Electromechanical coupling factor

The contribution to the stress from electromechanical coupling is readily estimated from the constitutive relation [Eq. (4.2)]. Under conditions of uniaxial strain and field, and for an open circuit, we find that the elastic stiffness is increased by the multiplying factor (1 -i- K ) where the square of the electromechanical coupling factor for uniaxial strain, is a measure of the stiffening effect of the electric field. Values of for various materials are for x-cut quartz, 0.0008, for z-cut lithium niobate, 0.055 for y-cut lithium niobate, 0.074 for barium titanate ceramic, 0.5 and for PZT-5H ceramic, 0.75. These examples show that electromechanical coupling effects can be expected to vary from barely detectable to quite substantial. 

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...

ZnO is a wide band gap semiconductor, which is used for various applications. Based on textured ZnO films one can build highly effective piezo field emitters. On the other hand ZnO is a very effective electron-excited phosphor. ZnO films easily withstand electron fluence more than 1 W/cm. ZnO films doped with Al, Ga, or In have a low resistivity of about 10 " Qcm and a high transparency of about 90%. This is sufficient for applications as a front contact in solar cells, liquid crystal displays etc. Dielectric ZnO films have a high electromechanical coupling factor that allow using ZnO in various surface acoustic wave (SAW) devices such as delay lines, delay-line filters, resonators, transducers and SAW convolvers. 

Density (10 kg/m ) e/Eo Piezoelectricity (pC/N) Sound Velocity (km/s) Acoustic Impedance (10 Pa s/m) Mechanical Quality Factor Electromechanical Coupling Factor (%)... 

By using equations 12.3 and 12.4, the efficiency of energy conversion, representing the electromechanical coupling factor, is given by ... 

There are five important figures of merit in piezoelectrics the piezoelectric strain constant d, the piezoelectric voltage constant g, the electromechanical coupling factor k, the mechanical quality factor Qm, and the acoustic impedance Z. These figures of merit are considered in this section. 

The terms, electromechanical coupling factor, energy transmission coefficient, and efficiency are sometimes confused (5. All are related to the conversion rate between electrical energy and mechanical energy, but their definitions are different [6]. 

Relaxor-type electrostrictive materials, such as those from the lead magnesium niobate-lead titanate, Pb(Mgp 3Nb2/3)03-PbTi03 (or PMN-PT), solid solution are highly suitable for actuator applications. This relaxor ferroelectric also exhibits an induced piezoelectric effect. That is, the electromechanical coupling factor kt varies with the applied DC bias field. As the DC bias field increases, the coupling increases and saturates. Since this behavior is reproducible, these materials can be applied as ultrasonic transducers which are tunable by the bias field [12]. 

The electromechanical coupling factor ksi is calculated from the v value and the antiresonance frequency /a through Eq. 34. Especially in low-coupling piezoelectric materials, the following approximate equation is available ... 

It is important to note that the unimorph (a piezoceramic plate and a metal plate bonded together) bending actuation cannot provide high efficiency theoretically, because the electromechanical coupling factor k is usually less than 10%. Therefore, instead of the unimorph structure, a simple disk was... 

Fig. .5-33 (PbTi03)j (Pb(Sci/2Nbi/2)03)i 3 (ceramic), fcp versus x. is the planar electromechanical coupling factor...

PVDF polymer is used in copolymers with TrFE in certain range of its molar ratio. This procedure will increase crystallinity ratio of the polymer up to 90%. Therefore such copolymers exhibit much stronger piezoelectric activity. The most interesting molar ratio range is 60-80% of PVDF. In that range the thickness electromechanical coupling factor kt reaches its maximum value k is a measure for the electromechanical energy conversion). Copolymerized TrFE units decrease the Curie temperature of the polymer (e.g. c = 80°C for P(60%VDF/40%TrFE) polymer). 

IRE Standards on Piezoelectric Crystals Determination of the Elastic, Piezoelectric, and Dielectric Constants—the Electromechanical Coupling Factor, 1958. Proc. IRE. 46, 764-778, April 1958. 

Fig. 11. (a) Equivalent series resistance of quartz and langasite single crystals as a function of resonator vibration modes, (b) electromechanical coupling factor of langasite series as a function of piezoelectric constant. 

Fig. 12. (a) Electromechanical coupling factor vs. temperature coefficent of frequency of piezeelectric materials, (b) Frequency variation/equivalent series resistance as a function of... 

The fundamental parameters controlling operating characteristics of SAW-based sensors are the SAW velocity, the temperature coefficients of delay (TCD), the electromechanical coupling factor, and the propagation loss. In SAW applications, the coupling factor relates to the maximum bandwidth obtainable and the amount of signal loss between input and output that determines the fractional... 

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