Applications of Bayesian corrections for systematic errors in Rietveld refinements

Recently, a Bayesian statistics approach for correction of systematic errors in Rietveld refinements has been developed and implemented as a patch to GSAS-II. This paper demonstrates the benefits of the proposed method in a series of structural refinements from diffraction data collected for one sample using four different powder diffractometers, i.e. synchrotron and laboratory X-ray and two time-of-flight neutron instruments. Differences between the parameters estimated while fitting these four data sets provided magnitudes of the systematic errors while also highlighting the efficacy of the Bayesian procedure for their correction. Structural parameters estimated from the standard Rietveld refinements using the four data sets differed significantly. In all cases, the agreement improved markedly after applying the Bayesian error-correction procedure. The Bayesian refinements were paired with a Markov chain Monte Carlo algorithm, which was implemented as part of the same patch to GSAS-II, to confirm that uncertainties in the refined parameters obtained using the much faster least-squares minimization were realistic.