Rietveld Refinement - Peak Shape

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 y_i at position 2θ_i is:

where H_k is the full width at half peak height (full-width half-maximum), 2θ_k is the centre of the reflex, and I_k 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, A_s to account for this asymmetry

where P is the asymmetry factor and s is +1,0,-1 depending on the difference 2θ_i-2θ_k 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 2θ_i.