Bayesian Method for the Analysis of Diffraction Patterns using BLAND
Joseph E. Lesniewski, Steven M.T. Disseler, Dylan J. Quintanta, Paul Kienzle, William D. Ratcliff
Rietveld refinement of x-ray and neutron diffraction patterns is routinely used to solve crystal and magnetic structures of organic and inorganic materials over many length scales. Despite its success over the last several decades, conventional Rietveld analysis suffers from tedious iterative methodologies, and the unfortunate consequence of many least-squares algorithms discovering local minima that are not the most accurate solutions. Bayesian methods which allow the explicit encoding of a-priori knowledge pose an attractive alternative to this approach by enhancing the ability to determine the correlations between parameters and to provide a more robust method for model selection. Global approaches also avoid the divergences and local minima often encountered by practitioners of the traditional Rietveld technique. The goal of this work is to demonstrate the effectiveness of an automated Bayesian algorithm for Rietveld refinement of neutron diffraction patterns in the solution of crystallographic and magnetic structures. A new software package , BLAND (Bayesian Library for Analyzing Neutron Diffraction data) based on the Markov-Chain Monte-Carlo minimization routine is presented. The benefits of such an approach are demonstrated through several examples and compared with traditional refinement techniques.