## 3 Results
### Kinetic Analysis for the Formation Process of ss-C\({}_{4}\)A\({}_{3}\)S  
The reaction degrees \(\alpha\) of ss-C\({}_{4}\)A\({}_{3}\)S in the forming stage were calculated according to the contents of the phases in the clinkers obtained by the RQPA. Afterwards, the linear relationship between the reaction degrees and the holding times were fitted by Equation (2) (the integral form of kinetic models), and the correlation coefficients (R\({}^{2}\)) were compared to determine the potential optimal models.  
According to the comparison in Table 4, all diffusion models exhibited obviously higher correlation coefficients than other types of models. It should be also noted that the correlation coefficients of the D3 (Jander) model and the D4 (Ginstling-Brounstein) model were very close and higher than the results yielded from the D1 and D2 models. The results illustrate that the formation reactions of ss-C\({}_{4}\)A\({}_{3}\)S take place in a process of three-dimensional diffusion, which accords with st-C\({}_{4}\)A\({}_{3}\)S and several types of solid-solution ye\({}^{\prime}\)elimite [29; 30]. Considering the D3 model exhibited the most acceptable fitting results, the values for \(k\) in Equation (2) were determined by the D3 model, and the fitting results can be seen in Figure 6a. Afterwards, the values of \(E_{\rm a}\) were obtained through a linear fitting for Equation (3) (Arrhenius equation), and they are shown in Figure 6b. According to the results of the Arrhenius fitting, the \(E_{\rm a}\) of ss-C\({}_{4}\)A\({}_{3}\)S equaled 285.6 kJ/mol in this study.  
Influence of Sintering Temperature on Microstructural Morphologies of ss-C\({}_{4}\)A\({}_{3}\)S  
Microstructural morphologies of four types of clinkers containing over 90 wt.% of ss-C\({}_{4}\)A\({}_{3}\)S are compared in Figure 7. As shown in Figure 7a, the morphology features of ss-C\({}_{4}\)A\({}_{3}\)S sintered at 1200 \({}^{\circ}\)C for 240 min were identified as approximately 1-2 \(\upmu\)m polyhedral granules with clear boundaries. For ss-C\({}_{4}\)A\({}_{3}\)S sintered at 1250 \({}^{\circ}\)C for 240 min (shown in Figure 7b), the majority of granules still exhibited clear boundaries, but a few granules tended to fuse and combine with adjacent granules (shown by the arrow). When prolonged times extended to 240 min at 1250 \({}^{\circ}\)C (see Figure 7c), fusion among the granules  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Temperature**} & \multicolumn{6}{c}{**Kinetic Models**} \\ \cline{2-7} (\({}^{\circ}\)**C**) & **D1** & **D2** & **D3** & **D4** & **A3** & **R3** & **F1** \\ \hline
1150 & 0.9608 & 0.9791 & 0.9942 & 0.9848 & 0.7357 & 0.9031 & 0.9293 \\
1200 & 0.9314 & 0.9590 & 0.9869 & 0.9693 & 0.7655 & 0.9106 & 0.9442 \\
1250 & 0.9994 & 0.9886 & 0.9682 & 0.9800 & 0.8658 & 0.9888 & 0.9986 \\
1300 & 0.9937 & 0.9998 & 0.9961 & 0.9996 & 0.9195 & 0.9807 & 0.9931 \\ \hline Average & 0.9713 & 0.9816 & 0.9864 & 0.9834 & 0.8216 & 0.9458 & 0.9663 \\ Standard deviation & 0.0274 & 0.0150 & 0.0110 & 0.0109 & 0.0743 & 0.0392 & 0.0301 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Correlation coefficients (R2) fitted by different reaction models.  
Figure 6: Plot of kinetic analysis for ss-C\({}_{4}\)A\({}_{3}\)S, (**a**) Jander fitting of ss-C\({}_{4}\)A\({}_{3}\)S formation at different temperatures, (**b**) Arrhenius fitting for the formation of ss-C\({}_{4}\)A\({}_{3}\)S.  
of ss-C4A3$ was more evident (shown in the circles). As for ss-C4A3$ sintered at 1300 \({}^{\circ}\)C for 120 min (see Figure 7d), partial granules fused to be larger than 2 um; meanwhile, the boundaries of the granules tended to be more vague.