Front. Mater. Frontiers in Materials Front. Mater. 2296-8016 Frontiers Media S.A. 792714 10.3389/fmats.2021.792714 Materials Original Research The Establishment of Thermodynamic Model for Ti Bearing Steel-Slag Reaction and Discuss Zhao et al. Reaction Between Metal and Slag Zhao Mao-Guo 1 Wang Xu-Feng 1 Chen Gu-Jun 2 He Sheng-Ping 1 * 1 School of Materials Science and Engineering, Chongqing University, Chongqing, China 2 School of Materials Science and Engineering, Yangtze Normal University, Fuling, China

Edited by: Antonio Caggiano, Darmstadt University of Technology, Germany

Reviewed by: Il Sohn, Yonsei University, South Korea

Qifeng Shu, University of Oulu, Finland

 *Correspondence: Sheng-Ping He, heshp@cqu.edu.cn

This article was submitted to Structural Materials, a section of the journal Frontiers in Materials

 03 01 2022 2021 8 792714 11 10 2021 15 11 2021 Copyright © 2022 Zhao, Wang, Chen and He. 2022 Zhao, Wang, Chen and He

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A thermodynamic model for seven CaO-MgO-BaO-CaF2-SiO2-Al2O3-TiO2 ladle slags based on the Ion and Molecule Coexistence theory (IMCT) is establishment and validated by the experiment results at 1873K. The calculated activity of SiO2, Al2O3 and TiO2 in the slag can be approved by the experiment results and the IMCT model used in this study is reasonable. Then the influence factors such as the mass ratio of CaO to SiO2 (C/S ratio) ranging from 1 to 10, the mass ratio of CaO to Al2O3 (C/A ratio) ranging from 1 to 2.5, TiO2 content (wt pct) ranging from 0 to 30, BaO content (wt pct) ranging from 0 to 30 are investigated based on the thermodynamic calculating results. The raise of C/S ratio, TiO2 content and BaO content in the slag can increase the molar Gibbs energy change (ΔG) of Ti reacted with SiO2 and Al2O3 or Al reacted with SiO2. The effect of C/A ratio on the molar Gibbs energy change (ΔG) of Ti reacted with SiO2 and Al2O3 or Al reacted with SiO2 was less. Finally, the slag with higher C/S ratio and TiO2 content and appropriate BaO content can weaken the reaction between Ti and SiO2 or Al2O3 in the slag.

 thermodynamic model Ti-bearing steel slag IMCT ladel National Natural Science Foundation of China10.13039/501100001809 Introduction

TiC and TiN inclusion can be formed in the Ti bearing steel in the solidification process (Cavazos et al., 2011; Leban and Tisu, 2013), which can increase the strength of the final products, as the steel’s secondary phase (Huang et al., 2018). During the initial solidification period, the heterogeneous nucleation of delta ferrite could formed on the TiN inclusions and then the equiaxed fine-grained structure was generated (Fujimura et al., 2001). For this reason, the addition of titanium to the liquid steel in the ladle for improving properties has increased in recent years. Nevertheless the loss of Ti will persist in the ladle metallurgy process, mainly oxidized by the slag. Then the formed TiOx in the steel would reacted with Mg, Ca or Al2O3 in the steel and the complex inclusions such as MgAl2O4 spinal and MgO-TiOx spinal, surrounded by TiN and perovskite are formed. This would lead to the clogging of submerged nozzle and forming of surface defects on the steel products (Maddalena et al., 2000; Nunnington and Sutcliffe, 2001; Zheng et al., 2004). Thus, in order to obtain an optimal slag composition for the ladle refining of Al-killed and Ti bearing steel, it is important to investigate the reaction between slag and molten steel.

Kim et al. (1993) found that the SiO2 in the slag could oxidize the Titanium in the liquid steel. Park et al. (2004) also found that Aluminum and Titanium could be simultaneously oxidized by the SiO2 in the 14%CaO-35%Al2O3-10%MgO-%4SiO2 slag and the soluble oxygen was supersaturated during the course, particularly with respect to Al. Then the re-oxidation mechanism of Al and Ti in the liquid steel by SiO2 was depicted in Figure 1. It can be seen from Figure 1, the oxidation process of Al or Ti mainly include two ways, on the one hand, the Al or Ti in the metal reacted with the SiO2 in the slag directly; on the other hand, the SiO2 in the slag decomposed of Si and O, then they transferred to the liquid steel and oxidized the Al and Ti in the liquid steel. Park et al. (2009) also investigate the thermodynamic behavior of TiOx in the refining slag (CaO-SiO2-MgO-Al2O3-TiOx

The main mechanism for the re-oxidation of Ti and Al in metal.

-CaF2) equilibrated with Fe-11%Cr melts. They found that the equilibrium between silicon and titanium in steel melts and their oxides in the slags are theoretically expected and experimentally proved well. They also calculated the relationship between Aluminum and Titanium in the steel melts and their oxides in the slag. The slope of the line is 0.5, which is lower than 1. Therefore, they summarized that the activity coefficient of TiOx in the slag would be affected in the composition range investigated in their study. They also found that with the increase of (%SiO2)/(%SiO2+%Al2O3) in the slag, the activity coefficient of TiO2 gradually decreased. The attraction between TiO2 and SiO2 is greater than that between TiO2 and Al2O3 in the present slag system due to the electronegativity difference between each cation involved. The activity of TiO2 in the slag system containing 10% MgO shows a negative deviation from an ideality, while that in the CaO-SiO2-Al2O3-MgOsatd-CaF2 system is really close to the ideal behavior up to about x TiO 2 = 0.1 . This is mainly due to the relatively basic characteristic of TiO2.

Qian et al. (2014) found that when the TiO2 content in the slag reached to 8%, the oxidation of Ti in the Ti-stabilized stainless steel was minimum and the T. O (Total O in the steel) was constant with the time increase. They also found the influence of TiO2 adding to the slag on the oxidation rate change of Al has an opposite tendency compared with Ti. The activity change behavior of TiO2 in different TiO2 content slag, calculated by IMCT model, are in good agreement of the experiment results. Li and Cheng (2019) investigated the effect of the CaF2 contents in the CaO-SiO2- MgO-Al2O3-TiO2-CaF2 slag on the formation of inclusion in Ti-Stabilized 20Cr Stainless Steel. They found that with the increase of CaF2 content in the slag, the equilibrium content of Ti and Mg in the steel increased. When the CaF2 content in the slag changed from 0 to 9.57, the equilibrium content of Ti changed from 0.018 to 0.031% and the equilibrium content of Mg changed from 12ppm to 23ppm. Due to the increase of CaF2 content in the slag can decrease the lg ( a TiO 2 / a SiO 2 ) and lg ( a TiO 2 / a Al 2 O 3 2 / 3 ) , which would make the steel has higher Ti after the Slag-metal reaction reached to the equilibrium state. They suggested the optimal CaF2 content in the slag was 5–10%. Meanwhile they also investigated the dependence of the composition ratio of steel on the activity ratio of slag at different CaF2 contents, which was calculated by IMCT model, and the phenomena was found that the calculation results are consistent with the experimental results. Although the Ti could be oxidized by the SiO2 according to the literature (Kim et al., 1993)∼ (Li and Cheng, 2019), Ti would be oxidized by Al2O3 in other slags, such as ESR slag (Jiang et al., 2016). And they also obtained that clearly the calculated results by IMCT model are in good agreement with experimental results. Some previous reports found that the reaction between Ti and Al2O3 in the slag can also cause the loss of Ti in the steel (Bomberger and Froes, 1984; Carmack et al., 1996; Jiang, 2000; Li, 2010; Jiang et al., 2016).

According to the previous researches (Qian et al., 2014; Jiang et al., 2016; Li and Cheng, 2019), The IMCT model has been applied in CaO-SiO2-MgO-Al2O3-TiO2-CaF2 slag system successfully for Ti-bearing stainless steel and 825 alloy refining process. However, the CaO-SiO2-MgO-Al2O3-TiO2-CaF2-BaO slag for low alloy high Ti-bearing steel refining, has never been explored. Due to the adding of BaO in the ladle slag has a excellently ability for desulphurization (Gao et al., 2012), Therefore this study is mainly focused on the investigation of the reactive between CaO-SiO2-MgO-Al2O3-TiO2-CaF2-BaO slag and 0.361% Ti bearing steel (0.0361%Al) by use the thermodynamic model (IMCT model), which is needed to be approved by the experiment results.

 Thermodynamic Interaction for Metal-Slag

The composition of Al-killed and Ti-bearing steel used in this study was listed in Table 1. During the ladle metallurgy process, the reactions (1–3) between the liquid steel and slag would lead to the loss of Ti and Al in the steel (Qian et al., 2014; Li and Cheng, 2019). The slag composition assigned for this paper’s discussion section is shown in Table 2. [ Al ] + 3 4 ( SiO 2 ) = 3 4 [ Si ] + 1 2 ( Al 2 O 3 ) Reaction 1 K 1 = a S i 3 / 4 ⋅ a A l 2 O 3 1 / 2 a A l ⋅ a S i O 2 3 / 4 = f S i 3 / 4 ⋅ [ S i ] 3 / 4 ⋅ a A l 2 O 3 1 / 2 f A l ⋅ [ A l ] ⋅ a S i O 2 3 / 4 Δ G 1 0 = - 164575 + 26.8 T lg ( K 1 ) = 8596.75 T − 1.40 lg [ S i ] 3 / 4 [ A l ] = lg f A l f S i 3 4 + lg a S i O 2 3 / 4 a A l 2 O 3 1 / 2 + lg K 1 = lg f A l f S i 3 / 4 + lg a S i O 2 3 / 4 a A l 2 O 3 1 / 2 + 8596.75 T − 1.40 [ Ti ] + ( SiO 2 ) = [ Si ] + ( TiO 2 ) Reaction 2 K 2 = a S i ⋅ a T i O 2 a T i ⋅ a S i O 2 = f S i ⋅ [ S i ] ⋅ a T i O 2 f T i ⋅ [ T i ] ⋅ a S i O 2 Δ G 2 0 = - 3503.9 − 26.03 T lg ( K 2 ) = 183 T + 1.36 lg [ S i ] [ T i ] = lg f T i f S i + lg a S i O 2 a T i O 2 + lg K 2 = lg f T i f S i + lg a S i O 2 a T i O 2 + 183 T + 1.36 [ T i ] + 2 3 ( A l 2 O 3 ) = 4 3 [ A l ] + ( T i O 2 ) Reaction 3 K 3 = a A l 4 / 3 ⋅ a T i O 2 a T i ⋅ a A l 2 O 3 2 / 3 = f A l 4 / 3 ⋅ [ A l ] 4 / 3 ⋅ a T i O 2 f T i ⋅ [ T i ] ⋅ a A l 2 O 3 2 / 3 Δ G 3 0 = 225300 - 63.44 T lg ( K 3 ) = - 35300 T + 9.94 lg [ A l ] 4 / 3 [ T i ] = lg f T i f A l 4 / 3 + lg a A l 2 O 3 2 / 3 a T i O 2 + lg K 3 = lg f T i f A l 4 / 3 + lg a A l 2 O 3 2 / 3 a T i O 2 − 35300 T + 9.94

The chemical composition of Al-killed and Ti-bearing liquid steel, wt pct.

Steel C Al Mn Si P S Cr Mo Ni Ti N O
A 0.178 0.039 1.210 0.191 0.005 0.003 0.114 0.198 0.078 0.361 0.004 0.006

the design slag composition used for this paper’s discussion section.

Slag C/S ratio C/A ratio Al2O3(wt pct) BaO (wt pct) MgO(wt pct) CaF2(wt pct) TiO2(wt pct)
S1 1–10 - 25 0 6 5 5
S2 6–10 1–2.5 - 0 6 5 5
S3 6–10 1.7 - 0 6 5 0–30
S4 6–10 1.7 - 0–30 6 5 15–25

From Eqs. 1–12, K n is equilibrium constant of reaction (i); a M is the activity of element i in the liquid steel with respect to an infinite dilute of one mass% state and is calculated by Eq. 13; f M is the activity coefficient of solute element (M) with respect to an infinite dilute of one mass% state; and calculated by the classical Wagner formalism, as shown in Eq. 14. Where E M j was the first-interaction parameter and r M j was the second-interaction parameter (Hino, 2009), which are listed in Table 3. a M = f M × [ % M ] lg f M = ∑ i = C,Si,Mn,P,S,MO,Al,Ti,O ( ( e M i × [ % i ] ) + ( r M i × [ % i ] 2 ) + ( r M i , j × [ % i ] × [ % j ] ) ) r Al O,Al = − 0.021 − 13.87 T , r Al Al,O = 9.05

Interaction parameters used in this paper (Hino, 2009).

eij (rij) C Si Mn P S Mo Al Ti O
Al 0.091 0.056 0.035 0.033 0.035 - 0.038 0.004 -1.98 (39.82)
Si 0.180 0.132 0.002 0.110 0.056 2.36 -0.058 -0.013 -0.23
Ti 0.165 -0.025 -0.043 0.0064 -0.11 - 0.0037 0.048 -1.80 (-0.36)

In addition, a MO n is the activity of the MOn in the slag with respect to the pure solid state and its values can be calculated by different methods (Guo, 2006; Zhang, 2007), including molecular theory, ion theory, regular ionic solution model, Factsage software and IMCT model. Although the chemical properties can be reflected by the molecular theory, the structural of the slag can not be expressed. The ion theory thought, the charge particles were consisted in and the complex molecules was regarded as charged ion clusters. The thermodynamic data of BaO-TiO2 system (Barin, 1995; Lu and Jin, 2001; Ye, 2002; Cheng, 2010; Sahu et al., 2018) were not considered in the Factsage software (Bale et al., 2009). Therefore, it is necessary to established the IMCT model to calculate the activity of MOn in the slag due to its satisfying the essence of slag structure.

 IMCT Model Description Establishment of the IMCT Model for CaO-MgO-BaO-CaF<sub>2</sub>-SiO<sub>2</sub>-Al<sub>2</sub>O<sub>3</sub>-TiO<sub>2</sub> Slag

According to the IMCT hypotheses proposed by literature (Zaitsev et al., 1990; Li and Zhang, 2000; Zhang, 2004; Zhang, 2007; Yang et al., 2009) and phase diagrams (Eisenhüttenleute, 1995; Shukla, 2012; Boulay et al., 2014), there are 4 simple cation-anion couples, 3 simple molecules and 51 complex molecules in this model at 1800–1935K, as shown in Table 4. The mole fraction of theses studied slag’s components is assigned as a1 = ∑ n CaO , a2 = ∑ n MgO , a3 = ∑ n BaO , a4 = ∑ n CaF 2 , a5 = ∑ n SiO 2 ,a6 = ∑ n Al 2 O 3 ,a7 = ∑ n TiO 2 . The equilibrium mole numbers and mass action concentrations of all structural units in CaO-MgO-BaO-CaF2-SiO2-Al2O3-TiO2 slag are listed in Table 4. The chemical reaction equations of all structural units in CaO-MgO-BaO-CaF2-SiO2-Al2O3-TiO2 slag are summarized in Table 5. The standard molar Gibbs free energy changes Δ G i 0 and mass action concentrations expressed by Ki of this model’s complex molecules structural units are also listed in Table 5.

The kinds of structural units in this model, and their definition mole number and mass action concentration.

Item Structural units as ion couples or molecules Mole number of structure unit Mass action concentration of structural unit or ion couples
Simple cation and anion (Ca2++O2-) n 1 = 2 n C a O N 1 = n 1 / ∑ n i
(Mg2++O2-) n 2 = 2 n MgO N 2 = n 2 / ∑ n i
(Ba2++O2-) n 3 = 2 n B a O N 3 = n 3 / ∑ n i
(Ca2++2F−) n 4 = 3 n C a F 2 N 4 = n 4 / ∑ n i
Simple molecules SiO2 n 5 = n S i O 2 N 5 = n 5 / ∑ n i
Al2O3 n 6 = n A l 2 O 3 N 6 = n 6 / ∑ n i
TiO2 n 7 = n T i O 2 N 7 = n 7 / ∑ n i
Complex Molecules CaO·SiO2 n 8 N 8 = n 8 / ∑ n i
2CaO·SiO2 n 9 N 9 = n 9 / ∑ n i
3CaO·SiO2 n 10 N 10 = n 10 / ∑ n i
3Al2O3·2SiO2 n 11 N 11 = n 11 / ∑ n i
MgO·SiO2 n 12 N 12 = n 12 / ∑ n i
2MgO·SiO2 n 13 N 13 = n 13 / ∑ n i
2BaO·SiO2 n 14 N 14 = n 14 / ∑ n i
BaO·SiO2 n 15 N 15 = n 15 / ∑ n i
2BaO·3SiO2 n 16 N 16 = n 16 / ∑ n i
BaO·2SiO2 n 17 N 17 = n 17 / ∑ n i
CaO·6Al2O3 n 18 N 18 = n 18 / ∑ n i
CaO·2Al2O3 n 19 N 19 = n 19 / ∑ n i
CaO·Al2O3 n 20 N 20 = n 20 / ∑ n i
12CaO·7Al2O3 n 21 N 21 = n 21 / ∑ n i
3CaO·Al2O3 n 22 N 22 = n 22 / ∑ n i
MgO·Al2O3 n 23 N 23 = n 23 / ∑ n i
BaO·6Al2O3 n 24 N 24 = n 24 / ∑ n i
BaO·Al2O3 n 25 N 25 = n 25 / ∑ n i
3BaO·Al2O3 n 26 N 26 = n 26 / ∑ n i
Al2O3·TiO2 n 27 N 27 = n 27 / ∑ n i
CaO·TiO2 n 28 N 28 = n 28 / ∑ n i
3CaO·2TiO2 n 29 N 29 = n 29 / ∑ n i
4CaO·3TiO2 n 30 N 30 = n 30 / ∑ n i
2MgO·TiO2 n 31 N 31 = n 31 / ∑ n i
MgO·TiO2 n 32 N 32 = n 32 / ∑ n i
MgO·2TiO2 n 33 N 33 = n 33 / ∑ n i
2BaO·9TiO2 n 34 N 34 = n 34 / ∑ n i
BaO·4TiO2 n 35 N 35 = n 35 / ∑ n i
4BaO·13TiO2 n 36 N 36 = n 36 / ∑ n i
BaO·TiO2 n 37 N 37 = n 37 / ∑ n i
2BaO·TiO2 n 38 N 38 = n 38 / ∑ n i
2CaO·Al2O3·SiO2 n 39 N 39 = n 39 / ∑ n i
CaO·Al2O3·2SiO2 n 40 N 40 = n 40 / ∑ n i
CaO·SiO2·TiO2 n 41 N 41 = n 41 / ∑ n i
CaO·MgO·SiO2 n 42 N 42 = n 42 / ∑ n i
CaO·MgO·2SiO2 n 43 N 43 = n 43 / ∑ n i
2CaO·MgO·2SiO2 n 44 N 44 = n 44 / ∑ n i
3CaO·MgO·2SiO2 n 45 N 45 = n 45 / ∑ n i
2MgO·2Al2O3·5SiO2 n 46 N 46 = n 46 / ∑ n i
3CaO·3Al2O3·CaF2 n 47 N 47 = n 47 / ∑ n i
11CaO·7Al2O3·CaF2 n 48 N 48 = n 48 / ∑ n i
3CaO·2SiO2·CaF2 n 49 N 49 = n 49 / ∑ n i
BaO·3CaO·2SiO2 n 50 N 50 = n 50 / ∑ n i
2BaO·4CaO·3SiO2 n 51 N 51 = n 51 / ∑ n i
BaO·2CaO·4Al2O3 n 52 N 52 = n 52 / ∑ n i
3BaO·CaO·Al2O3 n 53 N 53 = n 53 / ∑ n i
BaO·Al2O3·2SiO2 n 54 N 54 = n 54 / ∑ n i
BaO·4SiO2·TiO2 n 55 N 55 = n 55 / ∑ n i
BaO·3SiO2·TiO2 n 56 N 56 = n 56 / ∑ n i
BaO·2SiO2·TiO2 n 57 N 57 = n 57 / ∑ n i
2BaO·2SiO2·TiO2 n 58 N 58 = n 58 / ∑ n i

The chemical reaction formulas of complex molecular in this model, and their Standard Molar Gibbs Free Energy Changes and Mass Action Concentrations of complex molecules expressed by Ki.

Reactions Δ G i 0 N i References
(Ca2++O2-)+(SiO2)=(CaO·SiO2) -81416-10.498T N 8 = K 1 N 1 N 5 Zhang, (2007)
2(Ca2++O2-)+(SiO2)=(2CaO·SiO2) -160431 + 4.160T N 9 = K 2 N 1 2 N 5 Zhang, (2007)
3(Ca2++O2-)+(SiO2)=(3CaO·SiO2) -92366-23.027T N 10 = K 3 N 1 3 N 5 Zhang, (2007)
3(Al2O3)+2(SiO2)=(3Al2O3·2SiO2) 8589.9-17.39T N 11 = K 4 N 6 3 N 5 2 Zhang, (2007)
(Mg2++O2-)+(SiO2)=(MgO·SiO2) 43400-40.T N 12 = K 5 N 2 N 5 Zhang, (2007)
2(Mg2++O2-)+(SiO2)=(2MgO·SiO2) -77403 + 11.0T N 13 = K 6 N 2 2 N 5 Zhang, (2007)
(Ba2++O2-)+(SiO2)=(BaO·SiO2) -148950-6.28T N 14 = K 7 N 3 N 5 Bale et al. (2009)
2(Ba2++O2-)+(SiO2)=(2BaO·SiO2) -259826-5.86T N 15 = K 8 N 3 2 N 5 Bale et al. (2009)
2(Ba2++O2-)+3(SiO2)=(2BaO·3SiO2) -337580 + 7.03T N 16 = K 9 N 3 2 N 5 3 Bale et al. (2009)
(Ba2++O2-)+2(SiO2)=(BaO·2SiO2) -169365 + 1.49T N 17 = K 10 N 3 N 5 2 Bale et al. (2009)
(Ca2++O2-)+6(Al2O3)=(CaO·6Al2O3) -17430-37.2T N 18 = K 11 N 1 N 6 6 Zhang, (2007)
(Ca2++O2-)+2(Al2O3)=(CaO·2Al2O3) -16400-26.8T N 19 = K 12 N 1 N 6 2 Zhang, (2007)
(Ca2++O2-)+(Al2O3)=(CaO·Al2O3) -18120-18.62T N 20 = K 13 N 1 N 6 Zhang, (2007)
12(Ca2++O2-)+7(Al2O3)=(12CaO·7Al2O3) -86100-205.1T N 21 = K 14 N 1 12 N 6 7 Zhang, (2007)
3(Ca2++O2-)+(Al2O3)=(3CaO·Al2O3) -17000-32.0T N 22 = K 15 N 1 3 N 6 Zhang, (2007)
(Mg2++O2-)+(Al2O3)=(MgO·Al2O3) -35530-2.09T N 23 = K 16 N 2 N 6 Zhang, (2007)
(Ba2++O2-)+6(Al2O3)=(BaO·6Al2O3) -126813-24.29T N 24 = K 17 N 3 N 6 6 Bale et al. (2009)
(Ba2++O2-)+(Al2O3)=(BaO·Al2O3) -124264-6.694T N 25 = K 18 N 3 N 6 Bale et al. (2009)
3(Ba2++O2-)+(Al2O3)=(3BaO·Al2O3) -212125-18.83T N 26 = K 19 N 3 3 N 6 Bale et al. (2009)
(Al2O3)+(TiO2)=(Al2O3·TiO2) -25271 + 3.93T N 27 = K 20 N 6 N 7 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
(Ca2++O2-)+(TiO2)=(CaO·TiO2) -74392-10.13T N 28 = K 21 N 1 N 7 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
3(Ca2++O2-)+2(TiO2)=(3CaO·2TiO2) -148365-24.14T N 29 = K 22 N 1 3 N 7 2 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
4(Ca2++O2-)+3(TiO2)=(4CaO·3TiO2) -292880-17.57T N 30 = K 23 N 1 4 N 7 3 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
2(Mg2++O2-)+(TiO2)=(2MgO·TiO2) -25500 + 1.26T N 31 = K 24 N 2 2 N 7 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
(Mg2++O2-)+(TiO2)=(MgO·TiO2) -26400 + 3.14T N 32 = K 25 N 2 N 7 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
(Mg2++O2-)+2(TiO2)=(MgO·2TiO2) -27600 + 0.63T N 33 = K 26 N 2 N 7 2 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
2(Ba2++O2-)+9(TiO2)=(2BaO·9TiO2) -406802 + 40.53T N 34 = K 27 N 3 2 N 7 9 Lu and Jin, (2001)
(Ba2++O2-)+4(TiO2)=(BaO·4TiO2) -194314 + 14.87T N 35 = K 28 N 3 N 7 4 Lu and Jin, (2001)
4(Ba2++O2-)+13(TiO2)=(4BaO·13TiO2) -74326 + 49.07T N 36 = K 29 N 3 4 N 7 13 Lu and Jin, (2001)
(Ba2++O2-)+(TiO2)=(BaO·TiO2) -166210 + 14.14T N 37 = K 30 N 3 N 7 Yang et al. (2009)
2(Ba2++O2-)+(TiO2)=(2BaO·TiO2) -202924-T N 38 = K 31 N 3 2 N 7 Yang et al. (2009)
2(Ca2++O2-)+(Al2O3)+(SiO2)=(2CaO·Al2O3·SiO2) -17092 + 8.778T N 39 = K 32 N 1 2 N 6 N 5 Zhang, (2007)
(Ca2++O2-)+(Al2O3)+2(SiO2)=(CaO·Al2O3·2SiO2) 28006-74.195T N 40 = K 33 N 1 N 6 N 5 2 Zhang, (2007)
(Ca2++O2-)+(SiO2)+(TiO2)=(CaO·SiO2·TiO2) -114683 + 7.32T N 41 = K 34 N 1 N 5 N 7 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
(Ca2++O2-)+(Mg2++O2-)+(SiO2)=(CaO·MgO·SiO2) -124766 + 3.768T N 42 = K 35 N 1 N 2 N 5 Zhang, (2007)
(Ca2++O2-)+(Mg2++O2-)+2(SiO2)=(CaO·MgO·2SiO2) -80387-51.916T N 43 = K 36 N 1 N 2 N 5 2 Zhang, (2007)
2(Ca2++O2-)+(Mg2++O2-)+2(SiO2)=(2CaO·MgO·2SiO2) -73668-63.639T N 44 = K 37 N 1 2 N 2 N 5 2 Zhang, (2007)
3(Ca2++O2-)+(Mg2++O2-)+2(SiO2)=(3CaO·MgO·2SiO2) -315469 + 24.786T N 45 = K 38 N 1 3 N 2 N 5 2 Zhang, (2007)
2(Mg2++O2-)+2(Al2O3)+5(SiO2)=(2MgO·2Al2O3·5SiO2) -14422-14.808T N 46 = K 39 N 2 2 N 6 2 N 5 5 Zhang, (2007)
3(Ca2++O2-)+3(Al2O3)+(Ca2++2F−)=(3CaO·3Al2O3·CaF2) -44492-73.15T N 47 = K 40 N 1 3 N 6 3 N 4 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
11(Ca2++O2-)+7(Al2O3)+(Ca2++2F−)=(11CaO·7Al2O3·CaF2) -228760-155.8T N 48 = K 41 N 1 11 N 6 7 N 4 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
3(Ca2++O2-)+2(SiO2)+(Ca2++2F−)=(3CaO·2SiO2·CaF2) -255180-8.2T N 49 = K 42 N 1 3 N 5 2 N 4 Cheng, (2010); Jiang et al. (2016); Li and Cheng, (2019)
(Ba2++O2-)+3(Ca2++O2-)+2(SiO2)=(BaO·3CaO·2SiO2) -376298 + 8.75T N 50 = K 43 N 3 N 1 3 N 5 2 Bale et al. (2009)
2(Ba2++O2-)+4(Ca2++O2-)+3(SiO2)=(2BaO·4CaO·3SiO2) -533550 + 269.29T N 51 = K 44 N 3 N 1 4 N 5 3 Bale et al. (2009)
(Ba2++O2-)+2(Ca2++O2-)+4(Al2O3)=(BaO·2CaO·4Al2O3) -157255-85.11T N 52 = K 45 N 3 N 1 2 N 6 4 Bale et al. (2009)
3(Ba2++O2-)+(Ca2++O2-)+(Al2O3)=(3BaO·CaO·Al2O3) -139905-42.19T N 53 = K 46 N 3 3 N 1 N 6 Bale et al. (2009)
(Ba2++O2-)+(Al2O3)+2(SiO2)=(BaO·Al2O3·2SiO2) -198791-38.49T N 54 = K 47 N 3 N 6 N 5 2 Bale et al. (2009)
(Ba2++O2-)+4(SiO2)+(TiO2)=(BaO·4SiO2·TiO2) -291417-72.91T N 55 = K 48 N 3 N 5 4 N 7 Barin, (1995); Ye, (2002); Sahu et al. (2018)
(Ba2++O2-)+3(SiO2)+(TiO2)=(BaO·3SiO2·TiO2) -284166-55.31T N 56 = K 49 N 3 N 5 3 N 7 Barin, (1995); Ye, (2002); Sahu et al. (2018)
(Ba2++O2-)+2(SiO2)+(TiO2)=(BaO·2SiO2·TiO2) -249835-59.44T N 57 = K 50 N 3 N 5 2 N 7 Barin, (1995); Ye, (2002); Sahu et al. (2018)
2(Ba2++O2-)+2(SiO2)+(TiO2)=(2BaO·2SiO2·TiO2) -458720-7.14T N 58 = K 51 N 3 2 N 5 2 N 7 Barin, (1995); Ye, (2002); Sahu et al. (2018)

According to the definition of mass action concentration and mass conservation, Eq. 15–22 can be obtained, which could be solved with Matlab. a 1 = ( 0.5 N 1 + N 8 + 2 N 9 + 3 N 10 + N 18 + N 19 + N 20 + 12 N 21 + 3 N 22 + N 28 + 3 N 29 + 4 N 30 + 2 N 39 + N 40 + N 41 + N 42 + N 43 + 2 N 44 + 3 N 45 + 3 N 47 + 11 N 48 + 3 N 49 ) ∑ n i = ∑ n C a O a 2 = ( 0.5 N 2 + N 12 + 2 N 13 + N 23 + 2 N 31 + N 32 + N 33 + N 42 + N 43 + N 44 + N 45 + 2 N 46 ) ∑ n i = ∑ n M g O a 3 = ( 0.5 N 3 + N 14 + 2 N 15 + 2 N 16 + N 17 + N 24 + N 25 + 3 N 26 + 2 N 34 + N 35 + 4 N 36 + N 37 + 2 N 38 + N 50 + 2 N 51 + N 52 + 3 N 53 + N 54 + N 55 + N 56 + N 57 + 2 N 58 ) ∑ n i = ∑ n B a O a 4 = ( 1 3 N 4 + N 47 + N 48 + N 49 ) ∑ n i = ∑ n C a F 2 a 5 = ( N 5 + N 8 + N 9 + N 10 + 2 N 11 + N 12 + N 13 + N 14 + N 15 + 3 N 16 + 2 N 17 + N 39 + 2 N 40 + N 41 + N 42 + 2 N 43 + 2 N 44 + 2 N 45 + 5 N 46 + 2 N 49 + 2 N 50 + 3 N 51 + 2 N 54 + 4 N 55 + 3 N 56 + 2 N 57 + 2 N 58 ) ∑ n i = ∑ n S i O 2 a 6 = ( N 6 + 3 N 11 + 6 N 18 + 2 N 19 + N 20 + 7 N 21 + N 22 + N 23 + 6 N 24 + N 25 + N 26 + N 27 + N 39 + N 40 + 2 N 46 + 3 N 47 + 7 N 48 + 4 N 52 + N 53 + N 54 ) ∑ n i = ∑ n A l 2 O 3 a 7 = ( N 7 + N 27 + N 28 + 2 N 29 + 3 N 30 + N 31 + N 32 + 2 N 33 + 9 N 34 + 4 N 35 + 13 N 36 + N 37 + N 38 + N 41 + N 55 + N 56 + N 57 + N 58 ) ∑ n i = ∑ n T i O 2 N 1 + N 2 + N 3 + N 4 + N 5 + N 6 + ...... + N 54 + N 55 + N 56 + N 57 = ∑ N i = 1

The Validation of IMCT Model for CaO-MgO-BaO-CaF<sub>2</sub>-SiO<sub>2</sub>-Al<sub>2</sub>O<sub>3</sub>-TiO<sub>2</sub> Slag

According to Eq. 8 and Eq. 12, the dependence of the activity ratio of steel on the activity ratio of slag at different experiment heats, which includes JY. Li’s (Li and Cheng, 2019), ZH. Jian’s (Jiang et al., 2016),J.Park’s (Park et al., 2008) and this author’s experiment data, are shown in Figure 2. The activity of SiO2, Al2O3 and TiO2 in the slag are calculated by the IMCT model according to the final slag composition and the activity of Si, Al and Ti in the steel calculated by Eq. 13 and Eq. 14 according to the final steel composition, at different experiment heats. The magenta lines in this Figure are derived From Eq. 8 and Eq. 12. And we can find that the activity of the slag calculated by IMCT Model are approved by the experiments.

The relationship between the activity ratio of steel and the activity ratio of slag in the experiment.

The data of blue sphere is calculated by using this author’s experiment results as shown in Table 6 and the experiment method is described in Table 7. The CaO-MgO-BaO-CaF2-SiO2-Al2 O3-TiO2 slags before reacting with steel were pre-melted in a carbon crucible and the composition was shown in Table 8, which are marked as No.1∼No.13. The steel sample A, described in Table 1, and the pre-melted CaO-MgO-BaO-CaF2-SiO2-Al2O3-TiO2 slags were equilibrated in MgO crucible by using resistance furnace under Ar atmosphere for 1 h.

This author’s experiment result (wt pct).

NO. CaO MgO BaO CaF2 SiO2 Al2O3 TiO2 [Ti] [Al] [Si]
1 40.5 8.8 3.2 3.9 5.2 20.2 18.2 0.128 0.009 0.186
2 35.1 9.3 9.1 4.5 4.3 19.7 17.8 0.169 0.011 0.208
3 28.6 8.3 14.7 5.3 4.3 20.1 18.5 0.232 0.011 0.232
4 28.3 7.7 18.3 4.9 4.1 15.4 21.3 0.24 0.018 0.233
5 46.3 7.8 0 4.4 4.4 17.8 19.3 0.178 0.016 0.217
6 49.6 8.4 0 4.5 15.1 17.4 5.0 0.091 0.018 0.345
7 37.0 10.5 0 4.2 7.8 35.9 4.6 0.083 0.010 0.23
8 40.9 12.0 0 4.0 7.6 26.7 8.6 0.133 0.011 0.245
9 33.8 11.7 0 3.9 7.0 23.4 20.4 0.206 0.011 0.20
10 34.0 - 19.05 5.52 5.25 14.62 21.26 0.506 0.024 0.228
11 30.81 - 19.88 4.10 4.66 14.00 26.55 0.264 0.017 0.231
12 33.63 - 20.38 4.98 2.08 10.64 28.30 0.235 0.015 0.193

This author’s experiment methods.

Experiment heats Temperature (K) Atmosphere Crucible Steel (g) Slag Time
Resistance furnace 1873 Ar MgO 400 32 g pre-melted slags 1 h

The initial slag composition (%).

No CaO MgO BaO CaF2 SiO2 Al2O3 TiO2
1 43.7 6.0 6.0 5.0 4.0 20.3 15.0
2 36.7 6.0 13.0 5.0 4.0 20.3 15.0
3 29.7 6.0 20.0 5.0 4.0 20.3 15.0
4 30.0 6.0 20.0 5.0 4.0 15.0 20.0
5 49.7 6.0 0 5.0 4.0 20.3 15.0
6 54.0 6.0 0 5.0 18.0 17.0 0
7 42.0 6.0 0 5.0 8.0 39.0 0
8 46.8 6.0 0 5.0 8.0 29.2 5.0
9 37.5 6.0 0 5.0 8.0 23.5 20.0
10 34.43 19.13 4.55 6.00 15.28 20.61
11 31.61 20.39 4.43 5.01 14.44 24.11
12 35.25 21.36 5.19 1.51 11.26 25.43

The detailed process of slag/metal experiment can be described as follows. At first, 400 g steel were placed in a MgO crucible. Then, the slag/metal reaction chamber was filled by Ar gas and followed by resistance heating. After temperature reached 1873K, the initial steel sample was taken by quartz tube and then 32 g pre-melted slag was added. After the slag was melted at 1873K for 60 min, steel sample and slag sample were taken out. During the metal-slag reacting process, the steel sample were taken at 5, 20 and 40min after slag melting completely. The contents of silicon, soluble aluminum, titanium in steel samples were measured by the inductively coupled plasma optical emission spectrometry (ICP-OES) with ±5% relative standard deviation. The compositions of slag samples were measured by an X-ray fluorescence spectrometer. During the metal-slag reacting process, the composition change behavior of the silicon in the steel was shown in Figure 3. From Figure 3, the experiment equilibrium state has realized.

The Silicon content of the steel in different heats.

In addition, the activity of SiO2, Al2O3 and TiO2 in 2–5 dimensional slag from the literature (Gzieo and Jowsa, 1984; Nomura et al., 1991; Hino, 1994; Kishi et al., 1994; Ohta and Suito, 1994; Ohta and Suito, 1998a; Ohta and Suito, 1998b; Moeizane et al., 1999; Jung and Fruehan, 2001; Stolyarova et al., 2005; Sun et al., 2015; Safarin, 2019) are calculated by this paper’s IMCT model, and compared with their experiment results (Gzieo and Jowsa, 1984; Nomura et al., 1991; Hino, 1994; Kishi et al., 1994; Ohta and Suito, 1994; Ohta and Suito, 1998a; Ohta and Suito, 1998b; Moeizane et al., 1999; Jung and Fruehan, 2001; Stolyarova et al., 2005; Sun et al., 2015; Safarin, 2019) and Factsage-7.0 calculating values, as shown in Figure 4. In Figure 4A or Figure 4B, the activity of SiO2 or Al2O3 in the CaO-BaO-Al2O3-SiO2 slag system calculated by the IMCT model are in good agreement with the Factsage-7.0 calculating values. It also can be found that, the activity of low system slag calculated by IMCT model are in accordance to the experimental results. In summary, the IMCT model for CaO-MgO-BaO-CaF2-SiO2-Al2O3-TiO2 slag in this paper is reasonable.

The comparison of specie’s activity in slag between measured and calculated values. (A) The activity of SiO2; (B) The activity of Al2O3; (C) The activity of TiO2.

 Result and Discussion Influence of the C/S Ratio in the Slag

The dependence of C/S ratio in the slag (S1), listed in Table 2, on the ΔG of reactions 1–3 was shown in Figure 5. With the increase of C/S ratio in the slag, the ΔG of reactions 1–2 increased and the ΔG of reaction 3 decreased. In general, the C/S ratio in the slag was suggested to be higher 4 for Al-killed steel refining process. But Zhang et al. (Zhang, 2019) found that the C/S ratio of 6 was the most effective to improve the steel cleanliness. When the C/S ratio was higher 6, the ΔG of reaction 1 was higher than 0 kJ/mol and the ΔG of reactions 2–3 were about -25 kJ/mol, Therefore Ti in the steel will be oxidized by the SiO2 and Al2O3 in the slag. Therefore it is necessary to investigate other factors such as C/A ratio, TiO2 content and BaO content to suppress the re-oxidation of Ti by SiO2 and Al2O3.

The effect of C/S ratio on the ΔG of reactions 1–3.

 Influence of the C/A Ratio in the Slag

The effect of C/A ratio in the slag (S2), listed in Table 2, on the ΔG of reaction 1–3 is shown in Figure 6. In this figure, the blue symbol-line represents the C/S ration in the slag is 6, the magenta symbol-line means the C/S ratio is 8, and the olive symbol-line means the C/S ratio is 10. From this figure we can found that, when the C/A ratio changed from 1 to 2.5, the ΔG of reaction 2 and 3 are also lower -20 kJ/mol. Yoon et al. (Yoon et al., 2002) reported that the most effective C/A ratio in the high basicity slag, in which the C/S ratio was higher than 4, was 1.7–1.8 to removing inclusions from bearing steel. Therefore, the mass ratio of CaO to Al2O3 in the slag (S3 and S4) was 1.7 in the following discussion.

The influence of C/A ratio on the ΔG of reactions 1–3.

 Influence of the w(TiO<sub>2</sub>) in the Slag

Figure 7 shows the variation behavior of ΔG for reactions 1–3 with the increase of TiO2 content in the slag (S3), listed in Table2. In this figure, the C/S ratio in the slag, marked in different color symbols, was the same with Figure 6. From Figure 7, with the increase of TiO2 content in the slag, the ΔG of reaction 1 decreased, And the ΔG of reaction 2 and 3 increased. When the TiO2 content in the slag was greater than 20%, the ΔG of reaction 2 are also lower than -10 kJ/mol. Therefore, it is necessary to increase the C/S ratio in the slag. However, the activity of CaO in the slag would increase and the solid calcium titanates (Li et al., 2018) would appear. This will lead to decrease the desulfurizer ability of the slag. In the basic slag TiO2 exits as TiO 6 8 − ions (Sommerville and Bell, 1982). In addition, TiO2 in slag forms anions, which will cause free O2- ions to decrease and the desulfurization ability of the slag decrease.

The effect of TiO2 content on the ΔG of reactions 1–3.

 Influence of the BaO Content in the Slag

Figure 8 shows the influence of BaO content in the slag (S4) on the ΔG of reactions 1–3. In this figure, the C/S ratio in the slag, marked in different color symbols, was the same with Figure 6. It is clear that, the ΔG of reaction 1 changed less and the ΔG of reactions 2 and 3 increased with the addition of BaO to the slag. It is clear that from Figure 8A, when the slag contained 15%TiO2, the C/S ratio was higher than 10 and the BaO content was 25–30%, the ΔG of reactions 1–3 are higher than 0 kJ/mol. When the TiO2 content in the slag was higher than 20%, with the increase of BaO content in the slag, the ΔG of reaction 1 was still lower than 0. Therefore, when the BaO content and TiO2 content in the slag were controlled as 20–30% and 15–25%, the C/S ratio should be controlled as higher than 10 according to the thermodynamic results. However, the desulfurizer and inclusion absorption ability of the slag should be considered. When the TiO2 content was higher than 30%, a large amount of solid calcium titanates (Li et al., 2018) will formed in the slag, the viscosity of the slag increase. This would lead to the desulfurizer and inclusion absorption ability descend. BaO is more powerful desulfurizer than CaO. Adding BaO to the flux not only desulfurizers by itself, but also enhances the desulphurization ability of CaO. In addition, BaO is more inclined to release the oxygen ion for less affinity to oxygen than CaO, which also favors desulfurization. However, the increase of BaO content in the flux may lead to the decrease of molar fraction of basic components because of its high molecular mass (153). Also, BaS is not stable and tends to decompose with the increase of BaS, which is disadvantageous to the desulfurization reaction (Gao et al., 2012).

The effect of BaO content on the ΔG of reactions 1–3.

 Conclusion

In this work, the thermodynamic interaction between ladle slag and 0.361%Ti bearing steel has been analyzed using IMCT model and the following conclusion are obtained.

1) According to the comparing results between thermodynamic calculation and experimental values, the IMCT model established in this paper is reasonable.

2) With the increase of C/S ratio in the slag, the ΔG of reaction for Al and Ti reacted with SiO2 increased, and Ti reacted with Al2O3 decreased; the effect of C/A ratio in the slag on the change of ΔG for Al or Ti reacted with slag is less; with the addition of TiO2 to the slag, the ΔG for Ti reacted with SiO2 and Al2O3 increase, and Al reacted with SiO2 decrease; with the increase of BaO in the slag, the ΔG change for reaction 1 is less, and the ΔG for reaction 2 and 3 increase.

3) When the BaO content and TiO2 content in the slag were controlled as 20–30% and 15–25%, the C/S ratio should be controlled as higher than 10 according to the thermodynamic results. However, the desulphurization and inclusion absorption ability of the slag should be considered.

Data Availability Statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

 Author Contributions

M-GZ was the first author and has made significant contribution to the manuscript. X-FW and G-JC have contributed towards the conception and review of the manuscript. S-PH provided correspondence and guidance on the manuscript.

 Funding

The authors gratefully express their appreciation to National Natural Science Foundation of China (No.52074054) and the fourth batch of major science and technology projects in panxi experimental base (low cost manufacturing technique of titanium alloyed high-strength and hightoughness steel and its application).

 Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

 Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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the mass ratio of CaO-SiO2

C/Al ratio

the mass ratio of CaO-Al2O3

Δ G i 0

the standard molar Gibbs free energy change of reaction i, (J/mol)

 Δ G i

the molar Gibbs free energy change of reaction i, (J/mol)

 K i

the equilibrium constant of reaction i

 f i

the activity coefficient of element i in the liquid steel.