Premium
Bayesian approach applied to the Rietveld method
Author(s) -
Wiessner Manfred,
Angerer Paul
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714020196
Subject(s) - rietveld refinement , lattice constant , materials science , lattice (music) , crystal structure , algorithm , computer science , crystallography , chemistry , physics , diffraction , optics , acoustics
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 an in situ high‐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.