TABLE 49.2 Properties of Well-Known PZT Formulations(Based on the Original Navy Designations and Now Used by Commercial Vendor Vern PZT5A PZT5H PZT8 1700 6444 A 330 10-3Vm/N 0.705 0.752 Application High signal Medium signal Receiver Highest signal 00d1 0 E1 00d3 (49.3) S 2(S1-S12)T」[00 Note that T and E are shown as column vectors for typographical reasons; they are in fact row vectors. This equation shows explicitly the stress-strain relation and the effect of the electromechanical conversion A similar equation applies when the material is used as a receiver -gT+(εr) (494) where T is the transpose and d the electric displacement. For all materials the matrices are not fully populated Whether a coefficient is nonzero depends on the symmetry. For PZT, a ceramic which is given a preferred direction by the poling operation( the z-axis), only d33, d13, and dis are nonzero. Also, again by symmetry, di3 =d and dis= dy Applications Historically the material which was used earliest for its piezoelectric properties was single-crystal quartz. Crude sonar devices were built by Langevin using quartz transducers, but the most important application was, and still is, frequency control. Crystal oscillators are today at the heart of every clock that does not derive its frequency reference from the ac power line. They are also used in every color television set and personal computer. In these applications at least one(or more)quartz crystal"controls frequency or time. This explains the label quartz"which appears on many clocks and watches. The use of quartz resonators for frequency control relies on another unique property. Not only is the material piezoelectric(which allows one to excite mechanical vibrations), but the material has also a very high mechanical"Q "or quality factor(Q>100,000). The actual value depends on the mounting details, whether the crystal is in a vacuum, and other details. Compare this value to a Q for PZT between 75 and 1000. The Q factor is a measure of the rate of decay and thus the mechanical losses of an excitation with no external drive. A high Q leads to a very sharp resonance and thus tight frequency control. For frequency control it has been possible to find orientations of cuts of quartz which reduce the influence of temperature on the vibration frequency. c 2000 by CRC Press LLC© 2000 by CRC Press LLC (49.3) Note that T and E are shown as column vectors for typographical reasons; they are in fact row vectors. This equation shows explicitly the stress-strain relation and the effect of the electromechanical conversion. A similar equation applies when the material is used as a receiver: E = –gT + (eT)–1D (49.4) where T is the transpose and D the electric displacement. For all materials the matrices are not fully populated. Whether a coefficient is nonzero depends on the symmetry. For PZT, a ceramic which is given a preferred direction by the poling operation (the z-axis), only d33, d13, and d15 are nonzero. Also, again by symmetry, d13 = d23 and d15 = d25. Applications Historically the material which was used earliest for its piezoelectric properties was single-crystal quartz. Crude sonar devices were built by Langevin using quartz transducers, but the most important application was, and still is, frequency control. Crystal oscillators are today at the heart of every clock that does not derive its frequency reference from the ac power line. They are also used in every color television set and personal computer. In these applications at least one (or more) “quartz crystal” controls frequency or time. This explains the label “quartz” which appears on many clocks and watches. The use of quartz resonators for frequency control relies on another unique property. Not only is the material piezoelectric (which allows one to excite mechanical vibrations), but the material has also a very high mechanical “Q” or quality factor (Q >100,000). The actual value depends on the mounting details, whether the crystal is in a vacuum, and other details. Compare this value to a Q for PZT between 75 and 1000. The Q factor is a measure of the rate of decay and thus the mechanical losses of an excitation with no external drive. A high Q leads to a very sharp resonance and thus tight frequency control. For frequency control it has been possible to find orientations of cuts of quartz which reduce the influence of temperature on the vibration frequency. TABLE 49.2 Properties of Well-Known PZT Formulations (Based on the Original Navy Designations and Now Used by Commercial Vendor Vernitron) Units PZT4 PZT5A PZT5H PZT8 e33 — 1300 1700 3400 1000 d33 10–2 Å/V 289 374 593 225 d13 10–2 Å/V –123 –171 –274 –97 d15 10–2 Å/V 496 584 741 330 g33 10–3 Vm/N 26.1 24.8 19.7 25.4 k33 — 70 0.705 0.752 0.64 TQ °C 328 365 193 300 Q — 500 75 65 1000 r g/cm3 7.5 7.75 7.5 7.6 Application — High signal Medium signal Receiver Highest signal S S S S S S sss sss sss s s s s T T T T T T 1 2 3 4 5 6 11 12 13 12 11 13 13 13 33 44 44 11 12 1 2 3 4 5 6 0 0 2 È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ = È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ (–) ˙ + È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 0 0 0 0 0 0 0 0 0 0 000 13 13 33 15 15 1 2 3 d d d d d E E E