PIEZOELECTRIC CR YSTA LS IN TENSOR FORM 97 



21 = rii 61 + 2fio ^1^2 + 2^13 oi-Js + ^i^H 'Ji'J4 + 2ri5 ^165 + 2ci6 oiOe 

 + r.?i'5l + 2c^fS,S, + 2r?4'^^2>S4 + 2c^_,''SoS, + 2f?6%56 



^33 -J3 "T" ^^^34 03^4 "T" ^^'35 0305 -f- Z('36 03O6 

 (■44 O4 i- Zf45 O4O5 -j- Zr46 O4O6 



+ D,(T ^2 I rj Z).ff o O ' 



+ f66''^'6 (55) 



-(2//Ii5,5'i + 2/;I,5i52 + 2//l35i.93 + 2/;l45i54 + 2li%5,S, + 2//l65i5-6) 



-(2//2l5,5l + 2J1U2S2 + 2//235253 + 2//24^2^^4 + 2111-^^3^ + 2//26526'6) 

 -(2//3l53.Si + 2hl.MS2 + 2//33^3^3 + 2/;345354 + 2//35636'5 + 2//3653^6) 



-(27i'%^/() + 272'%f/<3 + 2yl'^SsdQ 



+ 274'''6'4fi?(? + 275'°55rf() + 2y'l''S,dQ) 

 +iirWiUl + 2/3^;r6if2 + 2(Sf,'d,bs + /3^;r62 + 2f32zdod, + /Sf^^i] 



-(29f%r/C' + 2qt-''5,dQ + 2gt''''W0 + ~§r". 



Equations (53) can be derived from this expression by employing the partial 

 1 derivatives 



i The other form for writing the elastic, f)iezoelectric, pyroelectric and di- 



j electric relations is to take the strains, displacements, and entropy as the 



! fundamental variables and the stresses, fields and temperature increments 



■ as the dependent variables. If we develop them in terms of their partial 



j derivatives as was done in (44), use the relations between the partial deriva- 



t tives shown in equation (57). 



(57) 



and substitute for the partial derivatives their equivalent elastic, piezo- 

 electric, pyroelectric, temperature expansions, dielectric and specific heat 

 constants, there are 10 equations of the form 



