An analysis of pyroelectric figures of merit in oblique cuts of crystals belonging to the symmetry class m is presented. It is shown that the optimum cut and the gain depend on the dielectric anisotropy and the orientation of the pyroelectric axis with respect to the dielectric principal axes. Remarkable enhancements are possible in optimum cuts of crystals with large anisotropy ratio in the mirror plane and large deviation of the pyroelectric axis from the principal axes of the dielectric tensor.

A simple physical model of rod composite piezoelectrics is extended to the case where both the polymer matrix and the ceramic rods are piezoelectric. This model incorporates the physical picture that strains and electric field are equal in both materials along the direction of the rods, while the stresses are equal in the plane perpendicular to the rods. If one switches to a coordinate system in which strain and electric field along the rods and the stresses in the perpendicular plane are the independent coordinates, the material properties of the composite are a simple volume fraction weighted average over the constituents' properties. The hydrophone figure of merit is presented for a PZT5-rod/PVDF-matrix composite. The bulk of the piezoelectric response is provided by the piezoceramic; the anisotropic elastic properties of PVDF make it particularly suitable for the composite; and the fact that the piezoelectric constants of PZT and PVDF differ in sign would cause the two phases to act against each other if they were poled by the same bias field.<>

A simple physical model of 1-3 composite piezoelectrics that was advanced for the material properties relevant to thickness-mode oscillations is extended to address the hydrostatic response. The model is valid when the lateral spatial scale of the composite is sufficiently fine that the composite can be treated as an effective homogeneous medium. Expressions are derived for the composite's material parameters in terms of the volume fraction of piezoelectric ceramic and the properties of the constituent piezoelectric ceramic and passive polymer. The results are similar to those derived by Haun and Newnham (1983, 1986) using a parallel-series connectivity model. The model is illustrated by analyzing composites made from conventional PZT5 and anisotropic modified lead titanate piezoelectric ceramics. For PZT5, the composite structure enhances its hydrostatic charge coefficient, hydrostatic voltage coefficient, hydrophone figure of merit, and hydrostatic coupling coefficient, while three of these quantities fall short of their pure ceramic values in the modified lead titanate composites. The shortfall is due to an enhanced composite that arises from lateral stress on the polymer being transferred to a longitudinal stress along the ceramic rods by the Poisson effect in the polymer, thus producing a charge through the ceramic's d(33).

The case of a piezoelectric material with infinity m axial symmetry (applicable to piezoceramics and most piezocomposites) is analyzed, and formulae for the resulting structures are derived. In terms of transducer design, the constraints on the elastic and dielectric constants provide no blockage to achieving acoustic impedance matching to the medium and electric impedance matching to the electronics. Electromechanical coupling is shown to be limited by the material's maximal coupling factors. A simple formula is derived which facilitates evaluating the maximal electromechanical coupling factor when the electric field is applied along the polar axis from the planar coupling factor and the thickness coupling factor, which can be readily evaluated from the lateral and thickness resonances of a disk.< >

Piezoelectric materials lie at the heart of ultrasonic transducers. These materials convert electrical energy into mechanical form when generating an interrogating acoustic pulse and convert mechanical energy into an electric signal when detecting its echoes. This paper first surveys the piezoelectric materials in current use: piezoceramics, such as barium titanate, lead zirconate titanate, and modified lead titanate; piezopolymers, such as polyvinylidene difluoride and its copolymer with trifluroethylene; and piezocomposites, consisting of piezoceramic rods in a passive polymer matrix. Each material system has properties which commend them for use in the present single element transducers, annular arrays, sequenced linear arrays, and steered phased arrays. Looking to the future, new transducer possibilities are opening up due to recent piezoelectric material developments, such as, for example, synthesis techniques for fine-grained high-density piezoceramics, electrostrictive relaxor ferroelectric ceramics, novel piezoceramic forming methods, piezoceramic fiber synthesis, piezoceramic/metal multilayer structures, composite acoustoelectric materials, ferroelectric thin film growth and processing, and new piezopolymers. These innovations lead to fabrication of conventional transducers at high frequencies, fine-scale piezocomposites, 11/2-D and 2-D arrays, small intravascular transducers, as well as provide opportunities for new ultrasonic imaging techniques, using pitch-catch and non-resonant traveling wave transducers.

The stress patterns-two shears and one direct stress-that are maximally coupled to the electric field in piezoelectric ceramics are identified. This is achieved by a simplifying initial choice of coordinate axes in the ceramic's thermodynamic phase space and by a subsequent sequence of elementary coordinate changes-rotations and scale changes; simple physical arguments lead to the new coordinates. The utility of this perspective is pointed out in two important applications of piezoceramics in acoustic transducers: naval hydrophone sensors and pulse-echo ultrasonic transducers used in medical diagnostic imaging.

By using a new calcium-modified lead titanate ceramic with a near-zero planar coupling coefficient, a series of 1-3 piezocomposite samples was fabricated with a dice-and-fill technique. The ceramic rods were approximately 0.10 mm in size, and the percent of ceramic loading varied from 10 to 30%. Two epoxy resins with different glass transition temperatures and moduli were used. The dielectric properties and the piezoelectric d(h) and g(h) coefficients of the composites were measured as a function of pressure and temperature and were found to exhibit little variation, but 10-25% lower than theoretical predictions. A prototype hydrophone made from one of the piezocomposite samples was tested to show a constant free-field voltage sensitivity of -201 dB re V/muPa from 100 Hz to 6 kHz.

The invention of methods to make new materials with an engineered microstructure that yields a negative Poisson ratio opens a new avenue to optimize the performance of piezoelectric-rod/polymer-matrix composites. Such negative Poisson's ratio materials can be used as the passive phase in the composite to redirect the external stress acting on the piezocomposite so that the resulting stress bearing on the piezoceramic rods produces a maximal piezoelectric response. To project the properties of such a piezocomposite, a simple physical model that assumes constant strain along the rods and constant stress in the perpendicular plane is used. Interesting opportunities to improve the performance of devices made from 1-3 piezocomposites are seen in results calculated for the thickness-mode electromechanical coupling constant relevant to pulse-echo ultrasonic applications and for the hydrostatic electromechanical coupling constant relevant to passive hydrophones.< >

A simple physical model of 1-3 composite piezoelectrics is advanced for the material properties that are relevant to thickness-mode oscillations. This model is valid when the lateral spatial scale of the composite is sufficiently fine that the composite can be treated as an effective homogeneous medium. Expressions for the composite's material parameters in terms of the volume fraction of piezoelectric ceramic and the properties of the constituent piezoelectric ceramic and passive polymer are derived. A number of examples illustrate the implications of using piezocomposites in medical ultrasonic imaging transducers. While most material properties of the composite roughly interpolate between their values for pure polymer and pure ceramic, the composite's thickness-mode electromechanical coupling can exceed that of the component ceramic. This enhanced electromechanical coupling stems from partially freeing the lateral clamping of the ceramic in the composite structure. Their higher coupling and lower acoustic impedance recommend composites for medical ultrasonic imaging transducers. The model also reveals that the composite's material properties cannot be optimized simultaneously; tradeoffs must be made. Of most significance is the tradeoff between the desired lower acoustic impedance and the undesired smaller electromechanical coupling that occurs as the volume fraction of piezoceramic is reduced.

A series of 1-3 piezocomposite samples was fabricated by using lead titanate ceramic with a dice-and-fill technique. The ceramic rods were approximately 0.10 mm in size, and the ceramic volume fraction varied from 10% to 30%. Two different epoxy resins were used. The piezoelectric d/sub h/ and g/sub h/ coefficients of the composites were found to be stable with pressure from ambient to 20 MPa. The temperature dependence of the composite properties was similar to that of the solid ceramic. The free-field voltage sensitivity of a prototype hydrophone made from the composite was calibrated and shown to be constant up to 6 kHz.< >

This review focuses the 1-3 piezocomposites, consisting of long thin rods of electrically active ceramic held parallel to each other by a passive matrix phase. Considered are situations where these piezocomposites function as true composite materials, that is, situations where all acoustic wavelengths are so large that the detailed structure is lost and the material may be considered as a new homogeneous medium with new effective material properties. Applications in naval sonar systems and medical ultrasonic imagers are illustrated with commercial product literature. Recent innovations highlighted include material fabrication techniques, finite-element modeling, and the use of electrostrictive ceramics

The potential for using first principles calculations for ferroelectrics is delineated. Significant insights into the microscopic origins of ferroelectricity are expected. In terms of practical matters, this theoretical approach provides a means to explore new ferroelectric material systems using computations alone.

Combining a piezoelectric ceramic and a passive polymer to form a piezocomposite allows the transducer engineer to design new piezoelectrics that offer substantial advantages over the conventional piezoelectric ceramics and polymers. The rod composite geometry provides materials with enhanced electromechanical coupling and with acoustic impedance close to that of tissue; these factors yield transducers for medical ultrasonic imaging with high sensitivity and compact impulse response. The dice-and-fill technique produces piezocomposites that can be readily formed into complex shapes to facilitate focusing the ultrasonic beam. Proper design of the rod spacing yields materials that exhibit low crosstalk between array elements formed by patterning the electrode alone, without cutting between the elements. In this way, curved annular arrays have been made that provide high-quality clinical images of substantial diagnostic value to physicians. Included is an extensive bibliography of papers documenting the role of piezocomposites in ultrasonic imaging transducers

The attenuation slope with frequency from the frequency decrease along the ultrasonic echo signal is evaluated in tissue. When the local frequency from the reflected waveform is evaluated, many data segments yield unreliable values because of interference between overlapping echo pulses. The authors advance an analysis based on the singular-value decomposition (SVD) of the Wigner distribution of the signal, which provides a criterion to filter out data segments corrupted by interference. When applied to clinical data, this SVD-Wigner filtering process reduces the scatter in the local frequency estimate sufficiently to produce a reliable estimate of the frequency slope along the signal with about one third of the data needed by conventional short-time Fourier techniques. The improvement is not larger because these clinical data were taken on a scanner with a large sample volume, so that most data segments are perturbed by interference artifacts. Simulations show that in a more tightly focused system, with fewer scatterers contributing to the echoes, the reduction in required data can be appreciable

Abstract Composite piezoelectrics made from Calcium-modified lead titanate rods embedded in a polymer matrix have been evaluated for hydrophone applications. These composites behave quite differently from the conventional 1–3 composites made with lead zirconate titanate ceramics. Specifically, in the modified lead-titanate case the magnitude of the d 31 coefficient is enhanced in the composite structure, and consequently the hydrostatic dh coefficient is suppressed. Nevertheless, these composites exhibit a large gh coefficient and a remark able pressure stability. An analysis shows that a substantial contribution to the composite's d 31 coefficient arises from internal stresses which develop along the ceramic rods and produce a piezoelectric charge through the d 33 coefficient of the ceramic. This effect is particularly pronounced in the composite structure of the modified lead-titanate ceramic since the ratio d 33/d 31 in this ceramic is exceptionally large.

Spherically curved annular-array transducers have been developed using a composite piezoelectric material. The composite material allows the construction of sensitive, high-resolution arrays with elements defined by the electrode pattern alone. The array elements exhibit uniform properties and clean thickness-mode oscillations uncoupled to spurious lateral resonances. A prototype 3-MHz array exhibits a minimum insertion loss of 8 dB with a 6-dB fractional bandwidth of 57%. The -20-dB and -40-dB ringdown times in this array correspond to 3.3 and 6.2 periods, respectively

An expression based on a perturbation method is employed to estimate the correlation of path length difference in a plane normal to the direction of wave propagation from measurements of ultrasonic scattering by model random media and calf liver. The expression gives the correlation function of path length difference in terms of an integral of the correlation function of the medium variations or an equivalent integral of the power spectrum of medium variations, both for a scattering angle of zero degrees. Power spectra derived from measurements of average differential scattering cross section over a spatial-frequency window are used to fit analytic functions that extend over all spatial frequencies. The results for the windowed and unwindowed data yield correlation functions and corresponding power spectra that are used to estimate the correlation function of path length difference. The results suggest that the correlation length in calf liver is less than 100 microns and that a root-mean-square path length variation of about 20 microns results from propagation through a 100-mm calf liver path.

1–3 piezoelectric-rod/passive-matrix composites offer advantages over the conventional piezoceramics and piezopolymers for the pulse-echo transducers used in medical ultrasonic imaging. Their benefits include high electromechanical coupling, acoustic impedance close to that of tissue, a wide range of dielectric constants, low dielectric and mechanical losses, an adjustable sound speed, low coupling to spurious oscillations, ease of subdividing into acoustically isolated array elements, and formability into complex curved shapes. Not all benefits are achieved simultaneously. In designing a material for a specific application, the material engineer can choose the piezoceramic, the passive matrix, their relative proportions and the spatial scale of the composite. We delineate the trade-offs in designing piezocomposites which enhance the performance of present ultrasonic transducers as well as make new transducer designs feasible.