Electromechanical Coupling Factor k

The electromechanical coupling factor (k) measures the ability of an E-M material to convert energy between the electrical and mechanical forms and is defined as [2]  

Depending on the direction of the eleetrie field and the direetions assoeiated with strain/ stress, there are many coupling factors. For a piezoelectric effect with electric field along direction i and the strain associated direction p, the k is  

If the electric field is applied along the 3-direction, the coupling factor is ka when the actuation is along the 3-direction and k i when the actuation is along the 1-direction, which are k = and k =d i/respectively. 

For the electrostrictive effect, the k is derived based on the indueed polarization level P and strain x induced by a given electrical field [11]  

The k is also related to the coefficients measured under different conditions. For instance, the elastic compliance and (measured under constant field and charge, respectively) are related to each other as = (l - kl )sf. Thus, under different external electric boundary conditions, a polymer with a large k will see a large difference in the elastic compliance. This can be used to tune the elastic modulus of the polymeric material by varying the electric conditions. For example, the elastic compliance of the electrostrictive material decreases with the DC bias. Similarly, E33 = (1 — which means the 

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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. 

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... 

Electromechanical coupling factor (k) This factor is related to the rate of conversion between electrical energy and mechanical energy. It is defined as... 

The electromechanical coupling factor k quantifies the efficiency of a piezoelectric material as a transducer, converting mechanical energy into electrical energy and vice versa. Thus... 

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. 

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...

The electrical impedance of the IDT depends on a variety of factors including the electromechanical coupling coefficient (K ), the dielectric permittivity of the substrate (e ), and the geometry of the IDT electrode width, spacing, number of finger pairs, and acoustic aperture (i.e., IDT finger overiap length). Table... 

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). 

The stiffness parameter C55 has, in effect, been increased by the factor (1 + K ) — an effect known as piezoelectric stiffening. The factor is the electromechanical coupling coefficient for the jt-propagating, z-polarized plane wave ... 

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