Bayesian approach to the Rietveld refinement of Poisson-distributed powder diffraction data

The Rietveld method is based on a weighted least-squares fit of a model diffraction pattern to the step-scan data of a complete experimental X-ray or neutron diffraction pattern. It is shown here that the weight most commonly used in Rietveld refinement of powder diffraction data leads to a biased background estimate. To overcome this bias, an alternative method for refinement of Poisson-distributed experimental data is suggested that only involves changes of the input data and the weights of least-squares refinement. Model calculations demonstrate that this novel method allows an improved refinement of the parameters describing the background and the Bragg reflections. The proposed method can be readily implemented in existing Rietveld programs.