Rietveldanalys

Rietveldanalys, also known as Rietveld analysis, is a quantitative method in powder X-ray and neutron diffraction used to refine crystal structures from diffraction data by fitting a calculated pattern to the observed one. It was developed by Dutch crystallographer Hugo Rietveld in 1969.

The method models the diffraction pattern as a sum of Bragg reflections from the crystal structure, with intensities calculated from structure factors and with peak shapes, background, and instrumental broadening explicitly treated. The refinement adjusts parameters such as lattice constants, atomic positions, site occupancies, thermal factors, peak-profile parameters, preferred orientation, and phase fractions to minimize the difference between observed and calculated intensities via least-squares.

A typical refinement yields refined crystallographic parameters, phase abundances for multiphase samples, and statistical measures of fit, including R-factors and chi-squared. Background is modeled with mathematical functions; peak profiles are often represented by pseudo-Voigt or similar functions; constraints and restraints help keep the solution physically reasonable.

Applications include quantitative phase analysis, determination of crystal structures from powder data, and quality control in materials science, metallurgy, ceramics, and geology. The method is widely implemented in software such as GSAS, FullProf, TOPAS, MAUD, and Jade.

Limitations include dependence on a reasonable starting model, parameter correlations, sensitivity to data quality, and potential non-uniqueness of solutions, particularly for complex or highly disordered systems. Overall, Rietveldanalys remains a foundational tool for extracting structural information from powder diffraction experiments.