PIEZOELECTRIC CRYSTALS IN TENSOR FORM 



115 



(133) 



Cn ; Ci2 ; C\3 ; Cu ; cis = 0; cie = 



Cn 5 ^22 = ^11 ; ^23 = C\3 ; C24 = Ci4 ; C25 =0; C26 = 



Ci3 ; ^23 = Ciz ; (^33 ; C34 = ; C35 = ; Cae = 



fi4 ; C24 = — Ci4 ; r34 = 0; <:44 ; C45 = 0; r46 = 



C15 = 0; ^26 = 0; f35 = 0; C45 = 0; C55 = ("44 ; C56 = Cu 



<^i6 = 0; C26 = 0; f36 = 0; Css = 0; C55 = ru ; Cee = 2 (<^ii~fi2)- 



vS.l Second Rank Tensors for Crystal Classes 



The symmetry relations have been calculated for all classes of crystals. 

 For a second rank tensor such as e,/, the following forms are required 



Triclinic Classes 1 and 2 eu , €12 , €13 



ei2 , ^22 , C23 



«13 , «23 , ^33 



fU , , €13 



, €22 , 



ei3 , , €33 



€11,0 ,0 



, 622 , (134) 



,0 , €33 



€11,0 ,0 

 , €„ , 



,0 , €33 

 €11,0 ,0 

 , €„ , 

 0,0, €„ 



5.2 Third Rank Tensors of the Piezoelectric Type for the Crystal Classes 



hn , hu , his , /'i4 , /'15 , /'le 



Monoclinic sphenoidal, 1' a binary axis, Class 3 

 MonocHnic domatic, Y a plane of symmetry. Class 4 

 Monoclinic prismatic, Center of symmetry, Class 5 



Orthorhombic 

 Classes 6, 7, 8 



Tetragonal, Trigonal 

 Hexagonal 

 Classes 9 to 27 



Cubic 



Classes 28 to 32 



Triclinic Assymetric (Class 1) No 

 Symmetry 



//21 , ^/22 , //23 , //24 , //26 , ^'26 

 /'31 , hsi , /?33 , //34 , //35 , hzr, 



