450 BELL SYSTEM TECHNICAL JOURNAL 



where 



Xx, Jy, z, = extensional strains = elongation per unit length, 

 Xx, Yy, Zz = extensional stresses = force per unit area, 

 yz = shearing strain = cos of an angle, 

 Y, = shearing stress = force per unit area, 

 Sij = elastic compliances = displacement per dyne, 

 dij = piezo-electric constants = e.s.u. charge per dyne, 

 Px = piezo-electric polarization = charge per unit area. 



The best measured values for these constants when the X axis coin- 

 cides with the electric axis of the crystal, the Faxis with the mechanical 

 axis and the Z axis with the optical axis, are 



^11 = ^22 = 127.2 X 10-" cm.Vdyne, 



5i2 = - 16.6 X 10-14 cm.Vdyne, 



sn = S23 = - 15.2 X 10-1" cm.Vdyne, 



^24 = - su = 43.1 X 10-14 cm.Vdyne, 



^33 = 97.2 X 10-14 cm.Vdyne, 



^34 = 0, (42) 



544 = 200.5 X 10-14 cm.Vdyne, 



^ ^ /c c!A v/ m-R^-S-u. charge 



an = — di2 = — 6.36 X 10^ -. 2_ , . 



dyne 



^13 = 



^:4 = 1.69 X 10-B "•^•": "^^'"g^^ 



dyne 



If, now, we maintain the direction of the electrical axis but rotate 

 the direction of the principal axis by some angle d, the resulting con- 

 stants of equations (40) and (41) undergo a change. 



Let the direction cosines for the new axes be given by 



(43) 



The convention is adopted that a positive angle is a clockwise rota- 

 tion of the principal axis of the crystal, when the electrically positive 

 face (determined by a squeeze) is up. For a left-handed crystal a 

 positive angle is in a counter clockwise direction, d is the angle be- 

 tween the previously unprimed and the primed axes. 



