*3.1. Effect of Temperature on the Viscosity of CaO–SiO2–FeO–Al2O3–MgO Slag*

Figure 2 shows the temperature dependence of viscosity in the CaO–SiO2–FeO–Al2O3– MgO system. Typically, slag viscosity decreases with increasing temperature. However, the effect of temperature on the viscosity change varies with slag composition. When both FeO and Al2O3 were 0 wt%, the viscosity increased steeply with decreasing temperature. However, when Al2O3 was added to the CaO–SiO2–MgO system, the temperature dependence of viscosity decreased. The addition of Al2O3 led to an increase in the temperature dependence of viscosity in the CaO–SiO2–FeO–MgO system. The relationship between temperature and viscosity can be quantitatively expressed by an Arrhenius-type equation, assuming that viscous shear is a thermally activated process [25]:

$$
\eta = \eta\_{\infty} \exp\left(\frac{E}{RT}\right),
\tag{1}
$$

where *η* is the viscosity, *η*<sup>∞</sup> is the pre-exponential constant, *R* is the ideal gas constant, *T* is the absolute temperature, and *E* is the activation energy. From Equation (1), the activation energies of the present slag system were calculated, as shown in Figure 3. The highest activation energy was found in the CaO–SiO2–MgO ternary slag system. When Al2O3 was added to this ternary system, the activation energy initially decreased. However, above 20 wt% Al2O3, higher Al2O3 concentrations increased the activation energy. In the CaO–SiO2–FeO–MgO systems, the activation energy increased with increasing Al2O3 concentration. As Equation (1) is based on vibrational frequency, the activation energy indicates the energy barrier to be overcome [25]. Turkdogan and Bills described the activation energy for viscous flow as the energy required to move the "flow-unit" from one equilibrium position to another [26]. According to Lee and Min [14], the activation energy was related to the distribution of the network structure and cation–anion interactions. Thus, the activation energy is also affected by the change in the equilibrium phase because the structure of the molten slag is similar to that of the thermodynamic equilibrium phase [14].

**Figure 2.** Relationship between viscosity and temperature in the (**a**) CaO–SiO2–Al2O3–MgO system, (**b**) CaO–SiO2–FeO– Al2O3–MgO system with 10 wt% FeO, and (**c**) CaO–SiO2–FeO–Al2O3–MgO system with 20 wt% FeO.

**Figure 3.** Activation energies of CaO–SiO2–FeO–Al2O3–MgO slag system with varying FeO and Al2O3 concentrations.

Using the thermodynamic calculation software FactSage 8.1 (Thermfact and GTT-Technologies, Montreal, QC, Canada), the thermodynamic equilibrium phases of the molten slags were evaluated. In the CaO–SiO2–MgO ternary system, the determined liquidus temperature was 1823.39 K and the equilibrium phase was merwinite (Ca3MgSi2O8). It can be inferred that this system showed the highest activation energy because merwinite has a rigid structure between cations and silicate anions. The equilibrium phase changed to MgO as Al2O3 was added to the ternary system. As the equilibrium structure was simplified, the activation energy decreased. However, above 20 wt% Al2O3, the equilibrium phase changed to spinel. Due to the high affinity between the Mg cations and aluminate anions, the activation energy was increased.

On the contrary, an increase in the activation energy was observed in the CaO–SiO2– FeO–MgO system as the Al2O3 concentration increased. In order to evaluate the effect of the slag structure on the viscosity, the structural change of the CaO–SiO2–FeO–Al2O3–MgO system was investigated and discussed in the following section.
