76 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



crystal. The magnitude and direction of the piezoelectric effect in 

 the cut depend upon its orientation with respect to the crystal axes. 

 Cuts are identified by the direction of the perpendicular drawn to the 

 largest face of the cut; if this direction falls into the direction of the 

 X axis of a crystal, the element is called X cut. Other more complex 

 cuts are identified by their angular orientation with respect to the 

 other two crystal axes. 1 The analytical evaluation of the properties of 



[c) 



(d) 



Fig. (1-2)59. Modes of operation of piezoelectric transduceis : (a) thickness or 

 longitudinal compression; (b) transversal compression: (c) thickness shear action; 

 (d) face shear action (leading to length expansion) (" Piezotronic Technical Data" 

 from Brush Electronics Corp., Cleveland,; by permission). 



crystal cuts is complicated because of the mechanical and electrical 

 anisotropy of the crystals and because of the variation of the crystal 

 constants with varying mechanical load. 



Piezoelectric elements made from barium titanate ceramics are 

 free from limitations imposed by the crystal structure. They can be 

 molded in different sizes and shapes, and the electrical axis can be 

 "built in" in the production process. 



modes of operation, single plates. In single piezoelectric slabs 

 or plates, four different modes of operation can be distinguished, 

 depending upon the material and upon the crystallographic orien- 

 tation of the plate. These modes are shown in Fig. (1-2)59. 

 1 See examples for quartz in Mason, op. cit., p. 83, fig. 6.3. 



