Piezoelectric strain constant

Values of piezoelectric constants are, however, very scattered among polymers. In the case of oriented poly(y-methyl L-glutamate) film, the piezoelectric strain constant (d-constant) amounts to as much as 10 x 10 8 cgsesu when elongated in a direction at 45° to the draw-axis (Fukada, 1970), which is comparable with d = 6.5 x 10 8 cgsesu for X-cut... 

Fig. 9. Piezoelectric strain constant of uniaxially drawn poly(y-methyl L-glutamate) film (a-helical form) plotted against the angle 6 between draw-axis and stress direction. Draw-ratio = 2. Drawn after Fukada, Date, and Hirai [Nature 211, 1079 (1966)] by permission of Macmillan (Journals) Ltd.

Fig. 11. Complex piezoelectric strain constant (20 Hz), complex Young s modulus (30 Hz), and complex dielectric constant (1kHz) of uniaxially drawn poly(D-propylene oxide) film plotted against temperature. Draw-ratio = 1.5. Degree of crystallinity=40%. Drawn after Furukawa and Fukada [Nature 221,1235 (1969)] by permission of Macmillan (Journals) Ltd.

Fig. 12. Complex piezoelectric strain constant of uniaxially drawn cellulose triacetate film plotted against temperature. Draw-ratio = 2. Plasticizer content = 10%. Frequency = 20 Hz. Drawn after Fukada, Date, and Emura [J. Soc. Mat Sci. Japan 17,335 (1968)] by permission of the Society of Materials Science, Japan...

Fig. 26. Correlation between increment of spontaneous polarization from 80° C to 15° C and piezoelectric strain constant at room temperature for /9-form polarized poly(vinylidene fluoride) films. Poling temperature = 90° C. Poling field = 700 kV/cm (Murayama, 1972)...

Fig. 29. Temperature dependence of complex piezoelectric strain constant of composite film of polyester resin and powdered PZT (50% of the volume) polarized at room temperature under a d.c. field of 100 kV/cm. Reproduced from Fukada and Date [Polymer Journal, 1,410 (1970)] by permission of the Society of Polymer...

Table 3. Piezoelectric strain constant of polymer films at room temperature...

Fig. 4. The effect of temperature on the piezoelectric strain constant, d3v for A, nylon-11 B, nylon-7 and C, poly(vinylidene...

Piezoelectricity links the fields of electricity and acoustics. Piezoelectric materials are key components in acoustic transducers such as microphones, loudspeakers, transmitters, burglar alarms and submarine detectors. The Curie brothers [7] in 1880 first observed the phenomenon in quartz crystals. Langevin [8] in 1916 first reported the application of piezoelectrics to acoustics. He used piezoelectric quartz crystals in an ultrasonic sending and detection system - a forerunner to present day sonar systems. Subsequently, other materials with piezoelectric properties were discovered. These included the crystal Rochelle salt [9], the ceramics lead barium titanate/zirconate (pzt) and barium titanate [10] and the polymer poly(vinylidene fluoride) [11]. Other polymers such as nylon 11 [12], poly(vinyl chloride) [13] and poly (vinyl fluoride) [14] exhibit piezoelectric behavior, but to a much smaller extent. Strain constants characterize the piezoelectric response. These relate a vector quantity, the electrical field, to a tensor quantity, the mechanical stress (or strain). In this convention, the film orientation direction is denoted by 1, the width by 2 and the thickness by 3. Thus, the piezoelectric strain constant dl3 refers to a polymer film held in the orientation direction with the electrical field applied parallel to the thickness or 3 direction. The requirements for observing piezoelectricity in materials are a non-symmetric unit cell and a net dipole movement in the structure. There are 32-point groups, but only 30 of these have non-symmetric unit cells and are therefore capable of exhibiting piezoelectricity. Further, only 10 out of these twenty point groups exhibit both piezoelectricity and pyroelectricity. The piezoelectric strain constant, d, is related to the piezoelectric stress coefficient, g, 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. 

Barium titanate (point group 4mm below the Curie temperature of 130 °C) has the (reduced) piezoelectric strain constant (d) matrix... 

Figure B.4 shows the theoretical temperature dependence of the spontaneous polarization P and the dielectric permittivity e. Considering that, for the ferroelectric state, e = C/2(Tc - T) and = >/((Tc -T)/eoCP), the temperature dependence of the piezoelectric strain constant d is obtained as...

Piezoelectric strain constants Planar piezoelectric strain constant Hydrostatic piezoelectric strain constant Direct current... 

Hguie 9 comperes Ihe tenqicrelurc dependence frf elastic modulus and piezoelectric strain constant for a phase nylon-9 and o-phasc nyloo-11. Nylao-9 has larger piezoeloctric strain constant than that of nylon-11, related to the larger dipole density ot in nykn-9 in the oystalline phase. 

Ihkase et al. [23] repotted high-temperature piezoelectric strain constant stress constant en, clectromechankal oou ding coefficients Ky, of nylon-11 and nylon-7. The films of nylons were prepared by melt-press process and then quenching molten films into ice and uniaxially stretching to a draw ratio of 3 1 al room temperature. The temperature dependence the elastk modulus (real part c and imaginary part of nylon-11 and nylon-7 films was measured at 104 Hz. Three relaxation processes were observed ... 

Figure 13 shows variation of piezoelectric strain constant du measured at 104 kHz from SOT to temperature near the melting points of nykm-ll, nykm-7, and PVDF. A large increase in d of nylons was observed around their glass transition temperatures. Similar features as a function of temperature appeared in data. Both d,i and tu exhibited a shoulder between 120 and 140 C The maximum du and e,i values were 14 pC/N and 21 mOm fix nylon-11 and 17 pCTN and 27 mOm for nylon-7, respectively. The dll of PVDF remained constant while the value of e i decreased linearly with increasing temperature. PVDF showed a d of S pCTN and en cd 7 mC/m at lOOT. The high-temperature dn and e,i values of nylon-11 and nykm-7 are larger than that of PVDF. 

In the following description, the piezoelectric constant d indicates the shear piezoelectric constant -d, or d . For symmetry C. and D the relation -d, d d holds. In most cases, a sinusoidal stress at 10 Hz is given to the sample and both in-phase component and v/2 out-of-phase component of the resulting sinusoidal polarization are detected. The ratio of polarization to stress is the conqdex piezoelectric strain constant d d - id, and the ratio of polarization to strain is the complex stress constant e t - id. ... 

The piezoelectric strain constants d of the a-b-a, a-c>a. and a-d-a systems were measured at room temperature for about 100 days after poling. The time dependence for these constants are presented in Figure 6S. It is seen in this figure that the initial values of du are 3, 4. and 20 pC/N for the a-c-a, a-b-a, and a-d-a systems, respectively. 

It is seen that the piezoelectric strain constant d cakulaicd from Eqs. (45) and (46) is about one order of magnitude smaller than the experimentally determined du constant. 

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