Search

The piezoelectric performance of polyvinylidene fluoride (PVDF) is shown to double through the controlled incorporation of carbon nanomaterial. Specifically, PVDF composites containing carbon fullerenes (C-60) and single-walled carbon nanotubes (SWNT) are fabricated over a range of compositions and optimized for their Young's modulus, dielectric constant, and d(31) piezoelectric coefficient. Thermally stimulated current measurements show a large increase in internal charge and polarization in the composites over pure PVDF. The electromechanical coupling coefficients (k(31)) at optimal loading levels are found to be 1.84 and 2 times greater than pure PVDF for the PVDF-C-60 and PVDF-SWNT composites, respectively. Such property-enhanced nanocomposites could have significant benefit to electromechanical systems employed for structural sensing, energy scavenging, sonar, and biomedical imaging. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4768923]

The piezoelectric performance of polyvinylidene fluoride (PVDF) is shown to double through the controlled incorporation of carbon nanomaterial. Specifically, PVDF composites containing carbon fullerenes (C-60) and single-walled carbon nanotubes (SWNT) are fabricated over a range of compositions and optimized for their Young's modulus, dielectric constant, and d(31) piezoelectric coefficient. Thermally stimulated current measurements show a large increase in internal charge and polarization in the composites over pure PVDF. The electromechanical coupling coefficients (k(31)) at optimal loading levels are found to be 1.84 and 2 times greater than pure PVDF for the PVDF-C-60 and PVDF-SWNT composites, respectively. Such property-enhanced nanocomposites could have significant benefit to electromechanical systems employed for structural sensing, energy scavenging, sonar, and biomedical imaging. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4768923]

The Frequency Control Symposium celebrated its Golden Anniversary in 1996. It began as an annual review of technical progress, largely by those who had been wartime contractors, and was held under the aegis of the Signal Corps Engineering Laboratories at Fort Monmouth, NJ. The first published proceedings started with the tenth. Program booklets have been recovered for five symposia predating the tenth; their contents are published, for historical purposes, in this report.

Future uses of modern ferroelectrics include thin film resonant microstructures for timimg, sensing, and actuation. The frequency range of interest extends from nearly DC through the UHF band. At high frequencies especially, it is difficult to obtain precise material parameters from broadband electrical measurements. We have developed highly accurate lumped equivalent networks for these frequencies, for the two canonical cases of thickness and lateral field excitation. Measurements on these circuits permit extraction of the complex dielectric, piezoelectric, and elastic parameters of the material. In this report we discuss both traditional and modern electrical network descriptions of piezoelectric resonators; we also treat how they are modified by the conditions of excitation and inclusion of loss mechanisms. The more general networks are then specialized to yield lumped circuit versions tailored to the particular attributes of ferroelectrics: high coupling and moderate loss. A numerical example is worked by means of illustration., Prepared in collaboration with Rutgers Univ. Piscataway, NJ.

General expressions for Poisson's ratio are derived for arbitrary orientations in hexagonal point groups; simplified forms are given for cases involving symmetry directions. Applications are made to piezoelectric ceramics.

General expressions for Poisson's ratio are derived for tetragonal crystals; simplified forms are given for cases involving symmetry directions. Poisson's ratio, v, is defined for isotropic media as the quotient of lateral contraction to longitudinal extension arising from application of a simple tensile stress; in most materials, this dimensionless number is positive. In crystals, v takes on different values, depending on the directions of stress and strain chosen. The ratio finds application in a variety of areas of applied elasticity and solid mechanics, for example, as indication of the mechanical coupling between various vibrational modes of motion. jg

General expressions for Poisson's ratio are derived for cubic crystals; simplified forms are given for cases involving symmetry directions. Crystals of cubic symmetry include many of the binary semiconductor systems with the piezoelectric zincblende structure, such as GaAs and related alloys. These are extremely important for high technology applications such as cellular radio and microwave collision avoidance radar. All cubic classes have the same elastic matrix scheme, so for our purposes it is not necessary to distinguish between the cubic point groups. The cubic elastic matrix scheme is identical in form to that of isotropic substances; the difference is that for isotropic materials the shear coefficient (s44 or c44) is related to the two other independent coefficients, whereas in cubic crystals it is a third independent quantity. jg

General expressions for Poisson's ratio are derived for hexagonal crystals; simplified forms are given for cases involving symmetry directions. Crystals of hexagonal symmetry include a number of the binary semiconductor systems with the piezoelectric wurtzite structure, such as GaN and AlN. These are becoming increasingly important for high technology applications. One of the most important representatives of this class is the family of poled electroceramics, including BaTiO3, PZT, and related alloys. All hexagonal classes have the same elastic matrix scheme, so for our purposes it is not necessary to distinguish between the different point groups; the presence of piezoelectricity is neglected. jg

A synopsis of the piezoelectric effect is presented in the context of its history, traditional uses, and relation to crystal symmetry. Associated effects are briefly noted. Future prospects, particularly in the area of microelectromechanical systems/structures (MEMS) are discussed.

The use of composite materials and structures to provide characteristics unattainable directly from the constituent materials is well known. Work has been undertaken to apply this principle to the development of new dielectric materials for use in capacitors with greater energy density, lower loss, and higher breakdown resistance. This report describes the numerical analysis of permittivity in isotropic binary composite dielectrics through three-dimensional computer simulation.

A powerful motivation for using equivalent circuits to characterize piezoelectric devices is that the using equipment is often itself completely electrical in nature. The whole ensemble thus becomes subject to analysis or synthesis from a single perspective, i.e., network theory. In this report are described a brief history of circuit equivalents through the Mason circuit, followed by a presentation of newer descriptions of piezoelectrically vibrating structures, specifically, analog networks and KLM circuits.

Lithium tetraborate is a tetragonal material of considerable promise for frequency control and signal processing applications. It exhibits piezoelectric coupling values that fall between those of lithium niobate and quartz, but possesses orientations for which the temperature coefficient of frequency and delay time is zero for bulk and surface acoustic waves. In this report, we discuss the properties of two doubly rotated bulk wave resonator orientations having both first- and second-order temperature coefficients equal to zero. These are suitable for shear and compressional wave transducers in applications where very low temperature sensitivity is required simultaneously with moderately strong piezocoupling coefficients. (js)

Stable local oscillators based on surface acoustic wave (SAW) resonators have been proposed for future use in Army electronic systems designed for airborne and vehicular applications. The vibration spectra of these systems in conjunction with the vibration sensitivity of the SAW resonators leads to a degradation in oscillator phase noise, which may then exceed the total allowable system phase noise. This report details a study of the vibration-induced phase noise in a group of SAW oscillators developed for a low-noise radar application. (r.h.)

The use of composite materials and structures to provide characteristics unattainable directly from the constituent materials is well known. Recently, work has been undertaken to apply this principle to development of dielectric materials for energy storage applications. It is anticipated that this technology will provide materials for use in capacitors with greater energy density, lower loss, and higher breakdown resistance. This report describes the results of an effort to analytically model the net or resultant dielectric behavior of such composite dielectric materials. A theoretical model of the composite dielectric is presented and computer code implementing the model is discussed along with preliminary results for the two-dimensional case.

AT-cut quartz plates, the most widely used vibrators for frequency selection and control, are singly rotated cuts. Increasingly stringent requirements on frequency tolerances motivate the report, which examines the effect on frequency-temperature behavior of small but nonnegligible second rotations that arise from inevitable manufacturing variations. The results presented permit formulation of practical and consistent specifications of tolerances on both angles to achieve a required temperature coefficient., GIDEP, 347.00.00.00-04-02

Analog networks for surface waves are introduced and illustrated. Transmission lines represent regions of propagation, and piezoelectric transduction appears as ideal transformers at electrode edges producing delta- functions of traction. Advantages of using an analog-type description are discussed.

Resonators for TCXO application are required to have accurately- characterized frequency-temperature (f-T) curves and equivalent network parameters. This report describes how the circuit parameters, critical resonator frequencies, and temperature coefficients depend on material constants of the crystal and geometrical factors. These constants are tabulated for AT- and SC- cut quartz. It further explains the observed f-T curve shift between resonator operation with and without series load capacitors. Simple relations are given for treating this effect, along with charts and other design aids. These are used in a practical example involving an AT-cut resonator for a typical TCXO application.

In analytical treatments of piezoelectric-acoustic transducers, signal processors, and resonators, the electromechanical transduction mechanism is most often expressed in terms of the elements of the piezoelectric (e) or (d) matrices. Molecular interpretations of piezoelectricity, and especially electrooptical applications, usually involve polarization as the preferred variable, and consequently the alternative (a) and (b) matrices are of interest. The elements of these latter sets are calculated for lithium niobate from measured elastopiezodielectric constants taken from the literature.

In analytical treatments of piezoelectric acoustic transducers, signal processors, and resonators, the electromechanical transduction mechanism is most often expressed in terms of the elements of the piezoelectric (e) or (d) matrices. Molecular interpretations of piezoelectricity, and especially electro- optical applications, usually involve polarization as the preferred variable, and consequently the alternative (a) and (b) matrices are of interest. The elements of these latter sets are calculated for lithium tantalate from measured elastopiezodielectric constants taken from the literature. Piezoelectric resonators; Piezoelectric transducers; Lithium tantalate; Acousto optics, Tantalum compounds, Lithium compounds.

In analytical treatments of piezoelectric-acoustic transducers, signal processors, and resonators, the electrochemical transduction mechanism is most often expressed in terms of the elements of the piezoelectric (e) or (d) matrices. Molecular interpretations of piezoelectricity, and especially electrooptical applications, usually involve polarization as the preferred variable, and consequently the alternative (a) and (b) matrices are of interest. The elements of these latter sets are calculated for lithium tetraborate from measured elastopiezodielectric constants taken from the literature. Keywords: Piezoelectric resonators; Piezoelectric transducers; Lithium tetraborate; Acousto-optics; Formula mathematics.

Ongoing work aimed at determining the physical properties of cultured quartz material from frequency measurements of bulk wave resonators has highlighted the need for accurate means of measuring the mass loading due to the electrodes. In this report, various methods of determining electrode mass loading are presented, and measurements of mass loading using several of these techniques are compared. Variations between the values of mass loading obtained by the various techniques are discussed and a model is proposed to explain the various differences. (rrh)

In analytical treatments of piezoelectric-acoustic transducers, signal processors, and resonators, the electromechanical transduction mechanism is most often expressed in terms of the elements of the piezoelectric (e) or (d) matrices. Molecular interpretations of piezoelectricity, and especially electrooptical applications, usually involve polarization as the preferred variable, and consequently the alternative (a) and (b) matrices are of interest. The elements of these latter sets are calculated for quartz from measured elastopiezodielectric constants taken from the literature. (RRH)

Contents: Plenary Session; R.D. Mindlin Memorial Session Piezoelectric Resonators and Filters; Quartz Material and Resonator Processing; Surface Acoustic Wave Devices/Magneto Static Waves and Dielectric Resonators; Frequency Stability, Noise and Measurements; Time Coordination; I.I. Rabi Memorial Session Atomic Frequency Standards; Superconductivity and Frequency Control; AUthor Index; Specifications and Standards Germane to Frequency Control; and Proceedings Availability Information; Symposia., See also Supplement, ADA217276.

Alpha aluminum phosphate (berlinite) has been investigated as a highly piezoelectric material potentially suitable for use in advanced bulk and surface acoustic wave devices. Areas of investigation include: (1) crystal structure, (2) methods of crystal growth, (3) defects in structure, (4) the presence of water impurities, (5) piezoelectric resonators, and (6) the equivalent electrical circuit. Calculations have been carried out for frequency constant, piezoelectric coupling factor, and linear temperature coefficient as functions of orientation for general, doubly rotated plate orientations, and disclose quartz-like properties with coupling factors appreciably larger than quartz. Measurements indicate larger than expected losses, indicative of incorporation of impurities during growth; suggestions for further work are given. (Author)

For precision applications, where ruggedness is required, it is necessary to mount AT-cut resonators at four points. This note considers mounts consisting of pairs of diametric edge attachments. A locus is found for the angles of attachment to circular plates such that radially directed edge forces are compensated. One locus point is found to be particularly frequency insensitive to mounting errors and defines the optimal setting for the four-point mount., Published in IEEE Transactions on Sonics and Ultrasonics, vSU-25 n4 p223-226, Jul 1978.

The effective frequency-temperature curve of a crystal resonator operated with series load capacitance differs from that of the crystal alone. Since the principal method of compensating for the crystal frequency-temperature behavior in a temperature compensated crystal oscillator (TCXO) employs series of varactors and a temperature-sensitive compensation network, it is of major importance to be able to understand and deal with this effect in the design of TCXOs. The necessary formulas and discussion are given in this paper., Published in IEEE Transactions on Sonics and Ultrasonics, vSU-25 n4 p185-191, Jul 1978.

The frequency-temperature (f-T) behavior of a crystal resonator depends upon temperature, and its spatial and temporal gradients. For quasi-isothermal changes the static f-T curve can be used to determine frequency shifts that occur, e.g., in oven-controlled units. The frequency then depends upon the parameters of the static f-T curve, the temperature range over which the oven cycles, and upon the oven setting point. The maximum frequency excursion has been computed for the AT and SC cuts of quartz in terms of these parameters as a function of the orientation angle. When thermal-transient-compensated cuts are not utilized, oven cyclings or other temperature perturbations introduce an additional nonnegligible component of the frequency shift. This effect is quantified by means of a simple mathematical model. The model is capable of predicting the thermal transient effects for AT cuts appearing in the literature. Simulations, using the model, disclose that sinusoidal temperature variations with periods of hours can readily lead to frequency instabilities much larger than would be expected using the static f-T curve for the AT cut. This effect should be greatly diminished in the vicinity of the SC cut., Published in IEEE Transactions on Sonics and Ultrasonics, vSU-26 n4 p299-306, Jul 1979.

This paper describes quartz resonators that provide simultaneous compensation against both dynamic and static conditions, and that are compensated, moreover, against rapid temperature transients encountered in fast-warmup oscillators for manpack use.

This report describes resonator configurations that are compensated for arbitrary directions of the acceleration field, and that require no additional electronics other than the oscillator circuitry normally used. This approach produces compensation with no changes in size, weight, and power, and applies to any crystal reference oscillator in any shock/vibration environment. (Author)

Doubly rotated cut quartz possesses many desirable features for acoustic wave devices. In addition to its excellent temperature behavior, it nonlinear elasticity produces mechanical and thermal stress-compensating effects. Doubly rotated cuts of quartz have been extensively used to construct bulk wave resonators for frequency-stable sources. In this report we will describe the acoustic properties of Surface Acoustic Waves (SAW) and Shallow Bulk Acoustic Waves (SBAW) on doubly rotated quartz. A number of delay lines have been constructed on various doubly rotated cuts of quartz. The frequency response of SAW is similar to that obtained on ST-cut quartz. The three SBAW modes predicted from theory were also observed. Both theoretical and experimental results are presented. (Author)

Some consequences of acoustic bulk wave propagation in piezoelectric semiconductors of class 4-bar 3m are investigated. Doubly rotated plate vibrators are considered, as are coupled modes and transmission line equivalent networks. It is shown how sensitive measurements of oxide films may be simply made in a nondestructive manner by use of such crystals as piezoelectric vibrators. Calculations are carried out using gallium arsenide as a typical compound. (Author)

Shallow bulk acoustic wave propagation in piezoelectric crystals is considered from the standpoint of work reported to date. It is compared to bulk and surface acoustic waves as to properties and device potential. Singly and doubly rotated cuts are considered, as are piezoelectric transduction, energy trapping equivalent networks, as well as areas of future work such as new materials, other than quartz, and nonlinear effects. (Author)

Singly rotated AT cut plates are most often used for frequency control in applications where moderate and high precision is required, but recent developments point to a greatly expanded role for doubly rotated cuts. Virtually all of these thickness mode cuts are of the form of thin circular discs mounted on their edges. Any forces communicated between the mounting supports and the quartz plate produce high stresses and stress-gradients resulting in significant frequency perturbations. This report describes crystal plate designs having a prescribed lateral contour for singly and doubly rotated plates. These designs provide a relatively large portion of the periphery for mounting, such that mounting stresses are greatly reduced with no detriment to the force immunity of the older-type mounts. (Author)

The frequency-temperature (f-t) behavior of a crystal resonator depends upon temperature, and its spatial and temporal gradients. For quasi-isothermal changes, the static f-t curve can be used to determine frequency shifts that occur. The frequency then depends upon the parameters of the static f-t curve, the temperature range over which the oven cycles, and upon the oven setting point. The maximum frequency excursion has been computed for the AT and SC cuts of quartz in terms of these parameters, as function of orientation angle. When oven cyclings, or other temperature perturbations occur at rates too rapid to be considered quasi-isothermal, additional non-negligible components of frequency shift are introduced. This effect is quantified by means of a simple model which is capable of predicting thermal transient effects for AT cuts. Simulations, using the model, disclose that sinusoidal temperature variations with periods of hours can lead to frequency instabilities much larger than would be expected using the static f-t curve. This effect should be greatly diminished in the vicinity of the SC cut. (Author)

The frequency- or immittance-temperature anomalies occurring in quartz crystal resonators are called activity dips. Testing for their presence can represent a considerable addition to the manufacturing cost. An electronic method is described that is rapid, simple, and well adapted to microprocessor control. It makes use of the fact that the desired mode of vibration is shifted in frequency by a variable series capacitor, while interfering modes that cause activity dips are nearly unaffected. (Author)

AT-cut quartz plate resonators are usually edge mounted. For precision applications, and especially where ruggedness is required, a four-point mount is necessary. This report investigates those mounts consisting of two pairs of diametric attachments. For this class of mount a locus is found for the angles of attachment of the circular plate with respect to the crystallographic axes such that radially directed edge forces are compensated. One point on the locus is found to be particularly frequency insensitive to mounting errors, and defines the optimum setting for the four-point mount. (Author)

Precision frequency control requirements for future digital communication systems require improved crystal resonator performance in a number of aspects. Accordingly, the potential of doubly rotated quartz cuts has begun to be explored. In the neighborhood of the SC-cut (YX omega L) phi/theta, phi approximately equals 21.9 degrees, theta approximately equals +33.9 degrees, a variety of effects having their bases in nonlinear elasticity have been shown, or are predicted, to be improved with respect to corresponding AT-cut values. The static frequency-temperature behavior also shows improvement. This report concerns the force-frequency effect, thus far not investigated in any detail for doubly rotated quartz plate vibrators. It relates initial stress produced by mounting supports to resonance frequency changes; it contributes to long-term aging, and is related to the frequency excursions produced in shock and vibration environments. In-plane diametric forces applied to the periphery of vibrating plates produce frequency changes that depend upon the azimuth angle psi in the plane of the plate. For the IT-cut at phi = 19.1 degrees, the maximum value was found previously to be only about one-third that of the AT-cut. This points to a reduced coefficient at the SC-cut as well. Measurements of the force-frequency effect coefficients have now been extended to doubly rotated quartz plates. Also given are charts of the mode spectra in the region of the thickness modes, and the modal temperature coefficients.

The imaginary part of the complex compliance matrix, denoted as the fluency, is defined, and the elements are computed for alpha-quartz. Its application to low frequency vibrators is discussed. The role of motional time constants in characterizing resonator behavior is also described and applied to the minus 18.5 degree bar. (Author)

This report comprises a doctoral dissertation in electrophysics at the Polytechnic Institute of Brooklyn, Brooklyn, NY 11201, June 1972. This study derives exact equivalent network representations for the electromechanical behavior of crystal stacks that are piezoelectrically driven in thickness modes of vibration. The stacked structure may consist of any number of layers; each layer consists of a homogeneous, but arbitrarily anisotropic crystal medium. The analysis shows that each layer is represented by three acoustic transmission lines; in general, these lines possess unequal characteristic immittances and propagation wavenumbers. At the interface between any two layers, the six transmission lines (three from each side) are interconnected by transformer elements. The circuit descriptions obtained constitute a first rigorous representation for the canonical cases of thickness- and lateral-field excitation of the three thickness modes of vibration of crystals with arbitrary anisotropy. The circuits have been realized in such a fashion that the overall result for a multi-layered structure is built up by the simple interconnection of basic blocks of identical form, with each block accounting for the behavior of one layer. An example demonstrates the application of these networks to the development of actual devices and illustrates the systematic, efficient and practical aspects of the network characterization developed. (Author)

In this report, attention is focused on the question of the spatial extent developed by an intermediate energy (5-20 keV) scattered electron beam in a lithographic e-beam resist material. Use is made of the multiple scattering theory of Bethe to calculate the average cosine between the actual direction of motion and the direction of the primary electron beam in terms of the average nuclear charge of the target and the depth of electron penetration into the target. Use is made of the average cosine calculation to establish an order-of-magnitude expression for the depth at which two electron-beam lines overlap to cause undercutting. (Author)

The report provides specific numerical results, in the form of data tables, obtained from the solution of the pertinent transcendental equations governing the vibration frequencies of mass-loaded piezoelectric plates, in the one-dimensional approximation. The tables refer to excitation of a single thickness plate mode by an electric field in the thickness direction. Resonance and antiresonance frequencies are given in normalized form, along with frequency deviations, as function of harmonic of operation, piezoelectric coupling factor and amount of mass-loading.

This report provides specific numerical results, in the form of data tables, obtained from the solution of the pertinent transcendental equations governing the vibration frequencies of mass-loaded piezoelectric plates, in the one-dimensional approximation. The tables refer to excitation of a single thickness plate mode by an electric field in the lateral direction. Resonance and antiresonance frequencies are given in normalized form, along with frequency deviations, as function of harmonic of operation, piezoelectric coupling factor, and amount of mass-loading.

The report considers a single thickness mode of a piezoelectric crystal plate, and relates both the characteristic frequencies and their temperature coefficients to the phenomenological material properties of the crystal and the electrode mass-loading. It is shown how mass-loading affects the frequency-temperature characteristics of the plate vibrator. Experimental results prove the existence of another factor, that depends on the electrode material, which contributes significantly to the temperature behavior.

The report discusses networks representing two types of acoustic structures used for filtering: the composite resonator, a one-port device comprising a thin film overlay of high coupling material atop a low loss substrate, and the stacked-crystal filter, a two-port device wherein two or more crystal plates are joined together mechanically at the major surfaces to take advantage of mechanical and piezoelectrical coupling effects. Computer simulations of stacked-crystal filter designs at 10 MHz disclose that both Chebyshev and Butterworth responses may be obtained using quartz plates.

The report treats a single-mode resonator plate with equal mass coatings on its surfaces and excited by an electric field in the thickness direction. The usual restriction to low piezoelectric coupling coefficient is not made. From simple considerations regarding the equivalent network, the exact equations for the critical frequencies of interest are shown to follow directly. These are used throughout without approximation and solved numerically. Use of the exact relations allows high coupling materials to be covered as easily as low. Families of curves showing the variations of the resonance and antiresonance frequencies over a wide range of values of mass-loading, coupling coefficient and harmonic number are given. A new plateback parameter, valid for all piezoelectric substances, is also introduced. (Author)