Composition Design and Property Investigation of Mold Fluxes for the Continuous Casting of Rare-Earth Weathering Steel

Abstract

Conventional CaO–SiO₂-based mold fluxes used in the continuous casting of rare-earth weathering steel are prone to severe slag–steel interfacial reactions, resulting in marked compositional changes and progressive property deterioration after rare-earth oxide pickup, which compromises lubrication stability and casting operability. In this study, a novel low-reactivity CaO–Al₂O₃-based mold flux was designed through phase-diagram-guided composition design, IMCT-based thermodynamic screening, and experimental investigation of melting, viscosity, and crystallization behavior. The originality of this work lies in establishing a design–validation framework for fluxes that remain stable after Ce₂O₃ absorption, rather than simply replacing the conventional CaO–SiO₂ system. Validation against literature SiO₂ activity data showed good trend consistency, supporting the use of the IMCT model as a semi-quantitative tool for composition screening. The results showed that CaO, Li₂O, and Ce₂O₃ exhibited relatively high activities, whereas B₂O₃ showed extremely low activity. When the Ce₂O₃ content exceeded 5 wt.%, the viscosity remained about 0.30 Pa·s, and when the w(CaO)/w(Al₂O₃) ratio was higher than 1.6, it stabilized at about 0.25 Pa·s. The minimum melting temperature, 1122.6 °C, was obtained at 5 wt.% Ce₂O₃. Compared with a conventional CaO–SiO₂-based flux, the developed flux showed similar initial processability but much better stability after absorbing 15 wt.% Ce₂O₃, with less severe deterioration in melting, viscosity, and crystallization behavior. These results provide scientific insight into mold-flux design under rare-earth oxide pickup conditions and practical guidance for improving the continuous casting of rare-earth weathering steels.

1. Introduction

Rare-earth (RE) steels, i.e., steels containing small additions of rare-earth elements, have attracted extensive attention because rare-earth elements can purify molten steel, modify non-metallic inclusions, and produce beneficial microalloying effects. As a result, even a small amount of rare-earth addition can significantly improve the strength, impact toughness, and corrosion resistance of steels, which has promoted their application in carbon steels, alloy steels, stainless steels, and, more recently, weathering steels [1]. Despite these advantages, the continuous casting of RE-bearing steels remains challenging because the high chemical activity of rare-earth elements can strongly disturb the steel/slag interfacial reactions and thereby affect mold-flux stability, lubrication, and heat transfer in the mold.

For conventional CaO–SiO₂-based mold fluxes, severe interaction with rare-earth elements and rare-earth oxides is difficult to avoid during continuous casting. On the one hand, dissolved rare-earth elements in molten steel can react readily with reactive slag components, especially SiO₂, causing significant slag compositional changes. On the other hand, rare-earth oxides generated in the steel can continuously enter the slag during casting, further altering the flux chemistry and its physicochemical properties [2]. These changes usually increase viscosity and crystallization tendency, impair slag consumption and lubrication, and destabilize mold heat transfer [3]. In practice, such instability may increase the risk of excessive slag-rim formation, unstable casting operation, surface longitudinal cracking, and deterioration of slab surface quality, which limits the wider application of RE-bearing steels in continuous casting [4,5].

Considerable efforts have been devoted to understanding the effects of rare-earth oxides on mold-flux behavior [6,7,8,9,10]. Previous studies have shown that rare-earth oxides can markedly influence melting temperature, viscosity, and crystallization behavior, and that the resulting trends depend strongly on slag basicity and composition. In parallel, CaO–Al₂O₃-based mold fluxes with Li₂O and/or B₂O₃ additions have been investigated as low-reactivity alternatives to conventional silicate-based systems, mainly because they can reduce the melting temperature without relying on highly reactive SiO₂. However, most previous studies have focused on the role of individual components or on the initial physicochemical properties of candidate fluxes, while comparatively less attention has been paid to the integrated design of mold fluxes for RE weathering steel under continuous rare-earth oxide pickup conditions. In particular, there is still a lack of clear understanding of how to design a low-reactivity flux system that can simultaneously maintain acceptable melting behavior, viscosity stability, and controllable crystallization behavior after absorbing substantial amounts of rare-earth oxides.

In view of the above issues, the present work aims to develop a dedicated low-reactivity mold flux for the continuous casting of rare-earth weathering steel based on the CaO–Al₂O₃–Li₂O–B₂O₃–Ce₂O₃ system. The study combines phase-diagram-guided composition design, thermodynamic analysis based on the ion and molecule coexistence theory (IMCT), and experimental investigation of melting, viscosity, and crystallization behavior. The originality of this work lies not simply in replacing the CaO–SiO₂ system with a CaO–Al₂O₃-based one, but in establishing an integrated design and validation framework for RE-steel mold fluxes that considers (i) reduced interfacial reactivity, (ii) physicochemical stability after Ce₂O₃ absorption, and (iii) the evolution of crystallization behavior compared with a conventional mold flux. By clarifying these relationships, this study is expected to provide both scientific insight into flux design under rare-earth oxide pickup conditions and practical guidance for improving lubrication stability, casting operability, and slab surface quality in the continuous casting of RE weathering steels.

2. Slag System Composition Design

To mitigate severe slag–steel interfacial reactions during the continuous casting of rare-earth weathering steels, reducing the intrinsic reactivity of the mold flux is a critical design objective. Thermodynamic analysis indicates that the standard Gibbs free energy for the reaction between rare-earth Ce and SiO₂ is significantly lower than that for its reactions with CaO and Al₂O₃, implying a much stronger reaction tendency between rare-earth elements and SiO₂ [11]. Consequently, in the present work, the composition design strategy was shifted from the conventional CaO-SiO₂-based low-melting region to the CaO-Al₂O₃-based low-melting region (Figure 1). According to the CaO-Al₂O₃ phase diagram in Figure 2, and considering both melting behavior and compositional tunability, the baseline composition was defined by a w(CaO)/w(Al₂O₃) ratio in the range of 0.6–2.0.

However, the CaO-Al₂O₃ base system inherently exhibits a relatively high melting temperature, which necessitates the introduction of suitable fluxing agents to reduce the melting temperature and to adjust other physicochemical properties. Thermodynamic evaluation shows that Na₂O has a strong reaction tendency with rare-earth Ce, as indicated by its large negative Gibbs free energy of reaction, and was therefore excluded from the flux design. In contrast, Li₂O exhibits a much weaker interaction with rare-earth Ce and can effectively suppress the reaction between the mold flux and rare-earth elements while maintaining the stability of slag properties. Furthermore, the Li₂O-Al₂O₃ phase diagram indicates that Li₂O can form low-melting-point compounds with Al₂O₃ in Figure 3, thereby significantly reducing the melting temperature of the slag [12,13,14]. Based on these considerations, Li₂O was selected as the primary fluxing agent, and its content was controlled within the range of 5–15 wt.%.

In addition, B₂O₃, which has a low melting point of approximately 450 °C and readily forms low-melting compounds with various oxides, was introduced to further decrease the melting temperature of the slag system [15,16,17]. Phase diagram analysis of the CaO-Al₂O₃-B₂O₃ system shows that increasing the B₂O₃ content from 0 to 10 wt.% can reduce the melting temperature of the system by as much as ~500 °C in Figure 4. Therefore, considering both melting performance and compositional stability, the B₂O₃ content in the new mold flux was determined to be in the range of 0–10 wt.%.

To further suppress the reaction between rare-earth elements and the mold flux, in addition to lowering the activity of the reactants, the reaction driving force can also be reduced by increasing the activity of the reaction products [18,19]. On this basis, an appropriate amount of rare-earth oxide Ce₂O₃ was introduced into the mold flux to inhibit further transfer and reaction of rare-earth elements into the slag and to reduce the overall reactivity of the slag system. Taking into account both thermodynamic considerations and process adaptability, the Ce₂O₃ content was controlled within the range of 0–20 wt.%.

On the basis of the above design principles, a novel low-reactivity mold flux system with the composition CaO-Al₂O₃-Li₂O-B₂O₃-Ce₂O₃ was finally established.

3. Thermodynamic Analysis of Slag Components

3.1. Model Assumptions

Based on the Ion and Molecule Coexistence Theory (IMCT), the CaO-Al₂O₃-Li₂O-B₂O₃-Ce₂O₃ slag system was analyzed by integrating published thermodynamic information with calculations performed using FactSage 8.2, and the corresponding structural units of the melt were identified as summarized in

Table 1. Structural Units in the CaO-Al₂O₃-Li₂O-B₂O₃-Ce₂O₃ System.

System	Structural Units
	Ca2+, Li+, Ce3+, O2−, Al2O3, B2O3
Al2O3-CaO	CaO·Al2O3, 3CaO·Al2O3, 12CaO·7Al2O3, CaO·2Al2O3, CaO-6Al2O3
Al2O3-B2O3	2Al2O3·B2O3, 9Al2O3 ·2B2O3
B2O3-CaO	CaO-2B2O3, CaO-B2O3, 2CaO ·B2O3, 3CaO ·B2O3
Ce2O3-Al2O3	Ce2O3·Al2O3, Ce2O3·11Al2O3
Li2O-Al2O3	Li2O·Al2O3
Li2O-B2O3	Li2O·B2O3, Li2O·2B2O3, Li2O·3B2O3, Li2O·4B2O3

[20,21]. After determining the structural units that may exist in the molten slag, equilibrium-constant expressions were formulated for all relevant reactions, and an activity-calculation model for the mold flux was subsequently established according to the principle of mass balance.

Assume that $$\begin{gathered} m_1=\sum X_{CaO},m_2=\sum X_{A{l}_2{O}_3},m_3=\sum X_{L{i}_{2}O},m_4=\sum X_{B_2{O}_3}, \\ {m}_5=\sum X_{C{e}_2{O}_3},N_1=N_{CaO},N_2=N_{A{l}_2{O}_3},N_3=N_{L{i}_{2}O},N_4=N_{B_2{O}_3},N_5=N_{C_2{O}_3}, \\ {N}_6=N_{CaO6A{l}_2{O}_3},N_7=N_{CaOA{l}_2{O}_3},N_8=N_{3CaOA{l}_2{O}_3},N_9=N_{12CaO7A{l}_2{O}_3},N_{10}=N_{CaO2A{l}_2{O}_3}, \\ {N}_{11}=N_{2A{l}_2{O}_3\cdot B_2{O}_3},N_{12}=N_{9A{l}_2{O}_3\cdot 2B_2{O}_3},N_{13}=N_{CaO2B_2{O}_3},N_{14}=N_{CaO{B}_2{O}_3},N_{15}=N_{2CaO{B}_2{O}_3}, \\ {N}_{16}=N_{3CaO{B}_2{O}_3},N_{17}=N_{C{a}_2{O}_3\cdot A{l}_2{O}_3},N_{18}=N_{C_2{O}_3\cdot 11H_2{O}_3},N_{19}=N_{L{i}_{2}O\cdot d{l}_2{O}_3},N_{20}=N_{L{i}_{2}O\cdot B_2{O}_3}, \\ {N}_{21}=N_{L{i}_{2}O\cdot 2B_2{O}_3},N_{22}=N_{L{i}_{2}O\cdot 3B_2{O}_3},N_{23}=N_{L{i}_{2}O\cdot 4B_2{O}_3}. \end{gathered}$$

Here, ∑X denotes the total moles of all structural units at equilibrium for an assumed 100 g of slag. xi (i = 1, 2, 3… 22) represents the moles of a given substance in the melt after reaction equilibrium is reached. mi (i = 1, 2, 3, 4, 5) denotes the total moles of CaO, Al₂O₃, Li₂O, B₂O₃, and Ce₂O₃, respectively, before reaction. Ni (i = 1, 2, 3, 4, 5) is the effective concentration of each component in the slag, which is defined as the activity of that component.

According to the Ion and Molecule Coexistence Theory, CaO, Ce₂O₃, and Li₂O exist as face-centered cubic ionic lattices in the solid state, and in the molten slag these compounds occur as ionic species such as Ca²⁺, Ce³⁺, Li⁺, and O²⁻, remaining independent rather than existing in molecular form.

The mass-action concentration expressions of the structural units and the corresponding equilibrium reactions used in the model are summarized in

Table 2. The reaction equations involved in the model mainly include.

Project	Structural Units	No	Mass Action Concentration of Structural
Ionic species.	$\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-}=\mathrm{CaO}$	(1)	${\mathrm{N}}_1={\mathrm{N}}_{\mathrm{C}{\mathrm{a}}^{2+}}+{\mathrm{N}}_{{\mathrm{O}}^{2-}}=2{\mathrm{x}}_1/\sum \mathrm{X} { \mathrm{x}}_1={\mathrm{N}}_1\sum \mathrm{X}/2$
	$2\mathrm{L}{\mathrm{i}}^{+}+{\mathrm{O}}^{2-}=\mathrm{L}{\mathrm{i}}_2\mathrm{O}$	(2)	${\mathrm{N}}_3=2{\mathrm{N}}_{\mathrm{L}{\mathrm{i}}^{+}}+{\mathrm{N}}_{{\mathrm{O}}^{2-}}=3 {\mathrm{x}}_3/\sum \mathrm{X} {\mathrm{x}}_3={ \mathrm{N}}_3\sum \mathrm{X}/3$
	$2{\mathrm{Ce}}^{3+}+3{\mathrm{O}}^{2-}={\mathrm{Ce}}_2{\mathrm{O}}_3$	(3)	${\mathrm{N}}_5=2{\mathrm{N}}_{\mathrm{C}{\mathrm{e}}^{3+}}+3{\mathrm{N}}_{{\mathrm{O}}^{2-}}=5 {\mathrm{x}}_5/\sum \mathrm{X} { \mathrm{x}}_5={\mathrm{N}}_5\sum \mathrm{X}/5$
Molecular species.	$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$	(4)	${\mathrm{N}}_2={ \mathrm{x}}_2/\sum \mathrm{X}{\mathrm{x}}_2={\mathrm{N}}_2\sum \mathrm{X}$
	${\mathrm{B}}_2{\mathrm{O}}_3$	(5)	${\mathrm{N}}_4={ \mathrm{x}}_4/\sum \mathrm{X}{\mathrm{x}}_4={ \mathrm{N}}_4\sum \mathrm{X}$
Ion–molecule and molecule–molecule chemical equilibrium reactions	$(\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-})+6\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3=\mathrm{C}\mathrm{a}\mathrm{O}\cdot$	(6)	$6\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ ${\mathrm{N}}_6={\mathrm{K}}_1{\mathrm{N}}_1{\mathrm{N}}_2^6{\mathrm{x}}_6={\mathrm{N}}_6\sum \mathrm{X}$
	$(\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-})+\mathrm{A}{\mathrm{l}}_2\mathrm{O}=\mathrm{Ca}\mathrm{O}\cdot {\mathrm{Al}}_2{\mathrm{O}}_3$ △G0 = −16380 − 37.58T (J/mol)	(7)	${\mathrm{N}}_7={\mathrm{K}}_2{\mathrm{N}}_1{\mathrm{N}}_2{\mathrm{x}}_7={\mathrm{N}}_7\sum \mathrm{X}$
	$3(\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-})+\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3=3\mathrm{C}\mathrm{a}\mathrm{O}\cdot \mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ △G0 = −18000 − 18.83T (J/mol)	(8)	${\mathrm{N}}_8={\mathrm{K}}_3{\mathrm{N}}_1^3{\mathrm{N}}_2{\mathrm{x}}_8={\mathrm{N}}_8\sum \mathrm{X}$
	$12(\mathrm{C}{\mathrm{a}}^{2+} + {\mathrm{O}}^{2-}) + 7\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3 = 12\mathrm{CaO}\cdot 7\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ △G0 = −12600 − 24.69T (J/mol)	(9)	${\mathrm{N}}_{9 }={\mathrm{K}}_4{\mathrm{N}}_1^{12}{\mathrm{N}}_2^7{\mathrm{x}}_9={ \mathrm{N}}_9\sum \mathrm{X}$
	$(\mathrm{C}{\mathrm{a}}^{2+}+ {\mathrm{O}}^{2-}) + 2\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_{3 }= \mathrm{CaO}\cdot 2\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ △G0 = −86100 − 205.1T (J/mol)	(10)	${\mathrm{N}}_{10 }={ \mathrm{K}}_5{\mathrm{N}}_1{\mathrm{N}}_2^2{\mathrm{x}}_{10}={\mathrm{N}}_{10}\sum \mathrm{X}$
	$2\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3 + {\mathrm{B}}_2{\mathrm{O}}_3 = 2\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3\cdot {\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −16700 − 25.52T (J/mol)	(11)	${\mathrm{N}}_{11}={ \mathrm{K}}_6{\mathrm{N}}_2^2{\mathrm{N}}_4{\mathrm{x}}_{11}={\mathrm{N}}_{11}\sum \mathrm{X}$
	$9\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3 + {\mathrm{B}}_2{\mathrm{O}}_{3 }= 9\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3\cdot {\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −90958.9 + 36.79T (J/mol)	(12)	${\mathrm{N}}_{12}={ \mathrm{K}}_7{\mathrm{N}}_2^9{\mathrm{N}}_4{\mathrm{x}}_{12 }={ \mathrm{N}}_{12}\sum \mathrm{X}$
	$\left(\mathrm{C}{\mathrm{a}}^{2+} +{ \mathrm{O}}^{2-}\right) + 2{\mathrm{B}}_2{\mathrm{O}}_{3 }= \mathrm{CaO}\cdot 2{\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −132385.55 − 28.7T (J/mol)	(13)	${\mathrm{N}}_{13}={ \mathrm{K}}_8{\mathrm{N}}_1{\mathrm{N}}_4^2{\mathrm{x}}_{13}={ \mathrm{N}}_{13}\sum \mathrm{X}$
	$(\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-}) +{ \mathrm{B}}_2{\mathrm{O}}_3 = \mathrm{CaO}\cdot {\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −109694.16 − 0.67T (J/mol)	(14)	${\mathrm{N}}_{14}={\mathrm{K}}_9{\mathrm{N}}_1{\mathrm{N}}_4{\mathrm{x}}_{14 }={\mathrm{N}}_{14}\sum \mathrm{X}$
	$2(\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-}) +{ \mathrm{B}}_2{\mathrm{O}}_3 = 2\mathrm{CaO}\cdot {\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −75362.4 − 20.77T (J/mol)	(15)	${\mathrm{N}}_{15 }={\mathrm{K}}_{10}{\mathrm{N}}_1^2{\mathrm{N}}_4{\mathrm{x}}_{15 }={\mathrm{N}}_{15}\sum \mathrm{X}$
	$3(\mathrm{C}{\mathrm{a}}^{2+}+{\mathrm{O}}^{2-}) + {\mathrm{B}}_2{\mathrm{O}}_3 = 3\mathrm{CaO}\cdot {\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −108019.44 − 46.56T (J/mol)	(16)	${\mathrm{N}}_{16} = {\mathrm{K}}_{11}{\mathrm{N}}_1^3{\mathrm{N}}_4{\mathrm{x}}_{16} = {\mathrm{N}}_{16}\sum \mathrm{X}$
	$(2\mathrm{C}{\mathrm{e}}^{3+}+3{\mathrm{O}}^{2-}) + \mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3 = \mathrm{C}{\mathrm{e}}_2{\mathrm{O}}_3\cdot \mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ △G0 = −129790.8 − 54.6T J/mol)	(17)	${\mathrm{N}}_{17 }={ \mathrm{K}}_{12}{\mathrm{N}}_2{\mathrm{N}}_5{\mathrm{x}}_{17}={ \mathrm{N}}_{17}\sum \mathrm{X}$
	$(2\mathrm{C}{\mathrm{e}}^{3+}+3{\mathrm{O}}^{2-}) + 11\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_{3 }= \mathrm{C}{\mathrm{e}}_2{\mathrm{O}}_3\cdot 11\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ △G0 = −60240.99 − 14.19T(J/mol)	(18)	${\mathrm{N}}_{18}={\mathrm{K}}_{13}{\mathrm{N}}_2^{11}{\mathrm{N}}_5{\mathrm{x}}_{18 }={ \mathrm{N}}_{18}\sum \mathrm{X}$
	$(2\mathrm{L}{\mathrm{i}}^{+}+{\mathrm{O}}^{2-}) + \mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3 = \mathrm{L}{\mathrm{i}}_2\mathrm{O}\cdot \mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ △G0 = 49331.82 − 80.56T (J/mol)	(19)	${\mathrm{N}}_{19}={\mathrm{K}}_{14}{\mathrm{N}}_2{\mathrm{N}}_3{\mathrm{x}}_{19}={\mathrm{N}}_{19}\sum \mathrm{X}$
	$(2\mathrm{L}{\mathrm{i}}^{+}+{\mathrm{O}}^{2-}) +{ \mathrm{B}}_2{\mathrm{O}}_3 = \mathrm{L}{\mathrm{i}}_2\mathrm{O}\cdot {\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −107100 − 10.59T (J/mol)	(20)	${\mathrm{N}}_{20}={\mathrm{K}}_{15}{\mathrm{N}}_3{\mathrm{N}}_4{\mathrm{x}}_{20}={ \mathrm{N}}_{20}\sum \mathrm{X}$
	$(2\mathrm{L}{\mathrm{i}}^{+}+{\mathrm{O}}^{2-}) + 2{\mathrm{B}}_2{\mathrm{O}}_3 = \mathrm{L}{\mathrm{i}}_2\mathrm{O}\cdot 2{\mathrm{B}}_2{\mathrm{O}}_3\cdot$ △G0 = −134250 − 23.8T (J/mol)	(21)	${\mathrm{N}}_{21}={\mathrm{K}}_{16}{\mathrm{N}}_3{\mathrm{N}}_4^2{\mathrm{x}}_{21}={ \mathrm{N}}_{21}\sum \mathrm{X}$
	$(2\mathrm{L}{\mathrm{i}}^{+}+{\mathrm{O}}^{2-}) + 3{\mathrm{B}}_2{\mathrm{O}}_3=\mathrm{L}{\mathrm{i}}_2\mathrm{O}\cdot 3{\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −260640 + 66.97T (J/mol)	(22)	${\mathrm{N}}_{22}={\mathrm{K}}_{17}{\mathrm{N}}_3{\mathrm{N}}_4^3{\mathrm{x}}_{22}={ \mathrm{N}}_{22}\sum \mathrm{X}$
	$(2\mathrm{L}{\mathrm{i}}^{+}+{\mathrm{O}}^{2-}) + 4{\mathrm{B}}_2{\mathrm{O}}_3 = \mathrm{L}{\mathrm{i}}_2\mathrm{O}\cdot 4{\mathrm{B}}_2{\mathrm{O}}_3$ △G0 = −368200 + 156.9T (J/mol)	(23)	${\mathrm{N}}_{23}={\mathrm{K}}_{23}{\mathrm{N}}_3{\mathrm{N}}_4^4{\mathrm{x}}_{23}={ \mathrm{N}}_{23}\sum \mathrm{X}$

.

According to the mass-balance principle:

$${\displaystyle \sum _{i=1}^{23}} N_i=1$$

(24)

Each component obeys the law of mass conservation, and because the total moles of CaO remain unchanged before and after reaction, Equation (25) can be obtained.

$$\sum X={\displaystyle \frac{m_1}{N_1/2+N_6+N_7+3N_8+12N_9+N_{10}+N_{13}+N_{14}+2N_{15}+3N_{16}}}$$

(25)

Because the total moles of Al₂O₃ remain unchanged before and after reaction, Equation (26) can be obtained.

$$\sum X={\displaystyle \frac{m_2}{N_2+6N_6+N_7+N_8+7N_9+2N_{10}+9N_{11}+N_{17}+11N_{18}+N_{19}}}$$

(26)

Because the total moles of Li₂O remain unchanged before and after reaction, Equation (27) can be obtained.

$$\sum X={\displaystyle \frac{m_3}{N_3/3+N_{19}+N_{20}+N_{21}+N_{22}}}$$

(27)

Because the total moles of B₂O₃ remain unchanged before and after reaction, Equation (28) can be obtained.

$$\sum X={\displaystyle \frac{m_4}{N_4+N_{11}+2N_{12}+2N_{13}+N_{14}+N_{15}+N_{16}+N_{20}+2N_{21}+3N_{22}}}$$

(28)

Because the total moles of Ce₂O₃ remain unchanged before and after reaction, Equation (29) can be obtained.

$$\sum X={\displaystyle \frac{m_5}{N_5/5+N_{17}+N_{18}}}$$

(29)

Equations (1)–(29) (Table 2) constitute the activity-calculation model for the CaO–Al₂O₃–Li₂O–B₂O₃–Ce₂O₃ system. Finally, the effective concentrations of all structural units can be calculated using the fsolve function in Matlab 2024.

The nonlinear system of equations was solved using Matlab, and the Newton iterative method was adopted as the computational approach. The Newton iterative method is a successive linearization technique for solving the nonlinear system f(x) = 0. Performing a Taylor expansion at an approximate solution x^(k) yields

$$f\left(x\right)\approx f\left(x^{\left(k\right)}\right)+f\prime \left(x^{\left(k\right)}\right)\left(x-x^{\left(k\right)}\right)$$

(30)

Thus, the approximate equation for f(x) = 0 can be expressed as

$$f\left(x\right)\approx f\left(x^{\left(k\right)}\right)+f\prime \left(x^{\left(k\right)}\right)\left(x-x^{\left(k\right)}\right)$$

(31)

where f′(x^(k)) is the Jacobian matrix of f(x), given by

$$f\prime \left(x^{\left(k\right)}\right)={\left[\begin{array}{cccc}{\displaystyle \frac{\partial f_1}{\partial x_1}}& {\displaystyle \frac{\partial f_1}{\partial x_2}}& \Lambda & {\displaystyle \frac{\partial f_1}{\partial x_n}}\\ {\displaystyle \frac{\partial f_2}{\partial x_1}}& {\displaystyle \frac{\partial f_2}{\partial x_2}}& \Lambda & {\displaystyle \frac{\partial f_2}{\partial x_n}}\\ ⋮& ⋮& \ddots & ⋮\\ {\displaystyle \frac{\partial f_n}{\partial x_1}}& {\displaystyle \frac{\partial f_n}{\partial x_2}}& \Lambda & {\displaystyle \frac{\partial f_n}{\partial x_n}}\end{array}\right]}_{x=x^{\left(k\right)}}$$

(32)

If the Jacobian matrix is nonsingular, the unique solution of the corresponding linearized system can be written as

$$x^{\left(k+1\right)}=x^{\left(k\right)}-\lambda {\left[f\prime \left(x^{\left(k\right)}\right)\right]}^{-1}f\left(x^{\left(k\right)}\right) \left(k=0,1,2,\Lambda \right)$$

(33)

where Equation (33) represents the Newton iterative scheme for solving the nonlinear system f(x) = 0.

3.2. Model Validation

Owing to the complexity of the slag-system compositions calculated by the present model, direct determination of the activities of its constituent components is difficult; therefore, in this study, the experimentally measured SiO₂ activity values for the Al₂O₃–CaF₂–CaO–SiO₂ slag system at 1823 K reported in Ref. [22] were compared with the values calculated by the present model, and a Pearson correlation analysis was performed. As shown in Figure 5 and Figure 6, Pearson correlation analysis of the experimentally measured values and the model-calculated values indicates that the two vary in the same direction, that is, when the experimental values increase, the simulated values also increase correspondingly; the correlation coefficient is 0.95, indicating an extremely strong positive correlation, as |r| ≥ 0.8 is generally considered to represent a strong correlation. This result demonstrates excellent consistency between the experimental observations and the simulation predictions, indicating that the simulation model can reliably reflect the experimental behavior.

3.3. Activities of Slag Components Under Different Conditions

Based on the established computational framework, the baseline mold flux with the composition listed in

Table 3. Activities of the components in the CaO-Al₂O₃-based mold flux.

Component(s)	Mass Fraction (wt.%)	Component Activity at Different Temperatures
		1100 °C	1200 °C	1300 °C	1400 °C	1500 °C
CaO	35	0.467723	0.466370	0.464943	0.463335	0.461468
Al2O3	35	0.000023	0.000041	0.000070	0.000110	0.000165
Li2O	15	0.240265	0.243249	0.246438	0.249878	0.253599
Ce2O3	10	0.073709	0.071970	0.070133	0.068257	0.066393
B2O3	5	0.000000	0.000000	0.000000	0.000000	0.000000
Li2O·Al2O3		0.178839	0.178281	0.177555	0.176655	0.175579
CaO·Al2O3		0.000314	0.000531	0.000836	0.001241	0.001753
3CaO·Al2O3		0.000075	0.000132	0.000214	0.000326	0.000470
Ce2O3·Al2O3		0.001280	0.001636	0.002009	0.002387	0.002761
2CaO·B2O3		0.004143	0.004637	0.005107	0.005552	0.005973
3CaO·B2O3		0.028500	0.028317	0.028090	0.027831	0.027547

was selected as the reference system. The activities of the primary oxide components in the newly designed flux (CaO, Al₂O₃, Li₂O, B₂O₃, and Ce₂O₃), together with those of the major composite oxides potentially present in the slag (e.g., Li₂O·Al₂O₃, 3CaO·B₂O₃, and 2CaO·B₂O₃), were calculated under varying temperatures and compositional conditions. The results are summarized in Figure 7.

3.3.1. Effect of Temperature on Component Activities

The calculations indicate that CaO, Li₂O, and Ce₂O₃ exhibit relatively high activities in the novel mold flux, whereas Al₂O₃ shows low activity and B₂O₃ remains close to zero across the investigated temperature range. The slag is predicted to contain several stable composite oxides, including Li₂O·Al₂O₃, 3CaO·B₂O₃, and 2CaO·B₂O₃. The low reactivity of the mold flux can be rationalized from two aspects. First, low-reactivity constituents such as CaO and Li₂O retain high activities, while the comparatively more reactive species B₂O₃ is thermodynamically suppressed to an extremely low activity, thereby reducing the overall driving force for slag reactions. Second, Ce₂O₃ is a key product of slag–metal interfacial reactions; its relatively high activity is expected to impede further interfacial reaction progress.

Notably, the activities of Al₂O₃ and B₂O₃ remain extremely low at all temperatures. This behavior is primarily attributed to the relatively high CaO fraction in the flux, which promotes the association of Al₂O₃ and B₂O₃ with CaO to form stable composite oxides. Consequently, the equilibrium concentrations of Al₂O₃ and B₂O₃ in the melt are substantially reduced, driving their activities toward zero.

3.3.2. Effect of w(CaO)/w(Al₂O₃) on Component Activities

Figure 7b shows the activity evolution of flux components as a function of w(CaO)/w(Al₂O₃). With increasing w(CaO)/w(Al₂O₃), the activities of CaO and Li₂O increase markedly, Ce₂O₃ decreases slightly, Al₂O₃ remains at an extremely low level and continues to decrease, and B₂O₃ stays near zero. These trends arise mainly from the compositional shift induced by increasing w(CaO)/w(Al₂O₃): the relative mass fraction of CaO increases while that of Al₂O₃ decreases, leading to a higher activity of CaO and a lower activity of Al₂O₃. In parallel, the reduced Al₂O₃ availability lowers the equilibrium concentrations of Al₂O₃-bearing composite oxides such as Li₂O·Al₂O₃ and CaO·Al₂O₃, resulting in decreased activities of these compounds. Moreover, because less Li₂O is consumed to form Li₂O·Al₂O₃, a larger fraction of free Li₂O remains in the melt, thereby increasing its activity. Overall, within an appropriate compositional window, elevating w(CaO)/w(Al₂O₃) increases the activities of the low-reactivity constituents CaO and Li₂O and thus contributes to reducing flux reactivity.

3.3.3. Effect of Fluxing-Agent Content (Li₂O and B₂O₃) on Component Activities

Figure 7c presents the activities of flux constituents at different Li₂O mass fractions. Increasing Li₂O leads to a pronounced rise in Li₂O activity, while Ce₂O₃ remains nearly constant and CaO and Al₂O₃ decrease slightly; B₂O₃ continues to exhibit an activity close to zero. The elevated Li₂O activity enhances its interaction with Al₂O₃, promoting the formation of Li₂O·Al₂O₃. As a result, the activity of Li₂O·Al₂O₃ increases, accompanied by a further decrease in Al₂O₃ activity. With continued Li₂O addition, the higher equilibrium concentration of Li₂O·Al₂O₃ suppresses the formation of other Al₂O₃-containing composite oxides (e.g., CaO·Al₂O₃, 3CaO·Al₂O₃, and Ce₂O₃·Al₂O₃), leading to reduced equilibrium concentrations and activities of these phases.

Figure 7d shows the activity changes induced by varying B₂O₃ content. As B₂O₃ increases, the activities of Li₂O and Ce₂O₃ increase (the former more significantly), whereas CaO and Al₂O₃ decrease. When B₂O₃ is below ~12 wt.%, its activity remains nearly zero, which is attributed to the strong stabilization of B₂O₃ through the formation of calcium borates (2CaO·B₂O₃ and 3CaO·B₂O₃). Above ~12 wt.% B₂O₃, the activity of B₂O₃ shows a slight increase but still remains at a very low level overall. Meanwhile, increasing B₂O₃ shifts the dominant borate species from 3CaO·B₂O₃ toward 2CaO·B₂O₃, as reflected by the increasing activity of 2CaO·B₂O₃ and the decreasing activity of 3CaO·B₂O₃.

3.3.4. Effect of Rare-Earth Oxide (Ce₂O₃) on Component Activities

Figure 7e illustrates the effect of Ce₂O₃ mass fraction on component activities. Increasing Ce₂O₃ markedly increases the activities of Ce₂O₃ and Li₂O, while decreasing those of CaO and Al₂O₃; B₂O₃ remains close to zero. The increase in Ce₂O₃ activity is a direct consequence of its higher concentration. In addition, Ce₂O₃ tends to associate with Al₂O₃ to form Ce₂O₃·Al₂O₃, which lowers Al₂O₃ activity while increasing the activity of Ce₂O₃·Al₂O₃. As Ce₂O₃·Al₂O₃ formation intensifies, the formation of Li₂O·Al₂O₃ is comparatively reduced, causing a decrease in Li₂O·Al₂O₃ activity and a concomitant increase in Li₂O activity. Moreover, the slight decrease in CaO activity with increasing Ce₂O₃ promotes the conversion of 3CaO·B₂O₃ to 2CaO·B₂O₃. Collectively, increasing Ce₂O₃ raises the activities of the low-reactivity constituents Li₂O and Ce₂O₃, providing a thermodynamic basis for mitigating slag–metal interfacial reactions and reducing the overall reactivity of the mold flux.

4. Composition Optimization of the Slag System and Investigation of Its Physicochemical Properties

4.1. Methodology

4.1.1. Preparation of Slag Samples

In this chapter, mold fluxes with different compositions were prepared by premelting reagent-grade pure chemicals. To remove moisture and impurities from the reagents, each reagent was calcined in a muffle furnace (National Engineering Research Center for Continuous Casting Technology, Beijing, China) at high temperature for 2 h. The calcined chemical reagents were weighed according to the designed compositions, thoroughly mixed, placed into a graphite crucible, and heated in a high-temperature tube furnace(National Engineering Research Center for Continuous Casting Technology, Beijing, China) at 1200 °C to 1450 °C, where they were held for 1 h to ensure complete melting of the slag samples. After premelting, the mold fluxes were quenched, dried, ground, and sieved to obtain a particle size of less than 0.074 mm for subsequent physicochemical property measurements.

4.1.2. Method for Viscosity Measurement

The viscosity characteristics of the mold fluxes were measured using the rotating cylinder method, and the experimental apparatus was an RTW-10 comprehensive melt property tester (National Engineering Research Center for Continuous Casting Technology, Beijing, China), as shown in Figure 8. The main heating unit was a MoSi₂ high-temperature furnace, and an S-type thermocouple was used for furnace temperature control and measurement, with a temperature control accuracy of ±0.5 °C. The temperature-measuring thermocouple was positioned at the bottom of the graphite crucible. The graphite crucible used to contain the slag had an outer diameter of 50 mm, an inner diameter of 40 mm, and a height of 80 mm.

The viscosity measurement procedure was as follows.

(1) Before heating, the graphite crucible lined with a molybdenum sheet was placed in the constant-temperature zone of the furnace, and approximately 140 g of premelted slag was weighed and loaded into the crucible. The power supply and control program were then turned on, and the temperature was raised to 1350 °C and held for 30 min to ensure complete melting of the slag sample.

(2) A molybdenum rod was used to stir the molten slag and adjust the slag height to 40 mm, after which the Mo probe and suspension rod were installed so that they were positioned exactly at the center of the furnace tube. The furnace height was then adjusted so that the distance between the lowest end of the Mo probe and the bottom of the graphite crucible was 10 mm.

(3) The viscosity measurement system was started, and the Mo probe was rotated at 200 rpm while the furnace temperature was decreased at a rate of 3 °C/min for viscosity measurement and data recording. The measurement was terminated when the viscosity increased to 10 Pa·s.

(4) After completion of the viscosity measurement, the furnace temperature was raised to a level at which the slag viscosity was relatively low, the molybdenum probe was removed, and the experiment was concluded. To protect the graphite crucible and sleeve, argon was used throughout the experiment as a protective atmosphere.

At high temperatures, the relationship between the viscosity of the mold flux and temperature follows the Arrhenius equation, showing a linear functional relationship. However, when the structure of the mold flux changes, such as when crystalline phases precipitate, the relationship between viscosity and temperature no longer follows the Arrhenius equation. Therefore, the temperature at which the functional relationship between viscosity and temperature begins to deviate from linearity is defined as the break temperature of the continuous casting mold flux. In addition, the apparent activation energy for viscous flow of the mold flux can be obtained by fitting the relationship between viscosity and temperature in the high-temperature region. The activation energy for viscous flow represents the energy required for one mole of particles in the molten slag to move from one equilibrium position to another.

4.1.3. Method for Testing Crystalline Phases

The raw material used in the crystalline phase test was premelted slag. An appropriate amount of slag sample was taken and fully melted at 1350 °C. Subsequently, with reference to the viscosity–temperature curve obtained during continuous cooling, the fully molten slag sample was cooled at a rate of 3 °C/min, and samples were collected at different characteristic temperatures according to the specific scheme. At the break temperature, slag samples were taken and water-quenched to analyze the initial crystalline phases of the mold flux. At the temperature corresponding to a viscosity of 10 Pa·s, slag samples were taken and water-quenched, and phase analysis was conducted on the mold flux after complete crystallization. The phase identification and analysis techniques were as follows.

(1) X-ray diffraction (XRD) analysis.

Phase identification of the mold flux was carried out using a D/max-2500PC X-ray diffractometer (Rigaku Corporation, Akishima, Tokyo, Japan) under the following conditions: Cu target Kα radiation with a wavelength of λ = 1.544426 Å, an operating voltage of 40 kV, a 2θ scanning range of 10–90°, and a scanning rate of 0.033°·s⁻¹.

4.1.4. Method for Measuring Melting Temperature

The melting temperature of the mold flux was determined by the hemisphere point method. As the temperature increased, the amount of liquid phase in the slag gradually increased and the sample softened, causing its shape to change progressively and its height to decrease continuously. After complete melting, the sample spread over the substrate. the temperature at which the sample height decreases to one-half of its original height is defined as the melting temperature.

The melting temperature of the mold flux was measured using a melting point and melting rate analyzer (National Engineering Research Center for Continuous Casting Technology, Beijing, China), and the experimental apparatus is shown in Figure 9. The equipment mainly consisted of a heating system, a temperature control system, an imaging system, and a rail transmission system. The heating device was a horizontal tube furnace equipped with U-shaped MoSi₂ heating elements, with a maximum operating temperature of 1550 °C. The furnace temperature was controlled by silicon-controlled rectifier components, with a temperature control accuracy of ±2 °C. The optical imaging system was an OLYMPUS high-definition camera. The transmission system was used to move the sample into and out of the heating furnace.

The melting temperature measurement procedure was as follows.

(1) A small amount of premelted slag with a particle size of less than 0.074 mm was mixed with alcohol and pressed into a cylindrical specimen with both diameter and height of 3 mm. The specimen was then placed at the center of an alumina substrate, and the alumina substrate was positioned in the groove of an alumina tube so that the temperature-measuring thermocouple was located directly beneath the alumina substrate.

(2) The temperature control program was set and operated so that the furnace heating rate was 10 °C/min. When the furnace temperature reached 550 °C, the slag sample was introduced into the constant-temperature zone of the furnace, and the positions of the eyepiece and objective lens were adjusted so that a clear projected image appeared on the computer screen, after which the image coordinates were entered.

(3) The temperature corresponding to the point at which the specimen height decreased to one-half of its original height during heating was recorded.

(4) The specimen was removed, and the temperature control program was turned off so that the furnace temperature decreased to room temperature.

4.2. Effect of w(CaO)/w(Al₂O₃) on Physicochemical Properties of the Mold Flux

Guided by the theoretical calculations, the w(CaO)/w(Al₂O₃) ratio of the slag system was systematically adjusted to improve the physicochemical performance of the mold flux. The corresponding melting temperatures are presented in Figure 10a. As w(CaO)/w(Al₂O₃) increased, the melting temperature exhibited a non-monotonic evolution, increasing initially and then decreasing before approaching a quasi-stable value. The highest melting temperature (1149.2 °C) was obtained at w(CaO)/w(Al₂O₃) = 1.2, whereas the lowest value (1125.5 °C) occurred at w(CaO)/w(Al₂O₃) = 0.6. When w(CaO)/w(Al₂O₃) was within 1.4–2.0, the melting temperature remained nearly constant at approximately 1140 °C.

Figure 10 shows the performance parameters of the mold flux under different w(CaO)/w(Al₂O₃) ratios. Figure 11 presents the viscosity–temperature curves of the mold flux at different w(CaO)/w(Al₂O₃) ratios. Figure 12 shows the fitting results for the relationship between mold flux viscosity and temperature. The viscosity–temperature behavior was strongly dependent on w(CaO)/w(Al₂O₃). For w(CaO)/w(Al₂O₃) = 0.6–1.0, viscosity decreased markedly with increasing temperature below 1300 °C, and the viscosity at 1300 °C exceeded 1 Pa·s; no distinct inflection point was observed in the viscosity curve. At w(CaO)/w(Al₂O₃) = 1.2, viscosity decreased rapidly with temperature up to ~1200 °C and then decreased more gradually at higher temperatures, again without a clear inflection. In contrast, when w(CaO)/w(Al₂O₃) increased to 1.4–2.0, a pronounced inflection emerged at around 1200 °C, indicating a transition in flow behavior; prior to the inflection point, viscosity decreased sharply with increasing temperature, whereas beyond the inflection it became relatively stable. Among these compositions, the flux at w(CaO)/w(Al₂O₃) = 1.60 showed the most stable viscosity before the inflection point, suggesting improved operational stability.

At 1300 °C, the viscosity decreased with increasing w(CaO)/w(Al₂O₃) and then exhibited a slight rebound before remaining essentially constant; when w(CaO)/w(Al₂O₃) exceeded 1.6, the viscosity stayed at a low level of ~0.25 Pa·s. The apparent activation energy for viscous flow decreased first and then increased with increasing w(CaO)/w(Al₂O₃), reaching a minimum of 132.1 kJ·mol⁻¹ at w(CaO)/w(Al₂O₃) = 1.6, which is consistent with enhanced melt fluidity in this compositional window.

Combined with the analysis of melt structure, as the w(CaO)/w(Al₂O₃) ratio increases, the mass fraction of CaO in the slag increases, the proportion of O²⁻ ions rises, and the degree of dissociation of the mold flux is enhanced. Moreover, the increase in O²⁻ ions promotes the formation of two-dimensional BO₃³⁻ triangular structural units, disrupts the three-dimensional network structure, and leads to a decreasing trend in the viscosity of the mold flux.

4.3. Effect of Fluxing-Agent Content on Physicochemical Properties of the Mold Flux

The influence of B₂O₃ content on melting temperature is shown in Figure 13. The melting temperature decreased progressively with increasing B₂O₃ mass fraction and reached a minimum of 1118 °C at 10 wt.% B₂O₃. Relative to the B₂O₃-free composition, the addition of 5 wt.% B₂O₃ reduced the melting temperature by 50.7 °C; increasing B₂O₃ from 5 to 10 wt.% produced an additional reduction of 22.4 °C, indicating that the fluxing efficiency of B₂O₃ diminishes at higher additions.

Figure 13 shows the performance parameters of the mold flux at different mass fractions of B₂O₃. Figure 14 presents the viscosity–temperature curves of the mold flux under different B₂O₃ mass fractions. Figure 15 shows the fitting results for the relationship between mold flux viscosity and temperature.

For all B₂O₃ levels, viscosity decreased with increasing temperature, while the inflection temperature shifted to lower values as B₂O₃ increased, reaching the lowest inflection temperature of 1145 °C at 10 wt.% B₂O₃. At 1300 °C, viscosity decreased and then slightly increased to an approximately constant value; when B₂O₃ exceeded 5 wt.%, viscosity remained low at ~0.33 Pa·s. The apparent activation energy for viscous flow decreased with increasing B₂O₃, reaching a minimum of 115.2 kJ·mol⁻¹ at 10 wt.% B₂O₃, and remained essentially unchanged in the range of 5–10 wt.% B₂O₃.

Combined with the analysis of melt structure, it can be concluded that, in the absence of B₂O₃ addition, the slag contains a relatively large number of highly polymerized AlO₄⁵⁻ tetrahedra, resulting in a high degree of polymerization of the mold flux as well as relatively high viscosity and viscous flow activation energy. When 5% B₂O₃ is added, the proportion of two-dimensional BO₃³⁻ triangular structures increases, the degree of polymerization of the mold flux decreases significantly, and the viscosity is reduced. When the mass fraction of B₂O₃ increases from 5% to 10%, the viscosity increases slightly but remains relatively stable. When the mass fraction of B₂O₃ increases from 0 to 10%, the break temperature of the mold flux decreases continuously, mainly because B₂O₃ has an extremely low melting point, which can substantially reduce the melting temperature and increase the superheat of the molten slag.

The influence of Li₂O content on melting temperature is shown in Figure 16. With increasing Li₂O mass fraction, the melting temperature first decreased and then increased, reaching a minimum of 1139.5 °C at 10 wt.% Li₂O.

Figure 16 shows the performance parameters of the mold flux at different Li₂O mass fractions. Figure 17 presents the viscosity–temperature curves of the mold flux under different Li₂O mass fractions. Figure 18 shows the fitting results for the relationship between mold flux viscosity and temperature.

The viscosity results show that, for all Li₂O levels, viscosity decreased with increasing temperature and the inflection temperature gradually decreased as Li₂O increased, reaching a minimum of 1175 °C at 15 wt.% Li₂O. When Li₂O exceeded 10 wt.%, the inflection temperature became nearly invariant. The viscosity at 1300 °C decreased with increasing Li₂O and reached a minimum of 0.2753 Pa·s at 15 wt.% Li₂O; when Li₂O was >10 wt.%, the viscosity remained at a low level of ~0.30 Pa·s. The apparent activation energy for viscous flow decreased first and then increased with increasing Li₂O, reaching a minimum of 129.9 kJ·mol⁻¹ at 10 wt.% Li₂O and remaining essentially constant for 10–15 wt.% Li₂O.

Combined with the analysis of melt structure, it can be concluded that, as the mass fraction of Li₂O increases, the degree of polymerization of the mold flux shows a continuous decreasing trend, and consequently the viscosity of the mold flux continuously decreases. The break temperature gradually decreases, possibly because the increase in Li₂O mass fraction weakens the crystallization ability of the mold flux and alleviates the abrupt change in its viscous characteristics.

4.4. Effect of Ce₂O₃ Content on Physicochemical Properties of the Mold Flux

Figure 19a shows the dependence of melting temperature on Ce₂O₃ mass fraction. As Ce₂O₃ increased, the melting temperature decreased slightly at first, then increased, and finally approached a stable plateau. The minimum melting temperature (~1122.6 °C) was obtained at 5 wt.% Ce₂O₃. When Ce₂O₃ exceeded 10 wt.%, the melting temperature remained relatively stable at approximately 1140 °C.

Figure 19 shows the performance parameters of the mold flux at different Ce₂O₃ mass fractions. Figure 20 presents the viscosity–temperature curves of the mold flux under different Ce₂O₃ mass fractions. Figure 21 shows the fitting results for the relationship between mold flux viscosity and temperature.

The viscosity trends further corroborate the compositional effect. With increasing Ce₂O₃ mass fraction, the viscosity–temperature curves consistently decreased with increasing temperature, and the inflection temperature shifted downward, reaching a minimum of 1155 °C at 20 wt.% Ce₂O₃. At 1300 °C, viscosity decreased with increasing temperature, and when Ce₂O₃ exceeded 5 wt.%, the viscosity remained low at ~0.30 Pa·s. The apparent activation energy for viscous flow exhibited a decrease followed by an increase with temperature, reaching a minimum of 132.2 kJ·mol⁻¹ at 5 wt.% Ce₂O₃; moreover, it was nearly invariant when Ce₂O₃ was within 5–15 wt.%.

Combined with the analysis of melt structure, it can be concluded that when the mass fraction of Ce₂O₃ does not exceed 10%, the increase in its mass fraction leads to an increase in O²⁻ ions generated by slag dissociation, and the low-polymerization AlO₄⁵⁻ tetrahedra Q² and Q³ gradually transform into AlO₆⁹⁻ octahedra, thereby disrupting the network structure, reducing the degree of polymerization, and gradually lowering the viscosity. When the mass fraction of Ce₂O₃ exceeds 10%, the structural units in the slag tend to reach a stable distribution, the degree of polymerization remains relatively stable, and the viscosity also remains relatively stable.

5. Comparison of Physicochemical Properties Between the Novel Mold Flux and the Conventional Mold Flux

5.1. Development of the Novel Mold Flux

This work used an industrial mold flux applied in the continuous casting of rare-earth weathering steel at a steel plant as a benchmark and carried out the design and development of a new CaO–Al₂O₃-based mold flux.

Table 4. Composition and properties of the mold flux for rare-earth weathering steel continuous casting.

Mass Fraction %						Properties
CaO	SiO2	Al2O3	Na2O	F	C	Melting temperature/°C	viscosity (1300 °C)/Pa·s
30~40	25~35	5~10	5~15	5~10	4~5	1100~1180	0.15~0.25

summarizes the composition and primary properties of the reference flux, in which CaO accounts for 30–40 wt.% and SiO₂ for 25–35 wt.%, and the principal fluxing additives are CaF₂ and Na₂O.

The reference flux shows a melting temperature range of 1100–1180 °C and a viscosity of ~0.15–0.25 Pa·s at 1300 °C, which are sufficient to satisfy the baseline processing requirements for continuous casting of rare-earth weathering steel at the initial stage.

Nevertheless, prolonged casting aggravates slag–steel interfacial reactions, which induces substantial variations in flux chemistry and properties and makes it difficult to maintain stable and smooth casting operation.

Guided by the performance targets of the plant-used flux (Table 4) and informed by the foregoing findings, an optimized new mold flux for rare-earth weathering steel casting was formulated, and the main compositional ranges are presented in

Table 5. Composition of the new mold flux for rare-earth weathering steel continuous casting (mass fraction)%.

CaO	Al2O3	Li2O	B2O3	Ce2O3
43.1~49.2	26.9~30.8	5~10	5~10	0~10

.

5.2. Comparison of Physicochemical Properties Between the Novel and Conventional Mold Fluxes

Figure 22 compares the melting temperatures of the novel CaO–Al₂O₃-based mold flux and the conventional mold flux.

As shown in the figure, the melting temperatures are comparable, and the novel flux exhibits a melting temperature of 1140 °C, indicating that its melting behavior is consistent with that of the industrially used flux.

Figure 23 shows a comparison of the viscosity characteristics of the two mold fluxes.

The novel flux exhibits viscosity characteristics broadly similar to those of the conventional flux, demonstrating good process compatibility in terms of the viscosity–temperature dependence and the workable viscosity window.

To further elucidate the crystallization behavior, XRD analyses were conducted on quenched samples of the conventional flux at the break temperature (1250 °C) and after full crystallization at 1100 °C, as shown in Figure 24.

The results indicate that the conventional flux remains a homogeneous liquid at the break temperature with no detectable crystalline phases, whereas after cooling to 1100 °C and full crystallization, a large amount of cuspidine (3CaO·2SiO₂·CaF₂) precipitates.

Similarly, Figure 25 presents the XRD patterns of quenched samples of the novel flux near the break temperature and after full crystallization at 1100 °C.

The novel flux also behaves as a homogeneous liquid near the break temperature without crystal precipitation; after full crystallization at 1100 °C, two precipitated phases are observed, with LiAlO₂ as the dominant phase and a minor amount of CaCeAlO₄.

Overall, the novel CaO–Al₂O₃-based flux exhibits a crystallization behavior broadly similar to that of the conventional SPH flux, in that no crystalline phases precipitate above the break temperature and a single liquid phase is maintained, whereas below the break temperature after full crystallization, the main precipitates in the novel flux are LiAlO₂ and CaCeAlO₄.

5.3. Stability Comparison Between the Novel and Conventional Mold Fluxes

Figure 22 compares the melting-temperature responses of the novel and conventional mold fluxes upon uptake of 15% Ce₂O₃.

The conventional silicate-based flux exhibits a pronounced increase in melting temperature of nearly 100 °C after 15% Ce₂O₃ uptake; in contrast, the novel flux maintains an almost unchanged melting temperature under the same uptake level, demonstrating excellent melting-temperature stability.

Figure 23 compares the viscosity behavior of the two fluxes following uptake of 15% Ce₂O₃.

After Ce₂O₃ uptake, the conventional flux exhibits markedly worsened viscosity characteristics, with ~2-fold higher viscosity at 1300 °C (exceeding 1 Pa·s) and an increase of ~100 °C in break temperature.

By comparison, the novel flux undergoes only minor variations in viscosity-related metrics, indicating superior viscosity stability.

To identify the cause of the deterioration in the conventional flux, quenched samples after 15% Ce₂O₃ uptake were examined by XRD near the break temperature (1270 °C) and after complete crystallization at 1200 °C, with the results shown in Figure 26.

The XRD results show extensive precipitation of lath- and block-like CaO·2Ce₂O₃·2SiO₂ at 1270 °C, and after complete crystallization at 1200 °C, a large amount of cuspidine (3CaO·2SiO₂·CaF₂) forms in addition to CaO·2Ce₂O₃·2SiO₂.

Extensive formation of high-melting rare-earth silicate phases significantly raises the solid-phase fraction and the degree of melt polymerization, resulting in pronounced viscosity increase and an elevated break temperature.

Likewise, Figure 27 shows the XRD patterns of quenched samples of the novel flux after 15% Ce₂O₃ uptake near the break temperature (1225 °C) and after complete crystallization at 1200 °C.

The results demonstrate that the novel flux is still a single homogeneous liquid phase near the break temperature with no crystallization detected, while after complete crystallization at 1200 °C, the precipitates become solely CaCeAlO₄.

In summary, the sharp rises in break temperature and viscosity of the conventional flux upon 15% Ce₂O₃ uptake mainly stem from massive precipitation of high-melting rare-earth silicate phases, exemplified by CaO·2Ce₂O₃·2SiO₂.

Over-crystallization elevates the solid fraction of the slag film, potentially causing inadequate lubrication and uneven heat transfer at the mold–strand interface and thus hindering stable continuous casting.

In contrast, even after 15% Ce₂O₃ uptake, the novel flux maintains a single liquid phase near the break temperature, better preserving its lubrication function; while precipitation of CaCeAlO₄ raises the break temperature to a certain extent, the effect is substantially less pronounced than in the conventional flux.

5.4. Industrial Implications and Current Limitations

Taken together, the above results indicate that the newly developed CaO–Al₂O₃-based mold flux not only exhibits lower reactivity toward rare-earth-bearing molten steel, but also maintains better physicochemical stability after rare-earth oxide uptake than the conventional CaO–SiO₂-based mold flux. From an industrial perspective, such stability is expected to be beneficial for maintaining lubrication consistency, reducing excessive crystallization of the slag film, and improving the operational stability of continuous casting for rare-earth weathering steels.

In addition to melting temperature, viscosity, and crystallization behavior, the steel–slag interfacial tension is also an important parameter for evaluating mold-flux applicability in continuous casting [23]. Interfacial tension affects slag entrapment tendency, interfacial stability, and lubrication behavior, and therefore has a direct influence on casting smoothness and slab surface quality [24]. In the present work, the improved physicochemical stability of the new mold flux after Ce₂O₃ absorption suggests that it may also be favorable for maintaining a more stable steel–slag interface during casting. However, because interfacial tension was not measured in this study, this implication remains qualitative. Further work combining interfacial-tension measurement with interfacial-reaction analysis is therefore needed to provide a more complete evaluation of the practical casting performance of the proposed flux.

Another issue that should be considered for industrial application is the compatibility between the CaO–Al₂O₃-based mold flux and refractory materials [25]. Compared with conventional silicate-based mold fluxes, CaO–Al₂O₃-rich systems may exhibit different wetting and corrosion behavior toward refractory or ceramic components under prolonged high-temperature service conditions [26]. In the present study, the proposed flux was designed and assessed mainly from the perspectives of slag–metal reactivity and physicochemical stability after rare-earth oxide pickup, whereas its interaction with refractory materials was not investigated. Therefore, although the present results demonstrate that the developed flux is a promising candidate for rare-earth weathering steel casting, its possible influence on refractory service life remains to be clarified. Dedicated compatibility and corrosion tests with representative refractory materials should be carried out before industrial implementation.

Overall, the present study provides a useful design route for developing low-reactivity mold fluxes with improved tolerance to compositional drift during the continuous casting of rare-earth steels. At the same time, the full industrial applicability of the proposed flux still requires further validation through interfacial-property characterization, refractory-compatibility assessment, and pilot-scale or plant-scale casting trials.

6. Conclusions

A low-reactivity CaO–Al₂O₃-based mold flux for the continuous casting of rare-earth weathering steel was designed and evaluated in the present study through thermodynamic analysis, model calculation, and experimental investigation. The results show that the proposed CaO–Al₂O₃–Li₂O–B₂O₃–Ce₂O₃ system provides a feasible composition framework for reducing the reactivity of mold fluxes toward rare-earth-bearing molten steel while maintaining acceptable melting, viscosity, and crystallization characteristics.

An activity calculation model for the CaO–Al₂O₃–Li₂O–B₂O₃–Ce₂O₃ system was established based on the ion and molecule coexistence theory (IMCT). The calculated results indicate that CaO, Li₂O, and Ce₂O₃ exhibit relatively high effective activities, whereas B₂O₃ remains at a very low level and Al₂O₃ also shows low activity within the present model framework. These results suggest that the newly designed flux system can suppress the contribution of highly reactive components and improve compositional tolerance under rare-earth oxide pickup conditions. However, the present IMCT analysis should be regarded as a semi-quantitative tool for composition screening and relative reactivity evaluation, rather than a direct substitute for experimentally measured absolute thermodynamic activities.

The physicochemical-property measurements show that the viscosity and melting behavior of the proposed flux can be controlled within an appropriate range through compositional optimization. When the Ce₂O₃ content exceeded 5 wt.%, the viscosity remained at about 0.30 Pa·s, and when the w(CaO)/w(Al₂O₃) ratio was higher than 1.6, the viscosity stabilized at about 0.25 Pa·s. The minimum melting temperature, approximately 1122.6 °C, was obtained at 5 wt.% Ce₂O₃. These results indicate that the proposed system is not only low-reactive in thermodynamic tendency, but also capable of maintaining a practically usable viscosity–melting window for continuous casting operation.

Compared with the conventional CaO–SiO₂-based mold flux, the newly developed CaO–Al₂O₃-based mold flux exhibits similar initial melting and viscosity characteristics but significantly improved stability after rare-earth oxide absorption. After absorbing 15 wt.% Ce₂O₃, the conventional mold flux showed a marked increase in melting temperature, viscosity, and break temperature, whereas the newly designed flux remained comparatively stable. This improved stability is associated with the different crystallization evolution of the two systems: the conventional flux tends to form high-melting rare-earth silicate phases, whereas the new flux evolves toward LiAlO₂- and CaCeAlO₄-related crystallization products, leading to less severe deterioration in flow and crystallization behavior.

From a practical perspective, the improved stability of the proposed flux after rare-earth oxide absorption is expected to be beneficial for maintaining lubrication consistency, reducing excessive crystallization, and improving casting operability during the continuous casting of rare-earth weathering steels. The present study demonstrates the feasibility of designing a low-reactivity CaO–Al₂O₃-based mold flux for rare-earth weathering steel continuous casting; however, several aspects still require further verification before industrial application. In particular, interfacial properties, refractory compatibility, and casting-scale performance were beyond the scope of the present work. Future studies should therefore focus on more comprehensive thermodynamic validation together with plant-relevant evaluation of interfacial behavior, refractory interaction, and slab-quality performance.