Appendix A: Future Directions
A.7.3 Example for the Interaction of Structural, Aerodynamic,
9.2 Smart Ceramics: Transducers, Sensors, and Actuators
9.2.3 Piezoelectric Materials
Th is section summarizes the current status of piezoelectric materials: single crystal materials, piezoceramics, piezopolymers, piezocomposites, and piezofi lms. Table 9.4 shows the material parameters of some representative piezoelectric materials described here [6,7].
9.2.3.1 Single Crystals
Piezoelectric ceramics are widely used at present for a large number of applications. However, single-crystal materials retain their utility; they are essential for applications such as frequency stabilized oscillators and surface acoustic devices. Th e most popular single-crystal piezoelectric materials are quartz, lithium
niobate (LiNbO3), and lithium tantalate (LiTaO3). Th e single crystals are anisotropic in general and have diff erent properties depending on the cut of the materials and the direction of bulk or surface wave propagation.
Quartz is a well-known piezoelectric material. α-Quartz belongs to the triclinic crystal system with point group 32 and has a phase transition at 537°C to the β-type that is not piezo- electric. Quartz has a cut with a zero temperature coeffi cient of the resonance frequency change. For instance, quartz oscillators using the thickness shear mode of the AT-cut are extensively used as clock sources in computers and as frequency stabilized oscillators in TVs and video cassette recorder (VCRs). On the other hand, an ST-cut quartz substrate that has X-propagation has a zero temperature coeffi cient for SAWs and so is used for SAW devices that have highly stabilized frequencies. Another distinguishing characteristic of quartz is its extremely high mechanical quality factor Qm > 105.
Lithium niobate and lithium tantalate belong to an isomor- phous crystal system and are composed of oxygen octahedron.
Th e Curie temperatures of LiNbO3 and LiTaO3 are 1210°C and 660°C, respectively. Th e crystal symmetry of the ferroelectric phase of these single crystals is 3 m and the polarization direction is along the c-axis. Th ese materials have high electromechanical coupling coeffi cients for SAWs. In addition, large single crystals can easily be obtained from their melts by using the conventional Czochralski technique. Th us, both materials are very important in SAW device applications.
9.2.3.2 Perovskite Ceramics
Most of the piezoelectric ceramics have the perovskite structure ABO3, shown in Figure 9.16. Th is ideal structure consists of a simple cubic unit cell that has a large cation A at the corner, a smaller cation B in the body center, and oxygens O in the centers of the faces. Th e structure is a network of corner-linked oxygen octahedra surrounding B cations. Th e piezoelectric properties of perovskite-structured materials can be easily tailored for appli- cations by incorporating various cations in the perovskite structure.
9.2.3.2.1 Barium Titanate
Barium titanate (BaTiO3) is one of the most thoroughly studied and most widely used piezoelectric materials. Figure 9.17 shows the temperature dependence of dielectric constants in BaTiO3
TABLE 9.4 Material Parameters of Representative Piezoelectric Materials
Parameter Quartz BaTiO3 PZT 4 PZT 5H (Pb, Sm)TiO3 PVDF-TrFE
d33 (pC/N) 2.3 190 289 593 65 33
g33 (10−3 V m/N) 57.8 12.6 26.1 19.7 42 380
kt 0.09 0.38 0.51 0.50 0.50 0.30
kp 0.33 0.58 0.65 0.03
e3T/e0 5 1700 1300 3400 175 6
Qm >105 500 65 900 3–10
TC (°C) 120 328 193 355
that demonstrate the phase transitions in BaTiO3 single crystals.
Th ree anomalies can be observed. Th e discontinuity at the Curie point (130°C) is due to a transition from a ferroelectric to a para- electric phase. Th e other two discontinuities are accompanied by transitions from one ferroelectric phase to another. Above the Curie point, the crystal structure is cubic and has no spontaneous dipole moments. At the Curie point, the crystal becomes polar and the structure changes from a cubic to a tetragonal phase.
Th e dipole moment and the spontaneous polarization are parallel to the tetragonal axis. Just below the Curie temperature, the vector of the spontaneous polarization points in the [001]
direction (tetragonal phase) and below 5°C, it reorients in the [011] (orthrhombic phase), and below −90°C in the [111] (rhom- bohedral phase). Th e dielectric and piezoelectric properties of ferroelectric ceramic BaTiO3 can be aff ected by its own stoichi- ometry, microstructure, and by dopants entering into the A or B site solid solution. Modifi ed BaTiO3 ceramics that contain dopants such as Pb or Ca ions have been used as commercial piezoelectric materials.
9.2.3.2.2 Lead Zirconate–Lead Titanate
Piezoelectric Pb(Ti, Zr)O3 solid solutions (PZT) ceramics are widely used because of their superior piezoelectric properties.
Th e phase diagram of the PZT system (Pb(ZrxTi1−x)O3) is shown in Figure 9.18. Th e crystalline symmetry of this solid solution is determined by the Zr content. PT also has a tetragonal ferroelectric phase of the perovskite structure. As the Zr content x increases, the tetragonal distortion decreases, and when x > 0.52, the structure changes from the tetragonal 4 mm phase to another ferroelectric phase of rhombohedral 3 m symmetry. Figure 9.19 shows the dependence of several d constants on the composition near the morphotropic phase boundary between the tetragonal and rhombohedral phases. Th e d constants have their highest values near the morphotropic phase boundary. Th is enhance- ment in the piezoelectric eff ect is attributed to the increased ease of reorientation of the polarization in an electric fi eld. Doping the PZT material with donors or acceptor changes the properties dramatically. Donor doping with ions such as Nb5+ or Ta5+
provides soft PZTs like PZT-5, because of the facility of domain motion due to the charge compensation of the Pb vacancy, which is generated during sintering. On the other hand, acceptor doping with Fe3+ or Sc3+ leads to hard PZTs such as PZT-8 because oxygen vacancies pin the domain wall motion.
9.2.3.2.3 Lead Titanate
PbTiO3 has a tetragonal structure at room temperature and has large tetragonality c/a = 1.063. Th e Curie temperature is 490°C.
Densely sintered PbTiO3 ceramics cannot be obtained easily because they break up into powders when cooled through the Curie temperature. Th is is partly due to the large spontaneous strain that occurs at the transition. PT ceramics modifi ed by small amounts of additives exhibit high piezoelectric anisotropy.
Either (Pb, Sm)TiO3 [8] or (Pb, Ca)TiO3 [9] has extremely low planar coupling, that is, a large kt/kp ratio. Here, kt and kp are thickness-extensional and planar electromechanical coupling A
B
O
FIGURE 9.16 Perovskite structure ABO3. (Modifi ed from Encyclo pedia of Smart Materials.)
FIGURE 9.17 Dielectric constants of BaTiO3 as a function of temperature. (Modifi ed from Encyclopedia of Smart Materials.) 10,000
5,000
0
Dielectric constant
Temperature (⬚C)
−150 −100 −50 0 50 100 150
Ps
Ps Ps
Rhombohedral Orthorhombic Tetragonal Cubic
ea
ec
factors, respectively. (Pb, Nd)(Ti, Mn, In)O3 ceramics that have a zero temperature coeffi cient of SAW delay have been developed as superior substrate materials for SAW devices [10].
9.2.3.2.4 Relaxor Ferroelectrics
Relaxor ferroelectrics diff er from normal ferroelectrics; they have broad phase transitions from the paraelectric to the ferro- electric state, strong frequency dependence of the dielectric constant (i.e., dielectric relaxation) and weak remanent polar- ization at temperatures close to the dielectric maximum. Lead- based relaxor materials have complex disordered perovskite structures of the general formula Pb(B1, B2)O3 (B1 = Mg2+, Zn2+, Sc3+, B2 = Nb5+, Ta5+, W6+). Th e B site cations are distributed
randomly in the crystal. Th e characteristic of a relaxor is a broad and frequency dispersive dielectric maximum. In addition, relaxor-type materials such as lead magnesium niobate Pb(Mg1/3Nb2/3)O3–lead titanate PbTiO3 solid solution [PMN-PT]
exhibit electrostrictive phenomena that are suitable for actuator applications. Figure 9.20 shows an electric-fi eld-induced strain curve that was observed for 0.9PMN-0.1PT and reported by Cross et al. in 1980 [11]. Note that a strain of 0.1% can be induced by an electric fi eld as small as 1 kV/mm and that hysteresis is negligibly small for this electrostriction.
Because electrostriction is the secondary electromechanical coupling observed in cubic structures, in principle, the charge is FIGURE 9.18 Phase diagram of the PZT system. (Modifi ed from Ceramics, transducers, in Encyclopedia of Smart Materials.)
500
400
300
200
100
0
0 10 20 30 40 50 60 70 80 90 100
PbTiO3 PbZrO3
Rhombohedral Tetragonal
Cubic a
a a
Morphotropic phase boundery
PbZrO3 (Mole %) c
a a
a
a Ps
Ps
Temperature (⬚C)
FIGURE 9.19 Piezoelectric d strain coeffi cients versus composition for the PZT system. (Modifi ed from Ceramics, transducers, in Encyclopedia of Smart Materials.)
48 50 52 54 56 58 60
dij (⫻ 10−12 C/N) 800
600
400
200
0
PbZrO3 (Mole %) d15
d33
−d31
0 5 10 15
−5
−10
−15
Electric field (kV/cm) Strain (⫻10−3) 1.00
0.50
FIGURE 9.20 Field-induced electrostrictive strain in 0.9PMN-0.1PT.
(Modifi ed from Ceramics, transducers, in Encyclopedia of Smart Materials.)
not induced under applied stress. Th e converse electrostrictive eff ect, which can be used for sensor applications, means that the permittivity (fi rst derivative of polarization with respect to an electric fi eld) is changed by stress.
In relaxor ferroelectrics, the piezoelectric eff ect can be induced under a bias fi eld, that is, the electromechanical coupling factor kt varies as the applied DC bias fi eld changes. As the DC bias fi eld increases, the coupling increases and saturates. Th ese materials can be used for ultrasonic transducers that are tunable by a bias fi eld [12].
Th e recent development of single-crystal piezoelectrics started in 1981, when Kuwata, Uchino, and Nomura fi rst repor- ted an enormously large electromechanical coupling factor k33 = 92%–95% and a piezoelectric constant d33 = 1500 pC/N in solid-solution single crystals between relaxor and normal ferroelectrics , Pb(Zn1/3Nb2/3)O3-PbTiO3 [13]. Aft er about 10 years, Y. Yamashita et al. (Toshiba) and T. R. Shrout et al. (Penn State) independently reconfi rmed that these values are true, and much more improved data were obtained in these several years, aimed at medical acoustic applications [14]. Important data have been accumulated for Pb(Mg1/3Nb2/3)O3 [PMN], Pb(Zn1/3Nb2/3) O3 [PZN], and binary systems of these materials combined with PbTiO3 (PMN-PT and PZN-PT) for actuator applications.
Strains as large as 1.7% can be induced practically for a morpho- tropic phase boundary composition of the PZN-PT solid-solution single crystals. Figure 9.21 shows the fi eld induced strain curve for [001] oriented 0.92PZN-0.08PT [14]. It is notable that the highest values are observed for a rhombohedral composition only when the single crystal is poled along the perovskite [001]
axis, not along the [111] spontaneous polarization axis.
9.2.3.3 Polymers
PVDF or PVF2 is a piezoelectric when stretched during fabrica- tion. Th in sheets of the cast polymer are drawn and stretched in the plane of the sheet in at least one direction and frequently also
in the perpendicular direction to convert the material into its microscopically polar phase. Crystallization from a melt forms the nonpolar α-phase, which can be converted into another polar β-phase by uniaxial or biaxial drawing; these dipoles are then reoriented by electric poling. Large sheets can be manufac- tured and thermally formed into complex shapes. Copoly- merization of vinilydene difl uoride with trifl uoroethylene (TrFE) results in a random copolymer (PVDF-TrFE) that has a stable, polar β phase. Th is polymer does not need to be stretched; it can be poled directly as formed. Th e thickness-mode coupling coef- fi cient of 0.30 has been reported. Such piezoelectric polymers are used for directional microphones and ultrasonic hydrophones.
9.2.3.4 Composites
Piezocomposites comprised of piezoelectric ceramics and polymers are promising materials because of excellent tailored properties. Th e geometry of two-phase composites can be classi- fi ed according to the connectivity of each phase (0, 1, 2, or 3 dimensionality) into 10 structures; 0-0, 0-1, 0-2, 0-3, 1-1, 1-2, 1-3, 2-2, 2-3, and 3-3 [15]. A 1-3 piezocomposite, or PZT–rod/
polymer–matrix composite is a most promising candidate. Th e advantages of this composite are high coupling factors, low acoustic impedance (square root of the product of its density and elastic stiff ness), a good match to water or human tissue, mechanical fl exibility, a broad bandwidth in combination with a low mechanical quality factor, and the possibility of making undiced arrays by structuring only the electrodes. Th e thick- ness-mode electromechanical coupling of the composite can exceed the kt (0.40–0.50) of the constituent ceramic and almost approaches the value of the rod-mode electromechanical cou- pling, k33 (0.70–0.80), of that ceramic [16]. Th e acoustic match to tissue or water (1.5 Mrayls) of typical piezoceramics (20–30 Mrayls) is signifi cantly improved by forming a composite structure, that is, by replacing a heavy, stiff ceramic by a light, soft polymer. Piezoelectric composite materials are especially useful for underwater sonar and medical diagnostic ultrasonic transducers.
9.2.3.5 Thin Films
Both zinc oxide (ZnO) and aluminum nitride (AlN) are simple binary compounds that have Wurtzite-type structures, which can be sputter-deposited in a c-axis-oriented thin fi lm on a variety of substrates. ZnO has reasonable piezoelectric coupling and its thin fi lms are widely used in bulk acoustic and SAW devices. Th e fabrication of highly c-axis oriented ZnO fi lms has been exten- sively studied and developed. Th e performance of ZnO devices is, however, limited due to their small piezoelectric coupling (20%–30%). PZT thin fi lms are expected to exhibit higher piezo- electric properties. At present, the growth of PZT thin fi lm is being carried out for use in microtransducers and microactua- tors. A series of theoretical calculations on perovskite-type ferroelectric crystals suggests that large d and k values of magni- tudes similar to those of PZN-PT can also be expected in PZT.
Crystal orientation dependence of piezoelectric properties was FIGURE 9.21 Field-induced strain curve for [001] oriented 0.92PZN-
0.08PT. (Modifi ed from Encyclopedia of Smart Materials.) 0.00
0.5 1.0
Strain (%)
1.5 2.0
20 40
Tetragonal d33~ 480 pC/N
60 Electric field (kV/cm)
80 100 120
phenomenologically calculated for compositions around the morphotropic phase boundary of PZT [17]. Th e maximum lon- gitudinal piezoelectric constant d33 (four to fi ve times the enhancement) and the electromechanical coupling factor k33
(more than 90%) in the rhombohedral composition were found at angles of 57° and 51°, respectively, canted from the spontane- ous polarization direction [111], which correspond roughly to the perovskite [100] axis.
Figure 9.22 shows the principle of the enhancement in electro- mechanical couplings. Because the shear coupling d15 is the high- est in perovskite piezoelectric crystals, the applied fi eld should be canted from the spontaneous polarization direction to obtain the maximum strain. Epitaxially grown, [001] oriented thin/thick fi lms using a rhomboherial PZT composition reportedly enhance the eff ective piezoelectric constant by—four to fi ve times.