Robust Rietveld refinement in the presence of impurity phases

A modified least-squares analysis is presented that allows reliable structu ral parameters to be extracted from a powder diffraction pattern even in th e presence of a substantial unmodelled impurity contribution. The algorithm is developed within the context of Bayesian probability theory. Experiment al points that fall above those calculated, and are thus more probably from impurity peaks, are systematically down-weighted. This approach is illustr ated with a two-phase example.