## 3 Results  
Thermodynamic Analysis of Reactive Mixtures Containing Components of Spinel-Forming Alumina Castables and Steel Slags and Thermal Analysis with Microscopic Heating (HMTA)  
FactSage thermochemical software was used to perform the thermodynamic analysis of the phase transformation of the spinel-forming alumina castables during heat treatment in the air in the presence of steel slag with the C/S mass ratio of 1.1 (S1), 3.5 (S2), 5.5 (S3). Although the phase composition of castables with 3, 5, and 7 wt.% of MgO was established as containing corundum and spinel phases, the phase changes of the reactive mixtures considered in the thermodynamic calculations were evaluated in the interest of proving the evolvement sequence of the resultants of reaction of MgO, Al\({}_{2}\)O\({}_{3}\), and SiO\({}_{2}\) from castables, and simple oxides from slags. Thermodynamic analysis of the phase transformation of the slag components S1, S2, and S3 was also performed. Hence, a thermodynamic calculation was performed to predict the possible phases formed during corrosion. All results are presented in Figures 3-6 and Table 2. The phase transformations with slags vs. temperature S1, S2, and S3 are summarized in Figure 3a-c, respectively. In Figure 4, thermodynamic predictions of the solid phases and liquid phase of the reactive mixtures containing components of the spinel-forming alumina 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 versus increasing temperature are presented. Castable C (7 wt.% of MgO) shown in Figure 4a-c was selected due to literature reports on the improvement of corrosion properties with the increase of spinel content. Castable C showed the highest corrosion resistance, which will also be presented later in this paper. Figure 5 show the 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, because only in these samples the CM\({}_{2}\)A\({}_{8}\) phase was calculated. Additionally, Figure 6 present content and chemical compositions of the liquid phase from the FactSage calculation in wt.% vs. temperature of the reactive mixtures containing components of the spinel-forming alumina castable with 7 wt.% of MgO (castable C) and steel slags with the C/S mass ratio of S1 (a), S2 (b), and S3 (c). Table 2 show the onset temperature for the formation of the liquid phase. The castable composition with slag used in the calculations was previously presented in Table 1. A schematic diagram of the eutectic temperatures for binary and ternary compounds based on the literature data [37; 38; 40; 44; 45; 46; 47] is presented in Figure 7, which will allow for the interpretation of the results. A thermodynamic analysis of the slag components in the temperature range of 1000-2000 \({}^{\circ}\)C was carried out. Based on this analysis, the phases C\({}_{3}\)MS\({}_{2}\), C\({}_{2}\)MS\({}_{2}\), CMS, the liquid phase for the slag S1 (Figure 3a), C\({}_{3}\)MA\({}_{2}\), C\({}_{2}\)S, C\({}_{3}\)MS\({}_{2}\), MA phase, liquid phase, small amounts of free oxides for the slag S2 (Figure 3b), C\({}_{3}\)A, C\({}_{3}\)MA\({}_{2}\), C\({}_{2}\)S, liquid phase, small amounts of free oxides for the slag S3 (Figure 3c) were calculated. The tested slags showed differences in both quantitative and qualitative composition. In the temperature range of 1300-1500 \({}^{\circ}\)C, an accelerated increase in the number of liquid phases was observed, along with an increase in the mass content of microsilica-rich phases in slags. The change in mass content of the liquid phase in the analyzed temperature range was 96.76 wt.%, 80.15 wt.%, and 65.94 wt.% for slags S1, S3, and S2, respectively.