Positions of oxygen atoms in rutile

In TiOj (rutile) the Ti atoms lie at the comers and at the body centre of the tetragonal unit cell and the O atoms lie on the (001) face diagonals, as shown in fig. 1. The fractional co-ordinates are as follows 

The intensities of the 111 and 301 reflections on a powder photograph taken with Cu Ka radiation (A = 1.54 A) are equal (Bunn, Chemical crystallography , Oxford, Clarendon Press, 1945, plate X and p. 214). For these reflections we have (compare problem 22) 

The scattering factors ( Internationale TabellenzurBestimmung von Kristallstrukturen , Bomtrager, 1935)/for Ti and O at these angles are as shown in fig. 1. 

The relative intensities I of reflections on a powder photograph are given by 

Since p has the same value for both reflections it cancels out in comparing relative intensities. 

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