## 2 Materials and Methods
### Chemical, Crystallographic, and Microstructural Characterization
Specific energy of iron melting, overall mass loss, iron melting temperature, and kinetics parameters were analysed as a function of C/Fe\({}_{2}\)O\({}_{3}\) ratio Figure 2. The analysis of these trends allowed us to highlight the best mixing condition (C/Fe\({}_{2}\)O\({}_{3}\)) that lead to the optimum reduction conditions. Specific energy and mass loss maximization were considered as the main aspects for optimum definition. With regard to the iron melting, the area of the ideal triangle formed by the valley at 1000 \({}^{\circ}\)C represents the total specific energy associated to the melting of the iron. The integral was computed with the trapezium method, and the results are reported in Figure 2a. Figure 1: Example of heat flow, thermogravimetry (TG) and first order derivate of thermogravimetry (dTG) curves for the sample with pure graphite (sample C2—0.85 C/Fe\({}_{2}\)O\({}_{3}\)) (**a**) and with blast furnace sludges (sample A3—1.18 C/Fe\({}_{2}\)O\({}_{3}\)) as reducing agent (**b**), argon atmosphere. Full line: heat flow; dash-dot line: TG; dotted line: dTG. TG-DSC results show different behaviour in samples with graphite and B.F. sludges. Increasing the C/Fe\({}_{2}\)O\({}_{3}\) ratio, the specific energy associated to the melting of iron increases up to 1.19 C/Fe\({}_{2}\)O\({}_{3}\) Figure 2a. The sample at 1.53 C/Fe\({}_{2}\)O\({}_{3}\) (C4) shows a value, similar to that observed for 0.51 C/Fe\({}_{2}\)O\({}_{3}\) ratio (sample C1). This behaviour is probably because in sample C1 the carbon is not enough to reduce all the hematite, while in samples with 1.53 C/Fe\({}_{2}\)O\({}_{3}\) there is an excess of carbon. The excess of C in sample C4, being the test in Ar and the mass constant for all the tests, reduces the amount of Fe\({}_{2}\)O\({}_{3}\) available for reduction. Fe\({}_{2}\)O\({}_{3}\) is totally reduced to Fe but the absolute amount is so small that it results in a weak endothermic valley. In other words, the formed iron is so in low amount that it gives a low energy associated with its formation. Therefore, the best result in terms of amount of attained iron seems obtained in the sample with 1.19 C/Fe\({}_{2}\)O\({}_{3}\). However, the behaviour relating to the loss of mass as a function of C/Fe\({}_{2}\)O\({}_{3}\) Figure 2b does not comply with the expected trend as reported in Figure 2a, and as observed during the reduction of jarosite [57]. The highest mass loss (\(\sim\)20% wt.) was registered for 0.85 C/Fe\({}_{2}\)O\({}_{3}\), for the sample with 1.19 (\(\sim\)18.5% wt.). The lowest mass loss observed for 1.53 C/Fe\({}_{2}\)O\({}_{3}\) (\(\sim\)16.5% wt.) confirms the hypothesis that in this sample the excess of carbon negatively affects the yield of the reduced product. Therefore, in relation to mass loss, the 0.85 C/Fe\({}_{2}\)O\({}_{3}\) sample seems to have the best conditions to maximize the reduction yield. For this reason, these two C/Fe\({}_{2}\)O\({}_{3}\) (0.85 and 1.19) were replicated by using B.F. sludges as a reducing agent. It is worth mentioning that the value of the specific energy for the sample with blast furnace sludges follows a similar trend to the graphite reduced sample in Figure 2a. This is the first suggestion that it is possible to recover the iron in the red mud using blast furnace sludges in the same way as with C, which has already been demonstrated in other papers by the same authors [53; 57]. Another aspect that plays in favour to the use of B.F. sludges as a reducing agent is that the amount of specific energy involved in the reduction and melting of iron is lower for samples A2 and A3 than for C2 and C3. This means, from an industrial scale up point-of-view, that the treatment of red muds by B.F. sludges will be less energy demanding than the same process with a conventional reducing agent. Figure 2: Specific energy of the cast iron melting peak (**a**), total mass loss (**b**), temperature of the iron melting, (**c**) and transformation rate parameters (**d**) as a function of C/Fe\({}_{2}\)O\({}_{3}\) ratio. Argon atmosphere.