Piezoelectric coupling constant

In these expressions eQ and are the static and high-frequency dielectric constants of the host, vs is a (mean) velocity of sound therein, Cpe is the piezoelectric coupling constant, CQ a numerical factor that depends on the crystal structure and kD the Debye inverse screening length. 

Here we demonstrate in two examples how symmetry considerations help eliminate coupling constants. The first example describes Frank s considerations in determining the relevant elastic constants of nematic liquid crystals, and the second example will show us how many piezoelectric coupling constants are possible in systems with different symmetries. In both cases the nonvanishing coefficients are determined by the symmetry of the material and using the Curie principle, which states that tensor coefficients characterizing material properties should be invariant under the symmetry transformations of the substance. ... 

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

This is the efficiency of energy conversion between mechanical and electrical forms. For PZTs, it ranges from 0.5 to 0.7, which are the most efficient of all known piezoelectric materials (see Table 9.1). For quartz, the coupling constant is about 0.1. 

In contrast to piezoelectric single crystals, such as quartz, the piezoelectricity of PZT ceramics decays with time due to relaxation. Experimentally it is found that on a large time scale (for example, months and years), the aging process can be accurately described by a logarithmic law. For example, the coupling constant k varies with time f as... 

See Local density of states Lead zirconate titanate ceramics 217—220 chemical composition 218 coupling constants 220 Curie point 218 depoling field 219 piezoelectric constants 220 quality number 219 Leading-Bloch-waves approximation 123 Level motion-demagnifier 271 Liquid-crystal molecules 338 Living cell 341... 

Even for poly(y-methyl L-glutamate) with a high piezoelectric constant (d= 10 7 cgsesu), the electro-mechanical coupling constant k defined by... 

Selected classes of asymmetric crystal structures exhibit the property of piezoelectricity. With the application of a mechanical strain, piezoelectric materials develop an electrical potential difference across them conversely, when a potential difference is applied to these materials, a displacement occurs. The efficiency of the conversion between mechanical energy and electrical energy is described by the electromechanical coupling constant, which practically ranges to values as high as 0.7 a value of 1 would imply complete conversion between mechanical and electrical energy. 

Crisler DF, Cupal JJ, Moore AR. Dielectric, piezoelectric, and electromechanical coupling constants of zinc oxide crystals. Proc IEEE 1968 56 225-6. 

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. 

KNbOi (LB Number 1A-2). This crystal is ferroelectric below about 418 °C. Further phase transitions take place at about 225 °C and about — 10°C, retaining ferroelectric activity. The crystal has large electromechanical coupling constants and is useful in lead-free piezoelectric elements and SAW (surface acoustic wave) filters in communications technology (Fig. 4.5-13,4.5-14). 

PIT (LB Number 1C-a63). Solid solutions Pb(Tii jZrj)03 with x = 0.5-0.6 are commonly called PZT. They have very large electromechanical coupling constants and are widely utilized as piezoelectric elements. Thin ceramic films are useful in memory devices (Fig. 4.5-31). 

Here, d and e are the matrices of piezoelectric coupling and dielectric constants, respectively. 

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