of the defects. Considering the highly attenuative nature of composite laminates, a pulse signal with major frequency content at or around the third harmonic of thickness mode resonance, 600∽700 kHz for the dimension of specimens used in this study, was found optimal for acousto-ultrasonic testing of CFRP-aluminum joints.

Progress in stacked piezocomposite ultrasonic transducers for low frequency applications

A stacked ultrasonic transducer comprises multiple individual layers connected mechanically in series and electrically in parallel to reduce the fundamental thickness mode resonance to a frequency corresponding to the transit time of the complete stack and the electrical impedance to a value which corresponds to that of the layers of the stack in parallel. In turn, this allows lower frequency resonant operation than would be possible with a single layer, and facilitates electrical impedance matching to typical transmission circuitry. On transmission, an ideal stack of uniform layers will have an output amplitude larger than that of the equivalent single layer by a factor equal to the . However, using conventional signal amplification circuitry on reception, the output voltage amplitude will be smaller than that of the equivalent single layer by a similar factor. In the past, stacks have commonly been assembled from layers of conventional piezoceramic material but more recently there have been reports of stacks of 1–3 piezocomposites and it is this type that is considered here. The work described in this paper is motivated by the need to operate at frequencies lower than are possible using conventional piezocomposite fabrication technology. Progress in comparison of experimental and simulated results is outlined and the highlights of a theoretical design study are presented. These show that although the general behaviour of a stacked structure is easily predicted, a rigorous theoretical analysis is essential to understand the detail of even a limited range of possible designs.

Microfluidic motion generation with acoustic waves

This paper presents a novel approach for producing microfluidic motion by loosely focused acoustic waves (generated by piezoelectric zinc oxide thin film). Results show that the acoustic waves generated by radio frequency (r.f.) sources with frequencies corresponding to the thickness-mode resonances of the piezoelectric film are very effective in moving liquid around when the waves are loosely focused. The device operates without any significant temperature increase in the liquid, and will be very attractive for mixing or transporting temperature-sensitive fluids.

Temperature behaviour of structural, dielectric and piezoelectric properties of sol-gel processed ceramics of the system LiNbO 3-NaNbO 3

Ceramics of the system LiNbO 3-NaNbO 3 were prepared from sol-gel derived powders in the whole range of compositions and structurally characterized by X-ray diffraction. The impedance of thin ceramic disks was measured as a function of the temperature from 1 kHz to 15 MHz up to 800 °C. An automatic iterative procedure was used to calculate the electromechanical coupling factor of the thickness mode resonance from impedance data. The solid solution limits of Na in LiNbO 3 and Li in NaNbO 3 were found to be 7mole% and 15mole%. As a consequence the materials whose nominal composition is Li 1− y Na x NbO 3 with 0.07 ≤ × ≤ 0.85 contain mixtures of the two limit solid solutions. For ceramics with Na content exceeding 10mole%, two dielectric anomalies at 300 and 400–450 °C are observed as local maximums in the real part of the dielectric permittivity when measurements are made while heating the sample. These are more enhanced as the Na content increases. There is a change of sign in the temperature coefficient of the conductivity of the ceramics giving place to a minimum at low temperature, 100–150 °C, which is not present at high frequency (> 5 MHz). There is a shift in the frequency number of the thickness mode of resonance towards higher values together with a minimum in the electromechanical coupling coefficient at about 350 °C. For high Na content ceramics (> 90mole%) an irreversible decrease to zero of the coupling coefficient is observed instead. The second anomaly in the real part of the dielectric permittivity and the anomalies in the electromechanical behaviour are related with the antiferroelectric-orthorhombic to paraelectric-orthorhombic transition reported for NaNbO 3 at 370 °C. The first anomaly in the real part of the dielectric permittivity and the change in the temperature coefficient of the conductivity are linked with a change in the conductivity mechanisms of localized charge carriers, allowed by a certain degree of structural disorder caused by the Na + substitution of the smaller Li + ion, or viceversa, as reported for similar systems.

Thick-film resonant piezo-layers as new gravimetric sensors

Resonant piezo-layers (RPLs) manufactured in thick-film technology are proposed as highly sensitive gravimetric sensors. RPLs rely on a PZT-based screen printable paste which is used for the fabrication of planar elements on alumina substrates behaving as thickness-mode resonators. When operated at resonance, these elements are sensitive to a mass load applied on their free moving face, working as resonant microbalances with a frequency output, reaching a mass sensitivity of 114 kHz . This paper describes the paste preparation, background theory, frequency-tracking oscillator and the characterization of the sensors and anticipates their application in sensing arrays for chemical measurements.

Thickness Mode Resonance of PZT Coatings on a Substrate

ABSTRACTThe analytical solution of the wave equation for a piezoelectric layer supported by a substrate is presented. Using the appropriate boundary conditions, the impedance for a piezoelectric layer driven in the thickness axis is derived and expressed in terms of the mechanical, electrical and piezoelectrical properties of the two materials. This solution allows for the extension of the free resonator IEEE impedance techniques and provides a nondestructive method for determining the material parameters of a piezoelectric film with mechanical support. The validity and universality of the model is demonstrated by measurements on composite sol gel PZT coatings within the thickness range of 15-70μm on aluminum substrates of varying thickness, and by simulating the mass loading of a quartz thickness resonator.

PZT/polymer composites for medical ultrasound

Piezoelectric ceramic polymer composites with 1–3 connectivity (i.e., parallel rods in polymer) using lead zirconate titanate and epoxy have been fabricated with different ceramic rod widths. The velocity of sound was measured for these composites using the Time-Delay technique. The values of acoustic impedance obtained by this method are compared with the results determined by the Resonance technique. The electromechanical coupling coefficient k tand planar coupling coefficient k p were determined from the thickness mode resonance and planar mode resonance peaks. The effect of addition of phenolic microballoons on these composites was also investigated. The microballoons had little effect on the acoustic impedance; however, they considerably improved the values of k t and k p.

Piezoelectric thickness resonance of aromatic polyurea films prepared by vapor deposition polymerization

Abstract By vapor deposition of a diisocyanate monomer (MDI) and a diamine monomer (MDA or MeMDA) onto a polyimide substrate, thin two-layer films of aromatic polyurea, P(MDA/MDI) or P(MeMDA/MDI), and polyimide were prepared. The polyurea layers acquired piezoelectric activity after poling treatment. The electric admittance of the films was measured as a function of frequency. Piezoelectric resonance and antiresonance were observed at the frequency of thickness mode resonance of the polyurea layer and at side-band frequencies corresponding to the harmonic thickness resonance frequencies of the polyimide layer. Theoretical analysis yielded the electromechanical coupling factor kt = 12%, the piezoelectric constant e 33 = 60 mC/m2, and the elastic constant C 33 = 6.87 GN/m2 for P(MDA/MDI). MDI: 4,4'-diphenyl methane diisocyanate, MDA: 4,4'-diamino diphenyl methane MeMDA: 4,4'-diamino-3,3'-dimethyl diphenyl-methane.

PdP133. Accuracy of the formulas used for the characterization of piezoelectric thickness mode resonators with impedance analyzers

Abstract The resonance method allows the determination of different elastic, dielectric, and piezoelectric constants of the material using an adequately shaped sample. The accuracy of the relationships between the measured electrical input impedance quantities and the material constants is of capital importance. In the International Standards1–2 these relations, and consequently the derived formulas, are based either on the exact one-dimensional expression of the input impedance of an ideal lossless resonator, or on the simplified (Butterworth-Van Dyke) equivalent circuit. In this paper, the accuracy of equations frequently used for the measurement of the longitudinal acoustic velocity, vD t, the thickness electromechanical coupling coefficient, kt, and the mechanical quality factor, Qm are analyzed. The exact one-dimensional model of a thickness expander piezoelectric resonator, with a rigorous account of the internal mechanical losses, is taken as a reference.

A modified thickness extensional disk transducer

Photolithography and chemical etching were investigated as a means of patterning miniature piezoelectric devices. Using a processing procedure analogous to that utilized in the production of integrated circuitry, concentrated hydrochloric acid and a commercially available photoresist were used to fabricate a number of complex structures from soft lead zirconate titanate (PZT) substrates. Among the devices produced in this manner was a modified thickness-mode resonator etched to destroy the simple geometry responsible for radial vibrations. The resultant transducer demonstrated significantly smaller amplitudes for lateral resonances and a marked reduction in the effective planar coupling coefficient over the unaltered disk. The results indicate that photolithographic patterning is useful both for eliminating spurious resonances from transducers for medical imaging or nondestructive evaluation and for engineering low planar coupling coefficients into a variety of substrate materials.

On the measurement of the mechanical losses of low Qmpiezoelectric materials

Abstract IRE and IEEE Standards on Piezoelectricity describe the characterization of relatively high mechanical Q (Qm) materials. The mechanical dissipation is the most important limitation on the validity of some analytical expressions derived for ideal piezoelectric materials. In this paper we propose an alternative expression for the mechanical quality factor (Qm) of the fundamental resonance of a thickness mode resonator which applies for high and low Qm materials.

Signal processing of ultrasonic signals with applications to surface metrology

A stacked ultrasonic transducer comprises multiple individual layers connected mechanically in series and electrically in parallel to reduce the fundamental thickness mode resonance to a frequency corresponding to the transit time of the complete stack and the electrical impedance to a value which corresponds to that of the layers of the stack in parallel. In turn, this allows lower frequency resonant operation than would be possible with a single layer, and facilitates electrical impedance matching to typical transmission circuitry. On transmission, an ideal stack of uniform layers will have an output amplitude larger than that of the equivalent single layer by a factor equal to the . However, using conventional signal amplification circuitry on reception, the output voltage amplitude will be smaller than that of the equivalent single layer by a similar factor. In the past, stacks have commonly been assembled from layers of conventional piezoceramic material but more recently there have been reports of stacks of 1–3 piezocomposites and it is this type that is considered here. The work described in this paper is motivated by the need to operate at frequencies lower than are possible using conventional piezocomposite fabrication technology. Progress in comparison of experimental and simulated results is outlined and the highlights of a theoretical design study are presented. These show that although the general behaviour of a stacked structure is easily predicted, a rigorous theoretical analysis is essential to understand the detail of even a limited range of possible designs.

Thermally generated transient frequency excursions in doubly-rotated quartz thickness-mode resonators

The temperature distribution in the electroded quartz plate is obtained from the uncoupled heat conduction equation subject to appropriate initial and boundary conditions. The time-dependent biasing state resulting from the transient temperature distribution is determined from the exact equations of static linear thermoelasticity for electrode films of zero thickness and from a system of approximate thermoelastic extensional plate equations for electrode films of finite thickness. The time-dependent change in resonant frequency resulting from the biasing state is determined from an equation for the perturbation of the eigenfrequency due to a bias. Results are presented for a number of thermally compensated as well as uncompensated cuts of quartz for some physically meaningful temperature inputs. In particular the calculations show that in thermally compensated cuts with electrodes of finite thickness, the frequency initially shifts considerably beyond the equilibrium resonant frequency for the final uniform temperature state.

Temperature dependence of the resonant frequency of electroded doubly-rotated quartz thickness-mode resonators

A system of approximate equations for the determination of thermal stresses in piezoelectric plates with large thin films of a different material plated on the surfaces is derived. The plate equations are obtained by making a suitable expansion of the pertinent variables in the thickness coordinate, inserting the expansion in the appropriate variational principle and integrating with respect to the thickness in the manner of Mindlin. Conditions resulting in both extensional and flexural stresses are considered and the full anisotropy of the quartz is included in the treatment. The particular case of purely extensional thermal stresses resulting from large electrodes of equal thickness plated on the major surfaces of doubly-rotated quartz thickness-mode resonators is treated in detail. The changes in resonant frequency resulting from the thermally induced biasing stresses and strains are determined from an existing perturbation equation. Calculations, using the newly defined first temperature derivatives of the fundamental elastic constants of quartz, are performed for large gold electrodes on doubly-rotated quartz plates.