An advanced approach to directly calculate eutectic points in quaternary and higher-order slags: A case study on CaF2–Al2O3–CaO–MgO–SiO2 slag systems

The stability of slag during the electroslag remelting (ESR) process significantly impacts the quality of the final ingot. Slag compositions that are closer to the eutectic point exhibit enhanced stability during the remelting process. However, traditional methods for identifying eutectic points rely on pseudo-ternary phase diagrams, which are time-consuming and fail to convert graphical information into numerical data, limiting computational screening. This study uses CaF 2 –Al 2 O 3 –CaO–MgO–SiO 2 quaternary slag as an example and sets a commonly used slag composition screening range based on industrial practice. By utilizing FactSage thermodynamic data and machine learning (ML), the liquidus temperatures of all slags within this screening range are calculated. A mathematical model incorporating the characteristics of eutectic points was established, converting the graphical position data of slag eutectic points into numerical data. This allows for the direct computation of slag eutectic points in high-dimensional space using a computer. The computational results showed that there are 13 eutectic points within the screening range. After validation, this method proved to be reliable and efficient for identifying eutectic points in quaternary and higher-order slags. Additionally, using the numerical position data of the slags, two methods were proposed to calculate the distance from any slag compositions to the nearest eutectic point. This allows researchers to quickly screen target slag compositions by setting filtering criteria, further advancing the field of slag computational science.