Ask an Expert: The Rietveld method
About 55 years ago the Dutch researcher Hugo Rietveld presented a new approach to structure refinement from powder diffraction data at the seventh Congress of the International Union of Crystallography (IUCr) in Moscow in 1966. The paper, titled ‘Line profiles of neutron powder-diffraction peaks for structure refinement’ was published in Acta Cryst. in 1967.
Rietveld originally worked with neutron diffraction data obtained from the research reactor at Petten, the Netherlands. His method was generally accepted only in 1977 when it was applied to X-ray diffraction data too. In that year the Commission on Powder Diffraction of the IUCr named the method after the author of the first publication. It took another ten years before people realized that the method can also be used for quantitative phase analysis, leading to a huge increase in popularity.
In the Rietveld method, the entire diffraction pattern is taken into account, not just the intensities of diffraction peaks. By comparing measured and calculated diffraction patterns, a crystal structure model can be refined and the composition of a sample can be quantified. Nowadays, Rietveld refinements (and derived methods) are widely applied for routine quantification of crystalline materials in science and production control (e.g. for cement or steel making) as well as for the analysis of crystal structures.
The main advantages of the Rietveld method
Some of the main advantages of the Rietveld method are:
- Differences between the experimental standard and the unknown substance are minimized, which is important for the quantification of mineralogical samples with high variability.
- The lattice parameters of the individual phases and the reflection profiles are refined.
- The accuracy of the quantitative phase analysis is improved since the entire diffractogram and not just one or a few reflections are included in the evaluation.
- The determination of amorphous amounts is included.
- Crystallite sizes are calculated.
- The chemical composition is calculated. A comparison to the X-ray fluorescence analysis of the sample can confirm the reliability of both results.
- It works well when implemented into routine processes, for instance for production control in cement plants.
- Errors of quantification of less than 1 % are achievable.
The currently available structure databases incorporate most of the common phases and can easily be extended by experimentally determined structure data, given for example as CIF or hkl files.1
Ask an expert
On March 30th, we will hold the second in a series of Ask an expert! webinars. During this webinar, we will fully focus on powder diffraction with Rietveld refinement. Do you need new ways to re-think materials analysis challenges, want to sharpen your analytical skills, or find out what more valuable information this method can bring you? This webinar’s just right.
‘Ask an expert’ is for students, researchers or professors who want to sharpen their analytical method, deepen their knowledge, or may be starting a new research and want to know what can help improve their data. After all, science moves faster when we share what we know.
We aim to provide basic coverage and tips about data collection practice and answering common questions about Rietveld refinement. You can send in your questions and/or data prior to the webinar by emailing askanexpert@malvernpanalytical.com or using the #MPexpert hashtag on Twitter. We will handle a selection of the incoming questions during the live webinar. In other words, this is the ultimate way of improving your quantitative phase analysis!
References
- Emrich, M., Opper, D., XRD for the analyst – Getting acquainted with the principles, Malvern Panalytical 2018, P. 67-68.