## 3 Results and Discussion  
### Comparison of Thermodynamic Calculations and Mineralogical Investigations  
Comparison of the performed FactSageTM equilibrium calculations (Figure 1a-c) with the mineralogical analysis of the phase composition and phase distribution (Figure 2) revealed that the phase proportions for samples A and C were best reproduced at 850 \({}^{\circ}\)C. Therefore, the influence of the quartz addition on the phase distribution and the amount of quartz sand required for the experiments was calculated at 850 \({}^{\circ}\)C in equilibrium mode.  
The calculations performed on sample A (laboratory experiments) and sample B (pilot scale experiments) at 850 \({}^{\circ}\)C with varying SiO\({}_{2}\) content are shown in Figure 1a',b'. Above 35 g and 30 g SiO\({}_{2}\), respectively, no wuestite (MeO\({}_{\text{-}}\)A), moderate spinel (SPINA), and more calcium silicates (olivine (OlivA), melilite (Mel\({}_{\text{-}}\)A), and clinopyroxene (cPyr; M\({}_{1}\)M\({}_{2}\)T\({}_{2}\)O\({}_{6}\), M\({}_{1}\) = Ca, Mg, Fe, Mn and M\({}_{2}\) = Al, Mn, Mg, Fe and T = Si, Al, Fe)) were formed. As it is assumed that melilites hydrate [10] and yield possible adsorption sites [9], the SiO\({}_{2}\) concentration corresponding to the highest melilite abundance (= 40 g SiO\({}_{2}\)) was chosen for the laboratory experiments (Figure 1), resulting in a normalized total SiO\({}_{2}\) content of 31.3 g. This changed the FeO/SiO\({}_{2}\) ratio from 3.66 to 1.12 and the CaO/SiO\({}_{2}\) ratio from above two (2.03) to below one (0.62). Taking into account the already present SiO\({}_{2}\), the input for the laboratory experiments was 56 g quartz sand (assumption: SiO\({}_{2}\) purity = 100%) and 204 g of sample A. For the pilot scale experiments, the same calculations were performed for sample B, resulting in a calculated SiO\({}_{2}\) amount of 27.3 kg per 100 kg of sample B and a changed FeO/SiO\({}_{2}\) ratio from 3.42 to 1.06 and a CaO/SiO\({}_{2}\) ratio from 2.38 to 0.74.  
Sample B (higher CaO input) could only be characterized chemically prior to the pilot scale experiments. Mineralogical examination afterward revealed that larnite and brownmillerite (Ca\({}_{2}\)(Al,Fe)\({}_{2}\)O\({}_{5}\)) were formed in sample B, instead of olivine and melilite (Figure 2a,b). The performed FactSageTM calculations (Figure 1b) showed that larnite (bC2 SA) with 99.6% Ca\({}_{2}\)SiO\({}_{4}\) (0.4% Mg\({}_{2}\)SiO\({}_{4}\) and 2.7\(\cdot\)10\({}^{-02}\)% Fe\({}_{2}\)SiO\({}_{4}\)) was formed at a transition temperature of 865.7 \({}^{\circ}\)C and that therefore, the calculations for the pilot scale experiments were not performed at the optimum temperature. The implementation of brownmillerite (C2 AF, not shown) resulted in low calculated concentrations of brownmillerite and melilite in both samples A and B, although no brownmillerite was identified experimentally in sample A and no melilite in sample B, respectively.  
Figure 1: FactSageTM calculations. (**a**) and (**a**\({}^{\prime}\)) sample A, (**b**) and (**b**\({}^{\prime}\)) sample B and (**c**) and (**c**\({}^{\prime}\)) sample C. (**a**–**c**) Mineral phase composition as a function of temperature. (**a**\({}^{\prime}\)**–**c**\({}^{\prime}\)) Mineral phase composition at 850 \({}^{\circ}\)C with varying SiO\({}_{2}\) content (not normalized); the normalized SiO\({}_{2}\) concentration of samples A–C as well as the target SiO\({}_{2}\) concentrations for samples A and B are marked. Abbreviations according to FactSageTM: liquid slag (SLAGA), olivine group (OlivA), melilite group (Mel_A), wheustite solid solution (MeO_A), spinel solid solution (SPINA), clinopyroxene (cPyrA), laronite (bC2 SA), and Fe(bcc) (Fe(s)). Plotted for publication with version 7.3 (FToxid, 2019 and FactPS, 2019) and calculated as described in Section 2.2.