high efficiency(electric energy to mechanical energy coupling factor k)and can generate higham Q A Ceramic materials of the PZT family have also found increasingly important applications. The piezo but not the ferroelectric property of these materials is made use of in transducer applications. PZT has a very -amplitude ultrasonic waves in water or solids. The coupling factor is defined by energy stored mechanica (49.5) total energy stored electri Typical values of k33 are 0.7 for PZT 4 and 0.09 for quartz, showing that PZT is a much more efficient transducer material than quartz. Note that the energy is a scalar; the subscripts are assigned by finding the energy conversion coefficient for a specific vibrational mode and field direction and selecting the subscripts accordingly. Thus k, refers to the coupling factor for a longitudinal mode driven by a longitudinal field. Probably the most important applications of PzT today are based on ultrasonic echo ranging Sonar uses the conversion of electrical signals to mechanical displacement as well as the reverse transducer property, which is to generate electrical signals in response to a stress wave. Medical diagnostic ultrasound and nondestructive testing systems devices rely on the same properties. Actuators have also been built but a major obstacle is the small displacement which can conveniently be generated. Even then, the required voltages are typically hundreds of volts and the displacements are only a few hundred angstroms. For PZt the strain in the z-direction due to an applied field in the z-direction is (no stress, T=0) d33E3 (496) (49.7) where s is the strain, E the electric field, and V the potential; d33 is the coupling coefficient which connects the △d=d3V (49.8) field is parallel to the displacement. Let the applied voltage be 100V and let us use PZt8 for which d33 is 225 (from Table 49.2). Hence Ad= 225 A or 2. 25 A/V, a small displacement indeed. We also note that Eq (49.6)is a special case of Eq (49.2)with the stress equal to zero. This is the situation when an actuator is used in a force-free environment, for example, as a mirror driver. This arrangement results in the n displacement. Any forces which tend to oppose the free motion of the PZT will subtract from the available displacement with the reduction given by the normal stress-strain relation, Eq (49.1) It is possible to obtain larger displacements with mechanisms which exhibit mechanical gain, such laminated strips(similar to bimetallic strips). The motion then is typically up to about 1 millimeter but at a cost of a reduced available force. An example of such an application is the video head translating device provide tracking in VCRs There is another class of ceramic materials which recently has become important. PMN (lead [Pb],magne sium niobate), typically doped with =10% lead titanate)is an electrostrictive material which has seen appli cations where the absence of hysteresis is important. For example, deformable mirrors require repositioning of the reflecting surface to a defined location regardless of whether the old position was above or below the Electrostrictive materials exhibit a strain which is quadratic as a function of the applied field. Producing a displacement requires an internal polarization. Because the latter polarization is induced by the applied field c 2000 by CRC Press LLC© 2000 by CRC Press LLC Ceramic materials of the PZT family have also found increasingly important applications. The piezoelectric but not the ferroelectric property of these materials is made use of in transducer applications. PZT has a very high efficiency (electric energy to mechanical energy coupling factor k) and can generate high-amplitude ultrasonic waves in water or solids. The coupling factor is defined by (49.5) Typical values of k33 are 0.7 for PZT 4 and 0.09 for quartz, showing that PZT is a much more efficient transducer material than quartz. Note that the energy is a scalar; the subscripts are assigned by finding the energy conversion coefficient for a specific vibrational mode and field direction and selecting the subscripts accordingly. Thus k33 refers to the coupling factor for a longitudinal mode driven by a longitudinal field. Probably the most important applications of PZT today are based on ultrasonic echo ranging. Sonar uses the conversion of electrical signals to mechanical displacement as well as the reverse transducer property, which is to generate electrical signals in response to a stress wave. Medical diagnostic ultrasound and nondestructive testing systems devices rely on the same properties. Actuators have also been built but a major obstacle is the small displacement which can conveniently be generated. Even then, the required voltages are typically hundreds of volts and the displacements are only a few hundred angstroms. For PZT the strain in the z-direction due to an applied field in the z-direction is (no stress, T = 0) s3 = d33E3 (49.6) or (49.7) where s is the strain, E the electric field, and V the potential; d33 is the coupling coefficient which connects the two. Thus Dd = d33V (49.8) Note that this expression is independent of the thickness d of the material but this is true only when the applied field is parallel to the displacement. Let the applied voltage be 100 V and let us use PZT8 for which d33 is 225 (from Table 49.2). Hence Dd = 225 Å or 2.25 Å/V, a small displacement indeed. We also note that Eq. (49.6) is a special case of Eq. (49.2) with the stress equal to zero. This is the situation when an actuator is used in a force-free environment, for example, as a mirror driver. This arrangement results in the maximum displacement. Any forces which tend to oppose the free motion of the PZT will subtract from the available displacement with the reduction given by the normal stress-strain relation, Eq. (49.1). It is possible to obtain larger displacements with mechanisms which exhibit mechanical gain, such as laminated strips (similar to bimetallic strips). The motion then is typically up to about 1 millimeter but at a cost of a reduced available force. An example of such an application is the video head translating device to provide tracking in VCRs. There is another class of ceramic materials which recently has become important. PMN (lead [Pb], magne￾sium niobate), typically doped with ª10% lead titanate) is an electrostrictive material which has seen appli￾cations where the absence of hysteresis is important. For example, deformable mirrors require repositioning of the reflecting surface to a defined location regardless of whether the old position was above or below the original position. Electrostrictive materials exhibit a strain which is quadratic as a function of the applied field. Producing a displacement requires an internal polarization. Because the latter polarization is induced by the applied field k 2 = energy stored mechanically total energy stored electrically s d d d V d 3 = = 33 D