## 3 Results and Discussion
### Diffusivity  
Each experiment was evaluated according to the model proposed in Ref. [11] to determine the diffusivity of magnesia. The average diffusivities of magnesia in S1-S3 at 1450, 1500, and 1550 \({}^{\circ}\)C are presented in Figure 4a. In a particular slag, the diffusivity of magnesia increased with increasing experimental temperature because of its lowered viscosity at higher temperatures. In addition, no trend was observed in the case of diffusivity with slag basicity; however, slag viscosities can explain the trend in diffusivities. Figure 4b shows the Arrhenius plots of the magnesia diffusivities in S1-S3 as a function of reciprocal temperature (K). The linear tendency of the Arrhenius plot confirms the plausibility of the trend in diffusivities. The activation energies of magnesia diffusion calculated from the Arrhenius plots are 213, 185, and 259 kJ/mol for S1, S2, and S3, respectively.  
Table 4 shows the diffusivities of magnesia obtained from the rotating finger test and CLSM. Magnesia diffusivities determined using a rotating finger test were obtained from Ref. [8], which were determined for slag S1, as used here; however, they are not exactly valid for the virgin slag composition. In Ref. [10], the magnesia concentration of the slag increased during the experiment, which was negligible for the CLSM investigation performed in this study. Therefore, they were converted to diffusivities of the virgin slag viscosity using the Stokes-Einstein relation, where the product of the diffusivity and viscosity is constant. In addition to the diffusivity determination model (M3) proposed in Ref. [11], shrinking core models with (M2) and without (M1) Stefan flow, both exemplified in Ref. [11], were employed to determine the diffusivities from the CLSM studies. M3 showed good agreement with the rotating finger test results, where the effective boundary layer thickness could be accurately controlled. However, M1 and M2 overestimated diffusivity in all cases.  
Figure 4: (**a**) Magnesia diffusivity and (**b**) Arrhenius plot of magnesia diffusivity in S1, S2, and S3 slags at 1450, 1500, and 1550 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Temperature**(\({}^{\circ}\)C) & **Slag** & \(t_{tot^{*}}\)**(s)** & \(B/\eta\) **(1/Pa-s)** & \(B/(\eta\)-\(\delta\))-(1/Pa-s-m)** & \(B/f\)**(\(\eta\)-\(\delta\))-(1/Pa-s-m)** \\ \hline \multirow{4}{*}{1450} & S1 & 188.1 & 0.275 & 6.38 \(\times\) 10\({}^{3}\) & 2.84 \(\times\) 10\({}^{4}\) \\  & S2 & 439.5 & 0.181 & 2.67 \(\times\) 10\({}^{3}\) & 8.18 \(\times\) 10\({}^{3}\) \\  & S3 & 412.6 & 0.346 & 7.79 \(\times\) 10\({}^{3}\) & 2.25 \(\times\) 10\({}^{4}\) \\ \hline \multirow{4}{*}{1500} & S1 & 111 & 0.390 & 1.19 \(\times\) 10\({}^{4}\) & 5.35 \(\times\) 10\({}^{4}\) \\  & S2 & 245.7 & 0.272 & 5.04 \(\times\) 10\({}^{3}\) & 1.52 \(\times\) 10\({}^{4}\) \\  & S3 & 172.4 & 0.481 & 1.27 \(\times\) 10\({}^{4}\) & 3.60 \(\times\) 10\({}^{4}\) \\ \hline \multirow{4}{*}{1550} & S1 & 66.1 & 0.547 & 1.73 \(\times\) 10\({}^{4}\) & 7.38 \(\times\) 10\({}^{4}\) \\  & S2 & 91.4 & 0.400 & 1.30 \(\times\) 10\({}^{4}\) & 3.73 \(\times\) 10\({}^{4}\) \\ \cline{1-1}  & S3 & 115.7 & 0.680 & 2.08 \(\times\) 10\({}^{4}\) & 5.78 \(\times\) 10\({}^{4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dissolution parameters to rank the slag aggressiveness.