## 3 Results
Thus, the most accelerated increase in the share of the liquid phase was observed for slag S1, for which, at 1000 \({}^{\circ}\)C, the highest mass content (about 70 wt.%) of microsilica-rich phases was calculated. On the other hand, the smallest increase in the mass content of the liquid phase was calculated for S2 slag, for which, at 1000 \({}^{\circ}\)C, the lowest mass content (about 20 wt.%) of the microsilica-rich phases was observed. As shown in Figure 4, for the castable C with all the slags used in the experiment, few changes in phase composition were identified. For castables A and B, the obtained qualitative results exhibited similar trends in relation to the slag with the same C/S mass ratio. However, significant qualitative and quantitative changes in the curve corresponding to the phases, both solid and liquid, were established between the same castable under the influence of three different slags (S1, S2, and S3). As a result of the thermodynamic analysis of reactive mixtures composed of castable Cand slags S1, S2, and S3 (Figure 4a-c, respectively) via FactSage software, within the temperature range between 1250 \({}^{\circ}\)C and 1650 \({}^{\circ}\)C, the spinel (MA), CM\({}_{2}\)As, CA, CA\({}_{2}\), gehlenite (C\({}_{2}\)AS), anorthite (CAS\({}_{2}\)), and liquid phases were calculated. From the data presented in Figures 4a and 5, two possible MgO-containing phases, i.e., MA and CM\({}_{2}\)As, in the reactive mixtures containing simple oxides with the chemical composition derived from the mixture of 50 wt.% slag and 50 wt.% castables can coexist in equilibrium in the samples A_S1, B_S1, C_S1, A_S2, and B_S2. Based on the data presented in Table 1, an obvious relationship between the four variables, i.e., MgO/Al\({}_{2}\)O\({}_{3}\), CaO/Al\({}_{2}\)O\({}_{3}\), CaO/SiO\({}_{2}\), and CaO/MgO mass ratios, can be noticed. CM\({}_{2}\)As\({}_{8}\) can exist with the MA phase within the temperature range 1250-1550 \({}^{\circ}\)C when the M/A, C/A, C/S, and C/M mass ratios are within the range of 0.15-0.19, 0.27-0.42, 1.08-3.21, and 1.67-2.76, respectively, (Table 1) for castable compositions A_S1, B_S1, C_S1, A_S2, and B_S2 (Figure 5) can be drawn. However, for the reactive mixtures A and B with slag S2, this dependency exists in the temperature range 1250-1450 \({}^{\circ}\)C. Furthermore, as shown in Figure 5 and Table 2, it can be observed that the possibility of the CM\({}_{2}\)As formation decreases with increasing MgO content in the reactive mixtures. In addition, it has been recognized that the formation of the CM\({}_{2}\)As phase is favored as the C/S mass ratio decreases in the reactive mixtures. Such dependency was observed in A_S1 and A_S2. Figure 3: Thermodynamic predictions of the solid phases and liquid phase of the steel slags with the C/S mass ratio of 1.1_S1 (**a**), 3.5_S2 (**b**), 5.5_S3 (**c**), when exposed to an oxidizing atmosphere vs. an increasing temperature. Figure 4: Thermodynamic predictions of the solid phases and liquid phase of the reactive mixtures containing components of the cement-free corundum-spinel refractory castable with 7 wt.% of MgO (castable C) and steel slags with the C/S mass ratio of 1.1_S1 (a), 3.5_S2 (b), 5.5_S3 (c), when exposed to an oxidizing atmosphere vs. increasing temperature. Figure 5: Thermodynamic predictions of the CM\({}_{2}\)A\({}_{8}\) solid phase of the reactive mixtures A_S1, B_S1, C_S1, A_S2, and B_S2 versus increasing temperature. Based on the results presented by [PERSON] et al. [47,48], the CM\({}_{2}\)A\({}_{8}\) phase can be generated by the high temperature (1200 \({}^{\circ}\)C) reaction between MA and C\({}_{2}\)AS. The possible mechanism involves the interaction between MA and C\({}_{2}\)AS-rich at ca. 1200 \({}^{\circ}\)C by the Mg\({}^{2+}\) ions incorporation into the liquid phase. While analyzing Figures 4a and 5 simultaneously, it can be noticed that the amount of CM\({}_{2}\)As phase for the C\({}_{\text{-}}\)S1 mixture increases to the temperature of 1350 \({}^{\circ}\)C, with a decrease in C\({}_{2}\)AS and MA phases.