MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



27 



Phombis System 

 .T3 binary 

 9 modulii 



Tetragonal System 

 X3 a fourfold axis 

 (Classes 9, 10, 13) 

 7 modulii 



5 - 



5ii 



'S'12 



'S'23 















s = 



(Sn 





 



Tetragonal System 

 X3 a fourfold axis 

 .Ti a twofold axis 

 (Classes 11, 12, 

 14, 15) 



6 modulii 



Trigonal System 

 .T3 trigonal axis 

 (Classes 16, 17) 



7 modulii _ 



5 = 



Sn 



S12 



Sn 















512 S\3 

 »->22 S23 



Siz S33 



S44 











•5*12 Si3 



Sn Siz 



513 033 



Sii 

 

 -Si, 



Sn Si3 

 Sn Si3 



Ol3 O33 



Sii 

 

 



The C matrix is 

 entirely analogous 



(8.15) 





 

 

 



Su 

 





 

 

 



Su 

 ^ei 



'•5' 16 





 

 



The C matrix is 

 entirely analogous 



(8.16) 



The C matrix is 

 entirely analogous 



(8.17) 



Trigonal System 

 .T3 trigonal axis 

 ;Vi binary (Classes 

 18, 20, 21) ^ 



6 modulii 

 (alpha quartz) 



Hexagonal System 

 .T3 a sixfold axis 

 -Ti a twofold axis 

 (Classes 19, 22, 

 23, 24, 25, 26, 27) 

 5 modulii 



Sn S12 Sis Su — oi5 



012 On Oi3 Su 025 



^13 SnSss 



Ol4 — Ol4 O44 2o25 



■025 ■J25 044 2oi4 



23-26 2Su 2(Sn 



On O12 Oi3 Oi4 



S-i2 Sn Si3 —Su 

 ^13 SnSzs 



5,4 -^14 ^44 



^44 2Su 

 2^14 2(Sn 



■Sr 



-Sr 



The C matrix 

 is analogous 

 except that 

 C46 = C25 



^56 = Cu 



Cee = 2 

 (Cn —Cis) 

 (8.18) 



The C matrix 

 is analogous 

 except that 



^56 = Cu 



Cee = 2 

 {Cn ~Cj2) 

 (8.19) 



S = 



SnSnSnO 

 Su Sn SnO 

 Si3 Si3 S33 

 6"44 

 544O 

 2(Sn -Si-2)} 



The C matrix 

 is analogous 

 except that 

 Cee = 2 

 (Cn -Cn) 

 (8.20) 



