The software package ESPEI has been developed for efficient evaluation of thermodynamic model parameters within the CALPHAD method. ESPEI uses a linear fitting strategy to parameterize Gibbs energy functions of single phases based on their thermochemical data and refine the model parameters using phase equilibrium data through Bayesian optimization within a Markov Chain Monte Carlo machine learning approach. In this paper, the methodologies employed in ESPEI are discussed in detail and demonstrated for the Cu-Mg system down to 0 K using unary descriptions based on segmented regression. The model parameter uncertainties are quantified and propagated to the Gibbs energy functions. a − J J J , where J is the chemical potential of the target hyperplane calculated in step 1.
In this work, an automated image analysis procedure for the quantification of microstructure evolution during creep is proposed for evaluating scanning electron microscopy micrographs of a single crystal Ni-based superalloy before and after creep at 950 °C and 350 MPa. scanning electron microscopy-micrographs of γ/γ′ microstructures are transformed into binary images. Image analysis, which involves pixel by pixel classification and feature extraction, is then combined with a supervised machine learning algorithm to improve the binarization and the quality of the results. The binarization of the gray scale images is not always straight forward, especially when the difference in gray levels between the γ-channels and the γ′-phase is small. To optimize feature extraction, we utilized a series of bilateral filters as well as a machine learning algorithm, known as the gradient boosting method, that was used for training and classifying the micrograph pixels. After testing the two methods, the gradient boosting method was identified as the most effective. Subsequently, a Python routine was written and implemented for the automated quantification of the γ′ area fraction and the γ channel width. Our machine learning method is documented and the results of the automatic procedure are discussed based on results which we previously reported in the literature.
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