QUARTZ CRYSTAL CIRCUIT ELEMENTS 



463 



angle between the Z' and Z axis (Fig. 2). 



CU — ^26 — <"3B — CH) — 0, 



Cse' = Cii(cos- 6 — sin^ 0) + (cee — C44) sin 6 cos 0, 

 Cee' = C44 sin^ + fee cos^ 6 — Icu sin 6 cos 0. 



(4) 



Piezo-Electric Equations 

 The inverse piezo-electric relations for the X' , Y', Z' system of axes 

 can be expressed by the following equations: 



= di^'EJ + di^Ry + dzi'EJ 

 = dis'E/ + dizEy + dzi'E/ 

 — d\i Ex -\- da Ey -\- dzi E^ 

 = d,,'EJ + d2'JEy' + d,,-EJ 

 = die Ex' + di&'Ey' + ds&EJ. 



(5) 



When in quartz X', F', Z' coincide with the crystallographic axes, 

 eq. 5 reduces to the following: 



Xx = d\\Ex 



Jy = — dnEx 



z, = 



y^ = dnEx 



Zx = — diiEy 



(6) 



where 



^11 = - 6.36 X 10- 



esu 



dyne ' 



du = 1.69 X 10-8 



esu 

 dyne 



For rotation about the X axis, 



d^Q — (dii sin d — 2dii cos 6) cos 6. 



(7) 



