B.K. Mukherjee

• B.Sc. Ph.D
• Professor Emeritus at Royal Military College of Canada

We present a procedure for determining the reduced piezoelectric, dielectric, and elastic coefficients for a C(∞) material, including losses, from a single disk sample. Measurements have been made on a Navy III lead zirconate titanate (PZT) ceramic sample and the reduced matrix of coefficients for this material is presented. In addition, we present...

We present a technique to measure the piezoelectric strain (charge) coefficient using an optical lever technique. The optical lever consists of a laser source, a levered mirror connected to the sample and a linear CCD array detector (pixel size = 13 μm). A field on the sample creates a displacement due to the piezoelectric effect. The displacement...

This article gives a review of the research done in our lab over the past few years on the characterization of the transverse elongation of polymeric electrostatic actuators induced by Maxwell stress. Dielectric elastomers are known to produce large transverse strains in response to Maxwell stresses and thus provide a useful form of electromechanic...

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We present a procedure for determining the reduced piezoelectric, dielectric and elastic coefficients for a C_∞ material, including losses, from a single disk sample. Measurements have been made on a Navy III PZT (Channel 5804) ceramic sample and the reduced matrix of coefficients for this material is presented.

The relative permittivity and dielectric loss tangent of transparent lead lanthanum zirconate titanate (PLZT) (9.5/65/35) and (9.0/65/35) ceramics were measured as a function of temperature, ranging from -60 to 100 ° C , and as a function of frequency, ranging from 0.12 to 5000 kHz. Diffuse maxima were observed in the complex permittivity plots of...

The continuing need for large actuation and a continually increasing variety of applications has seen the use of piezoelectric materials under a growing range of conditions. These include large applied AC fields, DC bias fields, applied stresses as well as a wider range of frequencies and temperatures. Under these conditions the behaviour of the ma...

Review of techniques for characterizing piezoelectric/electrostrictive material for transducer applications.

Resonance characterisation has been used to determine the variation of the independent piezoelectric, elastic, and dielectric material coefficients, as well as the electromechanical coupling factors, of typical soft and hard lead zirconate titanate (PZT) ceramics as a function of temperature ranging from -165degC to 195degC. The piezoelectric coeff...

We have used resonance methods to determine the variation of all the independent piezoelectric, elastic, and dielectric material coefficients, as well as the corresponding electromechanical coupling factors, of soft and hard doped piezoelectric lead zirconate titanate (PZT) ceramics with compositions near the morphotropic phase boundary, as a funct...

Different cations doped lead-free piezoelectric (Bi1/2Na1/2)TiO3 ceramics with the general formula Na0.4995Bi0.4995Ba0.001Ti0.998M0.002O3 (M=Nb, Ta, and Sb) were fabricated. The effects of processing parameters and doping on phase content, microstructure, dielectric and piezoelectric properties of the materials were discussed. Experimental results...

Resonance methods were used to determine the variation of several piezoelectric, elastic and dielectric constants, as well as the corresponding electromechanical coupling factors of soft and hard doped Pb(ZrxTi1-x)O3 (PZT) ceramics, with compositions near the morphotropic phase boundary (MPB), as a function of temperature ranging from -165 °C to 19...

Some dielectric elastomers produce large electric-field-induced strains that can be used for electromechanical actuation. When an electric field E is applied on an electroactive polymer film electroded on both sides, the film is subjected to a stress T due to the electrostatic force (Maxwell stress) and this causes it to deform, producing a strain...

Acoustic sensors and actuators often utilize piezoelectric transducers in active methods of noise and vibration control and in other smart applications. The increasing range of these applications requires the piezoelectric materials to be used under a variety of conditions that include large applied AC fields, DC bias fields, applied stresses and a...

Single crystals of Pb(Zn 1/3 Nb 2/3 )O 3 -PbTiO 3 (PZN-PT) produce high levels of strains with large electromechanical coupling coefficients and they exhibit high dielectric permittivity. These properties make PZN-PT single crystals promising materials for transducer and actuator applications. The large strains in these materials are partly due to...

Dielectric elastomers are known to produce large transverse strains in response to electrically induced Maxwell stresses and thus provide a useful form of electromechanical actuation. The transverse strain response of silicone (Dow Corning HS III RTV) based Maxwell stress actuators have been measured earlier as a function of driving electric field,...

Electric-field-induced phase transitions and piezoelectric properties of <001>-oriented Pb(Mg1/3Nb2/3)O3-32%PbTiO3 (PMN-PT) single crystals have been investigated as a function of temperature. It was found that the phase transitions and piezoelectric properties for PMN-PT crystals are strongly dependent on temperature. The measurements of polarizat...

The structure and dielectric properties of CaCu₃Ti₄O₁₂ ceramics have been investigated. The starting CaCu₃Ti₄O₁₂ powders were synthesized by a modified glycine nitrate process. The ceramics obtained exhibit a cubic perovskite structure. Dielectric constant up to 57,200 and dielectric...

Some electroactive polymers show large electric-field-induced strain. However, it is difficult to characterize the transverse strain response, especially the dynamic response, under high driving electric fields. In this work, a transverse strain measurement system based on a ZYGO laser Doppler interferometer has been developed. This system can meas...

Some electroactive polymers produce large electric-field-induced strains that can be used for electromechanical actuation. The measurement of the strain response, especially the dynamic response under high driving fields, is difficult. We have developed a transverse strain measurement system based on the Zygo laser Doppler interferometer. The syste...

Large, high-quality single crystals of (1−x)Pb(Zn1/3Nb2/3)–xPbTiO3 [PZN–PT] relaxors (with the composition range from ∼6 to ∼10% mol. PT) have been grown with a high degree of reproducibility by the gradient cooling method in a specially designed furnace from high-temperature solution. The crystal size is limited by the crucible diameter only. A pr...

The piezoelectric d15 coefficients of 〈111〉-oriented (1−x)Pb(Zn1/3Nb2/3)O3–xPbTiO3 single crystals for x = 0.045 and x = 0.08 (PZN-4.5%PT and PZN-8%PT) have been measured as functions of dc bias field and frequency using a Zygo laser interferometer system. High d15 values ( ∼ 5500 pC/N for PZN-4.5%PT and ∼ 7500 pC/N for PZN-8%PT) were obtained in t...

Single crystals of the relaxor ferroelectric solid solution family Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) have been shown to produce very high levels of electric field induced strains with large electromechanical coupling coefficients when poled aong the direction. These materials also exhibit a high dielectric permittivity and they are therefore very pr...

The nonlinear behaviors of the dielectric and piezoelectric responses of oriented Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT) single crystals for x=4.5% and 8% have been investigated as a function of ac electric fields and dc bias fields. At relatively low applied fields, the polarization and strain of PZN-PT single crystals poled along the direction show li...

We have investigated the electromechanical response of piezoelectric ceramics as a function of the amplitude and frequency of large electric fields and studied the effects of dc bias fields. In order to characterize the materials under these conditions, a ZMI 2000 laser interferometer system from Zygo Corp. has been installed and modified to direct...

A previously described model of hysteresis [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 106, 3317-3327 (1999); 106, 3328-3334 (1999)] is generalized to apply to a dynamical system. The original model produces theoretical hysteresis loops that agree well with laboratory measurements acquired under quasi-static conditions. The loops are pr...

A simple physical picture, useful for extended applications of a well-demonstrated phenomenological polarization model [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 101, 289 (1997)] is presented. The Weiss model of interacting dipoles (orginally suggested by Weiss for magnetic dipoles but applied here to electric dipoles) is generalized f...

Laser Doppler interferometry has been used to determine the strain and piezoelectric response of Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) electrostrictive ceramics as a function of electric fields up to 4 MV m-1, frequencies between 0.1 Hz and 2.5 kHz and DC bias fields up to 3 MV m-1. The strain and polarization of PMN-15 with a composition of 0.9PMN-0.1P...

Electric-field-induced phase transitions and piezoelectric properties of 〈001〉-oriented Pb(Zn1/3Nb2/3)O3–xPbTiO3 single crystals for x = 4.5% and 8% (PZN–4.5%PT and PZN–8%PT) have been investigated as a function of temperature. It was found that the piezoelectric properties and phase transitions for both crystals are strongly dependent on temperatu...

Various piezoelectric, elastic and dielectric constants of typical soft and hard lead zirconate titanate (PZT) ceramics have been determined as a function of applied AC field, DC bias field, pre-stress, temperature and frequency. Our results show significant non-linear effects and many of the effects are caused by extrinsic, or domain related effec...

The piezoelectric d coefficients of 〈111〉 oriented (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 single crystals for x = 0.045 and x = 0.08 (PZN-4.5%PT and PZN-8%PT) have been measured as functions of DC bias field and frequency using a Zygo laser interferometer system. The d coefficients decreased as the DC bias was increased, perhaps because of domain wall clamp...

The temperature dependence of dielectric properties and phase transitions of <001> oriented (1-x)Pb(Zn₁3/Nb₂3/)O₃-xPbTiO₃ (PZN-PT) single crystals for x = 4.5% and x = 8% have been investigated as a function of DC bias field. These crystals exhibit frequency dispersion and increasing the PT content in die...

The piezoelectric d coefficients of <111> oriented (1-x)Pb(Zn₁3/Nb₂3/)O₃-xPbTiO₃ single crystals for x = 0.045 and x = 0.08 (PZN-4.5%PT and PZN-8%PT) have been measured as functions of DC bias field and frequency using a Zygo laser interferometer system. The d coefficients decreased as the DC bias was inc...

The problem of determining the drive waveform that produces a desired output from a hysteretic, saturating material is considered both theoretically and experimentally. The specific problem of interest is the production of a high-amplitude, but monofrequency, sinusoidal polarization response. (The techniques presented could also be used to control...

Sensors and actuators based on piezoelectric ceramics are finding an increasingly large variety of applications under a very wide range of environmental conditions and applied signals. Some actuator applications require the piezoelectric materials to support large mechanical loads and produce high strain output. In order to accomplish this requirem...

The temperature and electric field dependence of the piezoelectric properties and phase transitions of 〈001〉 oriented Pb(Zn_1/3Nb_2/3)O₃-xPbTiO₃ single crystals for x = 4.5% and 8% have been investigated. Both piezoelectric properties and phase transitions are strongly dependent on temperature and electric...

Piezoelectric ceramics are often used under compressive stress. It is therefore important to know the properties of these materials as a function of applied stress. We have developed an experiment that allows us to find the piezoelectric charge coefficient d33, elastic compliance S 33, and dielectric constant ϵ 33 as a function of uniaxial stress i...

The temperature dependence of the material properties of PMN-PT-La (0.85/0.15/1%) electrostrictive ceramics manufactured by TRS Ceramics Inc. have been investigated. The measurements reported here include: the temperature and frequency dependence of dielectric permittivity and dissipation, the quasi-static strain as a function of applied electric f...

A laser Doppler interferometer system has been used to measure the strains of ferroelectric ceramics. The strains and polarisation of piezoelectric and electrostrictive ceramics have been investigated as a function of electric fields up to 4 MV/m in the frequency range from 0.01 Hz up to 1 kHz. The field and frequency dependence of the appropriate...

We have measured some of the dielectric, elastic, and piezoelectric constants of several types of PZT piezoelectric ceramics, manufactured by EDO Corporation, as a function of applied electric field and mechanical stress. Both the high frequency impedance resonance method and the low frequency response of the material under electrical and mechanica...

A Zygo laser interferometer system has been used to measure the strain induced in piezoelectric lead zirconate titanate (PZT) and electrostrictive lead magnesium niobate (PMN) based ceramics. The piezoelectric coefficients d₃₃, d₃₁ and d₁₅ of PZT ceramics have been determined as a function of electric field and fre...

Piezoelectric ceramics are often used under compressive stress. We have measured the dynamic value of the piezoelectric charge coefficient, d₃₃, as a function of uniaxial stress in the poled direction. Results on two types of PZT ceramics manufactured by EDO Corporation are presented; in general, they show a nonlinear behaviour with an i...

Large scale actuated structures often require piezoelectric elements in the thickness range 10-50μm. For manufacturing purposes, the chemical solution deposition of sol gel composites can create such structures using methods compatible with semiconductor fabrication technology. The piezoelectric characteristics of structures fabricated by patternin...

Complex material constants are now being used to accurately model the dynamic response of piezoelectric materials. A simple physical model of piezoelectric materials will be used to show how complex material constants can be conveniently used to characterize losses in the dielectric, elastic, and piezoelectric response of piezoelectric materials. T...

An experiment has been developed to measure the piezoelectric d coefficient as a function of uniaxial stress on a piezoelectric or electrostrictive ceramic material. Measurements on piezoelectric ceramic specimens show that there is a very significant enhancement in the value of the piezoelectric coefficient as a function of applied stress with the...

Smart structures based on piezoelectric materials are now finding applications in a wide variety of environmental conditions. We have used the impedance resonance technique to measure the impedance spectra of lead zirconate titanate ceramic specimens over temperatures ranging between 0ºC and 100ºC. The analysis of the radial, thickness, thickness s...

We present an analytical expression of the electromechanical coupling constant of a piezoelectric bimorph. A simplified impedance equation is presented that allows for the determination of the electromechanical coupling, flexural rigidity, and free permittivity of the bimorph.

We have measured the electromechanical properties of the “reversible” electrostrictive ceramic (TRS Ceramics Inc) PMN/PT/La (0.9/0.1/1%) at room temperature, which is slightly above Tmax, the temperature at which the real part of the material's low frequency permittivity has a maximum. Under DC bias fields up to about 0.5 MV/m, the material behaves...

We present a non-linear theory for electromechanical materials based on a Taylor's series expansion of the thermodynamic potentials to 3rd and higher order terms in field and stress, and we show that this general theory is applicable to both piezoelectric and ideal electrostrictive materials depending with an appropriate choice of material coeffici...

Electrostrictive materials, such as the ceramic PMN/PT/La, operating above Tmax with a DC bias field behave as a piezoelectric ceramic materials with CINF symmetry. The effective piezoelectric and electromechanical coupling coefficients are found to be linear as a function of the DC bias field up to about 0.5MV/m, while the elastic constant and the...

We describe an experiment in which a ramped or step stress can be applied to a piezoelectric sample and the charge generated on the sample can be determined by measuring the short-circuit current with a very high impedance electrometer. The low frequency direct piezoelectric charge coefficient, d33, can then be determined and is found to be substan...

A set of thickness resonators of PVDF-TrFE copolymer have been characterized as a function of the frequency and DC bias. The first six resonance peaks in the impedance spectra were analyzed to determine the degree of frequency dispersion in the complex elastic, piezoelectric, and dielectric constants. Modeling the dispersion in the material constan...

This paper discusses the use of complex material constants to model the response of piezoelectric materials to alternating fields. The various material constants needed to describe the behavior of piezoelectric materials in transducers are introduced. The reasons for using complex coefficients to characterize the frequency dependent dielectric, ela...

Quantitative validation is critical to the effective utilization of large-scale modeling in advanced biomedical ultrasonic imaging applications. This work describes an incremental “model-build-test” validation exercise centered around a nonproprietary, 5 MHz, 1D linear array design. The step-by-step sequence reported here includes piezoceramic sliv...

The design, construction, performance, and comparison to FEM simulation of a broadband 375 kHz, 100 element, composite based, 115 mm radius curved receive array is described. This array was designed for use in a forward-looking, mine-hunting application with 60, 1.5° beams scanning a 900 sector. A 150° sector can be scanned with beamwidths widening...

Equivalent circuit models for unloaded piezoelectric vibrators are presented. The new circuit model includes terms which take into account the dielectric and piezoelectric loss as well as the mechanical loss found in the standard Van Dyke's model. The new model contains two branches, the motional branch and the static branch, like the Van Dyke's mo...

The results of our analysis of a set of lead zirconate titanate (PZT-5H)/hard polyurethane 1 - 3 piezoelectric composites produced by injection molding are presented. Two groups of samples with 15 and 30 volume percent PZT were analyzed using impedance resonance techniques. Results from the thickness, radial, length thickness, thickness shear, and...

This paper reports on our determination of the small signal properties of Motorola 3203 HD, including the effects of losses and dispersion, and it shows the limitations imposed by assuming that the material is loss-less. A set of PZT 3203 HD unloaded resonators manufactured by Motorola was cut to specifications outlined in the IEEE Standard on Piez...

An alternative method to determine the electromechanical coupling constant k13 for the length-thickness piezoelectric resonator is presented. Data relating the electromechanical coupling constant k13 to the parallel resonance frequency ratios are tabulated. A third order polynomial was found to represent the relationship accurately for k13 = 0.01 t...

The design of ferroelectric/piezoelectric smart structures is limited by the accuracy to which the material properties of the sensor/actuator materials are determined. In particular, it is important to understand the effects of losses, dispersion, and the non-linearities that become significant when large fields are applied. This paper presents the...

A set of thickness resonators of PVDF-TrFE copolymer have been characterized as a function of the frequency and DC bias. The first six resonance peaks in the impedance spectra were analyzed to determine the degree of frequency dispersion in the complex elastic, piezoelectric, and dielectric constants. Modeling the dispersion in the material constan...

We have compared the measured effective dielectric, piezoelectric and hydrostatic properties of 0.500 mm thick P(VDF-TrFE) copolymer with flexible electrodes manufactured by AMP Sensors Inc. with similar properties of three different thicknesses of the same polymer with stiff electrodes manufactured by the same company. The presence of the stiff el...

A plasma-spray process was used to produce piezoelectric lead zirconate titanate (PZT)-glass composite thick films. The films were found to have the same crystal structure as the PZT (Navy-type V) and lead-based glass starting powder mixture. The films showed good adhesion to stainless steel and silver-coated glass slides and poor adhesion to alumi...

The recent past has seen the introduction of many new types of piezoelectric materials with relatively high dissipation and low mechanical Q (PVDF, ceramic?polymer composites). In order for designers to predict the performance of these materials in transducers, the imaginary components of the dielectric,elastic, and piezoelectric constants need to...

We describe a new method for determining the real and imaginary parts of the material constants of piezoelectric resonators. Our method is applicable to any of the common resonator geometries, it is non-iterative and its accuracy is comparable to that of other methods which are currently in use.

Piezoelectric 0–3 ceramic-glass composites have been developed by firing a mixture of modified Lead Zirconate Titanate (PZT) and a lead based glass powder. Composites with 58 to 92 volume percent PZT were fabricated and their dielectric, piezoelectric and hydrostatic properties have been determined. The hydrostatic properties were pressure independ...

We describe a new piezoelectric hydrophone material, a 1-3 type Lead Zirconate Titanate (PZT)-Air composite, which is constructed in such a way that the PZT rods are isolated from stresses in the 1 and 2 directions. The theory for these new composites predicts a hydrophone figure of merit that is substantially greater than that of PZT. Measurements...

The usual methods for determining the electromechanical coupling constants of piezoelectric materials are described in the IEEE standard on piezoelectricity (IEEE Standard on Piezoelectricity 176-1987). When spurious resonances are present, the standard recommends the use of a method that involves the use of a numerical table of corresponding value...

Chemical coprecipitation and gel processing techniques have been used to synthesize precursor powders of a modified lead titanate composition. The effects of powder processing parameters and sintering conditions on the microstructure and dielectric, piezoelectric, and pyroelectric properties of the products are discussed. Powders and products produ...

The time dependence of PZT (lead zirconate titanate) (Navy I and III) was investigated in the case of a high stress applied parallel to the poling axis. The time dependence was found to be linear in ln(t), with slope activated in temperature with an activation energy of 0.29-0.32 eV for the Navy I material and 0.62-0.80 eV for the Navy III material...

It has recently been shown that the selective reduction of one surface of a high-lead-containing piezoelectric or electrostrictive ceramic wafer results in a stress-biased wafer with a unique domed structure that leads to high electromechanical displacement and enhanced load-bearing capability. These ceramics have been called rainbow ceramics and t...

The standard IEEE procedure for determining the piezoelectric, dielectric, and elastic constants associated with the radial mode resonance of piezoelectric materials treats these constants as real rather than complex quantities. This approach is valid in the case of piezoelectric materials with low losses such as Lead Zirconate Titanate. However ne...

Summary form only given. The authors used the pyroelectric properties of beta-phase polyvinylidene fluoride (PVdF) to construct a relatively fast response cryogenic thermometer. The temperature dependence of the pyroelectric coefficient of 9 μm and 28 μm PVdF films was measured over the temperature range from 20 K to 300 K. Repeated cycling of the...

The effect of electrodes on the measurement of dielectric, piezoelectric, and mechanical properties of lead zirconate-titanate (PZT) ceramics and of 1-3 connectivity ceramic-polymer composites was studied. While fired silver and evaporated silver electrodes were found to have little effect on the measurements, silver epoxy electrodes resulted in a...

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Measurements have been made of the total time required for the penetration of magnetic flux into cylindrical specimens of pure indium and pure tin, both type I superconductors, when an overcritical axial magnetic field is suddenly applied. Whereas previous measurements covered small excess fields, the present measurements extend over magnetic field...

We have measured the in-phase component of the low frequency a.c. impedance of the d.c. current-induced intermediate state in indium-lead alloy wires. The theory developed by Gauthier and Rochon, which is based on London's model of the intermediate state, predicts theoretical values considerably larger than our observations, particularly near the c...

Landau has recently suggested that a static periodic structure of the direct current-induced intermediate state cannot explain experimental measurements and he has revived the dynamic structure originally proposed by Gorter. We point out that experimental results can, for the most part, be understood reasonably well on the basis of the Baird-Mukher...

We have measured the in-phase component of the low-frequency ac impedance of the dc current-induced intermediate state in indium-lead alloy wires. The specimens were mounted in a specific configuration that allowed a proper calculation of their dynamic resistances following the theory developed by Gauthier and Rochon, which is based on London's the...

We have measured the in-phase component of the low-frequency ac impedance of the dc current-induced intermediate state in wires of pure and impure type I superconductors. We find that this dynamic resistance of the intermediate state is greater than the normal state resistance of the wire. The linear response theory for the dynamic resistance devel...

We have measured the time required for the destruction of type I superconductivity in high purity indium wires by a current greater than the critical current. Our results are not in agreement with theoretical treatments presented by Pippard and by Rothen and Bestgen and we suggest possible inadequacies in the theoretical models.

Experimental studies of the kinetics of flux jumps in type II superconducting disks have shown that flux penetration into the specimen can be described by an exponential function of time. We present a phenomenological theory which uses the concepts of flux pinning and flux flow viscosity to derive a function of the same form as that found experimen...

When superconductivity in a type I wire is destroyed by a current i greater than the critical current i c the wire enters into an intermediate state whose structure, and consequently the resistance of the wire, is a function of the reduced current \(p=(i-{{i}_{c}})/{{i}_{c}}.\)

Several theoretical models have been put forward for the destruction of type-I superconductivity in a wire by the passage of a large enough current through it. In an attempt to discriminate between the various models, an experimental investigation has been carried out of the transition in one thallium wire and in a series of indium wires of differe...

Several models have been proposed for the intermediate state which occurs when superconductivity is destroyed in type I wires by a current. Experimental testing of these models has, so far, only been possible through measurements of the resistance and the intermediate state core radius during the transition. We describe an experiment in which a wir...

We have improved our previous model of the intermediate state in type-1 current-carrying superconductors. In addition to predicting a resistance transition in reasonable agreement with experimental observations, the model gives good agreement with experimental values for the radius of the intermediate-state core as obtained by Rinderer.

A revised form of the London theory of the destruction of superconductivity by a current is presented. Numerical methods are used to find the optimum phase boundary configuration. The result specifies the scale of the structure and the resistance of the intermediate state.