## 3 Discussion
This is in line with the majority composition of Fe\({}_{2}\)SiO\({}_{4}\) found in the earlier investigation. Additionally, a spatial depiction of the primary components is provided by the elemental mapping). The micrographs' high concentrations of Fe, Si, and O support the idea that Fe\({}_{2}\)SiO\({}_{4}\) is the predominant mineralogical phase. In accordance with the compounds found in the XRD analysis (Figure 4a), such as Cu\({}_{6}\)Si\({}_{2}\)S\({}_{7}\), trace amounts of Cu are also detected, indicating the potential presence of copper sulfides or silicates in the sample. When these methods are combined, it is confirmed that the examined slag retains a composition rich in Si and Fe, mostly in the form of Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{2}\)SiO\({}_{4}\), with (Mg\({}_{2}\)Fe)\({}_{2}\)SiO\({}_{4}\) and KAl\({}_{2}\)[AlSi\({}_{3}\)O\({}_{10}\)](OH)\({}_{2}\) as secondary minerals. This information is essential for evaluating the slags possible industrial uses and value as well as its reactivity in particular environmental settings. The oxidation of a metal or metal oxide at high temperature is influenced by (i) the temperature, (ii) the composition of the gases generated, (iii) the time of exposure to the corrosive environment, and (iv) the pressure of the system, and is characterized by the reduction in the thickness (penetration) of the metal and the rate of formation of corrosion products. The oxidation rate increases significantly with increasing temperature [52], creating a homogeneous medium and improving the thermodynamic equilibrium [53]. When a metal is exposed to oxidation at high temperatures (corroded metal or thermal degradation), considering the reaction xM + yH\({}_{2}\)O \(\rightarrow\) MxOy + yH\({}_{2}\)[52], a value of the Gibbs free energy (activation energy) is obtained, as determined by Equations (1) and (2):  
\[\Delta G^{\circ}=-RT\ln(K) \tag{1}\]  
\[\Delta G^{\circ}=-yRT\ln(PH_{2}/PH_{2}O) \tag{2}\]  
During the oxidation process of a metal (M) exposed to water vapor, H\({}_{2}\) can be produced by the following reaction [54]:\[MO_{(x-1)}+H_{2}O{\rightarrow}MO_{x}+H_{2} \tag{3}\]  
where the expression for the Gibbs free energy is as follows:  
\[\Delta G^{\circ}=\Delta H^{MO_{x}}-\Delta H^{MO_{(x-1)}}-\Delta H^{H_{2}O}-T(S^{ H_{2}}-S^{H_{2}O})\leq 0 \tag{4}\]  
where MO\({}_{x}\) is the oxidized metal and MO\({}_{x-1}\) is the reduced oxide, respectively. The gas data published by [PERSON] et al. in 1970 [PERSON] et al. (1970) regarding the behavior of copper in the direct smelting process at 1300 \({}^{\circ}\)C considers among its analyses materials such as iron silicate and magnetite. However, specific thermodynamic data for copper slag have been presented in studies focused on metal recovery using the direct reduction smelting method [1]. The lack of information regarding thermodynamic data related to the oxidation of copper slag in water vapor and at high temperatures provides an interesting line of research that would significantly contribute to generating valuable information regarding the reduction in mining pollutants resulting from the use of slag in electrochemical processes, providing unprecedented added value. However, it is known that the generated copper slag normally contains metal oxides (FeO, Fe\({}_{3}\)O\({}_{4}\), SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), MgO, CaO, and Cu\({}_{2}\)O), with its mineralogical phases being mainly Fe\({}_{2}\)SiO\({}_{4}\) and Fe\({}_{3}\)O\({}_{4}\)[PERSON] et al. (2018). Figure 4: XRD analysis and EDX analysis of Chilean copper slag. Figure 5: SEM-EDS indicates that the elements with the greatest presence are Fe, Si, O, and other primary components. \begin{table}
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The analysis of the SEM-EDS image shown in Figure 5 confirms the presence of Fe\({}_{2}\)SiO\({}_{4}\) and small traces of Cu in the sample.