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For every space group and every structure and every reflection (*hkl*) we know:

(3) |

where

*F*(*hkl*) is the amplitude and phase for a reflection with indices (*h*,*k*,*l*).*F*(*hkl*) is called the structure factor.*f*_{j}is the scattering factor of atom*j*.*N*is the number of atoms in the unit cell.*x*_{j}*y*_{j}*z*_{j}are the*x*-,*y*- and*z*-coordinates of atom*j*.

In the following (*hx* + *ky* + *lz*) is often written **hx** to make the
formulae shorter.

The structure factor depends on

- 1. The kinds of atom in the unit cell.
- 2. The position of the atoms within the unit cell.

Since the space group symmetry gives information about the relative positions of
the atoms, *F*(*hkl*) will become dependent on the symmetry. This holds both for
the phase and amplitude of *F*(*hkl*). The form of this dependence will come
clear from the following pages.

**Copyright © 1981, 1998 International Union of
Crystallography**