The origin of the solubility minimum of oxide (MxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_x\text{O}_y$$\end{document}) in liquid Fe-M-O alloy was investigated, and the minimum was predicted based on thermodynamic calculations. Due to the characteristic property of activities of M and O in the liquid, a maximum exists in the product between the two activities if the affinity of M to O is significantly high, as most deoxidizing elements are. A critical activity product is defined, which is an indicator of the solubility minimum of the MxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_x\text{O}_y$$\end{document} in the liquid Fe-M-O alloy according to the following relationship: max(aMx×aO̲y)=KMxOy×aMxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\text{max}}}(a_M^x \times a_{\underline{{{\text{O}}}}}^y) = {K_{M_x{{\text{O}}}_y}\times a_{M_x{{\text{O}}}_y}}$$\end{document}, where the aMxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{M_x{{\text{O}}}_y}$$\end{document} is unity if the alloy is in equilibrium with the pure MxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_x{{\text{O}}}_y$$\end{document}. The origin of the solubility minimum was explained using the change of the activity product by composition. Available CALPHAD assessments for several binary Fe-M liquid alloys and Wagner’s solvation shell model were combined to calculate the activity product in the Fe-M-O alloy, which can be used to predict the solubility minimum of MxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_x\text{O}_y$$\end{document}. A favorable agreement was obtained when M=Al\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M = {\text{Al}}$$\end{document}, B, Cr, Mn, Nb, Si, Ta, Ti, V, and Zr. The Gibbs energy of dissolution of O in pure liquid M (ΔgO̲(M)∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta g^\circ _{\underline{{{\text{O}}}}(M)}$$\end{document}) and the Gibbs energy of the formation of MxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_x\text{O}_y$$\end{document} per mole of atoms (ΔgMxOy∘/(x+y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta g^\circ _{M_x{{\text{O}}}_y}/(x+y)$$\end{document}) play important roles in determining the solubility minimum, as long as an interaction between Fe and M is less significant than the interaction between metal (Fe and M) and O. Predictions of the solubility minima of CaO and MgO were not satisfactory, requiring further improvement of the present analysis.

中文翻译：

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液态铁钼合金中的氧化物溶解度最小值

氧化物溶解度最小值的起源 (MxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage {upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_x\text{O}_y$$\end{document})是根据热力学计算预测的。由于液体中 M 和 O 活性的特性，如果 M 与 O 的亲和力显着高，则两种活性之间的产物中存在最大值，就像大多数脱氧元素一样。定义了一个关键活动产品，其中 aMxOy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\ oddsidemargin}{-69pt} \begin{document}$$a_{M_x{{\text{O}}}_y}$$\end{document} 是统一的，如果合金与纯 MxOy\documentclass[12pt ]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \开始{文档}$$M_x{{\text{O}}}_y$$\end{文档}。溶解度最小值的起源是用活性乘积随组成的变化来解释的。将几种二元 Fe-M 液态合金的可用 CALPHAD 评估和 Wagner 的溶剂化壳模型结合起来计算 Fe-MO 合金中的活度积，可用于预测 MxOy\documentclass[12pt]{minimal}\ usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ $ {M}_x\text{O}_y$$\end{document}。当 M=Al\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{ upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M = {\text{Al}}$$\end{document}, B, Cr, Mn, Nb, Si, Ta, Ti, V 和 Zr。