TY - JOUR
T1 - 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
AU - Wiessner, Manfred
AU - Angerer, Paul
AU - van der Zwaag, Sybrand
AU - Gamsjäger, Ernst
N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Bayesian statistics
KW - Dislocation densities
KW - Levenberg-Marquardt
KW - Markov Chain Monte Carlo
KW - Rietveld method
KW - Stainless steels
UR - http://www.scopus.com/inward/record.url?scp=85098967119&partnerID=8YFLogxK
U2 - 10.1016/j.matchar.2020.110860
DO - 10.1016/j.matchar.2020.110860
M3 - Article
AN - SCOPUS:85098967119
VL - 172
JO - Materials Characterization
JF - Materials Characterization
SN - 1044-5803
M1 - 110860
ER -