Testing different methods for estimating uncertainties on Rietveld refined parameters using SrRietveld
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Peng Tian
Abstract
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.
© by Oldenbourg Wissenschaftsverlag, 1116 East Lansing, Germany
Articles in the same Issue
- Preface: Modern Rietveld Analysis
- Preface: Modern Rietveld Analysis
- Obtaining models suitable for Rietveld refinement: the EXPO2011 techniques
- Complex inorganic structures from powder diffraction:case of tetrahydroborates of light metals
- Recent developments targeting new and experienced users in EXPGUI, an open source Rietveld analysis interface
- Testing different methods for estimating uncertainties on Rietveld refined parameters using SrRietveld
- Understanding anisotropic microstrain broadening in Rietveld refinement
- On the modelling of the powder pattern from a nanocrystalline material
- Rietveld refinement of energy-dispersive synchrotron measurements
- Description and survey of methodologies for the determination of amorphous content via X-ray powder diffraction
- A case study of parameterized Rietveld refinement:The structural phase transition of CuInSe2
Articles in the same Issue
- Preface: Modern Rietveld Analysis
- Preface: Modern Rietveld Analysis
- Obtaining models suitable for Rietveld refinement: the EXPO2011 techniques
- Complex inorganic structures from powder diffraction:case of tetrahydroborates of light metals
- Recent developments targeting new and experienced users in EXPGUI, an open source Rietveld analysis interface
- Testing different methods for estimating uncertainties on Rietveld refined parameters using SrRietveld
- Understanding anisotropic microstrain broadening in Rietveld refinement
- On the modelling of the powder pattern from a nanocrystalline material
- Rietveld refinement of energy-dispersive synchrotron measurements
- Description and survey of methodologies for the determination of amorphous content via X-ray powder diffraction
- A case study of parameterized Rietveld refinement:The structural phase transition of CuInSe2
