STRUCTURES The intensity of a powder diffraction ring is then written as: IðhklÞ¼ I0ðhklÞexp �2B sin#l 2' # 1þcos2 2# sin2#cos# �p Another correction factor arises because the X- ray beam is absorbed as it passes through the sample. The effect of this is to reduce the inten- sities of reflections that pass through large volumes of sample compared to those that pass through small volumes. Correction factors will depend upon sample shape and size, and a general formula applicable to all sample geometries can- not be given.

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However, this term must be included in careful work. In essence, a powder diffractogram contains as much information as a single crystal experiment. When the intensity and the positions of the diffraction pattern are taken into account, the pattern is unique for a single substance. The X- ray diffraction pattern of a substance can be likened to a fingerprint. In effect, the pattern of lines on the powder diffraction pattern of a single phase is virtually unique, and mixtures of different crystals can be analysed if a refer- ence set of patterns is consulted. To illustrate this, the powder diffraction pat- terns of two materials with closely similar struc- tures and unit cells are shown in Figure 6.19. These are the rutile form of PbO2, with a tetra- gonal unit cell, a ¼ 0:4946 nm, c ¼ 0:3379 nm and SnO2, which also adopts the rutile structure with a ¼ 0:4737 nm; c ¼ 0:3186 nm.