## 3 Results
The combination of these phases was calculated in the C_S1 mixture (Figure 4a). Therefore, for the reactive C_S1 mixture, it was the reason for a clear shift in the formation of the liquid phase towards lower temperatures, compared to the C_S2 and C_S3 mixtures, where the eutectic temperatures (Figure 7) between components CA, CA\({}_{2}\), C\({}_{2}\)AS, MA were higher and exceeded 1500 \({}^{\circ}\)C [38; 46; 47]. Based on the thermochemical calculation using FactSage software, the chemical composition of the total liquid phase, besides its content, vs. temperature, was also established and presented in Figure 6. The changes in the oxide content of the total liquid phase in the individual reactive mixtures were mainly related to C\({}_{2}\)AS and CAS\({}_{2}\) in C_S1 (Figures 4a and 6a); CA\({}_{2}\), C\({}_{2}\)AS, CA in sample C_S2 (Figures 4b and 6b) and CA, C\({}_{2}\)AS, CA\({}_{2}\) in sample C_S3 (Figures 4c and 6c). For C_S1, C_S2, and C_S3 mixtures, the content of SiO\({}_{2}\)-containing phases C\({}_{2}\)AS and CAS\({}_{2}\) (Figure 4a-c) decreases when the C/S mass ratio is increased (Table 1). At a temperature of 1450 \({}^{\circ}\)C, the highest content of SiO\({}_{2}\) was found for sample C_S1 (above 19 wt.%), while for samples C_S2 and C_S3, the content of SiO\({}_{2}\) was less than 1 wt.% (Figure 6). Based on this data, it was found that increasing SiO\({}_{2}\) content in the mixture decreased the temperature at which the liquid phase commenced. It can be assumed that MgO for sample C_S1 comes from both MA and CM\({}_{2}\)A\({}_{8}\), while for samples C_S2 and C_S3, it only comes from the MA phase. The lower the Al\({}_{2}\)O\({}_{3}\) content in the mixtures (Table 1), 63.66, 60.83, 49.33 wt.% for the temperature of 1450 \({}^{\circ}\)C, the higher the observed content of the liquid phase (Figure 6) 7.83, 16.83, 64.24 wt.% by weight in reactive mixtures, C_S2, C_S3, C_S1, respectively. The melting process of the reactive mixtures containing components of the spinel-forming alumina castables and steel slag was evaluated by heating microscopy thermal analysis (HMTA). From the micro-processed images, the relative height changes of the samples (8h) versus temperature were presented in the form of shrinking curves, as shown in Figure 8. This figure contains, as examples, the heating microscope images registered at 1410 \({}^{\circ}\)C and 1420 \({}^{\circ}\)C. According to the data presented in the experimental section, the characteristic transformation points of samples were determined at the HMTA curves and summarized in Table 3.  
Figure 8: Shrinkage curves of castable compositions (A, B, and C) with slags (S1, S2, and S3) versus increasing temperature. It can be seen that the values of the temperatures for the characteristic points of the castables A, B, and C vary significantly when they are in the mixtures containing slags S1 or S2 and S3. A distinguishing property of the A_S1, B_S1, and C_S1 HMTA curves is the possibility of the determination of characteristic transformation points of reactive mixtures. Based on the comparative study of the 3,5 and 7 wt.% MgO-containing castablesbehavior in contact with slag S1, it should be indicated that the thermal stability and corrosion resistance at high temperatures of castables can be arranged in increasing order of the MgO content up to ca. 1410 \({}^{\circ}\)C (Figure 8). As was evidenced by photographic images made with a camera, compared to the respective initial height of each sample, there was a mean shrinkage of ca. \(-\)64.87% (A_S1), ca. \(-\)27.2% (B_S1), and \(-\)19.1% (C_S1) at ca. 1410 \({}^{\circ}\)C, which was promoted by the liquid phase formation during corrosion processes. While at the temperature of around 1420 \({}^{\circ}\)C, a reversal of the tendency was observed and a smaller shrinkage of the B_S1 sample (\(-\)31.2%) than the C_S1 sample (\(-\)57.95%).