132 



BELL SYSTEM TECH NIC A L JOURNAL 



investigated by the writer and Miss E. J. Armstrong by measuring the 

 temperature expansion coefficients of the Y and Z axes and comparing their 

 average with the expansion coefficient at 45° from these two axes. The 

 difference between these two expansion coefficients measures the change 

 in angle between the Y and Z axes caused by the spontaneous shearing 

 strains. The results are shown by Fig. 7. Above and below the ferro- 

 electric region, the expansion of the 45° crystal coincides with the average 

 expansion of the Y and Z axes measured from 25°C as a reference tempera- 

 ture. Between the Curie temperatures a difference occui^ indicating thai 

 the Y and Z crystallographic axes are no longer at right angles. The dif- 

 ference in expansion per unit length at 0°C (ihe maximum point) corresponds 

 to 1.6 X 10"* cm per cm. This represents an axis d istortion of 1 .1 minutes 



700 



600 



t3 



No 



<5 500 



-II- 



Q.O 



a. 

 m 



400 



DO 



^ai 300 



0<J 200 

 O- 7 



100 



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



TEMPERATURE IN DEGREES CENTIGRADE 



Fig. 6.- — Spontaneous polarization in Rochelie Salt along the X axis. 



of arc. Correspondingly smaller values are found at other temperatures 

 in agreement with the smaller spontaneous polarization at other tempera- 

 tures. It was also found that practically the same curve resulted for either 

 45° axis, indicating that the mechanical bias put on by the optometer used 

 for measuring expansions introduced a bias determining the direction of the 

 largest number of domains. 



The second order terms caused by the square of the spontaneous polariza- 

 tion is given by the expression 



S,i = QlnP\ (168) 



Since Q is a fourth rank tensor the possible terms for an orthorhombic 

 bisphenoidal crystal (the class for Rochelie salt) are 



5u = QinxPl ; ^22 = Q2inP\ ; ^33 = QunPl (169) 



