## 2 Materials and Methods
### Preparation of Synthetic Steel Slags
Each of the castables was weighed to 10 g and mixed with each of the slag types, also  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{**SiO\({}_{2}\)**} & \multirow{2}{*}{**CaO**} & \multirow{2}{*}{**MgO**} & \multirow{2}{*}{**Al\({}_{2}\)O\({}_{3}\)**} & \multirow{2}{*}{**TiO\({}_{2}\)**} & \multirow{2}{*}{**Fe\({}_{2}\)O\({}_{3}\)**} & \multirow{2}{*}{**MnO**} & \multirow{2}{*}{**CaF\({}_{2}\)**} & \multirow{2}{*}{**C/S**} & \multirow{2}{*}{**M/A**} & \multirow{2}{*}{**C/A  
10 g, which resulted in nine castable-slag mixtures. Then, the obtained mixtures were each homogenized for approximately1 h. The compositions of the mixtures obtained (A_S1, A_S2, A_S3, B_S1, B_S2, B_S3, C_S1, C_S2, C_S3) are shown in Table 1. Then, cylindrical samples of these mixtures with a diameter of 2.54 cm were pressed using a hydraulic hand press. The cylindrical samples were fired at 1350 \({}^{\circ}\)C for 2 h. Then, the samples were crushed to a powder with a grain size of less than 63\(\upmu\)m.XRD analysis was performed on the powder after corrosion. The ex situ XRD measurement was carried out at room temperature using an X'Pert Pro PANalytical X-ray diffractometer, with Cu K\(\alpha\) radiation, 0.02\({}^{\circ}\) per step, and 3 s time per step (20-range of 10\({}^{\circ}\)-90\({}^{\circ}\)). High Score Plus software (PANalytical) with the PDF-2 database supported by ICDD was used for data analysis. For the HMTA, cubic samples were formed from the obtained reactive mixtures of 50 wt.% castable and 50 wt.% slag. The homogenized mixtures were wetted using ethanol and compacted into cubes of approximately 3 mm\({}^{3}\) using a hand press. The high-temperature analysis study was conducted in the temperature range of 25-1450 \({}^{\circ}\)C. The samples were placed on a corundum plate and placed on a high-temperature microscope. The test was carried out in an oxidizing atmosphere, and the heating rate was 10 \({}^{\circ}\)C/min. The device's camera captured a live image of the sample's changes as the temperature rises. The geometrical changes of the samples during heating were estimated by observing changes in the height and shape of the sample at different temperatures throughout the experiment. The images were recorded with a digital camera. Figure 1 show the shapes of the samples at characteristic temperatures. Figure 1a show the initial shape of the sample at room temperature. The initial deformation temperature (Figure 1b) is the first temperature at which the shape factor changed by 1.5% with respect to the first image. The softening point (Figure 1c) is the temperature at which the sample becomes more rounded during heating and the surface of the sample changes. The sphere temperature (Figure 1d) is the temperature at which the upper corners of the sample are completely rounded, and the height of the sample equals its width. The hemisphere temperature (Figure 1e) is the temperature at which the height of the sample is half of its base width. The flow temperature (Figure 1f) is the first temperature at which the sample is melted to a third of its original height. Formula (1) was used to determine changes in the shape of the tested samples. Based on Formula (1) and the image from a digital camera, the calculation formula was estimated, and with the help of the MATLAB program, the changes in the shape of the samples at specific temperatures were determined. Each analysis was repeated three times, and the standard deviation was within the range of the marker size used in the figures. \[\delta_{T}=\frac{h(T)-h_{0}}{h_{0}}\times 100\;[\%] \tag{1}\]  
where:  
\(\delta_{T}\)--change of sample linear dimensions,  
\(h_{0}\)--sample height at room temperature,  
\(h(T)\)--sample height at temperature T.  
Figure 1: Shape changes of the sample during measurements with the heating microscope. (**a**) starting shape; (**b**) deformation temperature; (**c**) softening temperature; (**d**) sphere temperature; (**e**) hemisphere temperature; (**f**) flow temperature [43].