## 2 Materials and Methods
### Reduction Tests
By observing the trend of Fe\({}_{\mathrm{Met}}\) as a function of C/Fe\({}_{2}\)O\({}_{3}\), it can be noted that it agrees with the variation of the specific energy Figure 7b. For instance, at 1200 \({}^{\circ}\)C, it proportionally increases with the C/Fe\({}_{2}\)O\({}_{3}\) ratio whereas at 1500 \({}^{\circ}\)C, the final amount of metallic fraction is weakly lower, confirming that at higher temperature a part of the new formed iron reoxidizes during the cooling step. The residual C amount was determined through elemental analysis and plotted in Figure 7c. The figure confirms the results derived from TG-DSC analysis and visual inspection. Increasing the amount of C available, the amount of residual C in the reduced product increases. In addition, increasing the temperatures lead to an increase of the residual carbon mass in the reduced material. Probably, this happen because the exceeding carbon cannot completely burn out due to a sort of protection of the already formed CO. In addition, during the cooling step of the roasting treatment, part of the unreacted CO decomposes again, below 700 \({}^{\circ}\)C, depositing C. This behaviour was evident in the control batch samples (C series) whereas for the B.F. sludge reduced samples, the residual C was almost constant and at a very low concentration. Probably, since in the B.F. sludge the C-bearing material is coke, it starts to form CO at a lower temperature than graphite (as stated in Figure 4d) giving time to completely reacts with reducible oxides thus, by consuming itself more homogenously during the heating step. Figure 6: Stereo microscope images of the sample reduced through graphite (C2) at (a) 1200 \({}^{\circ}\)C; (b) 1500 \({}^{\circ}\)C and blast furnace sludges (A2) (c) 1200 \({}^{\circ}\)C; (d) 1500 \({}^{\circ}\)C.  
Finally, the metallization degree (MD) was plotted as a function of the C/Fe\({}_{2}\)O\({}_{3}\) ratio Figure 7d. The maximum metallization degree (nearly 85%) was measured at C/Fe\({}_{2}\)O\({}_{3}\) of 0.85, in correspondence of the maximum mass loss registered in TG-DSC. As well, the behaviour of B.F. sludge reduced samples follows the trend of mass loss: The maximum (80%) corresponds to the 1.19 C/Fe\({}_{2}\)O\({}_{3}\) ratio. As a confirmation of the partial reoxidation during the cooling step from 1500 \({}^{\circ}\)C, the metallization degree is tendentially lower than the values obtained at 1200 \({}^{\circ}\)C. In addition, the maximum was obtained for the sample at 15% C (C1) likely as here the amount of metal was the lowest, hence its reoxidation was limited. Starting from the weight of each sample charged in the muffle furnace at 1500 \({}^{\circ}\)C, the mass loss was determined and compared with the theoretical one, by accounting:  
* the loss of the oxygen contained in the Fe\({}_{2}\)O\({}_{3}\) when it is reduced to Fe (reaction c, Section 2.3);
* the loss of all the oxygen contained in the oxides owing a standard oxygen potential higher than CO at 1500 \({}^{\circ}\)C (ZnO, PbO, P\({}_{2}\)O\({}_{5}\), SO\({}_{3}\), Cr\({}_{2}\)O\({}_{3}\), MnO and V\({}_{2}\)O\({}_{5}\)) (reactions d to j, Section 2.3);
* the loss of all the C contained in the mix to form CO (reaction a, Section 2.3). In this case, the computed mass loss was underestimated, a systematic error of about 5%, with respect to the experimental results. Mass loss does not depend only on reduction reactions, but at 1500 \({}^{\circ}\)C also the non-reducible oxides undergo some transformation forming the slag. Probably, some of the reactions lead to a change in the oxidation state of certain oxide species, resulting in a further loss of oxygens. In addition, part of the Na\({}_{2}\)O could sublimate, over 1275 \({}^{\circ}\)C, if it is not bound in a complex oxide, as was observed by [PERSON] and [PERSON] [67]. For example, a study analyzed the kinetics of Na\({}_{2}\)O evaporation in a COREX(r) process slag [68].