The Rietveld Method in Powder X-ray Diffraction
Kevin Henke, Bob Jewell, Shelly Hopps
University of Kentucky
Center for Applied Energy Research
Wednesday, November 20, 2008 3:00 am
Ben Bandy Conference Room
UK Center for Applied Energy Research
Bob Jewell, Shelley Hopps and Kevin Henke recently went to a training session to learn how to use Rietveld software. The equipment and software must be updated before using the technique described below. This seminar will provide information on the software’s capabilities.
The Rietveld method is a powerful computer-based tool that uses least-squares refinements to recover information from powder X-ray diffraction (XRD) data. The method is capable of: 1) calculating the ratios of elements in mineral solid solutions; 2) estimating the weight percentages (wt%) of amorphous and up to 24 crystalline phases in cements and other complex mixtures; 3) determining the crystalline structures of new phases (similar to single crystal XRD) and 4) estimating the sizes of microscopic crystals in conjunction with transmission electron microscopy (TEM). Based on reasonable guesses and chemical data entered by the operator, Rietveld generates a calculated powder XRD pattern and then adjusts the entered parameters to match the calculated pattern to the measured pattern of the sample. When the calculated and measured patterns agree within 5-10%, the data from the calculated pattern (e.g., chemical composition, crystalline space groups and atomic coordinates, etc.) are believed to accurately represent the contents of the measured sample.
In the CAER ECT group, Rietveld will be especially important in studying the mineralogy and chemistry of coal combustion byproducts and cements. With cements, the method might be able to determine the wt% of Al3+ and Fe3+ in brownmillerite and other solid solution phases. When compared with other methods that estimate the wt% of crystalline and amorphous phases in a sample, Rietveld uses fewer assumptions and generally obtains more accurate results on many more phases. For estimating the wt% of amorphous materials in a flyash or another sample, a mineral standard must be mixed with the sample prior to powder XRD analysis. Other Rietveld analyses often do not require the addition of standards.