Peak Shape
The shape of a powder diffraction reflection is influenced by the characteristics of the beam, the experimental arrangement, and the sample size and shape. In the case of monochromatic neutron sources the convolution of the various effects has been found to result in a reflex almost exactly Gaussian in shape. If this distribution is assumed then the contribution of a given reflection to the profile yi at position 2θi is:
where Hk is the full width at half peak height (full-width half-maximum), 2θk is the centre of the reflex, and Ik is the calculated intensity of the reflex (determined from the structure factor, the Lorentz factor, and multiplicity of the reflection)
At very low diffraction angles the reflections may acquire an asymmetry due to the vertical divergence of the beam. Rietveld used a semi-empirical correction factor, As to account for this asymmetry
where P is the asymmetry factor and s is +1,0,-1 depending on the difference 2θi-2θk being positive, zero or negative respectively.
At a given position more than one diffraction peak may contribute to the profile. The intensity is simply the sum of all reflections contributing at the point 2θi.
Read more about this topic: Rietveld Refinement
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