Original Article

Constructions of stability diagram for inclusions considering nucleation in Fe-Al-Mg-O system by integrating associate model and classical nucleation theory

¹ School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing (USTB), Beijing 100083, PR China
² School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, PR China

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Received: 9 October 2025
Accepted: 7 January 2026

Abstract

Low-density high-strength steels contain high aluminum contents, which interact with magnesium and strongly affects inclusion formation. Therefore, the associate model was coupled with classical nucleation theory to calculate the relationships among dissolved magnesium, aluminum, and oxygen under thermodynamic equilibrium and nucleation conditions in the Fe-Al-Mg-O system at 1600 °C. Three-dimensional stability diagrams were constructed for Al₂O₃, MgO, and MgAl₂O₄ inclusions. The diagrams show good agreement with experimental results and can be used to predict the types of inclusions and to determine the equilibrium dissolved oxygen content in molten iron. The calculations indicate that both homogeneous and heterogeneous nucleation of inclusions require compositional supersaturation to overcome the energy barrier. Increasing the interfacial energy between inclusions and liquid iron or the contact angle between inclusions and second-phase particles increases the required compositional supersaturation. In the Fe-Al-Mg-O system, Al₂O₃ and MgO inclusions can nucleate through both homogeneous and heterogeneous pathways. However, the nucleation of MgAl₂O₄ is dominated by heterogeneous nucleation at small contact angles. To minimize the formation of hard MgAl₂O₄ spinel inclusions and prevent deterioration of steels mechanical properties, the dissolved magnesium content should be controlled below 3 ppm.