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.

我们描述了暴露于加热，保持和冷却的复杂热循环的双相不锈钢的原位HT-XRD数据分析。对于使用的条件，只能收集低质量的衍射数据。峰位置，峰面积和峰展宽通过Rietveld方法建模。低信噪比和由于管尾造成的人工峰值的存在使数据评估复杂化。首次尝试通过局部优化程序（例如Levenberg-Marquardt）对参数进行优化。但是，此过程失败，因为陷入了几个局部最小值中的一个。接下来，使用具有马尔可夫链蒙特卡洛（MCMC）算法的贝叶斯方法作为全局优化过程，以细化模拟的Rietveld衍射图。通过该MCMC算法，可以准确估算出热循环所有阶段中马氏体和奥氏体中相分数和位错密度的演变。虽然基于多元二阶泰勒级数的方法完全低估了误差，但是可以通过MCMC方法获得的直方图适当估计模型参数的不确定性。