Duan et al. [
31,
32,
33] calculated the activity of components in CaF
2-CaO-Al
2O
3-B
2O
3-SiO
2 slag system by IMCT model and FactSage thermodynamic software, respectively. The calculated activity coefficient of B
2O
3 in the slag at 1600 °C is γ
B2O3 = 4.79 × 10
−4 by employing the IMCT model, which is much higher than that calculated by thermodynamic software. Peng et al. [
34] reported that the γ
B2O3 = 2.45 × 10
−4 in the CaF
2-CaO-Al
2O
3-B
2O
3-SiO
2 slag at 1600 °C using the agglomerated electron phase model. By comparing the activity coefficient of B
2O
3 calculated by different authors, the calculated γ
B2O3 by the IMCT model and the agglomerated electron phase model have the same order of magnitude. The value γ
B2O3 determined by Peng et al. is slightly lower than the result calculated by the IMCT model, which is likely due to the presence of MgO content reducing the activity coefficient of B2O3 in the 1600 °C slag. Duan et al. [
35] passed the accuracy of the calculated activity of TiO
2 in the CaF
2–CaO–Al
2O
3–TiO
2(–MgO) slags and that of Ce
2O
3 in the CaF
2–CaO–Al
2O
3–MgO–Ce
2O
3 slag by the IMCT model has been proved by the slag-metal experimental results. Meanwhile, although the calculated activity of B
2O
3 in the CaF
2–CaO–Al
2O
3–B
2O
3–SiO
2 slag by the IMCT model is higher than that by the thermodynamic calculation software at 1600 °C due to the experimental measurement of the activity of B2O3 in the slag is rarely reported, the calculated γ
B2O3 = 4.79 × 10
−4 by the IMCT model at 1600 °C is also testified by the slag-metal experimental results. These results imply that the IMCT model can be reliably applied to calculate the activity of components in slag. Therefore, it is ideal to use IMCT to calculate the slag melt containing CaF
2.
According to Nikolopoulos et al. [
36], 21 complex molecules exist in the CaO-CaF
2-MgO-Al
2O
3-SiO
2 slag system.
Table 7 shows the expressions for each structural unit, mole number, and mass action concentration in the slag.
The molar number of the five components in the slag is given by Equations (4)–(8).
Based on Equations (3)–(8), the mass action concentration of each component of the slag, that is, the bulk activity, can be obtained using MATLAB R2021b software. The surface phase activity of the slag component satisfies the coexistence theory, that is, the sum of the surface phase activities of all structural units is 1, as demonstrated in Equation (9).
After adding the deoxidation alloy during the refining of 15-5PH stainless steel, the Al in the molten steel reacts with oxide components in the slag, resulting in the continuous loss of Al via burning. Typically, SiO
2 and MgO in Al-deoxidized stainless steel refining slag react with Al in molten steel, as shown in Equations (10) and (13). These reactions are the main causes of aluminum burning in the molten steel. According to the theoretical model of slag coexistence, N
SiO2, N
Al2O3, and N
MgO can be used to represent the activities of the slag components a
SiO2, a
Al2O3, and a
MgO, respectively in Equations (12) and (14). The activity of each component in the slag at 1600 °C was calculated using the coexistence theory of the five-component slag established above. Accordingly, the activity changes of CaF
2, Al
2O
3, and MgO at various slag basicities were calculated, and the results are shown in
Figure 11. The calculation results show that with an increase in slag basicity, the activity of the CaF
2 and Al
2O
3 components in the slag gradually decreases, whereas the activity of MgO increases. Furthermore, the variation in log (
) and log (
) with the increase in slag basicity can be extrapolated from
Figure 11 (
Figure 12). With an increase in slag basicity, log (
) decreases. According to Equation (12), the decrease in log (
) results in a higher Si content and lower Al content in molten steel, which increases the burning loss of Al and destroys the “slag-steel” balance, thus affecting the cleanliness of molten steel. With an increase in the slag basicity content, log(
) increases. According to Equation (15), an increase in log (
) can increase the Mg content in molten steel and lower the Al content. After 90 min of reaction between the molten steel and slag, the experimental findings reveal that the steel sample A1 with the greatest Mg content was obtained from the slag sample SA1 with the lowest slag basicity. The Mg concentration in steel sample A1 reached 12 ppm at this point.
The production of inclusions in steel is substantially affected by the increase in the Mg concentration in molten steel. Using FactSage
TM 8.2 software, the Al-Mg stable phase diagram of 15-5PH stainless steel at 1600 °C was predicted (
Figure 13). The transition sequence of oxide inclusions changed from Al
2O
3 → MgAl
2O
4 → MgO when the Mg level in molten steel increased from 2 to 12 ppm.
Figure 13 shows the Mg content of the experimental steel samples. The composition of Samples A1 and A2 was in the spinel phase, whereas the composition of Sample A3 was in the MgO phase, as shown in
Figure 13. The experimental results were in strong agreement with the calculated results.