Testing Different Methods for Estimating Uncertainties on Rietveld Refined Parameters Using SrRietveld

The advent of fast computing allows more computationally expensive, though possibly more accurate, approaches for estimating uncertainties on Rietveld refined parameters. Here we compare three such methods, using two different refinement programs, FullProf and GSAS. This is facilitated by the use of a new Rietveld refinement package, SrRietveld, that provides Python wrappers for FullProf and GSAS. The refined values on the parameters from two different refinement engines match each other very well. The uncertainty estimates determined using the different methods are also consistent, though FullProf and GSAS estimate the parameter uncertainties slightly differently from each other, which is discussed. More importantly, we find that the refined results are very sensitive to the statistical weights used in the least squares equation. Different weights, for example from uncertain or incorrectly propagated random errors on the data, lead to significantly different refined values. This means that uncertainty estimates on refined parameters should be increased when the random errors on the data are not well known, as for example in many cases where area detectors are used, and care should be taken to propagate errors correctly in any data preprocessing such as normalization by a smoothed spectrum. The computationally expensive bootstrap error estimation methods are facilitated by the use of SrRietveld, but are not required in most cases though may be useful in some cases, for example if the random errors on the data are not well known.