PIEZOELECTRIC CRYSTALS IN TENSOR FORM 



137 



For a 45*^ X-cut crystal we would expect a sudden change in the value of 

 522 as the crystal becomes spontaneously polarized between the two Curie 

 points due to the addition of the s^i and s^^ elastic compliances. Such a 

 change has been observed for Rochelle salt* as shown by Fig. 9 which shows 

 the frequency constant of a nonplated crystal for which the elastic com- 

 pliances s^j should hold. 



uj 217 



5 



Z 216 



UJ 



u 



QC 215 



O 209 



2 208 



q 207 



u. 

 o 



6 Hi 



3 



4 

 3 



2 

 1 



-20 -16 -12 



-8-4 4 8 12 16 20 24 28 32 

 TEMPERATURE IN DEGREES CENTIGRADE 



36 40 44 48 



Fig. 9. — Frequency constant and Q of an unplated 45°X cut Rochelle Salt ctystal 

 plotted as a function of temperature. 



Hence the sudden change in the elastic constant is a result of the two 

 second order terms s^ -f s^i , which are caused by the spontaneous polariza- 

 tion. The value of the sum of these two terms at the mean temperature 

 of the Curie range, 3°C is 



•^24 + ^34 = 4.1 X 10 cm"/ dyne 



(179) 



Crystals cut normal to the Y and Z axes should not show a spontaneous 

 change in their frequency characteristic since the spontaneous terms Su , 

 524 , 534 and 5b6 do not affect the value of Young's modulii in planes normal 

 to Y and Z. Experiments on a 45° F-cut Rochelle salt crystal do not show 

 a spontaneous change in frequency at the Curie temperature, although there 

 is a large change in the temperature coefficient of the elastic compliance 

 between the two Curie points. This is the result of third order term and is 



' "The Location of Hysteresis Phenomena in Rochelle Salt Crystals," W. P. Mason, 

 Phys. Rev., Vol. 50, p. 744-750, October 15, 1940. 



