206 BELL SYSTEM TECHNICAL JOURNAL 



For the piezoelectric constants 



^11 — dnifw — C12) + duCn ; en — 2dnC\\ + 6^14^44 ; 



and conversely 



— dn = en{sii — S12) + euSn ; —du = 2enSii + ^14^44 • 



The dielectric constant Ki denotes the clamped dielectric constant, i.e., 

 the constant measured when the crystal is free from strain. This is related 

 to the free dielectric constant Kl by the equation 



iTf = Kl - ^irldueu + 2dneu]. (A.9) 



In a similar way if we solve equations (A. 7) simultaneously, for the stresses 

 in terms of the strains, we have 



— Xx= CiiXx + Ciijy -\- CnZz + Cnjz — JnQx ; 



— Yy = Ci2Xx + Ciijy + CnZz — Ciijz + fnQx' ; 



— Zz = CizXx + Cizjy + CzzZz ; 



— Vz= CiiXx — Cwjy -j- C44>'z — 714^1 ; 



— Zx = CnZx -\- CuXy + JuQy I 



■Xy — C\iZx + I ]Xy + fllQy ', 



Ex = —^Qx - fnXx + fnyy - fuyz ; 

 Kl 



(A.10) 



47r 



k! 



Ey = :^Qy + fuZz + fnXy ; 



^'-Kz^" . \ 



where the c^ constants are related to the 5« constants as in equation (A.8). 

 The piezoelectric relations are 



/u = gn{Cii — C12) + guC\i ; /l4 = 2giiCi4 + §14^44 ; 



or conversely 1 



— gn = fn{sn — Sn) + euSu ; —gu = 2/ii5h + fuSii ; 



while the dielectric relation between the free and clamped crystal 



%=^- (gi4/i4 + 2gn/ii). (A.11) 



Ai Ai 



