Symmetry and reflection intensities

The atoms in the unit cell will determine the intensity of a diffracted beam of radiation via the structure factor, as described above. This means that there will be relationships between the various F(hid) values that arise because of the symmetry of the unit cell. The symmetry of the structure will therefore play an important part in the intensity diffracted. One consequence of this is Friedel s law, which states that the structure factors, F, of the pair of 

Such pairs of reflections are called Friedel pairs. Because of this, the intensities can be expressed as  

The intensities of Friedel pairs will be equal. This will cause the diffraction pattern from a crystal to appear centrosymmetric even for crystals that lack a centre of symmetry. Diffraction is thus a centrosymmetric physical property, which means that the point symmetry of any diffraction pattern will belong to one of the 11 Laue classes, (see Section 4.7). 

All crystallographic unit cells derived from a body-centred lattice give rise to the same systematic absences. Similar considerations apply to the other Bravais lattices. The conditions that apply for diffraction to occur from Qikt) planes in the Bravais lattices, called reflection conditions, are listed in Table 6.4. 

Apart from the Bravais lattice, other crystallographic features give rise to systematic absences. The symmetry elements that are responsible for systematic absences are (i), a centre of symmetry, 

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