## 2 Materials and Methods  
### Materials  
In this study, pore-free fragments of single-crystal fused magnesia particles close to the theoretical density of 3.58 g/cc, with a magnesia content of 98.66 wt% and sizes of 300-500 \(\upmu\)m, were investigated in three silicate slags. In this study, fused magnesia grains were used because dense spherical magnesia particles are not commercially available. Cubic-shaped particles were manually selected, which transformed into a spherical shape at the beginning of the experiment owing to the faster dissolution of the edges. Synthetic slags in the CaO-Al\({}_{2}\)O\({}_{3}\)-SiO\({}_{2}\)-MgO system were produced from quartz powder, calcined Al\({}_{2}\)O\({}_{3}\) powder, decarburized CaCO\({}_{3}\), and MgO powder (S3 Handel und Dienstleistungen UG, Bad Oeynhausen, Germany). The slag preparation procedure was adopted from Ref. [11]. Each of the raw materials was taken as per the target slag composition and mixed to prepare slag batches. To enhance the homogeneity, the pre-mixes were melted at 1450 \({}^{\circ}\)C for 15 min in a preheated furnace and quenched on a metal sheet. To enhance the uniformity and maintain the same slag quantity in all CLSM crucibles, the solidified slag was pulverized in a cup mill lined with tungsten carbide. In two steps (0.08 g + 0.12 g), the powdered slag was pre-molten in each platinum-10% Rhodium (Pt-Rh10) crucible at 1450 \({}^{\circ}\)C for 15 min in a preheated furnace for easy removal of bubbles, which are detrimental in CLSM dissolution experiments [11]. The chemical compositions, dynamic viscosities (\(\eta\)) at the three experimental temperatures, and liquids temperatures (\(T_{L}\)) are listed in Table 1, where C/S is the CaO/SiO\({}_{2}\) weight ratio. Table 2 represents the densities (\(\rho\)) of the slags and mass fractions of magnesia (\(w_{s}\)) in the saturated slags at 1450, 1500, and 1550 \({}^{\circ}\)C. The viscosities and thermochemical properties of the slags were calculated using FactSage(r) 7.3. The slag densities were determined according to the method reported in Ref. [27].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Slag No.**} & \multirow{2}{*}{**C/S**} & **CaO** & **Al\({}_{2}\)O\({}_{3}\)** & **SiO\({}_{2}\)** & **MgO** & **\(\boldsymbol{\gamma_{1450^{\circ}}}\)C & \(\boldsymbol{\gamma_{1500^{\circ}}}\)C & \(\boldsymbol{\gamma_{1500^{\circ}}}\)C & \(\boldsymbol{T_{L}}\) \\  & & **[wt\%]** & **[wt\%]** & **[wt\%]** & **[wt\%]** & **[Pa-s]** & **[Pa-s]** & **[Pa-s]** & **[Pa-s]** & **[\({}^{\circ}\)C]** \\ \hline S1 & 0.65 & 32.42 & 11.16 & 49.56 & 6.86 & 1.02 & 0.73 & 0.53 & 1265 \\ S2 & 0.93 & 38.07 & 21.00 & 40.93 & - & 1.28 & 0.88 & 0.62 & 1301 \\ S3 & 1.17 & 45.03 & 11.33 & 38.64 & 5.00 & 0.36 & 0.27 & 0.20 & 1317 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical compositions, viscosities, and liquidus temperatures of the slags.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Slag No.**} & \(\boldsymbol{\rho_{1450^{\circ}}}\)C & \(\boldsymbol{\rho_{1500^{\circ}}}\)C & \(\boldsymbol{\rho_{1550^{\circ}}}\)C & \(\boldsymbol{W_{s.1450^{\circ}}}\)C & \(\boldsymbol{W_{s.1500^{\circ}}}\)C & \(\boldsymbol{W_{s.1550^{\circ}}}\)C \\  & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[l]** & **[l]** & **[l]** \\ \hline S1 & 2595 & 2587 & 2579 & 0.2724 & 0.2749 & 0.2779 \\ S2 & 2611 & 2600 & 2589 & 0.1881 & 0.1932 & 0.1987 \\ S3 & 2671 & 2662 & 2653 & 0.1551 & 0.1592 & 0.1637 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Slag densities and mass fractions of magnesia in the saturated slags.