*2.1. Production Procedure and Materials*

The following process was adopted for the production of high-strength tire cord steel in Baosteel (Wuhan Branch): basic oxygen furnace (BOF) → tapping → ladle furnace (LF) → soft blowing → continuous casting (CC) → rolling. Figure 1 shows a schematic diagram of the production process.

**Figure 1.** Production process of high-strength tire cord steel.

Both the liquid steel and balanced slag were sampled at the end point of the LF refining process at about 1853 K. The orthonormal chemical components of molten steel and slags for 16 heats are given in Table 2.

**Table 2.** Chemical components of liquid steel and slags at the end point of LF refining (wt %).


#### *2.2. Establishment of the IMCT Model*

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


The calculations were based on actual production involving CaO–SiO2–Al2O3–MgO–FeO– MnO–TiO2 slag systems. The initial numbers of moles for each composition in 100 g of CaO–SiO2– Al2O3–MgO–FeO–MnO–TiO2 slag were *a* = *n*<sup>0</sup> CaO, *<sup>b</sup>* <sup>=</sup> *<sup>n</sup>*<sup>0</sup> SiO2 , *c* = *n*<sup>0</sup> Al2O3 , *d* = *n*<sup>0</sup> MgO,*<sup>e</sup>* <sup>=</sup> *<sup>n</sup>*<sup>0</sup> FeO, *<sup>f</sup>* <sup>=</sup> *<sup>n</sup>*<sup>0</sup> MnO, and *g* = *n*<sup>0</sup> TiO2 , respectively. The balanced mole number of each constituent unit in the slag was defined as *ni*, and *Ni* denotes the MAC of each constitutional unit. The MAC is equivalent to the classical definition of activity based on the IMCT and can be acquired as

$$N\_i = \frac{n\_i}{\sum n\_i} \tag{1}$$

where *ni* is the total mole number of each constitutional unit in equilibrium.

According to the IMCT, at 1853 K, the slag system contains five simple ions (Ca2+, Fe2+, Mg2+, Mn2<sup>+</sup>, and O2<sup>−</sup>) and three ordinary molecules (Al2O3, SiO2, and TiO2). Based on the reported phase diagrams, 44 types of complex molecules can be generated at the steelmaking temperature [24,25]. The abovementioned structural units and their parameters are listed in Table 3.


**Table 3.** Parameters of structural units in the slag system at 1853 K.

The MACs for all the complex molecules can be determined using the reaction equilibrium constants *Ki*, *N*1(*N*CaO), *N*<sup>2</sup> *N*SiO2 , *N*<sup>3</sup> *N*Al2O3 , *N*<sup>4</sup> *N*MgO , *N*5(*N*FeO), *N*6(*N*MnO), and *N*<sup>7</sup> *N*TiO2 , which are listed in Table 4.


**Table 4.** Reaction formulas, Gibbs free energies, and mass action–concentrations (MACs) [26–32].

The mass conservation equations for the CaO–SiO2–Al2O3–MgO–FeO–MnO–TiO2 slag balanced with bulk steel can be built based on the definitions of *ni* and *Ni* for each structural unit as

$$a = \sum n\_i \binom{0.5N\_1 + N\_8 + 3N\_9 + 2N\_{10} + 3N\_{11} + 3N\_{12} + 12N\_{13} + N\_{14} + N\_{15} + N\_{16} + }{N\_{17} + 3N\_{18} + 4N\_{19} + 2N\_{37} + N\_{38} + 2N\_{40} + N\_{41} + N\_{42} + N\_{44}} \tag{2}$$

$$b = \sum n\_i \binom{N\_2 + N\_8 + 2N\_9 + N\_{10} + N\_{11} + 2N\_{20} + N\_{22} + N\_{23} + N\_{28} + N\_{32} + \cdots}{N\_{33} + N\_{37} + 2N\_{38} + 2N\_{39} + 2N\_{40} + N\_{41} + 2N\_{42} + 5N\_{43} + N\_{44}} \tag{3}$$

$$c = \sum n\_i \binom{N\_3 + N\_{12} + 7N\_{13} + N\_{14} + 2N\_{15} + 6N\_{16} + 3N\_{20} + \dots}{N\_{21} + N\_{24} + N\_{29} + N\_{34} + N\_{37} + N\_{38} + 2N\_{43}} \tag{4}$$

$$d = \sum n\_i \binom{0.5N\_4 + 2N\_{22} + N\_{23} + N\_{24} + N\_{25} + 2N\_{26} + }{N\_{27} + N\_{39} + N\_{40} + N\_{41} + N\_{42} + 2N\_{43}} \tag{5}$$

$$\sigma = \sum n\_i (0.5N\_5 + 2N\_{28} + N\_{29} + N\_{30} + 2N\_{31}) \tag{6}$$

$$f = \sum n\_i (0.5N\_6 + N\_{32} + 2N\_{33} + N\_{34} + N\_{35} + 2N\_{36}) \tag{7}$$

and

$$\mathbf{g} = \sum n\_i \binom{N\_7 + N\_{17} + 2N\_{18} + 3N\_{19} + N\_{21} + N\_{25} + N\_{26} + \cdots}{2N\_{27} + N\_{30} + N\_{31} + N\_{35} + N\_{36} + N\_{44}} \tag{8}$$

Based on the theory that the total MAC of each constitutional unit in CaO–SiO2–Al2O3– MgO–FeO–MnO–TiO2 slag with a fixed amount is equal to unity, Equation (9) can be derived as

$$\sum\_{i=1}^{44} N\_i = 1\tag{9}$$

Equations (2)–(9) represent the MAC calculation model for each constitutional unit in CaO–SiO2–Al2O3–MgO–FeO–MnO–TiO2 slag systems. The activity of each constituent in the slag at the refining temperature can then be obtained.

Based on the IMCT, the simple molecule TiO2 in the refining slags can be combined with ordinary molecules—such as CaO, Al2O3, MgO, FeO, MnO, and CaO+SiO2—to form 13 stable de-titanium products as TiO2, CaO·TiO2, 3CaO·2TiO2, 4CaO·3TiO2, Al2O3·TiO2, MgO·TiO2, 2MgO·TiO2, MgO·2TiO2, FeO·TiO2, 2FeO·TiO2, MnO·TiO2, 2MnO·TiO2, and CaO·TiO2·SiO2, respectively. According to the reported expression of the manganese distribution ratio [10,11], the titanium distribution calculation model can be described as

*<sup>L</sup>*Ti <sup>=</sup> (%TiO2) [%Ti] = *L*Ti,TiO2 + *L*Ti,CaO·TiO2 + *L*Ti,3CaO·2TiO2 + *L*Ti,4CaO·3TiO2 + *L*Ti,Al2O3·TiO2 +*L*Ti,MgO·TiO2 + *L*Ti,2MgO·TiO2 + *L*Ti,MgO·2TiO2 + *L*Ti,FeO·TiO2 +*L*Ti,2FeO·TiO2 + *L*Ti,MnO·TiO2 + *L*Ti,2MnO·TiO2 + *L*Ti,CaO·TiO2·SiO2 = *M*TiO2 · *ni*(*N*TiO2 + *N*CaO·TiO2 + 2*N*3CaO·2TiO2 + 3*N*4CaO·3TiO2 +*N*Al2O3·TiO2 + *N*MgO·TiO2 + *N*2MgO·TiO2 + 2*N*MgO·2TiO2 + *N*FeO·TiO2 +*N*2FeO·TiO2 + *N*MnO·TiO2 + *N*2MnO·TiO2 + *N*CaO·TiO2·SiO2 )/[%Ti] (10)

where *L*Ti is the total titanium distribution ratio; *L*Ti,*<sup>i</sup>* represents the respective titanium distribution ratio of structure unit *i* containing TiO2; *Ni* stands for the MAC of structure unit *i*; *ni* denotes the sum of mole numbers for each structure unit in equilibrium (mol); and *M*TiO2 is the molar mass of TiO2 (g/mol). Based on the IMCT model, the total titanium distribution ratio can then be acquired.

According to the calculation results of the IMCT model, the MACs of 3CaO·2TiO2, 4CaO·3TiO2, Al2O3·TiO2, 2MgO·TiO2, MgO·2TiO2, 2FeO·TiO2, 2MnO·TiO2, and CaO·TiO2·SiO2 were lower than 10<sup>−</sup>5. Therefore, their changes were ignored in the following discussion. In this case, Equation (10) can be simplified as

$$L\_{\text{Ti}} = \frac{\text{(\%TiO2)}}{\text{[\%Ti]}} = L\_{\text{Ti,TiO2}} + L\_{\text{Ti,CaO,TiO2}} + L\_{\text{Ti,MgCO,TiO2}} + L\_{\text{Ti,FeO,TiO2}} + L\_{\text{Ti,MnO,TiO2}} \tag{11}$$

$$= M\_{\text{TiO2}} \cdot \frac{\sum n\_i \text{(N}\_{\text{TiO2}} + N\_{\text{CaO,TiO2}} + N\_{\text{MgCO,TiO2}} + N\_{\text{FeO,TiO2}} + N\_{\text{MnO,TiO2}})}{[\text{\%Ti]}} \tag{12}$$
