Chemical Forums
Chemistry Forums for Students => Analytical Chemistry Forum => Topic started by: memma on October 03, 2006, 05:01:22 AM
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Hello,
I am just wondering whether if someone can check the folloriwing paragraph that I have written on X-ray crystallography and Debye-waller factor; in fact, I am not sure whether if the content is right. If not, I would be grateful if someone could correct it. Thank you!
The intensity of scattering is reduced due to thermal vibrations of the atoms and crystal disorder. In fact, the Debye-Waller factor represents the decrease of intensity in diffraction due to static disorder of the crystal and disorder caused by thermal vibrations. According to this factor, the observed intensity I is proportional to exp[-2B(sin?/?)2] and thus:
I = I0 exp[-2B(sin?/?)2]
where I0 is the intensity observed for an ideally ordered crystal.
This loss of intensity increases as the angle increases and as the resolution 1/d increases (d decreases). In fact, from Bragg’s law, sin?/? is 1/d and therefore the previous equation can be rewritten as:
I = I0 exp[-2B(1/d)2]
The quantity B is called the temperature factor and it represents the breadth of smearing: in fact, if the atom has a root-mean-square displacement u, then B = 8?2u2.
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Bragg law is
2d sin ? = n?
henc sin?/? = 1/d only for n=2