Bayesian approach applied to the Rietveld method

Abstract

The application of the Rietveld method for lattice constant and crystal structure refinement has been undertaken with great success. More routinely, this method is used to estimate quantitative phase amounts and to get information on the coherent diffracting length and the lattice defect density. In this paper an innovative combination of the Rietveld method with the Bayes approach is presented, to obtain directly the distribution of the refined parameters from a measured diffractogram, while the conventional Rietveld technique enables only the deduction of the most probable parameter and the estimation of its precision by confidence intervals. Furthermore, the goal of this work is to promote the development of a robust and automatable Rietveld algorithm. A detailed description of the modified algorithm is presented. Such a modified Rietveld approach is applied to anin situhigh-temperature experiment on a steel sample, including the temperature-dependent α → γ phase transformation reaction during heating and the martensitic transformation during the cooling phase.