Structure Analysis from Powder Diffraction Data: Rietveld Refinement in Excel

Abstract

Powder diffraction is one of the most widely used analytical techniques for characterizing solid state materials. It can be used for phase or polymorph identification, quantitative analysis, cell parameter determination or even full crystal structure analysis using the powerful Rietveld refinement method.As with much of modern crystallography, the software used for Rietveld refinement is frequently treated as a "black box" that produces often-poorly-understood outputs. This paper shows how it is possible for students to perform a full Rietveld refinement against experimental powder diffraction data from scratch using a simple spreadsheet like Excel. It starts by reviewing the basic ideas of leastsquares fitting a straight line, develops these into fitting simple functions to peaks in simulated experimental data, then combines these ideas with crystallographic equations to enable Rietveld refinement of the structure of an inorganic material (rutile, TiO2). At each stage students can selflearn different fundamental aspects and pitfalls of data analysis that are widely re-applicable. The ideas can be taught as an online learning exercise, or could be incorporated in a laboratory class where students collect and analyze their own experimental data.

Potassium–carbonate co-substituted hydroxyapatite compositions: maximising the level of carbonate uptake for potential CO2 utilisation options

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Effects of annealing temperature on structural phase transition and microstructure evolution of hydrothermally synthesized barium titanate nanoparticles

“…The diffraction patterns obtained using the powerful Rietveld refinement method [29] were used to calculate the lattice parameter and lattice strain. Both the crystallite size and intrinsic strain were calculated using the sizestrain plot (SSP) method, which considered the XRD peak profile to be a combination of the Lorentzian function and Gaussian function, where the size-broadened XRD profile was labelled as the Lorentz function and the strain-broadened profile was labelled as the Gaussian function [30].…”

Maximising carbonate content in sodium-carbonate Co-substituted hydroxyapatites prepared by aqueous precipitation reaction

“…Absorbance spectra were collected at a 2 cm -1 resolution, averaging 7 scans per sample, between 4000 and 400 cm -1 . Peak deconvolution of the carbonate ν2 region of the spectra was performed by fitting Gaussian distributions, using the Solver extension in Excel [24], based on peak assignment described elsewhere [25].…”