Phase Transition and Phase Fraction Analysis Using Rietveld Refinement

Rietveld refinement has become an essential tool for the quantitative analysis of crystal structures in polycrystalline systems using X-ray diffraction data. This tutorial paper focuses on the background, case studies, and practical implementation of Rietveld refinement using the open-source software PROFEX. Key structural parameters, such as lattice constants and phase fractions, can be quantitatively extracted through full-pattern fitting. Case studies involving compositional variation, electric fields, temperature changes, and battery cycling demonstrate the broad applicability of Rietveld refinement in materials science, energy storage, and catalysis. A step-by-step procedure for performing Rietveld refinement is presented using Bi1/2Na1/2TiO3 perovskite ceramic as an example, providing guidance on software installation, preparing crystal structure information files, performing Rietveld refinement, evaluating results using R-factor and χ² values, and summarizing the results. This tutorial aims to improve understanding and accessibility of Rietveld refinement for researchers seeking to investigate structure–property relationships in complex material systems.