THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

16.5 Transducers 459probe is to gauge the characteristics of an acoustic field, so its dimensions must besufficiently small so as not to affect the field. A probe diameter is typically onlyabout one-tenth of the wavelength.Piezoelectric CrystalsIn 1880, the Curie brothers discovered that when a crystal having one or morepolar axes or lacking axisymmetry is subjected to mechanical stress, an electricalpotential difference occurs. Consider a segment of such a crystal, in the form of aslab or a disk, that is cut with its parallel surface running normal to a polar axis.When this segment undergoes a mechanical stress, equal and opposite electriccharges arise on the parallel surfaces. The magnitude of the charge density (i.e.,dielectric polarization) is directly proportional to the applied stress, provided theapplied stresses do not strain the crystal beyond its elastic limit.The opposite effect, predicted by Lippmann in 1881 and verified experimentallyby the Curie brothers the same year, occurs when an electric field is applied in thedirection of a polar axis, causing a mechanical strain in the crystal segment. Theamount of strain is directly proportional to the intensity of the applied electric field.From the viewpoint of the principle of conservation of energy, the piezoelectriceffect and its converse may be deemed to be equal and opposite. Such effectsoccur in crystals such as quartz (a member of the trigonal system, as shown inFigure 16.3), Rochelle salt, and lithium sulfate.Quartz is very commonly applied for ultrasonic generation. A quartz crystalis shown in Figure 16.3, with a hexagonal cross section normal to the nonpolarFigure 16.3. A hexagonal quartz crystal with x-cut rectangular and circular plates.