## 2 Materials and Methods
### Chemical, Crystallographic, and Microstructural Characterization  
The morphology of the sludges (red mud and B.F. sludge) and the six mixes before and after the roasting cycles, as well as the evaluation of the local chemical composition, were analyzed \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Mixes** & **Sample ID** & **RM (\% wt)** & **C Added (\% wt)** & **CaO Ling (\% wt)** & **C/Fe\({}_{2}\)O\({}_{3}\)** & **BBI** & **CBI** & **OB** \\ \hline
15\% C + 0.3\% CaO & C1 & 84.75 & 12.71 & 2.54 & 0.51 & 0.67 & 0.55 & 0.68 \\ \hline
25\% C + 0.3\% CaO & C2 & 78.13 & 19.53 & 2.34 & 0.85 & 0.67 & 0.55 & 0.68 \\ \hline
35\% C + 0.3\% CaO & C3 & 72.46 & 25.36 & 2.17 & 1.19 & 0.67 & 0.55 & 0.67 \\ \hline
45\% C + 0.3\% CaO & C4 & 67.57 & 30.41 & 2.03 & 1.53 & 0.67 & 0.55 & 0.67 \\ \hline
25\% C + 0.3\% CaO & A2 & 51.28 & 46.15 & 2.56 & 0.84 & 0.69 & 0.57 & 0.67 \\ \hline
35\% C + 0.3\% CaO & A3 & 34.84 & 62.72 & 2.44 & 1.18 & 0.70 & 0.59 & 0.66 \\ \hline \end{tabular}
\end{table} 
Table 4: Chemical composition (% weight), C/Fe\({}_{2}\)O\({}_{3}\) ratio, and basicity indexes of red mud/reducing agent mixes. BBI = Binary Basicity Index, CBI = Complex Basicity Index, OB = Optical Basicity. using an electronic scanning microscope (SEM, Zeiss EVO50, Carl Zeiss AG, Oberkochen, Germany) equipped with an energy dispersive spectroscopy (EDS) probe (Oxford INCA, Oxford Instruments, High Wycombe, UK). The crystallographic analysis was carried out by means of a Bruker D8 Advance in 0-0 configuration (Cu-K\(\alpha\) radiation: \(\lambda\) = 1.54 A) on 2 g of ground sample (size \(<\)100 \(\upmu\)m). The samples were analysed between 0 and 80 \({}^{\circ}\)20 with a Lynks-eye-1 detector and fixed 0.6\({}^{\circ}\) divergence slit. The qualitative analysis was performed by Crystal Impact Match! software (version is 3.8.3.151) based on the Crystallographic Open Database (COD, revision 218120, September 10, 2019). Sample grinding (\(<\)100 \(\upmu\)m) was performed using a Retsch PM 400 planetary ball mill (Retsch Technology GmbH, Haan, Germany), using a 100 mL grinding jar and 10 mm zirconia sphering balls. Grinding was carried out at 350 rpm for different times depending on the hardness of the sample. Iron metallization degree (MD) in the reduced samples was determined by dissolution analysis. Total iron (metallic iron (Fe\({}_{\text{Met}}\)) plus unreduced residual iron oxide (Fe\({}_{\text{Tot}}\))) was determined in accordance with ISO 2597 while metallic iron was determined in accordance with ISO 5416. The dissolution of 0.4 g of powdered sample (\(<\)100 \(\upmu\)m) occurs in an alkaline solution of 30 mL of hydrochloric acid (HCl), subject to subsequent thermal cycles and to the addition of other substances such as water and ammonia. The degree of metallization is determined as the ratio between metallic iron and total iron (4). \[MD=\ \frac{\ \  
The two valleys, in the range 200-400 \({}^{\circ}\)C, are due to the complete dihydroxylation of the residual gibbsite and boehmite from the previous red mud roasting step. The second peak also belongs to portlandite dihydroxylation, and is due to the lime that was hydrated after the preparation of the mixes. The valley at 650 \({}^{\circ}\)C, more intense in the sample with blast furnace sludges, is related to the lining of the magnesite. Magnesite can come from the contact of the red mud with the sea water, and is capable of significantly reducing the alkalinity of the muds. In blast furnace sludge blends, this peak appears more intense because MgO was intentionally added to the mix. The weak valley at about 900 \({}^{\circ}\)C and intense one at 1000 \({}^{\circ}\)C belong to the first reduction step of Fe\({}_{2}\)O\({}_{3}\) to Fe\({}_{3}\)O\({}_{4}\), and to the completing reduction and melting of the newly reduced iron [63, 64]. The aforementioned peaks are also detected in the dTG graphs whereas the TG clearly shows as a mass variation when the reduction process begins. From the TG-DSC data, some calculations were made.