Thermodynamic modeling of the La2O3-SiO2, Dy2O3-SiO2 and Er2O3-SiO2 systems is part of a broader effort to obtain thermodynamic databases of the rare earth silicates that can help offer insight on designing the environmental barrier coatings in gas turbine engines. The main aim of the present work is to focus on obtaining a set of self-consistent thermodynamic parameters of La2O3-SiO2, Dy2O3-SiO2 and Er2O3-SiO2 systems. The ionic two-sublattice model was accepted to express the liquid phase, and all the binary phases were described as stoichiometric compounds due to the negligible solubility. After a critical literature review on the experimental phase diagrams data and thermodynamic properties for the La2O3-SiO2, Dy2O3-SiO2 and Er2O3-SiO2 systems, thermodynamic optimizations were performed by means of the CALPHAD (CALculation of PHAse Diagram) method. The modeling was done using Thermo-Calc software with PARROT module. The comprehensive comparison between the experimental results and our calculations exhibits that the calculated phase diagrams and thermodynamic properties were in good agreement with the available experimental data, except for experimental data with doubtful quality. This means that our thermodynamic descriptions were reasonable and could provide a reliable basis for thermodynamic calculations in RE2O3-SiO2-based higher-order systems.
The prediction of the characteristic Martensite Start (Ms) temperature and Austenitic Nose Tip Temperature (ANTT) in steels is of scientific and technological importance; however, it faces significant challenges due to multiphysical complexity.
In this study, we introduced a structured framework for data classification and hierarchical iterations aimed at predicting Ms (Martensite start temperature) and ANTT (Austenite non-transforming temperature). This framework was incorporated into two optimization models, leading to enhancements in accuracy, extrapolation capabilities, and generalization performance. First, we classified the collected Ms datasets hierarchically based on the alloying elements presented in steels, including carbon, austenite stabilizers, non-austenitization elements, and data credibility. Regression analyses of Ms temperatures concerning chemical compositions were then carried out using phenomenological variables from binary systems to multi-component systems in alignment with the spirit of CALPHAD modeling, which is renowned for its robust extrapolation abilities. By iteratively fitting the hierarchically classified datasets and implementing hierarchical iterations, we developed the CALPHAD-guided phenomenological variable (CGPV) Ms regression model. This model achieved improved accuracy levels, with R2 values of 0.9 for training and 0.87 for testing, surpassing most conventional regression models that do not account for compositional interactions. Furthermore, the CALPHAD-guided machine learning (CGML) model, constructed based on the classified datasets and hierarchical iterations but without utilizing phenomenological variables, demonstrated strong performance with R2 values of 0.98 and 0.86 for training and testing, respectively. The CGML model was demonstrated not only to reliably filter out problematic data in a dataset but also to unveil the unnoticed coupling between carbon and other alloying elements on Ms. Finally, the CGML method has been readily transferred to predict ANTT with high accuracy as well.
The isothermal section at 900 °C of the Ti-poor part of the Ni−Ti−Ru ternary system was measured experimentally, combined with SEM-EDS, XRD, TEM and DSC techniques. Four three-phase equilibria regions were confirmed at 900 °C isothermal section and a ternary compound τ with Face-centered-cubic structure can existed stably. The isothermal section at 900 °C measured in this study and the experimental data from our previous work were adopted in the present optimization. The calculated Ni−Ti−Ru ternary system was summarily presented in the form of isothermal sections, liquids projection and reaction scheme, with appropriate comparisons with available experimental data.
As a core of the high entropy alloys, the Co-Cr-Fe-Ni system has been widely investigated. In the present work, the thermodynamics of the Co-Cr-Fe-Ni system and the atomic mobilities of its fcc phase have been evaluated by means of the CALPHAD approach. First-principles calculations were performed to obtain the total energies for the end-member compounds of the σ phase in the Co-Cr-Fe-Ni system. Combining with the experimental data and thermodynamic modeling of the sub-systems from the literature, a set of self-consistent thermodynamic parameters were derived and extrapolated to obtain a thermodynamic description of the Co-Cr-Fe-Ni quaternary system. In order to verify the accuracy of the model parameters, the phase equilibria of a series of the CoCrxFeNi alloys with different Cr contents were determined using DSC, BSE and XRD analysis. Subsequently, based on the diffusion experimental data, the atomic mobilities of the fcc Cr-Fe-Ni alloys were reassessed using the DICTRA software. A mobility database for the fcc Co-Cr-Fe-Ni quaternary system was constructed by directly extrapolating the atomic mobilities of all sub-systems, and comprehensive comparisons prove the consistency between the present assessments and the experiments. In addition to the direct extrapolation approach, extra four-body interaction parameters concerning all four components were added and assessed. The results demonstrate that the extra interaction contributions are ignorable, so that the direct extrapolation from the sub-systems to the quaternary system is feasible in the fcc Co-Cr-Fe-Ni quaternary system.