Numerical evaluation of structure factors

Although structure factor calculations are carried out by computer, it is valuable to evaluate a few examples by hand, to gain an appreciation of the steps involved. As an example, the 

There are two Ti atoms and four oxygen atoms in the unit cell. 

This procedure is repeated for all of the other hkl reflections from the unit cell. 

Atom Phase angle, / /radians Phase angle, / /° fa COS f — A10o 

That is, the waves scattered by the two Ti atoms are exactly out of step and will cancel. It is immediately apparent that the (100) reflection will be weak, as it will depend only upon the oxygen atoms. In fact these cancel too, so that the intensity turns out to be zero, (Table 6.3). The phase angle, 10o, equal to the sum of all of the separate phase angles, is equal to 5-7t (900°) = 7r (180°), (Table 6.3). 

---