## 4 Summary and Conclusions  
Castables with MgO content of 3-7 wt.% were prepared using tabular alumina and magnesia fume by casting, drying, and firing at elevated temperatures. In addition, three slags were prepared via classical ceramic route and calculated by FactSage to determine probable phase vs. temperature. Based on the analysis of the results, the thermodynamic changes in the solid and liquid phases of steel slags with a mass ratio of CaO/SiO\({}_{2}\) (C/S) 1.1 (S1), 3.5 (S2), and 5.5 (S3) were predicted, and an oxidizing atmosphere was formed as a result of the temperature increase. The presence of SiO\({}_{2}\)-rich phases, including C\({}_{3}\)MS\({}_{2}\), in the S1 sample in the analyzed temperature range from 1300-1500 \({}^{\circ}\)C can be associated with a significant increase in the liquid phase content for this sample, as much as 96.76 wt.%. Sample S3 and sample S2, for which the content of SiO\({}_{2}\)-rich phases was lower, showed in the analyzed temperature range 80.15 wt.% and 65.94 wt.%, respectively. Equweight mixtures of slags and castables (50 wt% slag and 50 wt.% castable) were calculated by FactSage, observed by heating microscopy thermal analysis (HMTA), fired at 1350 \({}^{\circ}\)C, and investigated by X-ray diffraction (XRD). Thermochemical simulations were performed using FactSage software, and on this basis, the graphs were created; 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 and steel slags with the C/S mass ratio of 1.1_S1, 3.5_S2, and 5.5_S3, as well as 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. In addition, the chemical composition of the liquid phase of the reactive mixtures containing components of the cement-free corundum-spinel refractory castable with 7 wt.% of MgO and steel slags with the C/S mass ratio of 1.1, 3.5, and 5.5 was determined. There were qualitative and quantitative differences between the samples, depending on the analyzed type of slag. An important observation was that more SiO\({}_{2}\)-rich phases were detected in the S1 slag compared to the S2 and S3 slags, as well as information that with increasing MgO content in the overall composition, the CM\({}_{2}\)A\({}_{8}\) content in the samples decreases. On the other hand, it was observed that with an increase in the SiO\({}_{2}\) content in the overall composition, the CM\({}_{2}\)A\({}_{8}\) content in the samples increased. Moreover, comparing the phase composition of the C_S1, C_S2, and C_S3 equiweight mixtures with the phase composition of the slags S1, S2, and S3, respectively, for a specific temperature of 1350 \({}^{\circ}\)C (the temperature at which the sintering processes took place, and the content of the liquid phase is so low that the analysis of the results could be reliably carried out), showed that the content of silica-rich phases is much lower for the equiweight mixtures than for the slags themselves. This is related to the widening of the temperature range in which the liquid phase forms. In sample C_S1, where the proportion of the SiO\({}_{2}\)-containing phase was the highest, the first amounts of the liquid phase were formed at the lowest temperature. In order to perform the HMTA, cubic samples were prepared from the mixtures of 50 wt% slag and 50 wt.% castable. Based on the thermal analysis of heating microscopy in the measuring range, it was found that the concretes showed shrinkage only in contact with the slag with the lowest C/S mass ratio, and it was observed that the higher the MgO mass content in the analyzed sample, the lower its shrinkage. Characteristic points of transformation of reactive mixtures were also determined. For castables with the highest mass content of MgO (7 wt.%), significant shrinkage occurred at higher temperatures than for other castables.