Atomic Ionic-scale Mechanism on Inclusion Modification by Calcium Treatment in the Electroslag Remelting Process Based on Ion and Molecule Coexistence Theory and Molecular Dynamics Simulation

Abstract

In the course of industrial electroslag remelting (ESR), large-size Ca–Al–Mg–O nonmetallic inclusions were prone to form in 4Cr13 die steels and will deteriorate mechanical properties and service life seriously. In order to reveal the underlying mechanism, this work delves into the origins of Ca–Al–Mg–O inclusions in 4Cr13 die steel, establishing a correlation between inclusion characteristics and ESR slag composition. Utilizing molecular dynamics simulations, this work examines the CaO–Al₂O₃–CaF₂–SiO₂–MgO slag system, analyzing slag microstructure and the mean square displacement of Ca²⁺ ions. Combining the ion and molecule coexistence theory (IMCT), it was demonstrated that the key factor determining the total calcium (T.Ca) content and large-size Ca–Al–Mg–O inclusions in ESR steel is the concentration of free Ca²⁺ ions in the slag. In addition, a model for calculating free Ca²⁺ ions concentration in slag has been formulated based on IMCT. This model elucidates the influence of CaF₂ and CaO on the concentration of free Ca²⁺ ions in slag. The empirical data facilitated the development of a modified slag composition with reduced CaF₂ content, aiming to lower the T.Ca content in steel and reduce the quantity and size of Ca–Al–Mg–O inclusions. These hypotheses have been verified through a series of laboratory and industrial trials. This is crucial for optimizing the ESR slag composition and enhancing the metallurgical quality of ESR steels.

1. Introduction

ESR is a sophisticated metallurgical process that effectively removes non-metallic inclusions from electrodes and improves the solidification structure of the steel,^1,2) positioning it as a leading method for producing special steel. 4Cr13 is a plastic die steel. Due to the requirements of the final product applications, this steel is expected to have better polishing properties. Consequently, it is critical to control the quantity and size of inclusions during the smelting process. The sporadic emergence of D and Ds inclusions, predominantly composed of Ca–Al–Mg–O, in 4Cr13 die steel from a factory has drawn our attention. D and Ds inclusions are typically spherical oxides. D inclusions usually have a maximum diameter ranging from 3 to 13 μm, while Ds inclusions have a maximum diameter exceeding 13 μm. Actually, D and Ds inclusions composed of Ca–Al–Mg–O are characterized by lower melting points than other nonmetallic inclusions,^3,4,5) often existing as liquid state in the liquid steel. Compared to solid inclusions, liquid inclusions exhibit a smaller wetting angle with liquid steel,^6,7) thus significantly increasing the difficulty of their removal.

The role of slag in the ESR process is crucial for the removal and modification of inclusions. Different slags exhibit various influences on the composition, size, and quantity of inclusions within ESR steel ingots. Previous research indicated that the interaction between inclusions and slag during the ESR process essentially reaches the equilibrium state. Consequently, the composition of the inclusions tends to approach the composition of the slag.^10,11,12) The slag-steel interaction modulates the composition of inclusions in electrode, altering their melting point, surface tension, and other physicochemical characteristics, which consequently influence the quantity and size of inclusions in ESR ingot. These findings have been robustly demonstrated in previous investigations.^13,14) Previous studies indicated that the Ca–Al–Mg–O inclusions in ESR ingots were mainly caused by the “calcium treatment” of MgO·Al₂O₃ and Al₂O₃ inclusions, which are intrinsic to the electrodes.^8,9) Therefore, the T.Ca content in the ESR ingot is a critical factor influencing the inclusions of Ca–Al–Mg–O in the ESR ingot. However, previous research primarily focus on the impact of slag on the characters of Al, Ti and Mg elements in ESR ingots,^15,16,17) with comparatively limited research dedicated to the relationship between slag and T.Ca content in ESR ingots. The mechanism on the relationship between calcium treatment and slag composition in the ESR process was still unclear.

In this investigation, by means of molecular dynamics simulations, we have probed into the intricate microstructure of molten slag and tracked the movement of various ions. Specifically, we quantitatively assessed this movement by calculating the mean square displacement (MSD) of the Ca²⁺ ions in different slags. This approach was inspired by the ion and molecule coexistence theory, considering the concentration of free Ca²⁺ ions in the slag is a crucial factor that influences both T.Ca content and large-size Ca–Al–Mg–O inclusions in 4Cr13 ESR ingot. Also, we built a computational model that could accurately quantify the Ca²⁺ ions concentration in the slag. Based on this model, we have formulated novel slags containing less CaF₂ to decrease T.Ca content and large-size Ca–Al–Mg–O inclusions. This theoretical framework was demonstrated to be reliable based on laboratory and industrial results. This work shed light on the ionic-scale mechanism inclusion modification by calcium treatment in the ESR process and provides a methodology for precise control of T.Ca content in ESR steel, thus decreasing the large-size Ca–Al–Mg–O inclusions in ESR steel.

2. Materials and Methods

2.1. Experiments and Materials

The composition of 4Cr13 die steel utilized in this study is shown in Table 1. The ingot was produced by the following steel making process: Electric Arc Furnace (EAF) → Ladle Furnace (LF) → Vacuum Degassing (VD) → Uphill Casting → Electroslag Remelting (ESR). The ESR furnace was equipped with a water-cooled mold of 750 mm diameter, corresponding to 5-ton ingot production. Following ESR, the ingot was forged into a slab with 300 × 800 mm cross section. For the purpose of inclusion assessment, specimens with dimensions of 20 × 10 × 10 mm³ were extracted from the core of both slab and electrode, in alignment with the NADCA # 207-2016 criteria. The inclusions were characterized and quantified using scanning electron microscope (FEI Apero-2C) and automated particle explorer (Phenom Particle-X).

Table 1. Chemical composition of 4Cr13 steel (mass%).

C	Si	Mn	Cr	Ni	V	S	P
0.393	1.04	0.61	13.47	0.21	0.29	0.003	0.013

In the laboratory experiment, four slags with different compositions (shown in Table 2) were chosen for a slag-steel equilibrium experiment. The process entailed housing 500 g of 4Cr13 die steel within a MgO crucible, which was then situated within a graphite crucible inside a MoSi₂ furnace. We incorporated a molybdenum sheet with a thickness of 0.2 mm onto the inner surface of the upper section of the MgO crucible, which is in contact with the slag. This addition was intended to mitigate any potential interactions between the crucible material and the slag. An oxidation-restrictive atmosphere was achieved by evacuating air from the setup and backfilling with Ar gas. Upon reaching a temperature of 1873 K, pre-melted slag was introduced, and the system was sustained at this thermal state for 40 minutes prior to the initiation of cooling. The ingot was subsequently extracted, with sampling deliberately concentrated on the core region to circumvent surface impurities. The T.Ca content of the sample was detected by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) analysis.

Table 2. The compositions of various slags used in the experiment (mass%).

mass%	CaO	CaF2	SiO2	Al2O3	MgO
A01	20	40	7	30	3
A02	30	40	0	30	0
A03	0	65	0	30	5
A04	0	70	0	30	0

2.2. Molecular Dynamics Simulation

To elucidate the microstructure of molten slag and track the movement of ions in different slags, molecular dynamics simulation was conducted on the slags listed in Table 2. During molecular dynamics simulation, the Newtonian equations of motion for every particle in the system are defined based on statistical mechanics. Solving these equations facilitates the determination of particle trajectories upon the attainment of dynamic equilibrium. Subsequent to reaching this state, it becomes feasible to evaluate the transport characteristics of the constituent elements within the slag system.

In the MD simulation, the approximation of the Buckingham form¹⁸⁾ was used as the pair potential, as shown in Eq. (1). U_ij is the atomic pair potential, q_i is the number of charges carried by particles, ε₀ is the dielectric constant, r_ij is the distance between particles i and j, and A_ij, ρ_ij, C_ij is the atomic potential parameter. Related research has obtained its specific values. The specific parameter values can be found in Table 3.^19,20,21,22)

  

$${\text{U}}_{\text{ij}}(r)=\frac{{\text{q}}_{\text{i}}{\text{q}}_{\text{j}}}{4\pi {\epsilon }_0{r}_{ij}}+A_{ij}exp\left(-\frac{r_{ij}}{{\rho }_{ij}}\right)-\frac{C_{ij}}{r_{ij}^6}$$(1)

Table 3. Potential parameters for BHM potential function.

	Aij (eV)	ρij (Å)	Cij (eV·Å6)
Si–Si	2163.320	0.16	0
Si–Ca	26674.680	0.16	0
Si–Mg	5489.810	0.16	0
Si–Al	2990.000	0.16	0
Si–O	62821.410	0.165	0
Si–F	43406.000	0.165	0
Ca–Ca	329193.320	0.16	4.3369
Ca–Mg	67720.910	0.16	0.8674
Ca–Al	36918.570	0.16	0
Ca–O	718136.080	0.165	8.67
Ca–F	496191.600	0.165	8.67
Mg–Mg	13931.400	0.16	0.1735
Mg–Al	7600.000	0.16	0
Mg–O	154984.640	0.165	1.7347
Mg–F	107085.519	0.165	1.7347
Al–Al	4142.149	0.16	0
Al–O	86057.580	0.165	0
Al–F	59481.584	0.165	0
O–O	1497693.500	0.17	17.34
O–F	1046135.400	0.17	17.34
F–F	730722.800	0.17	17.34
Mg–F	107085.519	0.165	1.7347

For computational analysis, three-dimensional periodic boundary conditions were imposed on fundamental cells containing approximately 5000 atoms, with the precise atom count detailed in Table 4. The long-range Coulombic forces were calculated using the Ewald summation method²³⁾ with an uncertainty of 0.01%. The fundamental cell is configured as a cubic lattice with each edge measuring 0.4 nm. The simulation step size is 2fs. The entire simulation was conducted under a constant atmospheric pressure of 101 kPa. At the commencement of the simulation, the system was subjected to a high temperature of 4273 K for 10000 steps to ensure thorough mixing and to mitigate any influence from the initial atomic arrangement. The system temperature was then methodically reduced to 1873 K over a span of 20000 steps. Following the achievement of equilibrium, the system underwent an additional relaxation phase for 50000 steps. Data collection ensued over the course of 100000 time steps at the equilibrated temperature of 1873 K, providing the basis for the simulated results.

Table 4. Atomic number of slag samples.

Name	Ca	F	O	Al	Mg	Si	Total
A01	1030	1214	1833	697	88	138	5000
A02	1284	1256	1738	721	0	0	4999
A03	987	1974	1194	698	147	0	5001
A04	1077	2155	1061	707	0	0	5000

3. Results and Discussion

3.1. Statistical Analysis on Inclusions in Electrode and Steel

Figure 1 illustrates the statistical distribution of inclusions in the ESR ingot and the electrode. The results reveal a shift towards larger inclusion in the ESR ingot relative to the electrode, alongside a higher calcium content in the inclusions of ESR ingot. Notably, inclusions surpassing 13 μm exhibit a calcium content exceeding 20%. Furthermore, inclusions with sizes exceeding 19 μm were found in the ESR ingot. In addition, some inclusions with a small volume and high calcium content should be the initial inclusions with adequate calcium treatment, while they have not yet undergone the collision and growth process. The SEM characterization results are illustrated in Fig. 2. It can be seen that there are primarily two types of inclusions in the electrodes. One type is small-size MgO·Al₂O₃ spinel, as depicted in Fig. 2(c). The other type is Al₂O₃ inclusions that are distributed in chains, as shown in Fig. 2(d). The inclusions in the electrodes are typically irregular in shape and small in size. After ESR using traditional high-fluorine slag (A04), Ca–Al–Mg–O inclusions become the predominant inclusions in the ESR ingot. Studies have determined that these Ca–Al–Mg–O inclusions primarily result from the calcium treatment of Mg–Al spinels or Al₂O₃, as described by Eqs. (2)²⁴⁾ and (3).^9,24) This modification process transforms the inclusions from irregular shapes to spherical or hemispherical, and it is accompanied by an increase in the size of the inclusions. Upon completion of the modification process, the Ca–Al–Mg–O inclusions are generally spherical, as shown in Fig. 2(b). In case of partial reactions, due to the incompatibility between MgO and CaO, such inclusions often retain MgO at their core and adopt spherical or hemispherical shapes, consistent with the observations in Fig. 2(a).

  

$$\begin{array}{l}\text{[Ca]}+(x\text{MgO}\cdot y{\text{Al}}_2{\text{O}}_3)(s)\\ =\text{CaO}\cdot (x-1)\text{MgO}\cdot y{\text{Al}}_2{\text{O}}_3(s)+[\text{Mg}]\end{array}$$(2)

  

$$[\text{Ca}]+(x+1/3){\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=\text{CaO}\cdot x{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}(\text{s)}+\text{2/3[Al]}$$(3)

Fig. 1. (a) Statistical results of inclusions component mole fractions in the electrode; (b) Statistical results of inclusions component mole fractions in the ESR ingots. (Online version in color.)

Fig. 2. Inclusions in electrode and ESR ingot: (a). Incomplete modification of Ca–Al–Mg–O inclusions in ESR ingot. (b). Completely modified Ca–Al–Mg–O inclusions in ESR ingot. (c). Al–Mg–O inclusions in electrode; (d). Al–O inclusions in electrode. (Online version in color.)

Undoubtedly, ESR can modify the composition and quantity of inclusions in ingot attributed to slag-steel reaction. Previous study²⁵⁾ has indicated that even marginal fluctuations of T.Ca content in the steel can markedly influence the quantity and sizes of calcium aluminate inclusions. Utilizing FactSage thermodynamic computation software, we investigated the variations in the quantity of calcium aluminate in steel at various T.Ca content, as illustrated in Fig. 3(a). The calculation results reveal an uptick in the quantity of calcium aluminate in steel with higher T.Ca content, in consistent with the findings of previous research.²⁵⁾ Given a fixed T.Ca content in the electrode, slag becomes the exclusive source of calcium in the ESR ingot, hence various slags exert a substantial impact on the T.Ca content in ESR ingots. The results of slag-steel equilibrium experiment have demonstrated this hypothesis, as depicted in Fig. 3(b).

Fig. 3. (a) Thermodynamic calculation results on the relationship between T.Ca content and calcium aluminate quantity in steel. (b) T.Ca content in sample after slag-steel equilibrium. (Online version in color.)

3.2. Mobility of Ca²⁺ Ions Based on Structure Analysis of Slag

To understand the effect of compositions on the mobility of Ca²⁺ ions in various slags, we utilized molecular dynamics simulation to investigate the structure of slag with various compositions shown in Table 2. The radial distribution function (RDF) profiles, which serve to quantify the atomic spatial correlations, were elaborated by Eq. (4).²⁶⁾ N_i and N_j represent the total number of particles i and j, V is volume of system and n_ij is the number of particles i and j within the range of r ± Δr/2. The RDF illustrates the likelihood of encountering atom pairs at a given radial distance and is interpreted as a measure of atomic pair density within a specified radial ambit. The RDF plots are depicted in Fig. 4, wherein a pronounced narrow peak denotes the atom pair with high stability. The RDF plots indicate that within the CaO–CaF₂–Al₂O₃–SiO₂–MgO quinary slag system, both Al–O and Si–O bonds exhibit robust peaks at smaller average bond distances, indicating their high stability. These observations suggest that Al–O and Si–O bonds predominantly constitute the framework structure of the slag. Instantaneous atomic snapshots have been captured during the simulations and presented in Fig. 5, demonstrating the existence of Al–O and Si–O framework.

  

$${\text{g}}_{\text{ij}}(r)=\frac{V}{N_i{N}_j}\sum \frac{n_{ij}\left(r-\frac{\mathrm{\Delta }r}{2},r+\frac{\mathrm{\Delta }r}{2}\right)}{4\pi r^2\mathrm{\Delta }r}$$(4)

  

$$\text{MSD}=\frac{1}{\text{N}}\left[{\sum }_{i=1}^N[r_i(t)-r_i(0){]}^2\right]$$(5)

Fig. 4. Radial distribution function of main particles in slag: (a) RDF of slag A01, (b) RDF of slag A02, (c) RDF of slag A03, (d) RDF of slag A04. (Online version in color.)

Fig. 5. An instantaneous snapshot of the atomic configuration in the equilibrium state of A01 slag: (a) Ca–Al–O–Si–F–Mg system; (b) Al–Si–O–F system; (c) Al–O system; (d) Si–O system. (Online version in color.)

Different from Al³⁺ and Si⁴⁺ ions, usually Ca²⁺ ions are identified as network modifiers and can readily diffuse via interstitial spaces within the slag framework. The mean square displacement (MSD) of ions calculated by Eq. (5)²⁷⁾ could provide quantitative evaluation on the mobility of ions. N_i is the total number of particles i, and r_i(t) is the position of the particle at time t. As illustrated in Fig. 6, the calculated MSD trajectories indicate the strongest diffusive abilities of F^– ions, likely attribute to its smaller atomic size and non-involvement in the slag’s network structure. Conversely, Al³⁺, O^2– and Si⁴⁺ ions exhibit diminished mobility and they frequently share similar MSD trajectories throughout the simulation because of strong Al–O and Si–O bonds. Notably, apart from F^– ions, Ca²⁺ ions also show strong mobility within the CaO–CaF₂–Al₂O₃–SiO₂–MgO quinary slag system. While, the slag compositions exert a remarkable influence on the MSD of Ca²⁺ ions.

Fig. 6. Atom mean square displacement of slag: (a) A01; (b) A02; (c) A03; (d) A04. (Online version in color.)

3.3. Calculation Model of Free Ca²⁺ Ions Concentrations in Molten Slag

According to Ions and Molecule Coexistence Theory (IMCT), the molten slag consists of simple ions, simple molecules and complex molecules, the latter of which are generally inert at the slag-steel interface. In molten slag, calcium is usually existing at both complex molecules and free Ca²⁺ions. In fact, the mean square displacement (MSD) calculations include all calcium ions within the slag. Due to the larger size of complex molecules, they are difficult to diffuse, resulting in very limited displacement distances for the Ca²⁺ ions in these complex molecules. In contrast, free Ca²⁺ ions with smaller sizes can diffuse easily via the interstices, making them the primary contributors to the mean square displacement of calcium ions in the slag. Therefore, complex molecules face challenges in diffusing across the slag-steel interface and participating into the slag-steel interaction. Consequently, the concentration of free Ca²⁺ ions in the slag is a crucial indicator for assessing its “calcium treatment” ability to transfer Ca²⁺ ions from molten slag into ESR ingot. To elucidate the influence of slag compositions on the T.Ca content in ESR ingots, we calculated the free Ca²⁺ ions concentration of slag in Table 2 based on IMCT.

IMCT assumes that metallurgical processes are governed by dynamic equilibrium, and slag compositions evolve in accordance with mass balance during reactions. The CaO–CaF₂–Al₂O₃–SiO₂–MgO slag system displays a range of potential structural units, as depicted in Table 5.^28,29) The activity coefficient of structural unit i is denoted by N_i, while n_i represents the molar quantity of each unit post-equilibrium. $\mathrm{\Delta }{G}_i^{\theta }$(j/mol) is the molar Gibbs free energy of possible chemical reactions within the slag, and the equilibrium constant for these reactions is K_i, as shown in Table 6.³⁰⁾ Leveraging the Gibbs-Helmholtz equation, the relationship between $\mathrm{\Delta }{G}_i^{\theta }$(j/mol) and K_i can be articulated as $\mathrm{\Delta }{G}_i^{\theta }$(j/mol)=−RTlnK_i. The second law of thermodynamics allows us to express $\mathrm{\Delta }{G}_i^{\theta }$(j/mol) as $\mathrm{\Delta }{G}_i^{\theta }$(j/mol)=ΔH−TΔS. Considering a specific reaction, the activity coefficient of a complex molecule is inferred from those of the constituent simple molecules and ions. Taking the (Ca²⁺+O²⁻)+(SiO₂)=(CaO·SiO₂) as an example, it can be expressed as $K_{\mathrm{c}1}=exp\left(-\frac{\mathrm{\Delta }{G}_{c1}^{\theta }}{RT}\right)$, N_c1=K_c1N₁N₄. The representations of other complex molecules are shown in Table 6.³⁰⁾ The molar numbers of CaO, MgO, CaF₂, SiO₂, and Al₂O₃ in 100 g of slag are expressed as $b_1=n{\prime }_{\text{CaO}}$, $b_2=n{\prime }_{\text{MgO}}$, $b_3=n{\prime }_{{\text{CaF}}_{\text{2}}}$, $b_4=n{\prime }_{{\text{SiO}}_2}$, $b_5=n{\prime }_{{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}}$, following equation is established from the mass balance between the structural units and the sum of the activity coefficients is 1:

  

$$\sum _i{N}_i=1$$(6)

  

$$\begin{array}{l}{b}_1=(0.5N_1+N_{\text{c1}}+N_{\text{c3}}+2N_{\text{c5}}+3N_{\text{c7}}+12N_{\text{c8}}+N_{\text{c9}}\\ +N_{\text{c10}}+3N_{\text{c12}}+3N_{\text{c13}}+N_{\text{c14}}+2N_{\text{c15}}+3N_{\text{c16}}+N_{\text{c17}}\\ +2N_{\text{c18}}+3N_{\text{c19}}+N_{\text{c20}}+11N_{\text{c21}}+3N_{\text{c22}})\sum n_i=n{\prime }_{\text{CaO}}\end{array}$$(7)

  

$$\begin{array}{l}{b}_2=(0.5N_2+N_{\text{c2}}+N_{\text{c4}}+2N_{\text{c6}}+3N_{\text{c14}}+N_{\text{c15}}+N_{\text{c16}}\\ \hspace{1em}+N_{\text{c20}}+2N_{\text{c23}})\sum n_i=n{\prime }_{\text{MgO}}\end{array}$$(8)

  

$$b_3=(1/3N_3+N_{\text{c21}}+N_{\text{c22}})\sum n_i=n{\prime }_{{\text{CaF}}_{\text{2}}}$$(9)

  

$$\begin{array}{l}{b}_4=(N_4+N_{\text{c1}}+N_{\text{c2}}+N_{\text{c5}}+2N_{\text{c11}}+N_{\text{c12}}+2N_{\text{c14}}+2N_{\text{c15}}\\ +2N_{\text{c16}}+2N_{\text{c17}}+N_{\text{c18}}+2N_{\text{c20}}+5N_{\text{c23}})\sum n_i=n{\prime }_{{\text{SiO}}_2}\end{array}$$(10)

  

$$\begin{array}{l}{b}_5=(N_5+N_{\text{c3}}+N_{\text{c4}}+N_{\text{c7}}+7N_{\text{c8}}+2N_{\text{c9}}+6N_{\text{c10}}+3N_{\text{c11}}\\ +N_{\text{c17}}+N_{\text{c18}}+3N_{\text{c19}}+7N_{\text{c21}}+2N_{\text{c23}})\sum n_i=n{\prime }_{{\text{Al}}_2{\text{O}}_3}\end{array}$$(11)

Table 5. Structural units in CaO–CaF₂–Al₂O₃–SiO₂–MgO slag system.

Structural unit classification	Structural units	Mole Number of Structural Unit ni (mol)	Mass action concentration of structural
Simple ions	Ca2++O2–	$n_1=n_{{\text{Ca}}^{\text{2+}}\text{,CaO}}=n_{{\text{O}}^{\text{2}-},\text{CaO}}=n_{\text{CaO}}$	$N_1=\frac{2n_1}{\sum n_i}=N_{\text{CaO}}$
	Mg2++O2–	$n_2=n_{{\text{Mg}}^{\text{2}+}\text{,MgO}}=n_{{\text{O}}^{\text{2}-},\text{MgO}}=n_{\text{MgO}}$	$N_2=\frac{2n_2}{\sum n_i}=N_{\text{MgO}}$
	Ca2++2F–	$n_3=n_{{\text{Ca}}^{\text{2}+}{\text{,CaF}}_2}=\frac{1}{2}{n}_{{\text{F}}^{-},{\text{CaF}}_2}=n_{{\text{CaF}}_2}$	$N_3=\frac{3n_3}{\sum n_i}=N_{{\text{CaF}}_2}$
Simple molecules	SiO2	$n_4=n_{{\text{SiO}}_2}$	$N_4=\frac{n_4}{\sum n_i}=N_{{\text{SiO}}_{\text{2}}}$
	Al2O3	$n_5=n_{{\text{Al}}_2{\text{O}}_3}$	$N_5=\frac{n_5}{\sum n_i}=N_{{\text{Al}}_2{\text{O}}_3}$
Complex molecules	CaO·SiO2	$n_{\text{c1}}=n_{\text{CaO}\cdot {\text{SiO}}_{\text{2}}}$	$N_{\text{c1}}=\frac{n_{\text{c1}}}{\sum n_i}=N_{\text{CaO}\cdot {\text{SiO}}_{\text{2}}}$
	MgO·SiO2	$n_{\text{c2}}=n_{\text{MgO}\cdot {\text{SiO}}_{\text{2}}}$	$N_{\text{c2}}=\frac{n_{\text{c2}}}{\sum n_i}=N_{\text{MgO}\cdot {\text{SiO}}_{\text{2}}}$
	CaO·Al2O3	$n_{\text{c3}}=n_{\text{CaO}\cdot {\text{Al}}_2{\text{O}}_3}$	$N_{\text{c3}}=\frac{n_{\text{c3}}}{\sum n_i}=N_{\text{CaO}\cdot {\text{Al}}_2{\text{O}}_3}$
	MgO·Al2O3	$n_{\text{c4}}=n_{\text{MgO}\cdot {\text{Al}}_2{\text{O}}_3}$	$N_{\text{c4}}=\frac{n_{\text{c4}}}{\sum n_i}=N_{\text{MgO}\cdot {\text{Al}}_2{\text{O}}_3}$
	2CaO·SiO2	$n_{\text{c5}}=n_{\text{2CaO}\cdot {\text{SiO}}_{\text{2}}}$	$N_{\text{c5}}=\frac{n_{\text{c5}}}{\sum n_i}=N_{\text{2CaO}\cdot {\text{SiO}}_{\text{2}}}$
	2MgO·SiO2	$n_{\text{c6}}=n_{\text{2MgO}\cdot {\text{SiO}}_{\text{2}}}$	$N_{\text{c6}}=\frac{n_{\text{c6}}}{\sum n_i}=N_{\text{2MgO}\cdot {\text{SiO}}_{\text{2}}}$
	3CaO·Al2O3	$n_{\text{c7}}=n_{\text{3CaO}\cdot {\text{Al}}_2{\text{O}}_3}$	$N_{\text{c7}}=\frac{n_{\text{c7}}}{\sum n_i}=N_{\text{3CaO}\cdot {\text{Al}}_2{\text{O}}_3}$
	12CaO·7Al2O3	$n_{\text{c8}}=n_{\text{12CaO}\cdot 7{\text{Al}}_2{\text{O}}_3}$	$N_{\text{c8}}=\frac{n_{\text{c8}}}{\sum n_i}=N_{\text{12CaO}\cdot 7{\text{Al}}_2{\text{O}}_3}$
	CaO·2Al2O3	$n_{\text{c9}}=n_{\text{CaO}\cdot 2{\text{Al}}_2{\text{O}}_3}$	$N_{\text{c9}}=\frac{n_{\text{c9}}}{\sum n_i}=N_{\text{CaO}\cdot 2{\text{Al}}_2{\text{O}}_3}$
	CaO·6Al2O3	$n_{\text{c10}}=n_{\text{CaO}\cdot 6{\text{Al}}_2{\text{O}}_3}$	$N_{\text{c10}}=\frac{n_{\text{c10}}}{\sum n_i}=N_{\text{CaO}\cdot 6{\text{Al}}_2{\text{O}}_3}$
	3Al2O3·2SiO2	$n_{\text{c11}}=n_{{\text{3Al}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{2SiO}}_{\text{2}}}$	$N_{\text{c11}}=\frac{n_{\text{c11}}}{\sum n_i}=N_{{\text{3Al}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{2SiO}}_{\text{2}}}$
	3CaO·SiO2	$n_{\text{c12}}=n_{\text{3CaO}\cdot {\text{SiO}}_{\text{2}}}$	$N_{\text{c12}}=\frac{n_{\text{c12}}}{\sum n_i}=N_{\text{3CaO}\cdot {\text{SiO}}_{\text{2}}}$
	3CaO·2SiO2	$n_{\text{c13}}=n_{\text{3CaO}\cdot 2{\text{SiO}}_{\text{2}}}$	$N_{\text{c13}}=\frac{n_{\text{c13}}}{\sum n_i}=N_{\text{3CaO}\cdot 2{\text{SiO}}_{\text{2}}}$
	CaO·MgO·2SiO2	$n_{\text{c14}}=n_{\text{CaO}\cdot \text{MgO}\cdot 2{\text{SiO}}_{\text{2}}}$	$N_{\text{c12}}=\frac{n_{\text{c14}}}{\sum n_i}=N_{\text{CaO}\cdot \text{MgO}\cdot 2{\text{SiO}}_{\text{2}}}$
	2CaO·MgO·2SiO2	$n_{\text{c15}}=n_{\text{2CaO}\cdot \text{MgO}\cdot 2{\text{SiO}}_{\text{2}}}$	$N_{\text{c15}}=\frac{n_{\text{c15}}}{\sum n_i}=N_{\text{2CaO}\cdot \text{MgO}\cdot 2{\text{SiO}}_{\text{2}}}$
	3CaO·MgO·2SiO2	$n_{\text{c16}}=n_{\text{3CaO}\cdot \text{MgO}\cdot 2{\text{SiO}}_{\text{2}}}$	$N_{\text{c16}}=\frac{n_{\text{c16}}}{\sum n_i}=N_{\text{3CaO}\cdot \text{MgO}\cdot 2{\text{SiO}}_{\text{2}}}$
	CaO·Al2O3·2SiO2	$n_{\text{c17}}=n_{\text{CaO}\cdot {\text{Al}}_2{\text{O}}_3\cdot 2{\text{SiO}}_2}$	$N_{{\text{C}}_{17}}=\frac{n_{{\text{C}}_{17}}}{\sum n_i}=N_{\text{CaO}\cdot {\text{Al}}_2{\text{O}}_{\text{3}}\cdot {\text{2SiO}}_2}$
	2CaO·Al2O3·SiO2	$n_{\text{c18}}=n_{\text{2CaO}\cdot {\text{Al}}_2{\text{O}}_3\cdot {\text{SiO}}_2}$	$N_{\text{c18}}=\frac{n_{\text{c18}}}{\sum n_i}=N_{\text{2CaO}\cdot {\text{Al}}_2{\text{O}}_3\cdot {\text{SiO}}_2}$
	3CaO·3Al2O3·CaF2	$n_{\text{c19}}=n_{\text{3CaO}\cdot 3{\text{Al}}_2{\text{O}}_3\cdot {\text{CaF}}_2}$	$N_{\text{c19}}=\frac{n_{\text{c18}}}{\sum n_i}=N_{\text{3CaO}\cdot 3{\text{Al}}_2{\text{O}}_3\cdot {\text{CaF}}_2}$
	CaO·MgO·SiO2	$n_{\text{c20}}=n_{\text{CaO}\cdot \text{MgO}\cdot {\text{SiO}}_{\text{2}}}$	$N_{\text{c20}}=\frac{n_{\text{c20}}}{\sum n_i}=N_{\text{CaO}\cdot \text{MgO}\cdot {\text{SiO}}_{\text{2}}}$
	11CaO·7Al2O3·CaF2	$n_{\text{c21}}=n_{\text{11CaO}\cdot 7{\text{Al}}_2{\text{O}}_3\cdot {\text{CaF}}_2}$	$N_{\text{c21}}=\frac{n_{\text{c21}}}{\sum n_i}=N_{\text{11CaO}\cdot 7{\text{Al}}_2{\text{O}}_3\cdot {\text{CaF}}_2}$
	3CaO·2SiO2·CaF2	$n_{\text{c22}}=n_{\text{3CaO}\cdot 2{\text{SiO}}_2\cdot {\text{CaF}}_2}$	$N_{\text{c22}}=\frac{n_{\text{c22}}}{\sum n_i}=N_{\text{3CaO}\cdot {\text{2SiO}}_{\text{2}}\cdot {\text{CaF}}_{\text{2}}}$
	2MgO·2Al2O3·5SiO2	$n_{\text{c23}}=n_{\text{2MgO}\cdot {\text{2Al}}_2{\text{O}}_3\cdot 5{\text{SiO}}_2}$	$N_{\text{c22}}=\frac{n_{\text{c23}}}{\sum n_i}=N_{\text{2MgO}\cdot 2{\text{Al}}_2{\text{O}}_3\cdot 5{\text{SiO}}_{\text{2}}}$

Table 6. Chemical reaction formulas to form complex molecules.

chemical reaction	$\mathrm{\Delta }{G}_i^{\theta }$ (J/mol)	Ni
(Ca2++O2−)+(SiO2)=(CaO·SiO2)	–21757–36.819T	NC1=KC1N1N4
(Mg2++O2−)+(SiO2)=(MgO·SiO2)	23849–29.706T	NC2=KC2N2N4
(Ca2++O2−)+(Al2O3)=(CaO·Al2O3)	59413–59.413T	NC3=KC3N3N5
(Mg2++O2−)+(Al2O3)=(MgO·Al2O3)	–18828–6.276T	NC4=KC4N2N5
2(Ca2++O2−)+(SiO2)=(2CaO·SiO2)	–102090–24.267T	$N_{\text{C5}}=K_{\text{C5}}{N}_1^2{N}_4$
2(Mg2++O2−)+(SiO2)=(2MgO·SiO2)	–56902–3.347T	$N_{\text{C6}}=K_{\text{C6}}{N}_2^2{N}_4$
3(Ca2++O2−)+(Al2O3)=(3CaO·Al2O3)	–21757–29.288T	$N_{\text{C7}}=K_{\text{C7}}{N}_1^3{N}_5$
12(Ca2++O2−)+7(Al2O3)=(12CaO·7Al2O3)	617977–612.119T	$N_{\text{C8}}=K_{\text{C8}}{N}_1^{12}{N}_5^7$
(Ca2++O2−)+2(Al2O3)=(CaO·2Al2O3)	–16736–25.22T	$N_{\text{C9}}=K_{\text{C9}}{N}_1{N}_5^2$
(Ca2++O2−)+6(Al2O3)=(CaO·6Al2O3)	–22594–31.798T	$N_{\text{C10}}=K_{\text{C10}}{N}_1{N}_5^6$
3(Al2O3)+2(SiO2)=(3Al2O3·2SiO2)	–4354.27–10.467T	$N_{\text{C11}}=K_{\text{C11}}{N}_5^3{N}_4^2$
3(Ca2++O2−)+(SiO2)=(3CaO·SiO2)	–118826–6.694T	$N_{\text{C12}}=K_{\text{C12}}{N}_1^3{N}_4$
(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(CaO·MgO·2SiO2)	–236814+9.623T	$N_{\text{C13}}=K_{\text{C13}}{N}_1{N}_2{N}_4^2$
2(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(2CaO·MgO·2SiO2)	–80333–51.882T	$N_{\text{C14}}=K_{\text{C14}}{N}_1^2{N}_2{N}_4^2$
2(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(2CaO·MgO·2SiO2)	–73638–63.597T	$N_{\text{C15}}=K_{\text{C15}}{N}_1^3{N}_2{N}_4^2$
3(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(3CaO·MgO·2SiO2)	–205016–31.798T	$N_{\text{C16}}=K_{\text{C16}}{N}_1^3{N}_2{N}_4^2$
(Ca2++O2−)+Al2O3+2(SiO2)=(CaO·Al2O3·2SiO2)	–4184–73.638T	$N_{\text{C17}}=K_{\text{C17}}{N}_1{N}_5{N}_4^2$
2(Ca2++O2−)+Al2O3+(SiO2)=(2CaO·Al2O3·SiO2)	–116315–38.911T	$N_{\text{C18}}=K_{\text{C18}}{N}_1^2{N}_5{N}_6$
3(Ca2++O2−)+3Al2O3+(Ca2++2F−)=(3CaO·3Al2O3·CaF2)	–44492–7315T	$N_{\text{C19}}=K_{\text{C19}}{N}_1^3{N}_5^3{N}_3$
(Ca2++O2−)+(Mg2++O2−)+(SiO2)=(CaO·MgO·SiO2)	–124683+3.766T	NC20=KC20N1N2N4
11(Ca2++O2−)+7Al2O3+(Ca2++2F−)=(11CaO·7Al2O3·CaF2)	–228760–155.8T	$N_{\text{C21}}=K_{\text{C21}}{N}_1^{11}{N}_5^7{N}_3$
3(Ca2++O2−)+2SiO2+(Ca2++2F−)=(3CaO·2SiO2·CaF2)	–114683+7.32T	$N_{\text{C22}}=K_{\text{C22}}{N}_1^3{N}_4^2{N}_3$
2(Mg2++O2−)+2Al2O3+5SiO2=(2MgO·2Al2O3·5SiO2)	–255180–8.2T	$N_{\text{C23}}=K_{\text{C23}}{N}_2^2{N}_5^2{N}_4^5$

These equations, solvable via Python 3.5-Scipy, allow for the determination of activity coefficients for all structural units in the quinary slag system. According to IMCT, calcium within CaF₂ and CaO is ionized in the molten state, except when part of larger molecules, permitting the calculation of free Ca²⁺ ions concentration using Eq. (12):

  

$$C_{{\text{Ca}}^{2+}}=(0.5N_1+1/3N_2)\sum _i{n}_i/100$$(12)

Based on calculation results, we plotted the variation in free Ca²⁺ ions concentration as a function of the CaO and CaF₂ content in A01 slag, as illustrated in Fig. 7. It is evident that the CaF₂ content in slag indicates much more remarkable effects on the free Ca²⁺ ions concentration, in comparison to CaO content in slag. In the CaO–CaF₂–Al₂O₃–SiO₂–MgO slag system, CaO would like to combine with Al₂O₃, SiO₂, and MgO to form 18 complex molecules, while CaF₂ forms only three molecules: 3CaO·3Al₂O₃·CaF₂, 11CaO·7Al₂O₃·CaF₂, and 3CaO·2SiO₂·CaF₂. Consequently, Ca²⁺ ions from CaO are more inclined to combine with other components to form complex molecules, whereas Ca²⁺ ions from CaF₂ tend to exist as free Ca²⁺ ions. Thus, lowering CaF₂ content would be effective method to decrease the free Ca²⁺ ions concentration in the slag.

Fig. 7. (a) Relationship between CaF₂ content and free Ca²⁺ ions concentration in slag; (b) Relationship between CaO content and free Ca²⁺ ions concentration in slag. (Online version in color.)

Furthermore, the calculated free Ca²⁺ ions concentrations and the mean square displacement of slags A01–A04 are presented in Fig. 8, indicating similar trend of free Ca²⁺ ions concentration and the mobility of Ca²⁺ ions within the slag. This also demonstrates the reliability of IMCT and MD simulation results. On this basis, it was proposed that slags with lower CaF₂ content typically have lower free Ca²⁺ ions concentrations and this would weaken the transfer of free Ca²⁺ ions from slag into liquid steel during the ESR process. In other words, when the T.Ca content in the electrode remains constant, using slags with lower CaF₂ content (such as A01) can effectively reduce the T.Ca content and control the large-size Ca–Al–Mg–O inclusions in the ESR ingot. Currently, there is no definitive conclusion regarding the transfer mechanism of Ca²⁺ from the slag pool to the molten pool. and we propose a possible transfer mechanism.

  

$$3\mathrm{C}{\mathrm{a}}^{2+}+6{\mathrm{F}}^{-}+\mathrm{A}\mathrm{l}=3\mathrm{C}\mathrm{a}+2\mathrm{A}\mathrm{l}{\mathrm{F}}_3\uparrow$$(13)

The reactions of Eq. (13) may occur in several distinct positions: at the electrode tip, at the interface between the slag and the metal, and during the process of metal droplets through the slag pool. The high concentration of Ca²⁺ ions in the slag contributes to an increased concentration of reactants for Eq. (13). Additionally, during the process, the gaseous product AlF₃ is removed by the protective gas in the controlled atmosphere, resulting in a lower concentration of products. These factors promote the reaction of Eq. (13). Moreover, as metal droplets pass through the molten pool, certain inclusions may come into contact with the slag. In such cases, Ca²⁺ from the slag can directly interact with these inclusions via an encapsulation mechanism.³¹⁾ Following this interaction, the inclusions may transport calcium into the molten pool. Collectively, these processes contribute to the increased calcium content in the electroslag remelting (ESR) ingots. A schematic representation of these reaction processes is provided in Fig. 9.

Fig. 8. The calculated concentration of Ca²⁺ ions based on IMCT and the mean square displacement of Ca²⁺ ions based on MD simulation. (Online version in color.)

Fig. 9. Schematic diagram of Ca²⁺ transfer during ESR. (Online version in color.)

3.4. Experimental Verification

To verify above theoretical analysis, industrial-scale ESR experiments using slags A01 and A04 have been performed. The results in Fig. 10 indicate that the typical inclusions in the ESR ingot utilizing slag A01 are dispersive small-size Ca–Al–O inclusions. Compared to the 4Cr13 die steel remelted with A04 slag, the 4Cr13 die steel produced with A01 slag exhibits a lower T.Ca content (6 ppm) and fewer inclusions with size exceeding 8 μm. The obtained results prove the usability of IMCT and MD simulation to evaluate the “calcium treatment” ability of slag in the ESR process. This deepens our understanding on the relationship between ionic-scale structure of slag and its effect on metallurgical quality of ESR steels.

Fig. 10. (a) Typical inclusions in ESR ingot using A01 slag (b) Mass fraction of T.Ca and the number density of inclusions in industrial ESR ingot. (Online version in color.)

4. Conclusion

Large-size Ca–Al–Mg–O nonmetallic inclusions were prone to form in 4Cr13 die steels in the ESR process using typical binary slag (70%CaF₂ + 30%Al₂O₃) because of its strong “calcium treatment” ability. IMCT and MD simulation have been combined to reveal the ionic-scale mechanism and try to establish the correlation between inclusion characteristics and slag structure. The following conclusions have been obtained.

(1) Various slags exert a markedly different influence on the T.Ca content and the inclusions characters in 4Cr13 ESR steels. The electrodes primarily contain MgO·Al₂O₃ and Al₂O₃ inclusions. Utilizing traditional high-fluoride slag (A04), during the ESR process, the predominant inclusions shift towards large-size Ca–Al–Mg–O inclusions because of strong “calcium treatment” and result in a higher T.Ca content in the ESR ingot than that of electrode.

(2) According to molecular dynamics simulation, within CaO–CaF₂–Al₂O₃–SiO₂–MgO quinary slag system, Al–O and Si–O atomic pairings form the basic structural framework, leading to the limited mobility of Al³⁺, Si⁴⁺ and O^2– ions in molten slag. While Ca²⁺ ions typically serve as modifiers within the framework, can easily diffuse across the interstitial spaces of the framework. The mobility of Ca²⁺ ions in various slags could be quantitively evaluated by means of mean square displacement (MSD).

(3) According to IMCT, in the molten CaO–CaF₂–Al₂O₃–SiO₂–MgO slag, Ca²⁺ ions predominantly exist in two forms: participate in large molecular complexes with other ions or as discrete free Ca²⁺ ions. Furthermore, Ca²⁺ ions from CaO are more inclined to combine with other components to form complex molecules, whereas Ca²⁺ ions from CaF₂ tend to exist as free Ca²⁺ ions. The free Ca²⁺ ions concentrations and the mean square displacement indicate similar trend with the change of slag composition.

(4) It was demonstrated that slags with lower CaF₂ content typically have lower free Ca²⁺ ions concentrations and this would weaken the transfer of free Ca²⁺ ions from slag into liquid steel during the ESR process. When the T.Ca content in the electrode remains constant, using slags with lower CaF₂ content (such as A01) can effectively reduce the T.Ca content and control the large-size Ca–Al–Mg–O inclusions in the ESR ingot.

Statement for Conflict of Interest

No potential conflict of interest was reported by the authors.

Acknowledgments

This work was supported by Science and Technology Research Projects of Liaoning Province (2023JH1/10400051), the Fundamental Research Funds for the Central Universities (N2425022), Program of Introducing Talents of Discipline to Universities (No.B21001), Joint Program of Science and Technology Plans in Liaoning Province (2023JH2/101700302) and Science and Technology Plans in Liaoning Province (2023012205-JH3/4600).

References

• 1)   R.S.E.  Schneider,  M.  Molnar,  S.  Gelder,  G.  Reiter and  C.  Martinez: Steel Res. Int., 89 (2018), 1800161. https://doi.org/10.1002/srin.201800161
• 2)   S.  Duan,  X.  Shi,  M.  Mao,  W.  Yang,  S.  Han,  H.  Guo and  J.  Guo: Sci. Rep., 8 (2018), 5232. https://doi.org/10.1038/s41598-018-23556-3
• 3)   G.  Yang,  X.  Wang,  F.  Huang,  D.  Yang,  P.  Wei and  X.  Hao: Metall. Mater. Trans. B., 46 (2015), 145. https://doi.org/10.1007/s11663-014-0181-1
• 4)   B.H.  Reis,  W.V.  Bielefeldt and  A.C.F.  Vilela: ISIJ Int., 54 (2014), 1584. https://doi.org/10.2355/isijinternational.54.1584
• 5)   T.  Yoshioka,  K.  Nakahata,  T.  Kawamura and  Y.  Ohba: ISIJ Int., 56 (2016), 1973. https://doi.org/10.2355/isijinternational.ISIJINT-2016-324
• 6)   C.B.  Shi,  S.J.  Wang,  J.  Li and  J. W.  Cho: J. Iron Steel Res. Int., 28 (2021), 1483. https://doi.org/10.1007/s42243-021-00700-4
• 7)   T.  Yoshioka,  T.  Ideguchi,  A.  Karasev,  Y.  Ohba and  P.G.  Jönsson: Steel Res. Int., 89 (2018), 1700287. https://doi.org/10.1002/srin.201700287
• 8)   S.  Yang,  Q.  Wang,  L.  Zhang,  J.  Li and  K.  Peaslee: Metall. Mater. Trans. B., 43 (2012), 731. https://doi.org/10.1007/s11663-012-9663-1
• 9)   G.  Ye,  P.  Jönsson and  T.  Lund: ISIJ Int., 36 (1996), S105. https://doi.org/10.2355/isijinternational.36.Suppl_S105
• 10)   D.  Hou,  D.Y.  Wang,  Z.H.  Jiang,  T.P.  Qu,  H.H.  Wang and  J.W.  Dong: Metall. Mater. Trans. B., 52 (2021), 478. https://doi.org/10.1007/s11663-020-02032-2
• 11)   B.  Jaka,  T.  Franc,  G.  Matjaž,  M.  Jožef,  P.  Bojan and  B.  Rok: J. Min. Metall. B., 54 (2017), 51. https://aseestant.ceon.rs/index.php/jmm/article/view/11225, (accessed 2024-04-25).
• 12)   Y.B.  Kang and  H.G.  Lee: ISIJ Int., 44 (2004), 1006. https://doi.org/10.2355/isijinternational.44.1006
• 13)   S.J.  Li,  G.G.  Cheng,  Z.Q.  Miao,  L.  Chen and  X.Y.  Jiang: Int. J. Miner. Metall. Mater., 26 (2019), 291. https://doi.org/10.1007/s12613-019-1737-5
• 14)   Y.W.  Dong,  Z.H.  Jiang,  Y.L.  Cao,  A.  Yu and  D.  Hou: Metall. Mater. Trans. B., 45 (2014), 1315. https://doi.org/10.1007/s11663-014-0070-7
• 15)   Z.H.  Jiang,  D.  Hou,  Y.W.  Dong,  Y.L.  Cao,  H.B.  Cao and  W.  Gong: Metall. Mater. Trans. B., 47 (2016), 1465. https://doi.org/10.1007/s11663-015-0530-8
• 16)   S.C.  Duan,  X.  Shi,  F.  Wang,  M.C.  Zhang,  Y.  Sun,  H.J.  Guo and  J.  Guo: Metall. Mater. Trans. B., 50 (2019), 3055. https://doi.org/10.1007/s11663-019-01665-2
• 17)   Y.  Kanbe,  H.  Todoroki,  Y.  Kobayashi and  K.  Shitogiden: ISIJ Int., 49 (2009), 837. https://doi.org/10.2355/isijinternational.49.837
• 18)   X.  Zhang,  C.  Liu and  M.  Jiang: Metall. Mater. Trans. B., 52 (2021), 2604. https://doi.org/10.1007/s11663-021-02184-9
• 19)   S.  He,  S.  Wang,  B.  Jia,  M.  Li,  Q.  Wang and  Q.  Wang: Metall. Mater. Trans. B., 50 (2019), 1503. https://doi.org/10.1007/s11663-019-01547-7
• 20)   H.  Fan,  R.  Wang,  Z.  Xu,  H.  Duan and  D.  Chen: J. Mater. Res. Technol., 15 (2021), 1046. https://doi.org/10.1016/j.jmrt.2021.08.032
• 21)   X.  Zhang,  C.  Liu and  M.  Jiang: ISIJ Int., 60 (2020), 2176. https://doi.org/10.2355/isijinternational.ISIJINT-2020-002
• 22)   K.  Li,  H.  Li,  C.  Jiang,  J.  Zhang,  Z.  Liu and  S.  Ren: Mol. Simulat., 46 (2020), 289. https://doi.org/10.1080/08927022.2019.1698739
• 23)   Y.  Min,  S.  Jiao,  P.  Guo,  F.  Chen and  C.  Liu: J. Non-Cryst. Solids., 628 (2024), 122843. https://doi.org/10.1016/j.jnoncrysol.2024.122843
• 24)   C.B.  Shi,  W.T.  Yu,  H.  Wang,  J.  Li and  M.  Jiang: Metall. Mater. Trans. B., 48 (2017), 146. https://doi.org/10.1007/s11663-016-0771-1
• 25)   Y.  Wang,  G.  Cheng,  S.  Li,  W.  Dai,  D.  Shang and  C.  Lu: ISIJ Int., 61 (2021), 1514. https://doi.org/10.2355/isijinternational.ISIJINT-2020-671
• 26)   J.  Liu,  Y.  Yu,  W.  Kong,  Q.  Wang,  Z.  He and  X.  Yang: J. Non-Cryst. Solids., 578 (2022), 121354. https://doi.org/10.1016/j.jnoncrysol.2021.121354
• 27)   H.  Sun,  J.  Yang,  R.  Zhang and  L.  Xu: J. Non-Cryst. Solids., 627 (2024), 122818. https://doi.org/10.1016/j.jnoncrysol.2023.122818
• 28)   Z.  Liu,  W.  Wu,  X.  Guo,  H.  Meng and  J.  Zhao: Iron Steel, 48 (2013), 34 (in Chinese). http://www.chinamet.cn/Jweb_gt/EN/Y2013/V48/I6/34 (accessed 2024.04.25)
• 29)   X.M.  Yang,  C.B.  Shi,  M.  Zhang and  J.  Zhang: Steel Res. Int., 83 (2012), 244. https://doi.org/10.1002/srin.201100233
• 30)   W.  Gong,  R.A.  Zhou,  P.F.  Wang,  Z. H.  Jiang and  X.  Geng: ISIJ Int., 62 (2022), 2255. https://doi.org/10.2355/isijinternational.ISIJINT-2022-158
• 31)   E.  Sjöqvist Persson,  A.V.  Karasev,  A.T.  Mitchell and  P.G.  Jönsson: Metals, 50 (2020), 50. https://doi.org/10.3390/met10121620