136 



BELL SYSTEM TECHNICAL JOURNAL 



Comparing these with the relation of (90) we see that the spontaneous 

 polarization has added the elastic constants 



D {Minn + Minii + Mnni + Mz2ni)Pi 



(175) 



Sb6 — 



(iWf21bl + -M'f32U + M3II2I + M312II 



+ Mf2i3i + Mf23ii + Mnni + A/^i3ii)/^i 



between the two Curie points. Hence while the spontaneous polarization 

 Pi exists, the resulting elastic constants are 



(176) 



Comparing this to equation (139) which shows the possible elastic constants 

 for the various crystal classes, we see that between the two Curie points, 

 the crystal is equivalent to a monoclinic sphenoidal crystal (Class 3) with 

 the X axis the binary axis. Outside the Curie region the crystal becomes 

 orthorhombic bisphenoidal. This interpretation agrees with the tempera- 

 ture expansion curves of Fig. 7. 



The sudden appearance of the polarization 1\ will affect the frequency 

 of a 45° ,Y-cut crystal, for with a crystal cut normal to the .Y axis and with 

 the length of the crystal at an angle B with the Y axis, the value of the 

 elastic compliance 522 along the length is 



522' = 5^2 cos* G -f 25^4 cos^ B sin B + (25^3 + 54*4) sin B cos B 



(177) 

 + 2^34 sin B cos B + Sn sin B 



Hence for a crystal with its length 45° between the Y and Z axes, elastic 

 compliance becomes 



'« _ 522 ~1~ 2(524 ~1~ 523 + 534) + ^44 + 533 

 S21 — 



(178) 



