PIEZOELECTRIC CRYSTALS IN TENSOR FORM 



111 



in which 



The four forms of the piezoelectric equations, and the relation between 

 them are given in Table I. 



Table I 



Four Forms of the Elastic, Dielectric, and Piezo Electric Equations 



AND their Interrelations 



Form 



Elastic Relation 



5,,- = Si,k(Tu( + d„,,E,, 



Electric Relation 



bn = -~ En+ dnkfTkf 



47r 



I 5. Effect of Symmetry and Orientation on the Dielectric Piezo- 

 j electric and Elastic Constants of Crystals 



j All crystals can be divided into 32 classes depending on the type of sym- 

 1 metry. These groups can be divided into seven general classifications 

 il depending on how the axes are related and furthermore all il classes can 

 ^ be built out of symmetries based on twofold (binary) axes, threefold (irig- 

 1 onal) axes, fourfold axes of symmetry, sixfold axes of symmetry, planes of 

 j' reflection symmetry and combinations of axis reflection symmetry besides 

 a simple symmetry through the center. Each of these types of symmetry 



