Electromechanical coupling coefficients

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... 

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 ... 

The last term is approximately equal to K when <4 1. Thus, the electromechanical coupling coefficient K ) has a second interpretation is approx-... 

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... 

As a consequence, the joins for (Pbi. (Bajc)Ti03 at low temperature and for Pb(Zri cTy03 at room temperature are interrupted by a morphotropic phase boundary (MPB), which separates tetragonal and rhombohedral phases (Fig. 14). The structural state of the oxides in the vicinity of the MPB is a subject of active inquiry, because many of the physical properties of PBZT ferroelectrics are maximized at the MPB. These include the dielectric constant, the piezoelectric constant, and the electromechanical coupling coefficients (Jaffe 1971, Thomann and Wersing 1982, Heywang and Thomann 1984). For industrial purposes, this behavior is exploited by annealing PBZT ferroelectrics with compositions near the MPB close to the Curie temperature in an... 

If the film cannot be freely deformed in its plane, the piezoelectric current is called t/33 or dj. If the variation in the electric field is measured per unit of stress, g coefficients are obtained that are connected by the correlation of g = d/e where e is the dielectric constant depending on the film thickness. Constants g and tf are most widely used in the design of electromechanical transducers. The yield from the conversion of mechanical energy into electrical energy is represented by the electromechanical coupling coefficient ATjby Eq. (3.3). 

One way to present a gray box model of IPMC is to use an equivalent beam and an equivalent bimorph beam model and combine them with important physical properties of IPMCs Young s modulus and electromechanical coupling coefficient, determined from the rule of mixture bi-... 

The piezoelectric generator coefficient d indicates the mechanical strains that are induced by electric potentials and the piezoelectric motorcoefficient e is a measure of the dipole moments that are created by strains. These two parameters are similar in nature and proportional to one another. The electromechanical coupling coefficient k is proportional to both d and e, its square giving the efficiency of conversion between mechanical and electrical energy that can be achieved with the ferroelectric... 

The electromechanical coupling coefficient ky represents the conversion of electrical energy into mechanical energy and vice versa. The electromechanical coupling can be considered a measure of transduction efficiency and is always less than unity as shown here ... 

J. Valasek (1920, 1921,1922,1924) discovered the ferroelectric effect of a single crystal in about 1921. Jaffe, who went to the United States in 1935, assisted Cady in the study of Rochelle salt. Rochelle salt was often used in various transducers because it has a great piezoelectric effect. In spite of being a piezoelectric crystal with the highest electromechanical coupling coefficient, Rochelle salt is of limited use because it is soluble in water, deliquescent and some parameters do not have a suitable temperature characteristic. 

Berlinite crystals are very much similar to quartz. Stmctural phase change takes place at the temperature 584°C (Blistanov et al. 1982). For material properties see Table 7.6. Similarly to quartz berlinite crystals undergo a- to jS-phase transition. Crystals are grown by hydrothermal method (Detaint et al. 1985 Motchary and Chvanski 2001) Berlinite crystals exhibit higher electromechanical coupling coefficient than quartz. 

Electromechanical coupling coefficient is higher for LGS than for quartz. Some of the LGS non-linear material coefficients are pubhshed in Sorokin et al. (1996). Temperature coefficients published by different authors show values widely scattered. For material properties and their temperature coefficierrts see Tables 7.7 and 7.8. (Adachi et al. 1999 Bohm et al. 1999, 2000 Ilyaev et al. 1986 Kaminskii et al. 1983a,b, 1984 Onozato et al. 2000 Pisarevskii et al. 1998 Silvestrova et al. 1986, 1987, 1993 Sorokin etal. 1996). 

Jayasundere N, Smith BV, Dunn JR (1994) Piezoelectric constant for binary piezoelectric 0-3 connectivity composites and the effect of mixed connectivity. J Appl Phys 76 2993-2998 Jiang W, Zhang R, Jiang B, Cao W (2003) Characterization of piezoelectric materials with large piezoelectric and electromechanical coupling coefficients. Ultrasonics 41 55-63 Jin J, Rajan KK, Lim LC (2006) Properties of single domain PZN-(6-7)%PT single ciystal. Jpn J Appl Phys 45(11) 8744-8747... 

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