MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



65 



A counterclockwise rotation about .r2 is given by: 



(21.2) 



A counterclockwise rotation about xz is given by: 



(21.3) 



In case one wants only the value of a tensor property in a given direction 

 not all the elements of a and a need be used, but only a row or column. A 

 special case is that of computing such a property in the direction {d, 0) 

 of polar coordinates. The .Vi axis is chosen in this direction; .vo and xz are 

 not determined. Writing ci for cos 6, d for cos 0, Si for sin d and .^2 for sin (/> 

 the required matrices are 



CiSi 



S1S2 



2 2 

 C1S2 



2 2 

 ^1^2 



") 



C2 

 Si S2 C2 

 Ci C2 S2 

 \ClSis\ 



(21.4) 



From these the (11) term can be computed for any tensor. 



A few special transformations needed constantly are: A rotation of 180^ 

 about .V3: 



«c 



(21.5) 



