Transient phase fraction and dislocation density estimation from in-situ X-ray diffraction data with a low signal-to-noise ratio using a Bayesian approach to the Rietveld analysis
Manfred Wiessner (Anton Paar GmbH)
Paul Angerer (Materials Center Leoben GmbH)
Sybrand van der Zwaag (TU Delft - Novel Aerospace Materials)
Ernst Gamsjäger (Montan University of Leoben)
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Abstract
We describe the analysis of in-situ HT-XRD data of a dual phase stainless steel exposed to a complex thermal cycle of heating, holding and cooling. For the conditions used only low quality diffraction data could be collected. Peak positions, peak areas and peak broadening are modeled by the Rietveld method. The low signal-to noise ratio and the presence of artificial peaks due to tube tails complicate the data evaluation. In a first attempt the parameters are refined by a local optimization procedure (e.g. Levenberg-Marquardt). However, this procedure fails by being caught in one of several local minima. Next, a Bayesian approach with a Markov Chain Monte Carlo (MCMC) algorithm is used as a global optimization procedure to refine the simulated Rietveld diffractograms. Accurate estimates of the evolution of the phase fractions and dislocation densities in martensite and austenite during all stages of the thermal cycle are obtained by this MCMC algorithm. While an approach based on multivariate second order Taylor series completely underestimates the error, the uncertainties in the model parameters could be estimated appropriately from histograms obtained by the MCMC method.