## 3 Results and Discussion
### Diffusivity  
The dissolution quantities calculated from the MCPs are tabulated in Table 2. Using these quantities, the diffusivities for all the individual corrosion steps at the three experimental temperatures were determined according to Equation (1) [15; 62]. Figure 5a shows the diffusivities (\(D_{i}\) and \(D_{0,i}\)) of magnesia for all the corrosion steps. The diffusivity amplified with a rise in the temperature. At a given temperature, the slag viscosity decreased with magnesia dissolution, which possibly led to moderate rise of diffusivity. The Arrhenius plot was obtained using the diffusivities (\(D_{0,i}\)) at the corresponding corrosion steps \(i_{T}\) (the corrosion step \(i\) at temperature \(T\)): the specimen mass loss with respect to the original mass at different temperatures was similar. The obtained diffusivities are functions of the temperature and slag composition, which change during the experiment [15]. For the Arrhenius plot, the diffusivities were transformed to those of the virgin slag composition, assuming that the product of the diffusivity and viscosity was constant, which is in agreement with the Stokes-Einstein relation [15]. This conversion eliminated the composition dependency: otherwise, the amount of magnesia in the slag would have been an additional influencing factor [15]. Figure 5b depicts the Arrhenius plot. The plausibility of the diffusivities was confirmed by the linear propensity of the Arrhenius plot [15]. The test intervals used for the Arrhenius plots, together with the associated mass loss, bulk concentrations of magnesia, and the corresponding activation energies, are listed in Table 3. The activation energy of diffusion decreases with a rise in the mass loss and bulk concentration. Figure 4: Change in (**a**) length, (**b**) the mean corroded radius, (**c**) volume, and (**d**) mass for the magnesia dissolution at 200 rpm and 1450, 1500, and 1550 \({}^{\circ}\)C. The numbers within the graphs indicate the average rate over the total dissolution time. It is of interest to compare the effective binary diffusivities of magnesia obtained using two different Sherwood relations (according to the modified Tachibana and Fukui equations [15,61] and [PERSON] et al. [62]) for the mantle of a cylindrical sample. The Sherwood relation, according to [PERSON] [63], was applied to the bottom of the cylinder in both cases. Table 4 shows a comparison between the diffusivities at individual corrosion steps at the three experimental temperatures. At 1450 \({}^{\circ}\)C, the error percentage was lower than that of the other temperatures. The errors were considerably larger for the final corrosion steps. This may be due to the deviation in the shape of the corroded sample from that of the cylinder. Results using the Sherwood relation proposed by [PERSON] et al. [62] are anticipated to be more correct here, because the Sherwood relation therein was derived from a simulation where the actual sample geometry was considered; the modified Tachibana and Fukui relations, in contrast, considered a cylindrical sample shape. When the average diffusivities of all the corrosion steps at a particular temperature were compared, the error percentages were 1.74, 19.02, and 16.92 at 1450, 1500, and 1550 \({}^{\circ}\)C, respectively, indicating that both the Sherwood relations work reasonably well. Equality of the means was tested statistically with help of an independent two-sample \(t\)-test that is two-tailed. At a 5% significance level, the means for all three cases were proven to be equal.