Piezoelectric Material Properties

The science and technology of piezoelectric materials has long been dominated by the availability of specific materials with particular properties. Piezoelectric polymers are the most recent class of piezoelectrics developed. 

The contrast in knowledge is a result of the degree of complexity of materials properties elastic piezoelectric solids have perhaps the least complex behaviors, whereas ferroelectric solids have perhaps the most complex mechanical and electrical behaviors of any solid under shock compression. This complexity is further compounded by the strong coupling between electrical and mechanical states. Unfortunately, much of the work studying ferroelectrics appears to have underestimated the difficulty, and it has not been possible to carry out careful, long range, systematic efforts required to develop an improved picture. 

The material properties appearing in Eqs. (6)-(9) are defined by the partial derivatives of the dependent variables (P, c, e) with respect to the independent variables. At this point, to maintain consistency with the literature on the P-phase of PVDF, we label c as the 1 axis, a as the 2 axis, and, b as the 3 axis. In evaluating the piezoelectric and pyroelectric responses we consider changes in polarization along the 3 axis only polarization along the 1 and 2 axes remains zero, by symmetry, for all the cases considered here. The direct piezoelectric strain 03 , pC/N) and stress (gaj, C/iiE) coefficients are defined in Eqs. (10) and (11),... 

Two types of contributions to dielectric and piezoelectric properties of ferroelectric ceramics are usually distinguished [6], [9-12], One type is called an intrinsic contribution, and it is due to the distortion of the crystal lattice under an applied electric field or a mechanical stress. The second type is called an extrinsic contribution, and it results from the motion of domain walls or domain switching [8], To provide an understanding of material properties of pzt, several methods to separate the intrinsic and extrinsic contributions were proposed. These methods are indirect, and are based on measurements of the dielectric and piezoelectric properties of ferroelectric ceramics [8], [10-12], In the experiments reported in this paper a different approach is adopted, which is based on measurements of high-resolution synchrotron X-ray powder diffraction. The shift in the positions of the diffraction peaks under applied electric field gives the intrinsic lattice deformation, whereas the domain switching can be calculated from the change in peak intensities [13,14],... 

FTMA is a forced vibration test method based on direct measurement of stress and strain spectra. As with all forced vibration methods, FTMA is subject to spurious wave effects at high frequencies. The lower frequency limit is determined by transducers, signal conditioners, etc. The lower limit in this research was 35 Hz as determined by the inherent properties of the piezoelectric transducers. With different transducers (for example load cell for the force and LVDT for displacement measurements) and signal conditioners, FTMA should measure material properties down to much lower frequencies. 

Coupling of mechanic stress and electrical polarization results in piezoelectricity. KDP type materials are piezoelectrics at room temperature and ADP was formerly used in submarine applications to emit and receive ultrasonic waves. Berlinite, AIPO4, is structurally related to the common piezoelectric a -Si02 (see Section 5.1.2) and has superior properties in some respects. 

The material properties of piezoelectric layer are shown in Table 1. Since the temperature variation in the piezoelectric layer is not so large, it is assumed that the properties are independent of temperature. 

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... 

We have seen that fiexoelectricity (and piezoelectricity) influences the material properties expressed in the coefficients of Eq. (5.16) and consequently influences quantitatively the pitch, the phase transition temperature and the tilt. But there are no qualitative changes, i.e. no new stable phases with qualitatively different structures appear due to these two interactions. Below we shall see that in systems where the interactions are more complex the role of the flexoelectric phenomenon can be very significant and it is crucial for the stability of many structures. 

Rocha (1996) used a piezoelectric sensor inserted into the needle bar of an industrial overedge sewing machine, a measurement system that was further developed by Carvalho (2010). With this equipment, it is possible to measure needle penetration and withdrawal force at industrial speeds. Rocha found that, among other material properties, bending rigidity and drape factor were related to needle penetration forces. It was possible to demonstrate the relationship among needle size, sewing... 

Tables 4.4-3-4.4-21 are arranged according to piezoelectric classes in order of decreasing symmetry (see Table 4.4-2), and alphabetically within each class. They contain a number of columns placed on two pages, even and odd. The following properties are presented for each dielectric material density q, Mohs hardness, thermal conductivity k, static dielectric constant Sij, dissipation factor tanS at various temperatures and frequencies, elastic stiffness Cmn, elastic compliance s n (for isotropic and cubic materials only), piezoelectric strain tensor di , elastooptic tensor electrooptic coefficients r k (the lat-...

---