Study of Thermodynamic for Low-Reactive CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O Mold Flux Based on the Model of Ion and Molecular Coexistence Theory

Abstract

A thermodynamic model was proposed to calculate the activity of components in low-reactive CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O mold flux, which was chosen to improve the castability of high Al steel, based on the ion and molecular coexistence theory. The model was indirectly validated, and the effects of the mass ratio of Al₂O₃/SiO₂, contents of CaF₂ and Li₂O on the reactivity of components were discussed. The results reveal that the reactivity of mold flux attenuated with the increase in the mass ratio of Al₂O₃/SiO₂. The decrease in reactivity was insignificant as the mass ratio was over 3.5. The steel–slag reaction experiment confirmed that the reactivity of mold flux is weakened when the content of SiO₂ below 8 wt%. The reactivity of mold flux increased nearly linearly with the increase in CaF₂ content, indicating that the proportion of CaF₂ should be kept to a minimum in the flux. In addition, the compositional regions involving around 6 wt% Li₂O should be avoided to develop low-reactive mold flux.

1. Introduction

Advanced high-strength steels with high content of aluminum have attracted much attention in the automobile industry owing to low density, high ductility, and strength for the sake of passenger safety and environmental friendliness [1,2,3]. However, aluminum in molten steel ([Al]) is prone to react with silicon dioxide in traditional CaO-SiO₂-based mold flux ((SiO₂)), resulting in sharply varied content of SiO₂ and Al₂O₃. The compositional variation of the mold flux leads to an increase in melting temperature and viscosity, consequently deteriorating its performances, such as heat transfer and lubrication [4,5,6,7]. Therefore, it is essential to develop a specified mold flux having low reactivity with high-Mn, high-Al molten steel [8,9]. Taking the reaction between [Al] and (SiO₂) for example:

4[Al] + 3(SiO₂) → 2(Al₂O₃) + 3[Si]

(1)

$$\Delta G=\Delta G^{\theta }+RT\ln \frac{a_{{}_{({\mathrm{Al}}_2{\mathrm{O}}_3)}}^2{a}_{{}_{[\mathrm{Si}]}}^3}{a_{{}_{({\mathrm{SiO}}_2)}}^3{a}_{{}_{[\mathrm{Al}]}}^4}$$

(2)

where $\Delta G$, $\Delta G^{\theta }$, R, T, a_i are the reaction Gibbs free energy change, standard reaction Gibbs free energy change, gas constant (8.314 J/(mol·K)), temperature, and activity of component i, respectively. Thus, for a certain steel, the activities of various components in mold flux are crucial parameters to determine the extent of reaction at the steel–slag interface. Currently, the application of thermodynamic software is a preferred approach to predict the activities of components in mold flux. However, the thermodynamic software has limited scope because of the lack of some databases. In order to make up for the shortcomings of the thermodynamic software, the ion and molecular coexistence theory (IMCT) was proposed by Chuiko. N.M. in 1960s [10], which could predict the activity of each component of multi-component flux system. When using IMCT, the activity of each component in the flux can be expressed by the mass action concentration [10]. The accuracy to predict activities of components has been confirmed for flux melts, such as FeO-Fe₂O₃-SiO₂ [10], CaO-SiO₂-Al₂O₃-MgO [10], Na₂O-SiO₂ [10], NiO-MgO [11], CaO–Al₂O₃–Ce₂O₃ [12], and CaO-SiO₂-Al₂O₃-FeO-CaF₂-La₂O₃-Nb₂O₅-TiO₂ [13]. Our previous studies [14] indicated that the flux system of CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O as a low-reactive flux system is expected to be applied for continuous casting of high-Mn high-Al steel. To deeply understand during the contact of steel and flux, the obtainment of activity data in flux melts is urgent. In this study, a thermodynamic model is established to calculate the activity of the components in CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O mold flux based on IMCT (Ion and molecular coexistence theory) at 1773 K. In addition, the steel–slag contact experiment was conducted to verify the accuracy of the prediction. The effects of mass ratio of Al₂O₃/SiO₂ and content of CaF₂ and Li₂O were discussed.

2. Methodology

2.1. Structural Units and Mass Action Concentration

IMCT assumed that structural units of molten flux consisted of simple ions, simple and complex molecules. The simple ions participate in the formation of complex molecules in the form of ion couples, and each pair of cation and anion occupies one structural unit. For CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O system, Ca²⁺, Ba²⁺, Li⁺, F⁻, and O²⁻ as simple ions, and SiO₂ and Al₂O₃ as simple molecules existed. On the basis of ternary phase diagrams of CaO-SiO₂-Al₂O₃, BaO-SiO₂-Al₂O₃, CaO-Al₂O₃-CaF₂, CaO-SiO₂-CaF₂, and Al₂O₃-SiO₂-Li₂O, and binary phase diagrams of CaO-SiO₂, CaO-Al₂O₃, BaO-SiO₂, BaO-Al₂O₃, Li₂O-SiO₂, and Li₂O-Al₂O₃ [15,16,17], there are 33 major species of complex molecules that form within the temperature range of 1673–1823 K. The structural units and corresponding mole numbers are listed in

Table 1. Mole number and mass action concentration of the structural units.

Items	Structural Units	Mole Number	Mass Action Concentration
Ion couples	(Ca2+ + O2−)	$n_1=2n_{\mathrm{CaO}}$	$N_1=n_1/{\displaystyle \sum n_i}$
	(Ba2+ + O2−)	$n_2=2n_{\mathrm{BaO}}$	$N_2=n_2/{\displaystyle \sum n_i}$
	(Ca2+ + 2F−)	$n_5=3n_{{\mathrm{CaF}}_2}$	$N_5=n_5/{\displaystyle \sum n_i}$
	(2Li+ + O2−)	$n_6=3n_{{\mathrm{Li}}_2\mathrm{O}}$	$N_6=n_6/{\displaystyle \sum n_i}$
Simple molecules	Al2O3	$n_3$	$N_3=n_3/{\displaystyle \sum n_i}$
	SiO2	$n_4$	$N_4=n_4/{\displaystyle \sum n_i}$
Complex molecules	CaO·SiO2	$n_7$	$N_7=n_7/{\displaystyle \sum n_i}$
	2CaO·SiO2	$n_8$	$N_8=n_8/{\displaystyle \sum n_i}$
	3CaO·SiO2	$n_9$	$N_9=n_9/{\displaystyle \sum n_i}$
	3CaO·2SiO2	$n_{10}$	$N_{10}=n_{10}/{\displaystyle \sum n_i}$
	CaO·Al2O3	$n_{11}$	$N_{11}=n_{11}/{\displaystyle \sum n_i}$
	CaO·2Al2O3	$n_{12}$	$N_{12}=n_{12}/{\displaystyle \sum n_i}$
	CaO·6Al2O3	$n_{13}$	$N_{13}=n_{13}/{\displaystyle \sum n_i}$
	3CaO·Al2O3	$n_{14}$	$N_{14}=n_{14}/{\displaystyle \sum n_i}$
	12CaO·7Al2O3	$n_{15}$	$N_{15}=n_{15}/{\displaystyle \sum n_i}$
	BaO·SiO2	$n_{16}$	$N_{16}=n_{16}/{\displaystyle \sum n_i}$
	BaO·2SiO2	$n_{17}$	$N_{17}=n_{17}/{\displaystyle \sum n_i}$
	2BaO·SiO2	$n_{18}$	$N_{18}=n_{18}/{\displaystyle \sum n_i}$
	2BaO·3SiO2	$n_{19}$	$N_{19}=n_{19}/{\displaystyle \sum n_i}$
	BaO·Al2O3	$n_{20}$	$N_{20}=n_{20}/{\displaystyle \sum n_i}$
	BaO·6Al2O3	$n_{21}$	$N_{21}=n_{21}/{\displaystyle \sum n_i}$
	3BaO·Al2O3	$n_{22}$	$N_{22}=n_{22}/{\displaystyle \sum n_i}$
	3Al2O3·2SiO2	$n_{23}$	$N_{23}=n_{23}/{\displaystyle \sum n_i}$
	Li2O·SiO2	$n_{24}$	$N_{24}=n_{24}/{\displaystyle \sum n_i}$
	Li2O·2SiO2	$n_{25}$	$N_{25}=n_{25}/{\displaystyle \sum n_i}$
	2Li2O·SiO2	$n_{26}$	$N_{26}=n_{26}/{\displaystyle \sum n_i}$
	Li2O·Al2O3	$n_{27}$	$N_{27}=n_{27}/{\displaystyle \sum n_i}$
	BaO·3CaO·2SiO2	$n_{28}$	$N_{28}=n_{28}/{\displaystyle \sum n_i}$
	2BaO·4CaO·3SiO2	$n_{29}$	$N_{29}=n_{29}/{\displaystyle \sum n_i}$
	BaO·2CaO·4Al2O3	$n_{30}$	$N_{30}=n_{30}/{\displaystyle \sum n_i}$
	3BaO·CaO·Al2O3	$n_{31}$	$N_{31}=n_{31}/{\displaystyle \sum n_i}$
	CaO·Al2O3·2SiO2	$n_{32}$	$N_{32}=n_{32}/{\displaystyle \sum n_i}$
	2CaO·Al2O3·SiO2	$n_{33}$	$N_{33}=n_{33}/{\displaystyle \sum n_i}$
	BaO·Al2O3·2SiO2	$n_{34}$	$N_{34}=n_{34}/{\displaystyle \sum n_i}$
	3CaO·2SiO2·CaF2	$n_{35}$	$N_{35}=n_{35}/{\displaystyle \sum n_i}$
	3CaO·3Al2O3·CaF2	$n_{36}$	$N_{36}=n_{36}/{\displaystyle \sum n_i}$
	11CaO·7Al2O3·CaF2	$n_{37}$	$N_{37}=n_{37}/{\displaystyle \sum n_i}$
	Li2O·Al2O3·2SiO2	$n_{38}$	$N_{38}=n_{38}/{\displaystyle \sum n_i}$
	Li2O·Al2O3·4SiO2	$n_{39}$	$N_{39}=n_{39}/{\displaystyle \sum n_i}$

. According to IMCT, free Me⁺/Me²⁺ and F⁻/O²⁻ remain independent, whereas ion couples (Me²⁺ + O²⁻) occupy two structural units and (2Me⁺ + O²⁻) or (Me²⁺ + 2F⁻) occupy three structural units (where Me²⁺ refers to Ca²⁺ or Ba²⁺ and Me⁺ refers to Li⁺). For the flux with six kinds of components, the ion couples include (Ca²⁺ + O²⁻), (Ba²⁺ + O²⁻), (2Li⁺ + O²⁻), and (Ca²⁺ + 2F⁻). Thus, the total mole number of structural units can be expressed as follows:

$${\displaystyle \sum n_i}=2n_{\mathrm{CaO}}+2n_{\mathrm{BaO}}+n_{{\mathrm{Al}}_2{\mathrm{O}}_3}+n_{{\mathrm{SiO}}_2}+3n_{{\mathrm{CaF}}_2}+3n_{{\mathrm{Li}}_2\mathrm{O}}+n_7+\dots +n_{39}$$

(3)

where n_i is the mole number of structural units for product i.

The mass action concentration of the 39 items in Table 1 are denoted as N₁, N₂, N₃, …, and N₃₉, respectively. N_i is calculated using Equation (4):

$$N_i=\frac{n_i}{{\displaystyle \sum n_i}}$$

(4)

As complex molecules are derived from simple ion couples and molecules by chemical reactions, the mass action concentration of the complex molecules can be expressed by their corresponding reaction equilibrium constant (K_i) and the values of N₁, N₂, N₃, N₄, N₅, and N₆. K_i can be obtained by:

$$K_i=\exp (-\frac{\Delta G_i^{\theta }}{RT})$$

(5)

2.2. Calculation of Standard Gibbs Free Energy for Complex Molecules

To calculate the standard Gibbs free energy change ($\Delta G_T^{\theta }$) for the formation of complex molecule by ion couples and simple molecules, the reactants and products are considered to be in dissolution state. For example, the formation of mMeO·nSiO₂ proceeds by the following way:

$$m({\mathrm{Me}}^{2+}+{\mathrm{O}}^{2-})+n({\mathrm{SiO}}_2)\to (m\mathrm{MeO}·n{\mathrm{SiO}}_2) \Delta G_{\mathrm{solution}}^{\theta }$$

(6)

where m and n are positive integers and $\Delta G_{\mathrm{solution}}^{\theta }$ is the standard Gibbs free energy change in dissolution state. However, obtaining $\Delta G_{\mathrm{solution}}^{\theta }$ data under such condition is often difficult. In contrast, if the reaction occurs in solid state, as shown in Equation (7), the standard Gibbs free energy change, $\Delta G_{\mathrm{solid}}^{\theta }$, is easier to acquire.

$$m{({\mathrm{Me}}^{2+}+{\mathrm{O}}^{2-})}_{(s)}+n{({\mathrm{SiO}}_2)}_{(s)}\to {(m\mathrm{MeO}·n{\mathrm{SiO}}_2)}_{(s)} \Delta G_{\mathrm{solid}}^{\theta }$$

(7)

It is well known that the dissolution of a certain component into flux melts can be divided into two steps. The first step involves melting the component from solid to liquid state, ${\Delta }_{\mathrm{fus}}{G}_{\mathrm{i}}^{\theta }$. The second step involves further dissolution into flux melts, ${\Delta }_{\mathrm{sol}}{G}_{\mathrm{i}}^{\theta }$. The changes of the standard Gibbs free energy for the above steps are equal, that is ${\Delta }_{\mathrm{fus}}{G}_{\mathrm{i}}^{\theta }=-{\Delta }_{\mathrm{sol}}{G}_{\mathrm{i}}^{\theta }$ [18,19]. Therefore, the following relation can be obtained:

$$\Delta G_{\mathrm{solution}}^{\theta }=\Delta G_{\mathrm{solid}}^{\theta }+{\Delta }_{\mathrm{fus}}{G}_{\mathrm{i}}^{\theta }+{\Delta }_{\mathrm{sol}}{G}_{\mathrm{i}}^{\theta }=\Delta G_{\mathrm{solid}}^{\theta }$$

(8)

Generally, $\Delta G_T^{\theta }$ could be expressed a function of temperature [20] by:

$$\Delta G_T^{\theta }=\Delta H_{298\mathrm{K}}^{\theta }-T\Delta {\Phi }_T$$

(9)

$$\Delta H_{298\mathrm{K}}^{\theta }={\displaystyle \sum {(n_i\Delta H_{i,298\mathrm{K}}^{\theta })}_{\mathrm{product}}-}{\displaystyle \sum {(n_j\Delta H_{j,298\mathrm{K}}^{\theta })}_{\mathrm{reactant}}}$$

(10)

$$\Delta {\Phi }_T={\displaystyle \sum {(n_i{\Phi }_{i,T})}_{\mathrm{product}}-}{\displaystyle \sum {(n_j{\Phi }_{j,T})}_{\mathrm{reactant}}}$$

(11)

where, n_j is the stoichiometric number of reactant j; $\Delta H_{298\mathrm{K}}^{\theta }$ is the standard enthalpy change of reaction at 298 K; $\Delta {\Phi }_T$ is the standard Gibbs function change of reaction at T; $\Delta G_T^{\theta }$ in the form of $\Delta G_T^{\theta }=A+BT$ for these reactions are listed in

Table 2. Reaction formulas for the formation of complex molecules.

Reaction	$\mathbf{\Delta }{\mathit{G}}_{\mathit{T}}^{\mathbf{\Theta }}$	Ki	Ni	Ref.
(Ca2+ + O2−) + (SiO2)→(CaO·SiO2)	−92,500 + 1.25T	$K_7=\frac{N_7}{N_1{N}_4}$	$N_7=K_7{N}_1{N}_4$	[10]
2(Ca2+ + O2−) + (SiO2)→(2CaO·SiO2)	−102,090 − 24.267T	$K_8=\frac{N_8}{N_1{}^2{N}_4}$	$N_8=K_8{N}_1{}^2{N}_4$	[21]
3(Ca2+ + O2−) + (SiO2)→(3CaO·SiO2)	−118,826 − 6.694T	$K_9=\frac{N_9}{N_1{}^3{N}_4}$	$N_9=K_9{N}_1{}^3{N}_4$	[21]
3(Ca2+ + O2−) + 2(SiO2)→(3CaO·2SiO2)	−236,814 + 9.623T	$K_{10}=\frac{N_{10}}{N_1{}^3{N}_4{}^2}$	$N_{10}=K_{10}{N}_1{}^3{N}_4{}^2$	[21]
(Ca2+ + O2−) + (Al2O3)→(CaO·Al2O3)	59,413 − 59.413T	$K_{11}=\frac{N_{11}}{N_1{N}_3}$	$N_{11}=K_{11}{N}_1{N}_3$	[21]
(Ca2+ + O2−) + 2(Al2O3)→(CaO·2Al2O3)	−16,736 − 25.522T	$K_{12}=\frac{N_{12}}{N_1{N}_3{}^2}$	$N_{12}=K_{11}{N}_1{N}_3{}^2$	[21]
(Ca2+ + O2−) + 6(Al2O3)→(CaO·6Al2O3)	−22,594 − 31.798T	$K_{13}=\frac{N_{13}}{N_1{N}_3{}^6}$	$N_{13}=K_{13}{N}_1{N}_3{}^6$	[21]
3(Ca2+ + O2−) + (Al2O3)→(3CaO·Al2O3)	−21,757 − 29.288T	$K_{14}=\frac{N_{14}}{N_1{}^3{N}_3}$	$N_{14}=K_{14}{N}_1{}^3{N}_3$	[21]
12(Ca2+ + O2−) + 7(Al2O3)→(12CaO·7Al2O3)	617,977 − 612.119 T	$K_{15}=\frac{N_{15}}{N_1{}^{12}{N}_3{}^7}$	$N_{15}=K_{15}{N}_1{}^{12}{N}_3{}^7$	[21]
(Ba2+ + O2−) + (SiO2)→(BaO·SiO2)	−154,238 − 2.926T	$K_{16}=\frac{N_{16}}{N_2{N}_4}$	$N_{16}=K_{16}{N}_2{N}_4$	[22]
(Ba2+ + O2−) + 2(SiO2)→(BaO·2SiO2)	−169,365 + 1.496T	$K_{17}=\frac{N_{17}}{N_2{N}_4{}^2}$	$N_{17}=K_{17}{N}_2{N}_4{}^2$	[22]
2(Ba2+ + O2−) + (SiO2)→(2BaO·SiO2)	−264,183 − 3.395T	$K_{18}=\frac{N_{18}}{N_2{}^2{N}_4}$	$N_{18}=K_{18}{N}_2{}^2{N}_4$	[22]
2(Ba2+ + O2−) + 3(SiO2)→(2BaO·3SiO2)	−337,580 + 7.039T	$K_{19}=\frac{N_{19}}{N_2{}^2{N}_4{}^3}$	$N_{19}=K_{19}{N}_2{}^2{N}_4{}^3$	[22]
(Ba2+ + O2−) + (Al2O3)→(BaO·Al2O3)	−99,760 − 25.413T	$K_{20}=\frac{N_{20}}{N_2{N}_3}$	$N_{20}=K_{20}{N}_2{N}_3$	[22]
(Ba2+ + O2−) + 6(Al2O3)→(BaO·6Al2O3)	−126,813 − 24.293T	$K_{21}=\frac{N_{21}}{N_2{N}_3{}^6}$	$N_{21}=K_{21}{N}_2{N}_3{}^6$	[22]
3(Ba2+ + O2−) + (Al2O3)→(3BaO·Al2O3)	−187,633 − 37.528T	$K_{22}=\frac{N_{22}}{N_2{}^3{N}_3}$	$N_{22}=K_{22}{N}_2{}^3{N}_3$	[23]
3(Al2O3) + 2(SiO2)→(3Al2O3·2SiO2)	−4354 − 10.467T	$K_{23}=\frac{N_{23}}{N_3{}^3{N}_4{}^2}$	$N_{23}=K_{23}{N}_3{}^3{N}_4{}^2$	[22]
(2Li+ + O2−) + (SiO2)→(Li2O·SiO2)	−143,757 + 3.796T	$K_{24}=\frac{N_{24}}{N_6{N}_4}$	$N_{24}=K_{24}{N}_6{N}_4$	[22]
(2Li+ + O2−) + 2(SiO2)→(Li2O·2SiO2)	−145,174 − 1.372T	$K_{25}=\frac{N_{25}}{N_6{N}_4{}^2}$	$N_{25}=K_{25}{N}_6{N}_4{}^2$	[22]
2(2Li+ + O2−) + (SiO2)→(2Li2O·SiO2)	−230,237 + 15.442T	$K_{26}=\frac{N_{26}}{N_6{}^2{N}_4}$	$N_{26}=K_{26}{N}_6{}^2{N}_4$	[22]
(2Li+ + O2−) + (Al2O3)→(Li2O·Al2O3)	−106,327 − 16.567T	$K_{27}=\frac{N_{27}}{N_6{N}_3}$	$N_{27}=K_{27}{N}_6{N}_3$	[22]
(Ba2+ + O2−) + 3(Ca2+ + O2−) + 2(SiO2)→(BaO·3CaO·2SiO2)	−376,298 + 8.751T	$K_{28}=\frac{N_{28}}{N_2{N}_1{}^3{N}_4{}^2}$	$N_{28}=K_{28}{N}_2{N}_1{}^3{N}_4{}^2$	[22]
2(Ba2+ + O2−) + 4(Ca2+ + O2−) + 3(SiO2)→(2BaO·4CaO·3SiO2)	−533,550 + 269.292T	$K_{29}=\frac{N_{29}}{N_2{}^2{N}_1{}^4{N}_4{}^3}$	$N_{29}=K_{29}{N}_2{}^2{N}_1{}^4{N}_4{}^3$	[22]
(Ba2+ + O2−) + 2(Ca2+ + O2−) + 4(Al2O3)→(BaO·2CaO·4Al2O3)	−157,255 − 85.113T	$K_{30}=\frac{N_{30}}{N_2{N}_1{}^2{N}_3{}^4}$	$N_{30}=K_{30}{N}_2{N}_1{}^2{N}_3{}^4$	[22]
3(Ba2+ + O2−) + (Ca2+ + O2−) + (Al2O3)→(3BaO·CaO·Al2O3)	−139,905 − 42.192T	$K_{31}=\frac{N_{31}}{N_2{}^3{N}_1{N}_3}$	$N_{31}=K_{31}{N}_2{}^3{N}_1{N}_3$	[22]
(Ca2+ + O2−) + (Al2O3) + 2(SiO2)→(CaO·Al2O3·2SiO2)	−4184 − 73.638T	$K_{32}=\frac{N_{32}}{N_1{N}_3{N}_4{}^2}$	$N_{32}=K_{32}{N}_1{N}_3{N}_4{}^2$	[23,24]
2(Ca2+ + O2−) + (Al2O3) + (SiO2)→(2CaO·Al2O3·SiO2)	−116,315 − 38.911T	$K_{33}=\frac{N_{33}}{N_1{}^2{N}_3{N}_4}$	$N_{33}=K_{33}{N}_1{}^2{N}_3{N}_4$	[23,24]
(Ba2+ + O2−) + (Al2O3) + 2(SiO2)→(BaO·Al2O3·2SiO2)	−198,791 − 38.497T	$K_{34}=\frac{N_{34}}{N_2{N}_3{N}_4{}^2}$	$N_{34}=K_{34}{N}_2{N}_3{N}_4{}^2$	[22]
3(Ca2+ + O2−) + 2(SiO2) + (Ca2+ + 2F−)→(3CaO·2SiO2·CaF2)	−255,180 − 8.20T	$K_{35}=\frac{N_{35}}{N_1{}^3{N}_4{}^2{N}_5}$	$N_{35}=K_{35}{N}_1{}^3{N}_4{}^2{N}_5$	[23,24]
3(Ca2+ + O2−) + 3(Al2O3) + (Ca2+ + 2F−)→(3CaO·3Al2O3·CaF2)	−44,492 − 73.15T	$K_{36}=\frac{N_{36}}{N_1{}^3{N}_3{}^3{N}_5}$	$N_{36}=K_{36}{N}_1{}^3{N}_3{}^3{N}_5$	[23,24]
11(Ca2+ + O2−) + 7(Al2O3) + (Ca2+ + 2F−)→(11CaO·7Al2O3·CaF2)	−228,760 − 155.8T	$K_{37}=\frac{N_{37}}{N_1{}^{11}{N}_3{}^7{N}_5}$	$N_{37}=K_{37}{N}_1{}^{11}{N}_3{}^7{N}_5$	[23,24]
(2Li+ + O2−) + (Al2O3) + 2(SiO2)→(Li2O·Al2O3·2SiO2)	−136,270 − 37.516T	$K_{38}=\frac{N_{38}}{N_6{N}_3{N}_4{}^2}$	$N_{38}=K_{38}{N}_6{N}_3{N}_4{}^2$	[19]
(2Li+ + O2−) + (Al2O3) + 4(SiO2)→(Li2O·Al2O3·4SiO2)	−128,739 − 48.253T	$K_{39}=\frac{N_{39}}{N_6{N}_3{N}_4{}^4}$	$N_{39}=K_{39}{N}_6{N}_3{N}_4{}^4$	[19]

.

2.3. Mass Action Concentration for Structural Units and Ion Couples

The initial mole contents of CaO, BaO, Al₂O₃, SiO₂, CaF₂, and Li₂O are denoted as a₁, a₂, a₃, a₄, a₅, and a₆, respectively. Based on the principle of mass conservation:

$$\begin{gathered} a_1 = (0.5N_1 + N_7 + 2N_8 + 3N_9 + 3N_{10} + N_{11} + N_{12} + N_{13} + 3N_{14} + 12N_{15} + 3N_{28} + 4N_{29} + 2N_{30} + N_{31} + N_{32} + 2N_{33} + \\ 3N_{35} + 3N_{36} + 11N_{37}){\displaystyle \sum n_i} \end{gathered}$$

(12)

$$a_2 = (0.5N_2 + N_{16} + N_{17} + 2N_{18} + 2N_{19} + N_{20} + N_{21} + 3N_{22} + N_{28}+2N_{29} + N_{30} + 3N_{31} + N_{34}){\displaystyle \sum n_i}$$

(13)

$$\begin{gathered} a_3 = (N_3 + N_{11} + 2N_{12} + 6N_{13} + N_{14} + 7N_{15} + N_{20} + 6N_{21} + N_{22} + 3N_{23} + N_{27} + 4N_{30} + N_{31} + N_{32} + N_{33} + N_{34} + 3N_{36} + \\ 7N_{37} + N_{38} + N_{39}){\displaystyle \sum n_i} \end{gathered}$$

(14)

$$\begin{gathered} a_4 = (N_4 + N_7 + N_8 + N_9 + 2N_{10} + N_{16} + 2N_{17} + N_{18} + 3N_{19} + 2N_{23} + N_{24} + 2N_{25} + N_{26} + 2N_{28} + 3N_{29} + 2N_{32} + N_{33} + \\ 2N_{34} + 2N_{35} + 2N_{38} + 4N_{39}){\displaystyle \sum n_i} \end{gathered}$$

(15)

$$a_5 = (1/3N_5 + N_{35} + N_{36} + N_{37}){\displaystyle \sum n_i}$$

(16)

$$a_6 = (1/3N_6 + N_{24} + N_{25} + 2N_{26} + N_{27} + N_{38} + N_{39}){\displaystyle \sum n_i}$$

(17)

To solve Equations (12)–(17), Matlab software was subsequently used for further calculations, and the unique solutions of N₁, N₂, N₃, N₄, N₅, and N₆ were obtained. Thus, the activity calculation model for CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O mold flux system could be developed.

2.4. Steel–Slag Contact Experiment

The schematic of the apparatus to conduct steel–slag contact experiment is shown in Figure 1. The compositions of mold flux and steel are listed in

Table 3. Initial composition of mold fluxes and steel for the contact experiment (wt%).

		CaO	BaO	Al2O3	SiO2	F	Li2O
Fluxes	S-1	36.5	24	21	6	8	4.5
	S-2	36.5	24	19	8	8	4.5
	S-3	36.5	24	17	10	8	4.5
	S-4	36.5	24	15	12	8	4.5
Steel		C	Al	Mn	Si	S	Fe
		0.17	1.49	22.7	0.22	0.02	Bal.

. Total content of Al₂O₃ and SiO₂ in the flux is designed to be constant as 27 wt%. The content of Al in steel is 1.49 wt%, which belongs to grades of high-Mn, high-Al steels. Before the contact experiment, 80 g of each mold flux was prepared using chemically pure reagents, and pre-melted in a silica-molybdenum furnace at 1573 K for compositional homogeneity. After cooling, the mold flux was ground into fine powder. For each run, approximately 320 g of steel sample was placed in a MgO crucible and heated. Then, the molten steel was maintained isothermally at 1773 K for 20 min. Subsequently, 80 g of pre-melted flux was dispensed onto the top surface of the molten steel, at which moment was recorded as the start time of steel–slag reaction. To avoid the effect of oxygen, the contact experiments were conducted under Ar atmosphere at a flow rate of 1 L/min. After the reaction time reached 12 min, the MgO crucible with molten steel and flux was taken out and cooled at room temperature. The compositions of mold flux before and after contact experiment were analyzed by the methods of ICP-OES (ICAP 6300 Duo made by Thermo Scientific IRIS Intrepid II, MA, USA) and XRF (ARL Perform X made by Thermo Fisher).

3. Model Validation

To validate the accuracy of established model to predict the activity of various components in flux melts, the comparisons between the prediction by the current study and the calculation by Factsage and the literature [17,25,26,27,28] were made on the activity of the reactive component, SiO₂. The flux melts were CaO-Al₂O₃-SiO₂-CaF₂, CaO-BaO-Al₂O₃-SiO₂, and Li₂O-SiO₂, respectively. It should be noted that the accuracy of the current model was indirectly validated, and all components in Table 3 were taken into consideration. At present, Factsage is a popular thermodynamic software to calculate the activity for simple flux systems with 2–4 components. However, as the data of BaO and CaF₂ belong to two separate databases, the activities of the components in the CaO-Al₂O₃-SiO₂-CaF₂ and CaO -Al₂O₃-SiO₂-BaO systems were validated, respectively. Rey [27] and Charles [28] have obtained the activity data of SiO₂ in Li₂O-SiO₂ binary system with the SRS model (sub-regular solution model).

CaO-Al₂O₃-SiO₂-BaO and CaO-Al₂O₃-SiO₂-CaF₂

Table 4. Composition of the CaO-Al₂O₃-SiO₂-BaO/CaF₂ quaternary flux system (wt%) and activity of SiO₂.

	CaO	BaO	Al2O3	SiO2	CaF2	ki,cal	ki,fit	ΔX
CaO-Al2O3-SiO2-BaO	20	30	10	40	0	−0.670	−0.884	0.242
	20	40	10	30	0	−1.241	−1.549	0.199
	20	50	10	20	0	−2.378	−2.234	0.064
	30	30	10	30	0	−1.494	−1.711	0.127
	40	20	10	30	0	−1.763	−1.943	0.093
	50	10	10	30	0	−2.093	−2.411	0.132
	50	20	20	10	0	−4.632	−4.653	0.005
	40	20	30	10	0	−3.983	−4.049	0.016
	30	20	40	10	0	−2.851	−3.383	0.157
CaO-Al2O3-SiO2-CaF2	36	0	16	40	8	−0.969	−1.006	0.037
	40	0	16	36	8	−1.297	−1.294	0.002
	40	0	22	30	8	−1.734	−1.623	0.068
	40	0	34	18	8	−2.552	−2.627	0.029
	40	0	40	12	8	−2.879	−3.236	0.110
	36	0	8	40	16	−0.876	−0.846	0.035
	40	0	8	36	16	−1.188	−1.111	0.069
	40	0	14	30	16	−1.729	−1.529	0.131
	40	0	26	18	16	−2.731	−2.795	0.023
	40	0	32	12	16	−3.106	−3.302	0.059

summarizes the compositions of the CaO-Al₂O₃-SiO₂-BaO and the CaO-Al₂O₃-SiO₂-CaF₂ quaternary flux systems and the corresponding activity of SiO₂. The deviation (ΔX) for the difference between IMCT model and Factsage was calculated by Equation (18), 0.5% to 24.2% for CaO-Al₂O₃-SiO₂-BaO melt, and 0.2% to 11.0% for CaO-Al₂O₃-SiO₂-CaF₂ melt. The close agreement indicates that the IMCT model is reliable for quaternary flux system.

$$\Delta X=\frac{\left|{{\displaystyle k}}_{i,cal}-{{\displaystyle k}}_{i,fit}\right|}{\left|{{\displaystyle k}}_{i,fit}\right|}\times 100\%$$

(18)

where N represents the number of the samples; k_i,cal is the value calculated from Factsage; k_i,fit is the fitted value derived from the relationship between calculated values of Factsage and IMCT model.

Due to the lack of measured activities for Li₂O-SiO₂ binary system, the calculated activity of (SiO₂) by the IMCT model was compared with those estimated by SRS model [27,28], as shown in Figure 2. When the Li₂O content was below 20 wt%, the values of SiO₂ activity predicted by SRS model were slightly higher than those predicted by the current study. When the Li₂O content was higher than 25%, the values of SiO₂ activity predicted by the IMCT model agreed more closely with those predicted by Ref. [27]. The comparison in Figure 2 indicated that the IMCT model has acceptable credibility to predict the SiO₂ activity in melts containing Li₂O.

In summary, the reliability of the established thermodynamic model based on IMCT was indirectly confirmed by separately validating three flux systems that contained all six interested components in Table 3.

4. Contact Experiment of Steel-Slag Reaction

The compositions of mold fluxes before and after the contact experiment are listed in

Table 5. Composition of mold flux before and after steel–slag reaction (wt%).

Mold Flux	Before/After	CaO	BaO *	Al2O3	SiO2	F	Li2O	MgO
S-1	Initial	36.70	24.00	20.82	6.07	8.00	4.08	0.00
	Final	35.20	23.00	22.31	5.05	7.60	3.78	2.55
S-2	Initial	36.41	24.00	19.12	8.21	6.90	4.12	0.00
	Final	35.80	23.00	21.01	6.90	6.80	3.81	2.46
S-3	Initial	36.23	24.00	17.09	10.11	7.20	4.05	0.00
	Final	35.10	23.00	20.24	7.09	7.00	3.35	2.32
S-4	Initial	36.15	24.00	15.24	12.18	7.00	4.07	0.00
	Final	33.71	23.00	20.45	8.58	6.80	3.74	2.89

* The BaO content is the analytical reference value.

. It is clearly shown that as the initial content of SiO₂ increased from 6.07% to 12.18%, the reduced content of SiO₂ after the contact experiment also increased from 1.02% to 3.60%. Because high content of SiO₂ favors the reaction between [Al] and (SiO₂) at the steel–slag interface, the oxidized Al₂O₃ dissolves into flux and the reduced Si enters into the steel pool. As the duration time of 12 min was short, the content of typical volatile components (Li₂O and F⁻) attenuated slightly (less than 1%). The detection of MgO was caused by the erosion of MgO crucible at a high temperature. Figure 3 shows the variation of SiO₂ and Al₂O₃ in the mold flux before and after contact experiments. When the content of SiO₂ in mold flux was no more than 8%, the increment of Al₂O₃ (ΔAl₂O₃) was approximately 7.1%, and the decrement of SiO₂ (ΔSiO₂) was approximately 16.8%. As soon as the content of SiO₂ rose to 10% and even higher, ΔAl₂O₃ changed obviously from 18.4% to more than 34.2%, and ΔSiO₂ reached 30%. The variation of ΔAl₂O₃ and ΔSiO₂ indicated clearly that critical content of components may play a part in determining the extent of steel–slag reaction. Some references reported that the steel–slag reaction did not occur once the content of (SiO₂) was less than 7 wt% [4] or in the range of 5–10 wt% [9] for conventional CaO-Al₂O₃-based flux.

5. Effect of Different Factors

Equation (1) can be expressed in the form of Equation (19):

$$\Delta G=\Delta G^{\theta }+RT\ln \frac{a_{{}_{[\mathrm{Si}]}}^3}{a_{{}_{[\mathrm{Al}]}}^4}+\Delta G_{\mathrm{react}}^{\theta }$$

(19)

$$\Delta G_{react}^{\theta }=RTln\frac{a_{\left({Al}_2{\mathrm{O}}_3\right)}^2}{a_{\left({SiO}_2\right)}^3}$$

(20)

where $\Delta G_{\mathrm{react}}^{\theta }$ denotes the Gibbs free energy change involving the activities of (SiO₂) and (Al₂O₃) in mold flux, and is a parameter characterizing the reactivity of mold flux.

5.1. Mass Ratio of Al₂O₃/SiO₂

When the CaO-SiO₂-based flux is applied to cast high-Mn, high-Al steel, the content of (SiO₂) decreases and that of (Al₂O₃) increases continuously during casting, resulting in changes in the composition of flux and the deterioration of physical properties of flux. Change in the flux composition is mainly related to the substitution of SiO₂ with Al₂O₃, that is, the change of Al₂O₃/SiO₂ ratio. In the present study, a promising flux for casting high-Mn, high-Al steel was selected as the original flux [29] and SiO₂ was gradually replaced with Al₂O₃ (the Al₂O₃/SiO₂ ratio ranges from 0.29 to 8.00) to investigate variations in the activities of (SiO₂) and (Al₂O₃) and the reactivity of mold flux. The contents of the other components in the original flux are listed in

Table 6. Composition of various flux systems for investigating the effect of components on the activities of Al₂O₃ and SiO₂ (wt%).

Variable	CaO	BaO	Al2O3	SiO2	CaF2	Li2O	Sum	Interval
Al2O3, SiO2	20	20	8–32	28–4	16	8	100	4
CaF2	CaO:BaO = 1:1		24	12	4–28	8	100	4
Li2O	CaO:BaO = 1:1		24	12	16	2–14	100	2

. Figure 4 shows that with the increase in mass ratio of Al₂O₃/SiO₂ from 0.29 to 8.0, the activity of (SiO₂) first decreased rapidly, and then decreased slowly when the mass ratio of the Al₂O₃/SiO₂ was beyond 3.5, and the activity of (Al₂O₃) changed slightly. Meanwhile, the decrease in the reactivity of flux was similar to that trend of (SiO₂). Figure 4 also demonstrates that increasing the mass ratio of Al₂O₃/SiO₂ could effectively weaken the reactivity of flux contacting steel with high content of [Al]. Although with further increase above 3.5, the effect on weakening the reactivity of mold flux was extremely limited, indicating that the reactivity of flux approached to the minimum. Therefore, for this six-component flux system, the mass ratio of Al₂O₃/SiO₂ of 3.5 can be regarded as the critical value, below which the reactivity of mold flux is prominent and the reaction between [Al] and (SiO₂) at the steel–slag interface occurs easily.

Figure 5 shows the mole fraction of complex molecules that rank the top three in amount as a function of the mass ratio of Al₂O₃/SiO₂. The top three were all silicates, when the content of Al₂O₃ was low and the ratio was 0.29. As the mass ratio of Al₂O₃/SiO₂ increased from 0.29 to 8.0, the total mole fraction of silicates decreased sharply, and aluminates (Li₂O·Al₂O₃, and 3BaO·Al₂O₃) became the main units whose mole fraction reached 17.8%. The increase in the proportion of aluminate-type complex molecules also attributed to the relative stable activity of (Al₂O₃) with the increase in the mass ratio of Al₂O₃/SiO₂ in Figure 4. The variation of silicates and aluminates demonstrates that the flux system gradually transformed from CaO-SiO₂-based to CaO-Al₂O₃-based mold flux.

5.2. Content of CaF₂

CaF₂ is a common fluxing agent that can greatly reduce the viscosity of flux. Moreover, it can form cuspidine (3CaO·2SiO₂·CaF₂) combining with CaO and SiO₂ and favor decreasing the horizontal heat transfer between the solidify strand and mold. The content of F⁻ in commercial flux typically ranges from 2 to 14 wt% [30], corresponding to a CaF₂ content range of 4–28 wt%. Figure 6 shows the effect of CaF₂ content on the activities of (SiO₂) and (Al₂O₃) and the reactivity of mold flux. The increased activities of (SiO₂) and (Al₂O₃) and the reactivity of flux indicated that the reaction between [Al] and (SiO₂) was enhanced with the addition of CaF₂. The decreased viscosity with CaF₂ addition is expected to intensify the kinetic condition of the steel–slag reaction. Hence, there is a need to keep the content of CaF₂ as low as possible, while ensuring appropriate lubrication and heat transfer of mold flux. Figure 7 shows the top three complex molecules with different contents of CaF₂. For the current flux system with fixed contents of 24 wt% Al₂O₃ and 12 wt% SiO₂, the main structure units were Li₂O·Al₂O₃ and 2CaO·SiO₂, while both of their contents attenuated gradually with increased content of CaF₂ from 4 wt% to 28 wt%. The decreased content of silicates and aluminates was consistent with the predicted increased activities of simple molecule (Al₂O₃ and SiO₂), indicating that the number of free SiO₂ and Al₂O₃ was enhanced with increased addition of CaF₂.

5.3. Content of Li₂O

It is well known that the common fluxing agents, Na₂O and B₂O₃, can react with [Al], whereas Li₂O does not participate in the steel–slag reaction, and is able to reduce the melting temperature and viscosity of mold flux [31]. Thus, Li₂O is a promising fluxing agent for designing low-reactivity flux. Figure 8 shows the effect of Li₂O content. The activities of (SiO₂) and (Al₂O₃) and the reactivity of mold flux decreased gradually, which indicated that the reactivity between [Al] and (SiO₂) was weakened. As the content of Li₂O increased from 2 wt% to 14 wt%, the reactivity of flux increased first and then decreased with a maximum at 6 wt%, indicating the compositional region around 6 wt% Li₂O should be avoided in the development of low-reactivity flux. Figure 9 lists the top three complex molecules. The increased addition of Li₂O made the mole fraction of silicate and aluminate containing Li₂O be enlarged obviously, and the mole fraction of (2CaO·SiO₂) and (BaO·Al₂O₃) decreased gradually.

6. Conclusions

A thermodynamic model to predict the activities of components in low-reactive CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O mold flux was established based on IMCT. The conclusions can be summarized as follows:

• The results calculated by IMCT model are good accordance to the experiment results and Factsage calculation. The thermodynamic model based on IMCT could predict the activity of each component in the low-reactive CaO-BaO-Al₂O₃-SiO₂-CaF₂-Li₂O mold flux accurately and has good reliability.
• With the increase in mass ratio of Al₂O₃/SiO₂, the decreases in the activity of SiO₂ and the reactivity of mold flux had a turning point when the ratio of Al₂O₃/SiO₂ was 3.5, where the content of SiO₂ was 8 wt%.
• The activities of SiO₂ and Al₂O₃ and the reactivity of mold flux increased continuously with an increase in the content of CaF₂, which is unfavorable for developing low-reactivity mold flux. However, to avoid compromising other physical properties, the CaF₂ should be kept to a minimum.
• The activities of SiO₂ and Al₂O₃ decreased with an increase in Li₂O content, whereas the reactivity of mold flux had a maximum with 6 wt% Li₂O content, indicating that the compositional regions involving around 6 wt% Li₂O content should be avoided to design the low-reactive flux system.