PIEZOELECTRIC CR YSTA LS IN TENSOR FORM 123 



A = 



Wi = ;^ ; ^"2 = —/ ; ^3 = ^ (142) 



Hence substituting equations (141) in equations (140) the transformation 

 equations between the new and old axes become 



rp' _ D dXk dXf dXi dXj , _ dx^ dxf dx^ / 



dXk ax I dXi axj dXk dXf dxn 



(143) 



These equations then provide means for determining the transformation of 

 constants from one set of axes to another. 



As an example let us consider the case of an ADP crystal, vibrating longi- 

 tudinally with its length along the xi axis, its width along the X2 axis and 

 its thickness along the X3 axis, which is also the X3 axis, and determine the 

 elastic, piezoelectric and dielectric constants that apply for this cut when 

 Xi is 9 = 45° from xi . Under these conditions 



dx'i dxi 

 A = z— = 3-/ = cos 9; 

 dxi 0x1 



dxi dXi . 

 mi = —- = —-, = sm 8; W2 



0x2 OXl 



dxi dxs 

 Ml =—- = —-,= 0; Hi = 



6x3 dxi 



(144) 



Since ADP belongs to the orthorhombic bisphenoidal (Class 6), it will have 

 the dielectric, piezoelectric and elastic tensors shown by equations (134), 

 (135), (139). Applying equations (143) and (144) to these tensors it is 



