*4.1. Thermodynamic Considerations*

The crystallization process of the molten slag is composed of nucleus formation and crystal growth, and is also determined by thermodynamic and kinetic factors. As shown in Figure 5, according to the calculation results of the solidification process through FactSage7.1, there are three phases including the liquid slag, spinel crystal, and α-C2S in the CaO-SiO2-MgO-Al2O3-Cr2O3-FeO system at 1450 ◦C. Combined with the preparation of synthetic slag, the nucleus could not form in the liquid phase, which transforms directly into the glassy matrix, whereas spinel crystal and α-C2S were high-temperature precipitated phases in the CaO-SiO2-MgO-Al2O3-Cr2O3-FeO system at 1450 ◦C. The heating time only affected the diffusion of the particles, and had little effect on mineral composition. These observations can explain why the mineral phases remained constant with the extension of heating time at 1450 ◦C.

**Figure 5.** Theoretical analysis of the slag solidification process and selection of temperature.

Spinel crystal is the main mineral phase for improving chromium stability in the CaO-SiO2-MgO-Al2O3-Cr2O3-FeO system [14–16]. Additionally, the reactions that form spinel crystals can occur between the MgO, Al2O3, Cr2O3, CaO, and FeO in the CaO-SiO2-MgO-Al2O3-Cr2O3-FeO system. The reactions are shown in Equations (1)–(5).

(MgO) + (Cr2O3) = MgO·Cr2O3(s) (1)

$$(\text{FeO}) + (\text{Cr}\_2\text{O}\_3) = \text{FeO} \cdot \text{Cr}\_2\text{O}\_3(\text{s}) \tag{2}$$

$$(\text{MgO}) + (\text{Al}\_2\text{O}\_3) = \text{MgO} \cdot \text{Al}\_2\text{O}\_3(\text{s}) \tag{3}$$

$$(\text{FeO}) + (\text{Al}\_2\text{O}\_3) = \text{FeO} \cdot \text{Al}\_2\text{O}\_3(\text{s}) \tag{4}$$

$$(\text{CaO}) + (\text{Cr}\_2\text{O}\_3) = \text{CaO} \cdot \text{Cr}\_2\text{O}\_3(\text{s}) \tag{5}$$

MgCr2O4 formed by MgO and Cr2O3 is the most stable phase at high temperature [15]. During the heating period, iron and calcium elements that evolve into spinels through the isomorphic substitution are gradually replaced by magnesium. Consequently, the magnesium content increases, while the contents of iron and calcium decrease. Furthermore, chromium stability is affected by calcium content to a large extent [15]. The silicate microcrystals containing calcium are adsorbed into the spinel lattice during spinel growth due to the formation of a finite solid solution with

MgO·Cr2O3 [17]. Compared with other silicate mineral phases, dicalcium silicate is more soluble in water. The dissolution of chromium increases significantly as the content of dicalcium silicate in chromium spinels increases [17,18]. Thus, prolonging the heating time can reduce the content of dicalcium silicate in chromium spinels and improve their stability.
