Generation Mechanism of MgO and Al₂O₃ Inclusions in 51CrV4 Spring Steel Based on the Ion–Molecule Coexistence Theory

Abstract

The presence of MgO·Al₂O₃ inclusions in 51CrV4 spring steel is detrimental to the alloy’s castability and fatigue properties. To effectively suppress these inclusions during production, accretions were collected from the immersion nozzle, and the MgO·Al₂O₃ inclusions in the steel billet were investigated. The generation mechanism of the inclusions was evaluated based on the ion–molecule coexistence theory, and the mass action–concentration model of CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag was developed. Industrial experiments showed that nozzle clogging was primarily caused by MgAl₂O₄ spinel inclusions, and the MgO·Al₂O₃ spinel inclusions in the steel billet were investigated by non-aqueous electrolysis. The model calculation results indicate that the Mg content increased with an increasing basicity, CaO/Al₂O₃ ratio, and Al content during the ladle furnace (LF) process. In contrast, the Mg content decreased with increasing CO pressure under Ruhstahl-Hausen vacuum degassing process (RH) conditions.

1. Introduction

In recent years, the increasing demand for alloyed steels with excellent properties has led to efforts to enhance the castability, surface quality, toughness, and fatigue behaviors of alloyed steels [1,2,3,4]. Due to the addition of Cr and V, 51CrV4 spring steel exhibits an excellent intensity, fatigue performance, and hardenability; thus, it has attracted considerable attention for use in large damping springs, suspension springs, and flat springs [5,6]. During the production of 51CrV4 steel, a high-basicity slag is adopted, as it is conductive to the removal of inclusions in bulk steel, desulfurization, and reducing the total oxygen content, but results in the formation of detrimental MgO·Al₂O₃ inclusions [7,8,9]. These inclusions have a steady face-centered cubic structure with a high melting point and are hard and un-deformable [10]. They tend to accumulate on the submerged entry nozzle (SEN) [2,11,12], resulting in nozzle clogging during casting. Furthermore, the accretions on the SEN might desquamate and become entrapped in the solidified shell, resulting in serious decreases in the internal quality [13]. Therefore, MgO·Al₂O₃ inclusions are detrimental to the final 51CrV4 product and its castability. Although a small amount of dissolved Ca can modify the MgO·Al₂O₃ spinel inclusions [9,14,15,16,17], the Ca treatment has a limited effect on large clusters of MgO·Al₂O₃ inclusions [18].

The generation and control of MgO·Al₂O₃ inclusions in stainless steels have been extensively investigated, because these inclusions are harmful to both the surface quality and forming properties of the final products [2,8,19,20,21,22]. They are thought to be generated from sources of Mg in liquid steel via the reduction of MgO in slag or MgO-based refractory [8,23,24,25]. Many studies have found that the compositions of top slag and refractory material strongly affect the inclusion composition [16,17,21,26,27,28,29,30,31,32,33,34,35,36,37], as summarized in Table 1.

Table 1. The relationships between compositions of slag or refractory and inclusions.

Steels	Slag/Refractory	Inclusions	Main Finding	Ref.
High strength alloyed structural steel	CaO–SiO2–Al2O3–MgO	MgO·Al2O3	log(XMgO/XAl2O3) of inclusions and log(aMgO/aAl2O3) in slag exhibiting a good linear relation.	[16]
High strength alloying steel	CaO–SiO2–Al2O3	MgO·Al2O3– CaO	MgO·Al2O3 inclusions can be modified to liquid ones by high-basicity slag.	[17]
Ferritic stainless steel	CaO–Al2O3–MgO	MgO·Al2O3	log(XMgO/XAl2O3) of inclusions and log(aMgO/aAl2O3) in slag showing a good linear relation.	[21]
Al-killed ferritic stainless steel	CaO–SiO2–Al2O3–MgO	MgO·Al2O3	MgO contents in inclusions decreased with the declining of CaO/SiO2 and CaO/Al2O3 ratio.	[26]
Mn and V alloyed steel	CaO–SiO2–Al2O3–MgO– CaF2	Spinel	The generation behavior of inclusion was influenced by aMgO in the initial slag.	[27]
Al-killed steel	CaO–SiO2–Al2O3–MgO– FeO	MgO·Al2O3	The content of FeO in slag plays an important role in the formation of MgO·Al2O3 inclusions.	[28]
Bearing steel	CaO–SiO2–Al2O3–MgO	CaO–SiO2–Al2O3–MgO	Thermodynamic for the formation of spinel inclusions was made.	[29]
Fe–Mn–S–C–Al steel	CaO–Al2O3–SiO2–CaF2– MgO/MgO–C refractory	MgAl2O4	The calculated results at different composition of slag and steel were in good agreement with the experimental results.	[30]
Extra-low- oxygen steel	MgO-based refractory and MgO bearing slag	MgO·Al2O3 spinel	MgO-based refractory supplied more Mg into liquid steel than refining slag.	[31]
Al deoxidized molten steel	MgO–C refractory	MgO·Al2O3	An internal oxidation-reduction occurs in the MgO–C refractory at elevated temperature.	[32]
Al-killed molten steel	Mg–Cr refractory	MgO·Al2O3 spinel	Mg and Cr dissolved from the refractory, and lead to the increasing contents of Mg and Cr in the liquid steel.	[33]
Fe–Al alloy	MgO-based refractory	MgO·Al2O3 spinel	The generation of a spinel layer at the interface was attributing to oxidation–reduction reactions and phase transformation.	[34]
Steels	MgO-based refractory	Spinel	Improving the resistance of MgO-based refractory to slag penetration is good to improve steel cleanness.	[35]
Al-killed steel	MgO refractory	Spinel	The decomposing of MgO refractory plays a key role in the dissolution of MgO refractory in Al-killed steels.	[36]
304 stainless steel	CaO–Al2O3-based slag	Spinel	A thermodynamic model was developed to predict slag–steel–inclusion reactions.	[37]

Compared to stainless steels, the suppression of MgO·Al₂O₃ inclusions in alloyed spring steels has the potential to provide a superior castability and fatigue performance. In this study, the generation mechanism of MgO·Al₂O₃ inclusions in 51CrV4 spring steel refined by CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag was investigated, based on the ion–molecule coexistence theory (IMCT) combined with industrial experiments, and influential factors were discussed.

2. Experimental and Methods

2.1. Nozzle Clogging

Nozzle clogging is occasionally observed during the production of 51Cr4V steel. To understand the causes of nozzle clogging, accretions taken from the SEN were identified by X-ray diffraction (XRD) and scanning electron microscopy (SEM) equipped with energy-dispersive X-ray spectroscopy (EDS). The XRD analysis indicated that the accretions primarily consisted of MgAl₂O₄ (Figure 1).

Figure 1. X-ray diffraction (XRD) pattern of the accretion collected from the submerged entry nozzle (SEN).

An image of the collected accretion is shown in Figure 2. The XRD and EDS analyses indicated that the accretion was composed of MgO·Al₂O₃ spinel (dark phase) and CaO·6Al₂O₃ hexa-aluminate (gray phase). Therefore, the XRD and SEM/EDS analyses indicated that nozzle clogging was primarily caused by the presence of MgAl₂O₄ spinel inclusions. Moreover, if the accretions desquamated from the nozzle wall, they would be entrapped by the solidified shell and lead to a decreased quality.

Figure 2. Scanning electron microscopy (SEM) images of the accretion.

2.2. Types of MgO·Al₂O₃ Spinel Inclusions in 51CrV4 Spring Steel

The smelting process of 51CrV4 spring steel can be described as BOF→LF→RH→calcium treatment (soft blow)→slab continuous casting. During basic oxygen furnace (BOF) tapping, Al ingots were employed for preliminary deoxidation and V–Fe and Cr–Fe as the alloying elements. When the ladle reached the ladle furnace (LF) station, a high-basicity slag was used, and Al particles were added into liquid steel for final deoxidation. During the LF process, V–Fe and Cr–Fe were added to final composition adjustment. After degassing in Ruhstahl-Hausen vacuum degassing process (RH) for 20 min, the Ca–Si wire was fed to modify the inclusions and the removal of inclusions by soft blowing about 15 min was done. Finally, the liquid steel was sent to the continuous casting (CC) platform. The average compositions of 51CrV4 spring steel and refining slag are given in Table 2 and Table 3, respectively.

Table 2. Average composition of 51CrV4 spring steel (wt%).

C	Si	Mn	P	S	Al	Cr	V	Fe
0.51	0.23	0.94	0.01	0.008	0.024	1.02	0.16	balance

Table 3. Average composition of refining slag (wt%).

CaO	SiO2	MgO	FeO	MnO	Al2O3	CaO/Al2O3
50.19	8.2	7.49	0.35	0.18	33.59	1.49

Three types of MgO·Al₂O₃ spinel inclusions in the steel billet were evaluated via non-aqueous electrolysis: Independent MgO·Al₂O₃ inclusions (Figure 3a); modified MgO·Al₂O₃ spinel inclusions primarily containing Mg, Ca, Al, and O (Figure 3b), which was the dominant inclusion type; and modified spinel inclusions mainly consisting of Al, Ca, and O (Figure 3c). The spinel-type inclusions exhibited three-dimensional shapes with spherical morphologies, and the energy spectra given in Figure 3 are all for point A.

Figure 3. Images and energy spectra of MgO·Al₂O₃ spinel-type inclusions extracted by non-aqueous electrolysis: (a) Independent MgO·Al₂O₃ inclusions; (b) modified spinel inclusions containing Mg, Ca, Al, and O; (c) modified spinel inclusions consisting of Al, Ca, and O.

To assess the inclusions during the LF refining process, RH, and calcium treatment, respectively, the steel specimens taken with pail samplers were also investigated before and after LF and RH after polishing; the schematic diagram of sampling locations is given in Figure 4.

Figure 4. Schematic diagram of sampling locations.

The evolution of mean mass fraction of inclusions in the specimens is shown in Figure 5. Figure 5 indicated that no MgO·Al₂O₃ spinel inclusions were found before LF; MgO·Al₂O₃ inclusions containing small amounts of CaO began to form after LF. The number of MgO·Al₂O₃ spinel inclusions increased after RH, and the dominant inclusion type was MgO–Al₂O₃–CaO, which was attributed to the calcium treatment after RH. Therefore, the inclusions transformed through Al₂O₃→MgO·Al₂O₃→MgO–Al₂O₃–CaO during the refining process.

Figure 5. Evolution of mean mass fraction of inclusions.

2.3. Generation Mechanism of MgO·Al₂O₃ Inclusions

There are four possible Mg sources in liquid steel (Figure 6) [8,13,25,26,38,39,40]: (1) The reduction of MgO in slag by Al in liquid steel; (2) the reduction of MgO in slag by C under RH conditions; (3) the reduction of MgO in the refractory by Al in liquid steel; and (4) the reduction of MgO in the refractory by C under RH conditions.

Figure 6. Diagram showing the four potential sources of Mg in liquid steel.

The reduced Mg in liquid steel is oxidized into MgO and reacts with Al₂O₃ to generate MgO·Al₂O₃ inclusions via the following reactions:

$$2\left[\mathrm{Al}\right]+3(\mathrm{MgO})=({\mathrm{Al}}_2{\mathrm{O}}_3)+3\left[\mathrm{Mg}\right],$$

(1)

$$\left[\mathrm{C}\right]+(\mathrm{MgO})=\left[\mathrm{Mg}\right]+{\mathrm{CO}}_{(\mathrm{g})},$$

(2)

$$\left[\mathrm{Mg}\right]+\left[\mathrm{O}\right]=(\mathrm{MgO}),$$

(3)

and

$$(\mathrm{MgO})+({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{MgO}·{\mathrm{Al}}_2{\mathrm{O}}_3).$$

(4)

Therefore, to suppress the formation of MgAl₂O₄ inclusions during steel production, it is essential to study the generation mechanism of inclusions along with the factors influencing their formation. However, it is difficult to determine the activity of each constituent in a complex refining slag. The IMCT provides an effective way to obtain the activity of a complicated slag [41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]. In the IMCT, the defined mass action–concentration (MAC) is consistent with the classical concept of activity in the slag. The MAC model based on the IMCT has been successfully applied to describe the manganese distribution, phosphate capacity, sulfide capacity, and so on [41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56].

2.4. MAC Model of the Constitutional Units in Slag Systems

Based on the assumptions inherent in the IMCT, the dominant features of the MAC model for the activities of the structural units in the slag can be summarized as follows:

(1) The constitutional units in the slag consist of simple ions, ordinary molecules, and complicated molecules;

(2) Complex molecules are generated by the reactions of bonded ion couples and simple molecules under kinetic equilibrium;

(3) The activity of each constituent in the slag equals the MAC of the structural unit at the steelmaking temperature;

(4) The chemical reactions comply with the law of mass conservation.

The calculations were based on actual production involving CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag systems. The initial numbers of moles for each composition in 100g of CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag were $a=n_{\mathrm{CaO}}^0$, $b=n_{{\mathrm{SiO}}_2}^0$, $c=n_{{\mathrm{Al}}_2{\mathrm{O}}_3}^0$, $d=n_{\mathrm{MgO}}^0$, $e=n_{\mathrm{FeO}}^0$, and $f=n_{\mathrm{MnO}}^0$, respectively. The balanced mole number of each constituent unit in the slag was defined as $n_i$, and N_i denotes the MAC of each constitutional unit. The MAC is equivalent to the classical definition of activity based on the IMCT and can be obtained as follows:

$$N_i=\frac{n_i}{{{\displaystyle \sum }}^{\text{}}{n}_i}$$

(5)

where ${{\displaystyle \sum }}^{\text{}}{n}_i$ is the total balanced mole number of each constitutional unit.

According to the IMCT, at an elevated temperature, the slag system contains four simple ions (Ca²⁺, Mg²⁺, Fe²⁺, Mn²⁺, and O²⁻) and two ordinary molecules (${\mathrm{Al}}_2{\mathrm{O}}_3$ and ${\mathrm{SiO}}_2$). Based on the reported phase diagrams, 25 types of complex molecules can be generated at the steelmaking temperature [57,58]. The above mentioned structural units and their parameters are listed in Table 4.

Table 4. Parameters of the structural units in the slag system.

Items	Constitutional Units	Balanced Mole Number	Mass Action–Concentrations (MACs)
Simple cations and anions	${\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-}$	$n_1=n_{{\mathrm{Ca}}^{2+}}=n_{{\mathrm{O}}^{2-}}=n_{\mathrm{CaO}}$	$N_1=\frac{2n_1}{{\displaystyle \sum }{n}_i}=N_{\mathrm{CaO}}$
	${\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-}$	$n_4=n_{{\mathrm{Mg}}^{2+}}=n_{{\mathrm{O}}^{2-}}=n_{\mathrm{MgO}}$	$N_4=\frac{2n_4}{{\displaystyle \sum }{n}_i}=N_{\mathrm{MgO}}$
	${\mathrm{Fe}}^{2+}+{\mathrm{O}}^{2-}$	$n_5=n_{{\mathrm{Fe}}^{2+}}=n_{{\mathrm{O}}^{2-}}=n_{\mathrm{FeO}}$	$N_5=\frac{2n_5}{{\displaystyle \sum }{n}_i}=N_{\mathrm{FeO}}$
	${\mathrm{Mn}}^{2+}+{\mathrm{O}}^{2-}$	$n_6=n_{{\mathrm{Mn}}^{2+}}=n_{{\mathrm{O}}^{2-}}=n_{\mathrm{MnO}}$	$N_6=\frac{2n_6}{{\displaystyle \sum }{n}_i}=N_{\mathrm{MnO}}$
Simple molecules	${\mathrm{SiO}}_2$	$n_2=n_{{\mathrm{SiO}}_2}$	$N_2=\frac{n_2}{{\displaystyle \sum }{n}_i}=N_{{\mathrm{SiO}}_2}$
	${\mathrm{Al}}_2{\mathrm{O}}_3$	$n_3=n_{{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_3=\frac{n_3}{{\displaystyle \sum }{n}_i}=N_{{\mathrm{Al}}_2{\mathrm{O}}_3}$
Complex molecules	$\mathrm{CaO}·{\mathrm{SiO}}_2$	$n_7=n_{\mathrm{CaO}·{\mathrm{SiO}}_2}$	$N_7=\frac{n_7}{{\displaystyle \sum }{n}_i}=N_{\mathrm{CaO}·{\mathrm{SiO}}_2}$
	$3\mathrm{CaO}·2{\mathrm{SiO}}_2$	$n_8=n_{3\mathrm{CaO}·2{\mathrm{SiO}}_2}$	$N_8=\frac{n_8}{{\displaystyle \sum }{n}_i}=N_{3\mathrm{CaO}·2{\mathrm{SiO}}_2}$
	$2\mathrm{CaO}·{\mathrm{SiO}}_2$	$n_9=n_{2\mathrm{CaO}·{\mathrm{SiO}}_2}$	$N_9=\frac{n_9}{{\displaystyle \sum }{n}_i}=N_{2\mathrm{CaO}·{\mathrm{SiO}}_2}$
	$3\mathrm{CaO}·{\mathrm{SiO}}_2$	$n_{10}=n_{3\mathrm{CaO}·{\mathrm{SiO}}_2}$	$N_{10}=\frac{n_{10}}{{\displaystyle \sum }{n}_i}=N_{3\mathrm{CaO}·{\mathrm{SiO}}_2}$
	$3\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{11}=n_{3\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{11}=\frac{n_{11}}{{\displaystyle \sum }{n}_i}=N_{3\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$12\mathrm{CaO}·7{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{12}=n_{12\mathrm{CaO}·7{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{12}=\frac{n_{12}}{{\displaystyle \sum }{n}_i}=N_{12\mathrm{CaO}·7{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{13}=n_{\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{13}=\frac{n_{13}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$\mathrm{CaO}·2{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{14}=n_{\mathrm{CaO}·2{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{14}=\frac{n_{14}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{CaO}·2{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$\mathrm{CaO}·6{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{15}=n_{\mathrm{CaO}·6{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{15}=\frac{n_{15}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{CaO}·6{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$3{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2$	$n_{16}=n_{3{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2}$	$N_{16}=\frac{n_{16}}{{\displaystyle \sum }{n}_i}=N_{3{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2}$
	$2\mathrm{MgO}·{\mathrm{SiO}}_2$	$n_{17}=n_{2\mathrm{MgO}·{\mathrm{SiO}}_2}$	$N_{17}=\frac{n_{17}}{{\displaystyle \sum }{n}_i}=N_{2\mathrm{MgO}·{\mathrm{SiO}}_2}$
	$\mathrm{MgO}·{\mathrm{SiO}}_2$	$n_{18}=n_{\mathrm{MgO}·{\mathrm{SiO}}_2}$	$N_{18}=\frac{n_{18}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{MgO}·{\mathrm{SiO}}_2}$
	$\mathrm{MgO}·{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{19}=n_{\mathrm{MgO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{19}=\frac{n_{19}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{MgO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$2\mathrm{FeO}·{\mathrm{SiO}}_2$	$n_{20}=n_{2\mathrm{FeO}·{\mathrm{SiO}}_2}$	$N_{20}=\frac{n_{20}}{{\displaystyle \sum }{n}_i}=N_{2\mathrm{FeO}·{\mathrm{SiO}}_2}$
	$\mathrm{FeO}·{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{21}=n_{\mathrm{FeO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{21}=\frac{n_{21}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{FeO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$\mathrm{MnO}·{\mathrm{SiO}}_2$	$n_{22}=n_{\mathrm{MnO}·{\mathrm{SiO}}_2}$	$N_{22}=\frac{n_{22}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{MnO}·{\mathrm{SiO}}_2}$
	$2\mathrm{MnO}·{\mathrm{SiO}}_2$	$n_{23}=n_{2\mathrm{MnO}·{\mathrm{SiO}}_2}$	$N_{23}=\frac{n_{23}}{{\displaystyle \sum }{n}_i}=N_{2\mathrm{MnO}·{\mathrm{SiO}}_2}$
	$\mathrm{MnO}·{\mathrm{Al}}_2{\mathrm{O}}_3$	$n_{24}=n_{\mathrm{MnO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$	$N_{24}=\frac{n_{24}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{MnO}·{\mathrm{Al}}_2{\mathrm{O}}_3}$
	$2\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{\mathrm{SiO}}_2$	$n_{25}=n_{2\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{\mathrm{SiO}}_2}$	$N_{25}=\frac{n_{25}}{{\displaystyle \sum }{n}_i}=N_{2\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{\mathrm{SiO}}_2}$
	$\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2$	$n_{26}=n_{\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2}$	$N_{26}=\frac{n_{26}}{{\displaystyle \sum }{n}_i}=N_{\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2}$
	$2\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2$	$n_{27}=n_{2\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2}$	$N_{27}=\frac{n_{27}}{{\displaystyle \sum }{n}_i}=N_{2\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2}$
	$3\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2$	$n_{28}=n_{3\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2}$	$N_{28}=\frac{n_{28}}{{{\displaystyle \sum }}^{\text{}}{n}_i}=N_{3\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2}$
	$\mathrm{CaO}·\mathrm{MgO}·{\mathrm{SiO}}_2$	$n_{29}=n_{\mathrm{CaO}·\mathrm{MgO}·{\mathrm{SiO}}_2}$	$N_{29}=\frac{n_{29}}{{{\displaystyle \sum }}^{\text{}}{n}_i}=N_{\mathrm{CaO}·\mathrm{MgO}·{\mathrm{SiO}}_2}$
	$\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2$	$n_{30}=n_{\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2}$	$N_{30}=\frac{n_{30}}{{{\displaystyle \sum }}^{\text{}}{n}_i}=N_{\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2}$
	$2\mathrm{MgO}·2{\mathrm{Al}}_2{\mathrm{O}}_3·5{\mathrm{SiO}}_2$	$n_{31}=n_{2\mathrm{MgO}·2{\mathrm{Al}}_2{\mathrm{O}}_3·5{\mathrm{SiO}}_2}$	$N_{31}=\frac{n_{31}}{{{\displaystyle \sum }}^{\text{}}{n}_i}=N_{2\mathrm{MgO}·2{\mathrm{Al}}_2{\mathrm{O}}_3·5{\mathrm{SiO}}_2}$

The MACs for all the complex molecules can be determined using the reaction equilibrium constants $K_i$, $N_1(N_{\mathrm{CaO}})$, $N_2(N_{{\mathrm{SiO}}_2})$, $N_3(N_{{\mathrm{Al}}_2{\mathrm{O}}_3})$, $N_4(N_{\mathrm{MgO}})$, $N_5(N_{\mathrm{FeO}}),$ and $N_6(N_{\mathrm{MnO}})$, which are listed in Table 5.

Table 5. Reaction formulas, Gibbs free energies, and mass action–concentrations (MACs) [56,59,60,61,62,63,64].

Reaction Formulas	$\mathbf{\Delta }{\mathit{G}}^{\mathit{\theta }}/(\mathbf{J}\mathbf{·}\mathbf{m}\mathbf{o}{\mathbf{l}}^{-\mathbf{1}})$	MACs
$({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(\mathrm{CaO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-21757-36.819T$	$N_7=K_1{N}_1{N}_2$
$3({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+2({\mathrm{SiO}}_2)=(3\mathrm{CaO}·2{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-236972.9+9.6296T$	$N_8=K_2{N}_1^3{N}_2^2$
$2({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(2\mathrm{CaO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-102090-24.267T$	$N_9=K_3{N}_1^2{N}_2$
$3({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(3\mathrm{CaO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-118826-6.694T$	$N_{10}=K_4{N}_1^3{N}_2$
$3({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)=(3\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=-21757-29.288T$	$N_{11}=K_5{N}_1^3{N}_3$
$12({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+7({\mathrm{Al}}_2{\mathrm{O}}_3)=(12\mathrm{CaO}·7{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=617977-612.119T$	$N_{12}=K_6{N}_1^{12}{N}_3^7$
$({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=59413-59.413T$	$N_{13}=K_7{N}_1{N}_3$
$({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+2({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{CaO}·2{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=-16736-25.522T$	$N_{14}=K_8{N}_1{N}_3^2$
$({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+6({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{CaO}·6{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=-22594-31.798T$	$N_{15}=K_9{N}_1{N}_3^6$
$3({\mathrm{Al}}_2{\mathrm{O}}_3)+2({\mathrm{SiO}}_2)=(3{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-4351-10.46T$	$N_{16}=K_{10}{N}_2^2{N}_3^3$
$2({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(2\mathrm{MgO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-56902-3.347T$	$N_{17}=K_{11}{N}_2{N}_4^2$
$({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(\mathrm{MgO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=23849-29.706T$	$N_{18}=K_{12}{N}_2{N}_4$
$({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{MgO}·{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=-18828-6.276T$	$N_{19}=K_{13}{N}_3{N}_4$
$2({\mathrm{Fe}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(2\mathrm{FeO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=-9395-0.227T$	$N_{20}=K_{14}{N}_2{N}_5^2$
$({\mathrm{Fe}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{FeO}·{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=-59204+22.343T$	$N_{21}=K_{15}{N}_3{N}_5$
$({\mathrm{Mn}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(\mathrm{MnO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=38911-40.041T$	$N_{22}=K_{16}{N}_2{N}_6$
2$({\mathrm{Mn}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)=(2\mathrm{MnO}·{\mathrm{SiO}}_2)$	$\Delta G^{\theta }=36066-30.669T$	$N_{23}=K_{17}{N}_2{N}_6^2$
$({\mathrm{Mn}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)=(\mathrm{MnO}·{\mathrm{Al}}_2{\mathrm{O}}_3)$	$\Delta G^{\theta }=-45116+11.81T$	$N_{24}=K_{18}{N}_3{N}_6$
$\begin{array}{l}2({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)+({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(2\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-116315-38.911T$	$N_{25}=K_{19}{N}_1^2{N}_2{N}_3$
$\begin{array}{l}({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Al}}_2{\mathrm{O}}_3)+2({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-4148-73.638T$	$N_{26}=K_{20}{N}_1{N}_2^2{N}_3$
$\begin{array}{l}2({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+2({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(2\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-73638-63.597T$	$N_{27}=K_{21}{N}_1^2{N}_2^2{N}_4$
$\begin{array}{l}3({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+2({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(3\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-205016-31.798T$	$N_{28}=K_{22}{N}_1^3{N}_2^2{N}_4$
$\begin{array}{l}({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(\mathrm{CaO}·\mathrm{MgO}·{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-124683+3.766T$	$N_{29}=K_{23}{N}_1{N}_2{N}_4$
$\begin{array}{l}({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+2({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(\mathrm{CaO}·\mathrm{MgO}·2{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-80333-51.882T$	$N_{30}=K_{24}{N}_1{N}_2^2{N}_4$
$\begin{array}{l}2({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})+2({\mathrm{Al}}_2{\mathrm{O}}_3)+5({\mathrm{SiO}}_2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=(2\mathrm{MgO}·2{\mathrm{Al}}_2{\mathrm{O}}_3·5{\mathrm{SiO}}_2)\end{array}$	$\Delta G^{\theta }=-14422-14.808T$	$N_{31}=K_{25}{N}_2^5{N}_3^2{N}_4^2$

The mass conservation equations for the CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag equilibrated with bulk steel can be built based on the definitions of $n_i$ and $N_i$ for each structural unit as follows:

$$\begin{array}{c}a={\displaystyle \sum }{n}_i(0.5N_1+N_7+3N_8+2N_9+3N_{10}+3N_{11}+12N_{12}+N_{13}+N_{14}+N_{15}\\ +2N_{25}+N_{26}+2N_{27}+3N_{28}+N_{29}+N_{30})\end{array}$$

(6)

$$\begin{array}{c}b={\displaystyle \sum }{n}_i(N_2+N_7+2N_8+N_9+N_{10}+2N_{16}+N_{17}+N_{18}+N_{20}+N_{22}+N_{23}\\ +N_{25}+2N_{26}+2N_{27}+2N_{28}+N_{29}+2N_{30}+5N_{31})\end{array}$$

(7)

$$\begin{array}{c}c={\displaystyle \sum }{n}_i(N_3+N_{11}+7N_{12}+N_{13}+2N_{14}+6N_{15}+3N_{16}+N_{19}+N_{21}+N_{24}+N_{25}\\ +N_{26}+2N_{31})\end{array}$$

(8)

$$d={\displaystyle \sum }{n}_i(0.5N_4+2N_{17}+N_{18}+N_{19}+N_{27}+N_{28}+N_{29}+N_{30}+2N_{31})$$

(9)

$$e={\displaystyle \sum }{n}_i(0.5N_5+2N_{20}+N_{21})$$

(10)

and

$$f={\displaystyle \sum }{n}_i(0.5N_6+N_{22}+2N_{23}+N_{24}).$$

(11)

Based on the theory that the total MAC of each constitutional unit in CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag with a fixed amount is equal to unity, Equation (12) can be derived as follows:

$${\displaystyle \sum }_{i=1}^{31}{N}_i=1.$$

(12)

Equations (5)–(12) represent the MAC calculation model for each constitutional unit in CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag systems. The activity of each constituent in the slag at the refining temperature can then be obtained.

3. Results and Discussions

3.1. Effect of Slag Composition on Mg Content in Liquid Steel

After final deoxidation with Al, the dissolved Mg is supplied by the reduction of MgO in slag by dissolved Al via the following reaction [65]:

$$2\left[\mathrm{Al}\right]+3{(\mathrm{MgO})}_{\mathrm{s}}={({\mathrm{Al}}_2{\mathrm{O}}_3)}_{\mathrm{s}}+3\left[\mathrm{Mg}\right],\Delta G^0=296752.4+21.69T(\frac{\mathrm{J}}{\mathrm{mol}}).$$

(13)

The equilibrium constant K for the above process is given by

$$K=\frac{(a_{{\mathrm{Al}}_2{\mathrm{O}}_3,\mathrm{slag}}·a_{\mathrm{Mg}}^3)}{(a_{\mathrm{MgO},\mathrm{slag}}^3·a_{\mathrm{Al}}^2)}=\frac{(a_{{\mathrm{Al}}_2{\mathrm{O}}_3,\mathrm{slag}}·f_{\mathrm{Mg}}^3·{[\%\mathrm{Mg}]}^3)}{(a_{\mathrm{MgO},\mathrm{slag}}^3·f_{\mathrm{Al}}^2·[\%\mathrm{Al}{]}^2)}=\exp (\frac{-\Delta G^0}{RT})$$

(14)

where $a_{\mathrm{MgO},\mathrm{slag}}$ and $a_{{\mathrm{Al}}_2{\mathrm{O}}_3,\mathrm{slag}}$ are the activities of MgO and Al₂O₃ in slag relative to the pure solid state, respectively; $a_{\mathrm{Mg}}$ and $a_{\mathrm{Al}}$ are the activities of Mg and Al in liquid steel relative to a 1% mass concentration, respectively; and $f_{\mathrm{Mg}}$ and $f_{\mathrm{Al}}$ are the activity coefficients of Mg and Al in molten steel, respectively. R is the ideal gas constant, whose value is 8.314 J/(mol·K).

The interaction coefficients $e_i^j$ are given in Table 6. The relationship between the activity coefficient $f_i$ and temperature can be described as follows [66]:

$$\lg f_i(T)=(\frac{2538}{T}-0.355)\lg f_i(1873\mathrm{K})$$

(15)

where

$$\lg f_i(1873\mathrm{K})={\displaystyle \sum }{e}_i^j\left[\%j\right].$$

(16)

Table 6. Interaction coefficients for bulk steel at 1873 K [29,58].

${\mathit{e}}_{\mathit{i}}^{\mathit{j}}$	C	Si	Mn	P	S	Al	Cr	V
C	0.14	0.08	−0.012	0.051	0.046	0.043	−0.024	−0.077
Mg	−0.24	−0.09	--	--	−1.38	−0.12	0.05	--
Al	0.091	0.0056	0.0065	0.033	0.030	0.045	0.012	0.06

By substituting the values of $f_{\mathrm{Mg}}$ and $f_{\mathrm{Al}}$ at 1853 K (0.781 and 1.198, respectively) into Equation (14), the effect of the slag composition on the content of Mg at 1853 K is obtained as follows:

$$\left[\%\mathrm{Mg}\right]=1.44\times {10}^{-3.17}{N}_{\mathrm{MgO}}{(\frac{{\left[\%\mathrm{Al}\right]}^2}{N_{{\mathrm{Al}}_2{\mathrm{O}}_3}})}^{\frac{1}{3}}.$$

(17)

Based on the constituents of refining slag shown in Table 3, the compositions of MgO, FeO, and MnO were fixed at 7.5 wt%, 0.35 wt%, and 0.2 wt%, respectively, in subsequent calculations.

Equation (17) gives the thermodynamic model of MgO in slag reduced by Al. Based on the MAC model, N_MgO and N_Al2O3 at various basicities and CaO/Al₂O₃ ratios were calculated, and the relationship between Al and Mg content was obtained (Figure 7). The content of Mg in liquid steel increased dramatically with increasing Al content (Figure 7a,b). When the CaO/Al₂O₃ ratio was fixed at 1.5, and the Al content remained the same, the Mg content increased slightly with increasing basicity, and the increasing trend was enhanced when the Al content increased (Figure 7a). When the basicity (B) was fixed at 6, the Mg content was clearly affected by the CaO/Al₂O₃ ratio; a higher CaO/Al₂O₃ ratio in slag corresponded to a higher Mg content in liquid steel (Figure 7b). This suggests that the effect of slag on liquid steel became stronger as the basicity and CaO/Al₂O₃ ratio increased.

Figure 7. Al–Mg equilibria at various basicities and CaO/Al₂O₃ratiosin the slag: (a) Effect of basicities at a fixed CaO/Al₂O₃ ratio; (b) effect of CaO/Al₂O₃ ratios at a fixed basicity.

In industrial production, the CaO/Al₂O₃ ratio of the refining slag was 1.49, the content of acid-soluble aluminum was 0.024 wt%, and the basicity was 6.12. Based on the IMCT, the calculated equilibrium Mg was about 0.82 ppm, which was lower than the measured value 1.4 ppm. It is because that the effect of the lining has not been taken into account, and this will be discussed in the next section.

3.2. Effect of Lining on the Mg Content in Liquid Steel

Currently, MgO is a common component in refractory materials. When the bulk steel has a high Al content, the MgO in the lining can be reduced, and can further lead to the generation of MgO·Al₂O₃ spinel inclusions. For the refractory, N_MgO = 1. According to Equation (17), the following thermodynamic model of MgO in the refractory reduced by Al can be obtained at T = 1853 K:

$$\left[\%\mathrm{Mg}\right]=1.44\times {10}^{-3.17}{(\frac{{\left[\%\mathrm{Al}\right]}^2}{N_{{\mathrm{Al}}_2{\mathrm{O}}_3}})}^{\frac{1}{3}}.$$

(18)

Based on Equation (18), the relationship between Mg and Al content was obtained (Figure 8). The influence of liquid steel on the refractory increases with an increasing content of Al, which leads to the supply of Mg, and the increasing trend is closely related to the slag compositions, especially the CaO/Al₂O₃ ratio, as shown in Figure 8b. For a fixed Al content, the Mg content is higher when the effect of the slag is considered compared to when this effect is ignored. This is attributed to the fact that the slag can absorb Al₂O₃ inclusions, and its ability to absorb inclusions increases with increasing basicity, resulting in an increased Mg content (Figure 8a).

Figure 8. Al–Mg equilibria at various basicities and CaO/Al₂O₃ ratios in the lining: (a) Effect of basicities at a fixed CaO/Al₂O₃ ratio; (b) effect of CaO/Al₂O₃ ratios at a fixed basicity.

According to the calculation result based on the IMCT, in industrial production, the equilibrium Mg content was 3.2 ppm. Although the real balance is not reached, it indicated that the MgO-based refractory has a greater potential to supply more Mg into liquid steel than refining slag, which has been verified by Liu [31]. Due to the simultaneous effect of slag and refractory, the Mg content in bulk steel has the enough chance to reach 1.4 ppm. Based on the reported phase stability diagram of Al₂O₃, MgO·Al₂O₃, and MgO [16,17,24,67], and calculated stability diagram of Mg–Al–O system in liquid steel [13,68], the [Mg%] and [Al%] mainly existed in the spinel generation zone, which is the dominating reason for the generation of MgO·Al₂O₃ inclusions. It shows a good agreement with the fact that No MgO·Al₂O₃ spinel inclusions were found before LF, and the MgO·Al₂O₃ inclusions began to occur during LF process (Figure 5). In order to verify the model at real equilibrium conditions, the laboratory experiment will be carried out in the future work.

3.3. Effect of C on the Mg Content Under RH Conditions

The reduction of MgO by C under RH conditions can be written as the following [69]:

$$(\mathrm{MgO})+\left[\mathrm{C}\right]=\left[\mathrm{Mg}\right]+{\mathrm{CO}}_{(\mathrm{g})},\Delta G^0=722976.29-281.59T (\frac{\mathrm{J}}{\mathrm{mol}}),$$

(19)

with

$$K=\frac{P_{\mathrm{CO}}·a_{\mathrm{Mg}}}{a_{\mathrm{MgO}}·a_{\mathrm{C}}}=\frac{f_{\mathrm{Mg}}·\left[\%\mathrm{Mg}\right]·P_{\mathrm{CO}}}{f_{\mathrm{C}}·\left[\%\mathrm{C}\right]·N_{\mathrm{MgO}}}.$$

(20)

Substituting $f_{\mathrm{C}}$ = 1.107, $f_{\mathrm{Mg}}$ = 0.781, and [%C] = 0.51 into Equation (20) gives the following formula for slag at 1853 K:

$$\left[\%\mathrm{Mg}\right]=0.72\times {10}^{-5.67}\frac{N_{\mathrm{MgO}}}{P_{\mathrm{CO}}}.$$

(21)

For the refractory, N_MgO = 1, which gives,

$$\left[\%\mathrm{Mg}\right]=0.72\times {10}^{-5.67}\frac{1}{P_{\mathrm{CO}}}$$

(22)

where P_CO is the pressure of CO. Equations (21) and (22) represent the theoretical models for the reduction of MgO by C under RH conditions. Based on the IMCT, the effect of C on Mg content under RH conditions at different P_CO values was obtained. The content of Mg increases dramatically with decreasing P_CO, when C reduces the MgO in slag or lining, and the reduction of MgO in the lining is more crucial. When log(P_CO/Pa) reached 3.7 (i.e., P_CO ≈ 5066.25 Pa), [%Mg] was about 0. Therefore, when the CO pressure was sufficiently high, the reduction of MgO in the slag or lining was insignificant. Figure 9 shows the effects of basicity and the CaO/Al₂O₃ ratio in the slag on the Mg content. For a fixed CO pressure, the effect of basicity and the CaO/Al₂O₃ ratio on Mg resulting from the reduction of MgO by C in the slag can be ignored.

Figure 9. Effects of C on Mg content under RH conditions at different P_CO: (a) Effect of basicities at a fixed CaO/Al₂O₃ ratio; (b) effect of CaO/Al₂O₃ ratios at a fixed basicity.

In actual production, the P_CO was about 67 Pa. In this case, the Mg content balanced with lining and slag can reach up to 17 ppm and 5 ppm, respectively, based on the IMCT. Therefore, the supply of Mg into bulk steel under RH conditions is more crucial. In this study, the number of MgO·Al₂O₃ spinel inclusions and the mass fraction of MgO in MgO·Al₂O₃ spinel inclusions (Figure 5) increased after RH. These were attributed to the fact that, under RH conditions, the MgO in the slag or lining was partly reduced by C to generate MgO·Al₂O₃ inclusions; on the other hand, the excess Mg can also combine with MgO·Al₂O₃ to increase the mass fraction of MgO in MgO·Al₂O₃ inclusions. The trend of the model calculation is in agreement with the industrial test results. After Ca treatment, some of the inclusions were not modified and existed as independent spherical MgO·Al₂O₃ inclusions, while others were partly modified (Figure 3). To inhibit the formation of undesirable MgO·Al₂O₃ spinel inclusions, the pressure of CO could be adjusted to decrease inclusion generation. Furthermore, the appropriate application of Ca treatment can ensure that MgO·Al₂O₃ spinel inclusions are completely modified into liquid MgO–Al₂O₃–CaO-type inclusions.

4. Conclusions

The causes of nozzle clogging during casting and the existent forms of MgO·Al₂O₃ spinel inclusions in the steel billet were investigated. Based on the IMCT, the MAC model of CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag was developed, and the generation mechanism of MgO·Al₂O₃ inclusions, along with the influential factors, were clarified. The conclusions of the present study are as follows:

• The XRD and SEM/EDS analyses indicated that the nozzle clogging for 51CrV4 spring steel production was primarily due to the presence of MgAl₂O₄ spinel inclusions;
• Three types of MgO·Al₂O₃ spinel inclusions were observed in steel billets by non-aqueous electrolysis: Pure MgO·Al₂O₃ inclusions; modified MgO·Al₂O₃ spinel inclusions containing Mg, Al, Ca, and O, which was the dominant inclusion type; and modified spinel inclusions primarily containing Al, Ca, and O. The assessment of the inclusions in the specimens before and after LF and RH indicated that the inclusions transformed through Al₂O₃→MgO·Al₂O₃→MgO–Al₂O₃–CaO during the refining process;
• The generation mechanism of MgO·Al₂O₃ inclusions in 51CrV4 spring steel refined by CaO–SiO₂–Al₂O₃–MgO–FeO–MnO slag was evaluated based on the IMCT combined with industrial results. The effects of slag composition, refractory, and RH conditions on the content of Mg in liquid steel were determined. Model calculation results indicated that the Mg content increased with an increasing basicity, CaO/Al₂O₃ ratio, and Al content during LF, with the CaO/Al₂O₃ ratio being the most critical factor. In contrast, under RH conditions, the effects of basicity and the CaO/Al₂O₃ ratio were insignificant, and the partial pressure of CO was the dominant factor.