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

16.5 Transducers 461Figure 16.4. Crystal divided into segments.The Electrostrictive EffectThe electrostrictive effect, which is the electrical analog of the magnetostrictiveeffect discussed in a later section, occurs in all dielectrics, but it is not a very pronouncedphenomenon in most materials except for a certain class of dielectrics. Theeffect is much more apparent in this class namely, the ferroelectrics. An electricfield applied along a given direction produces a mechanical strain. The magnitudeof the strain is proportional to the square of the strength of the applied electricfield and is therefore independent of the sense of the field. A positive strain maythus result for both positive and negative values of the excitation field. For a sinusoidallyvarying electric field, the waveform of the strain assumes that of a rectifiedbut unsmoothed alternating current, and its frequency is twice that of the appliedfield.It is possible to obtain a sinusoidal variation in the strain, and this is done bypermanently polarizing the transducer, namely, one that has magnetostrictive properties.The transducer is heated to a temperature above the Curie point, causing themagnetostrictive effect to vanish, and then it is cooled slowly in a strong direct fieldoriented in the direction along which it is intended to apply the exciting field. Ifthe exciting field is kept small compared with the initial polarizing field, the strainshould vary sinusoidally at the frequency of the exciting field. Because a polarizedferroelectric transducer appears to manifest the same effect as a piezoelectric