Electromechanical piezoelectrics

Ferroelectric Ceramic—Polymer Composites. The motivation for the development of composite ferroelectric materials arose from the need for a combination of desirable properties that often caimot be obtained in single-phase materials. For example, in an electromechanical transducer, the piezoelectric sensitivity might be maximized and the density minimized to obtain a good acoustic matching with water, and the transducer made mechanically flexible to conform to a curved surface (see COMPOSITE MATERIALS, CERAMiC-MATRix). 

Uncoupled solutions for current and electric field give simple and explicit descriptions of the response of piezoelectric solids to shock compression, but the neglect of the influence of the electric field on mechanical behavior (i.e., the electromechanical coupling effects) is a troublesome inconsistency. A first step toward an improved solution is a weak-coupling approximation in which it is recognized that the effects of coupling may be relatively small in certain materials and it is assumed that electromechanical effects can be treated as a perturbation on the uncoupled solution. 

From a constitutive relation of the form t = t(D, ri) (here t is stress not time) it can be readily shown that, since there is no change in electric displacement in an open-circuit, thick-sample configuration, there are no secondary stresses due to electromechanical coupling. Nevertheless, the wavespeed is that of a piezoelectrically stiffened wave. 

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

The major piezoelectric applications are sensors (pickups, keyboards, microphones, etc.), electromechanical transducers (actuators, vibrators, etc ), signal devices, and surface acoustic wave devices (resonators, traps, filters, etc ). Typical materials are ZnO, AIN, PbTiOg, LiTaOg, and Pb(Zr.Ti)03 (PZT). 

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... 

Fe which have full width 2r at 0.2 mm s . Other isotopes are less demanding, e.g., Au, for which the lines are ten times wider. Most spectrometers are equipped with electromechanical Mossbauer velocity transducers of the loudspeaker type. This technique is suitable for velocity variations ranging from less than 1 mm s full scale up to several cm s and covers the whole reach of hyperfine splitting for most of the common isotopes. Kalvius, Kankeleit, Cranshaw, and others [1-5] have been pioneers in the field, who laid foundations for the development of high-precision drives with feedback amplifiers for proper linear velocity scales with high stability and low hum. Other techniques for Doppler modulation have been developed for isotopes with extremely narrow hyperfine lines, e.g., Zn. For such isotopes, piezoelectric transducers are mostly used [6, 7], more details of which are found in Sect. 7.2.1. 

The two main types of electromechanical transducers are based on either the piezoelectric or the magnetostrictive effect. The more commonly used of which are piezoelectric transducers, generally employed to power the bath and probe type sonicator systems. Although more expensive than mechanical transducers, electromechanical transducers are by far the most versatile and widely used. 

Probably the best measure of the effectiveness of a piezoelectric material is its electromechanical coupling constant, k, defined as... 

Chen, C. J. (1992). Electromechanical deflections of piezoelectric tubes with quartered electrodes. Appl. Phys. Lett. 60, 132-134. 

Because of its piezoelectric properties, synthetic CC-quartz is used for frequency control in electrical oscillators and filters and in electromechanical transducers. When mechanically stressed in the correct direction, CC-quartz develops an electric polarization. The opposite is also tme an applied electric field gives rise to a mechanical distortion in the crystal. Thin sections of quartz are cut to dimensions that produce the desired resonance frequency when subjected to an alternating electric field the vibrating crystal then reacts with the driving circuit to produce an oscillation that can be narrowly controlled. Quartz is ideal for this application because it is hard, durable, readily synthesized, and can be tuned to high accuracy, for example, quartz crystal clocks can be made that are stable to one part in 109. 

The piezoelectric effect is an electromechanical effect in which mechanical evoke and reverse an electric reaction in a ferroelectric material and vice versa. The word piezo has been derived from the Greek piezein which means press . Compounds are composed of positive and negative ions and are electrically neutral as a whole. The fact that electrically charged particles are still present in the crystal can for example be demonstrated by means of the electric... 

The class of ferroelectric materials have a lot of useful properties. High dielectric coefficients over a wide temperature and frequency range are used as dielectrics in integrated or in smd (surface mounted device) capacitors. The large piezoelectric effect is applied in a variety of electromechanical sensors, actuators and transducers. Infrared sensors need a high pyroelectric coefficient which is available with this class of materials. Tunable thermistor properties in semiconducting ferroelectrics are used in ptcr (positive temperature coefficient... 

Far more frequently, however, measurements are made with a relatively thin film (often < 5 /rm) on a comparatively massive substrate (often > 400 //,m in thickness). In principle, the piezoelectric and electromechanical properties of the films can be extracted by fitting conventional resonance measurements. In practice, multiple resonances due to the film/substrate system are measured it is then necessary to deconvolute the data in order to extract information on the films itself. In practice, this is difficult to do unambiguously [21,22],... 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

IRE Standards on Piezoelectric Crystals determination of the elastic, piezoelectric and dielectric constants - the Electromechanical Coupling Factor, 1958, Proceedings IRE April 1958, 764-78. 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

In Sect. 7.3, Eqs. (18) and (19) describe the Maxwell stress forces acting on a conductive tip when a combined d.c./a.c. voltage is applied. For the PFM set-up we have to complete the total interaction force by the additional effects of piezoelectricity, electrostriction and the spontaneous polarisation. Both electromechanical effects cause an electric field-induced thickness variation and modulate the tip position. The spontaneous polarisation causes surface charges and changes the Maxwell stress force. If the voltage U(t)=U[)c+UAc sin((Ot) is applied, the resulting total force Ftotai(z) consists of three components (see also Eq. 19) Fstatic, F(0 and F2m. Fstatic is the static cantilever deflection which is kept constant by the feedback loop. F2a contains additional information on electrostriction and Maxwell stress and will not be considered in detail here (for details see, e.g. [476]). The relevant component for PFM is F(0 [476, 477] ... 

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