Piezoelectric properties

Piezoelectric effect is of fundamental importance for the piezoelectric measurements technology. General thermodynamic theory of a piezoelectric effect will be described more in details in this paragraph. Temperature or entropy a is held constant in the diagram according to Fig. 4.1. Hence the diagram is reduced just to the relationship between mechanical quantities or (stress or strain) and electrical quantities Ek or Dk (electric field or electric displacement). No special superscript for isothermal or adiabatic option is further used in linear piezoelectric equations of state. Omitting abovementioned thermal quantities, the system of 24 equations of state in Table 4.1 is reduced just to 8 equations - see Fig. 5.1 and Eqs. (5.1), (5.2), (5.3), (5.4), (5.5), (5.6), (5.7), and (5.8). 

Equations of state (5.1), (5.3), (5.5) and (5.7), belong to the description of direct piezoelectric effect. Equatiorrs (5.2), (5.4), (5.6) and (5.8) are due to the converse effect, on the contrary. Piezoelectric effect coitld be described by four different 

Independent variables Ek and 7 belong to the free mechanical and electrical conditions. Piezoelectric effect is characterized by the coefficient dif in this case. Such situation is especially important for piezoelectric measurements technology. It is more or less fulfilled or at least assumed as fulfilled. Direct piezoelectric effect is described by 

Realization of mechanically well-defined state is not easy. Sample is always kept in some holder (e g. between metallic jaws) in order to reach uniaxial homogeneous stress. Metallic jaws are deformed along with the sample. Normally isotropic metal is in contact with anisotropic piezoelectric material. Uniaxially acting force on metallic jaws results in shear components of the mechanical stress at the interface between metal and piezoelectric material due to the anisotropy of it. Stress components system therefore include more components in the piezoelectric sample (stress 

The fourth arrd last pair of equations of state (independerrt variables D, and S ) cortesporrds to the combination of mechanically as well as electrically clamped piezoelectric element. Piezoelectric effect is described by the piezoelectric coefficient /r/ u. 

---

Lead zirconate [12060-01 -4] PbZrO, mol wt 346.41, has two colorless crystal stmctures a cubic perovskite form above 230°C (Curie point) and a pseudotetragonal or orthorhombic form below 230°C. It is insoluble in water and aqueous alkaUes, but soluble in strong mineral acids. Lead zirconate is usually prepared by heating together the oxides of lead and zirconium in the proper proportion. It readily forms soHd solutions with other compounds with the ABO stmcture, such as barium zirconate or lead titanate. Mixed lead titanate-zirconates have particularly high piezoelectric properties. They are used in high power acoustic-radiating transducers, hydrophones, and specialty instmments (146). 

Zirconate compounds exhibit several interesting properties. Lead zirconate—titanate [12626-81 -2] compositions display piezoelectric properties which are utilized in the production of EM-coupled mode filters, resonators in microprocessor clocks, photoflash actuators, phonograph cartridges, gas... 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

In order to anticipate problems and to interpret observations under the extreme conditions of shock compression, it is necessary to consider structural and electronic characteristics of PVDF. Although the phenomenological piezoelectric properties of PVDF are similar to those of the piezoelectric crystals, the structure of the materials is far more complex due to its ferroelectric nature and a heterogeneous mixture of crystalline and amorphous phases which are strongly dependent on mechanical and electrical history. 

Chlorates and bromates feature the expected pyramidal ions X03 with angles close to the tetrahedral (106-107°). With iodates the interatomic angles at iodine are rather less (97-105°) and there are three short I-O distances (177-190 pm) and three somewhat longer distances (251-300 pm) leading to distorted perovskite structures (p. 963) with pseudo-sixfold coordination of iodine and piezoelectric properties (p. 58). In Sr(I03)2.H20 the coordination number of iodine rises to 7 and this increases still further to 8 (square antiprism) in Ce(I03)4 and Zr(I03)4. 

Most niobates and tantalates, however, are insoluble and may be regarded as mixed oxides in which the Nb or Ta is octahedrally coordinated and with no discrete anion present. Thus KMO3, known inaccurately (since they have no discrete MO3 anions) as metaniobates and metatantalates, have the perovskite (p. 963) stmcture. Several of these perovskites have been characterized and some have ferroelectric and piezoelectric properties (p. 57). Because of these properties, LiNb03 and LiTa03 have been found to be attractive alternatives to quartz as frequency filters in communications devices. 

Temperature can destroy the piezoelectric properties of the probe, although techniques for cooling probes (delay blocks), and development of temperature-resistant piezoelectric materials, are extending the temperature range. Differences of up to 5% in thickness can occur between hot and cold readings. 

Phase transition irreversible, 225 order - disorder, 224-228 reversible, 225, 229, Physicochemical properties of ammonium hydrofluoride, 39 deviations from ideal, 149 ideal system, 148 NbF5 and TaFs, 25 niobium containing melts, 150 tantalum containing melts, 151 M5Nb3OFlg, 234-235 Piezoelectric properties, 245-247 Plasma chemical decomposition equipment, 311... 

Zinc oxide (ZnO) has useful piezoelectric properties. It has an hexagonal structure (wurtzite type) with a density of 5.66 g/cm. It is relatively unstable and decomposes above 1700°C, which is below its melting point (1975°C). It is readily attacked by all common acids and bases. It has limited CVD applications at this time. 

Lead titanate (PbTi03) is a ferroelectric material with unusual pyroelectric and piezoelectric properties. It is deposited by MOCVD from ethyl titanate and lead vapor in oxygen and nitrogen at 500-800°C.[42]... 

Lead titanate (PbTiOg) with excellent pyroelectric and piezoelectric properties. 

The piezoelectric properties of collagen have been investigated in complex biological systems such as bone and tendon. The piezoelectric properties of bone have a great interest in view of their role in bone remodeling. The bone stress... 

PVDF is a difluoro derivative, leading to the following formula — (— CH2 — CF2-) - and a fluorine content of 59%. PVDF is semicrystalline with three possible crystal forms, one of which has interesting pyro- and piezoelectric properties. Copolymers are marketed for applications needing flexibility. 

PVDFs are good insulators even in wet environments, with high resistivities, dielectric constants and loss factors. Films with suitable crystallinity have pyro- and piezoelectric properties. 

These days the most common method employed for the generation and detection of ultrasound utilises the piezoelectric properties of certain crystals one of which is quartz [3]. A simplified diagram of a crystal of quartz is reproduced (Fig. 7.3) which shows three axes defined as x, y and z. If a thin section of this crystal is cut such that the large surfaces are normal to the x-axis (x-cut quartz) then the resulting section will show the following two complementary piezoelectric properties ... 

Barium titanate has many important commercial apphcations. It has both ferroelectric and piezoelectric properties. Also, it has a very high dielectric constant (about 1,000 times that of water). The compound has five crystalline modifications, each of which is stable over a particular temperature range. Ceramic bodies of barium titanate find wide applications in dielectric amplifiers, magnetic amplifiers, and capacitors. These storage devices are used in digital calculators, radio and television sets, ultrasonic apparatus, crystal microphone and telephone, sonar equipment, and many other electronic devices. 

Fig. 9.4. Dependence of piezoelectric properties of PbZrOj-PbTiOj on composition. The zirconate-rich phase is rhombohedral, whereas the titanate-rich phase is tetrahedral. The piezoelectric coefficients reach a maximum near the morphotropic phase boundary, approximately 45% PbZrOj and 55% PbTiOj. (After Jaffe et al., 1954.)...

The crystallographic and piezoelectric properties of the ceramics depend dramatically on composition. As shown in Fig. 9.4, the zirconate-rich phase is rhombohedral, and the titanate-rich phase is tetragonal. Near the morphotrophic phase boundary, the piezoelectric coefficient reaches its maximum. Various commercial PZT ceramics are made from a solid solution with a zirconate-titanate ratio near this point, plus a few percent of various additives to fine tune the properties for different applications. 

---