QUARTZ CRYSTAL APPLICATIONS 205 



"Both the formulation of (A. 6) and (A. 7) can be expressed in terms of 

 the strains rather than the stresses. Since these are useful forms and are 

 used later in this appendix, they are given below. Equations (A. 8) are 

 obtained directly from equations (A. 6) by solving them simultaneously to 

 replace the strain by the stress, while equations (A. 10) are obtained in the 

 same way from equations (A. 7). 



— Xx = CiiXx + cioVy + CisZz + cuyz — euEx 



— Fj, = cfo-Vx + CuVy + cuz, — cuy^ + enEi 



— Zj = CnXx + Cisyy + CzsZz 



— Yz = CnXx — cUjy + c^^y^ — euEx 

 Zx = CnZx ~r CnXy -\- eiiEy 



(E E \ 

 ^^ — -jXy^euEy (A.8) 



Ex Ex Ki 



Qx = -r -\- Px = -—. — + enXx — enjy + e^jz 

 47r 47r 



r\ V I 7-) ^-^y ■''■1 



Vv = -^, r ry = — — — eu Zi — 6ii Xy 



47r 47r 



47r 47r 



where the relations for the elastic constants are 



^ E _ Ssz _. Su ^ _ -33 -^44 _ — -^13 

 ^Cii 1^5 -^^12 -^ ', Ci3 — • ; 



a p a p a 



E E ^^ E E E 



E ^14 _ Sil -f- Si2 E S\i — Sl2 



Cl4 — — TT- ; C33 — ; C44 — 



a ' j8 



£■ _ I'll — <'12 _ .>44 _ / K I £ X ^ 2 



C66 — 7^ ~ tTd ' a — 533(^511 -\- S12) — Z5i3 



Cii — C12 _ 544 



£2 



^ — Sii{Sii — 512) — 2Si4 



Conversely we can also write the useful relation 



