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Rutile (TiO2)

Examine the output from symmetry. It should be obvious that you need local rotation matrices for both, Ti and O:

   ....
   Titanium   operation #  1     1                   
   Titanium   operation #  2     -1                  
   Titanium   operation #  5     2 || z              
   Titanium   operation #  6     m n z             
   Titanium   operation # 12     m n 110             
   Titanium   operation # 13     m n -110            
   Titanium   operation # 18     2 || 110            
   Titanium   operation # 19     2 || -110           
     pointgroup is mmm (neg. iatnr!!)
     axes should be: m n z, m n y, m n x

This output tells you, that for Ti a mirror plan normal to z is present, but the mirror planes normal to x and y are missing. Instead, they are normal to the (110) plane and thus you need to rotate x, y by $45^\circ$ around the z axis. (The required choice of the coordinate system for mmm symmetry is also given in Table 7.2)

   ....
   Oxygen     operation #  1     1                   
   Oxygen     operation #  6     m n z             
   Oxygen     operation # 13     m n -110            
   Oxygen     operation # 18     2 || 110            
     pointgroup is mm2 (neg. iatnr!!)
     axes should be: 2 || z, m n y

For O the 2-fold symmetry axes points into the (110) direction instead of z. The appropriate rotation matrices for Ti and O are:


\begin{displaymath}\left (
\begin{array}{ccc}
\frac{-1}{\sqrt 2} & \frac {1}{...
...t 2} & \frac {1}{\sqrt 2}\\
1 & 0 & 0
\end{array} \right )
\end{displaymath}




2000-04-11