## 3 Results and Discussion
### Calibration Model for Quantitative Estimation
#### 3.3.1 CA-CaS Sample  
Table 4 shows the results for CA-CaS samples, where the relative intensity ratio for CaS at 157 cm\({}^{-1}\) and at 524 cm\({}^{-1}\) for CA gave the highest linear regression coefficient of determination value and the lowest mean absolute error value was better than the other peak ratios. The peak ratio of 157/524 also provided generally better relative stability estimated values, as illustrated in Figure 9. A calibration curve constructed between the relative intensity ratios of the measured phase fractions for CaS in the CA-CaS samples is presented in Figure 10. Therefore, based on the evaluations for CA-CaS shown in Figures 9 and 10 and Table 4, the relative intensity ratio, between 157 cm\({}^{-1}\) for CaS and 524 cm\({}^{-1}\) for CA, demonstrated the most suitable Raman peaks for a phase content analysis of binary CA-CaS samples. Additionally, these peaks, according to Figure 5, were the phases' most intense peaks.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & & \multicolumn{3}{c}{**Training Data**} & \multicolumn{3}{c}{**Validation**} \\ \cline{3-8}
**Phases** & **Relative Intensity** & **Mean (R\({}^{2}\))** & **Mean (MAE)** & **Mean (R\({}^{2}\))** & **Mean (MAE)** & **Sum MAE** & **Relative Stability** \\ \hline C12A7-CaS & 517/157 & 0.98 & 2.76 & 0.98 & 2.96 & 5.72 & 0.98 \\ C12A7-CaS & 517/200 & 0.84 & 8.03 & 0.84 & 8.72 & 16.75 & 4.44 \\ C12A7-CaS & 781/157 & 0.90 & 6.06 & 0.90 & 6.43 & 12.49 & 1.54 \\ C12A7-CaS & 781/200 & 0.75 & 10.49 & 0.72 & 11.31 & 21.80 & 3.78 \\ C12A7-CaS & 774/157 & 0.76 & 10.30 & 0.80 & 11.10 & 21.40 & 4.78 \\ C12A7-CaS & 774/200 & 0.77 & 9.55 & 0.77 & 11.16 & 20.71 & 5.73 \\ \hline \end{tabular}
\end{table}
Table 6: Evaluation of the coefficient of determination (R\({}^{2}\)) and mean absolute error (MAE) for the prediction and validation between the phase content and relative intensity of the Raman peaks and phase content for C12A7–CaS.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & & \multicolumn{3}{c}{**Training Data**} & \multicolumn{3}{c}{**Validation**} \\ \cline{3-8}
**Phases** & **Relative Intensity** & **Mean (R\({}^{2}\))** & **Mean (MAE)** & **Mean (R\({}^{2}\))** & **Mean (MAE)** & **Sum MAE** & **Relative Stability** \\ \hline C3A–CaS & 510/157 & 0.96 & 4.03 & 0.97 & 4.07 & 8.10 & 0.67 \\ C3A–CaS & 766/157 & 0.88 & 6.50 & 0.88 & 6.92 & 13.42 & 0.09 \\ C3A–CaS & 510/190 & 0.87 & 7.72 & 0.86 & 8.74 & 16.46 & 0.16 \\ C3A–CaS & 766/190 & 0.85 & 8.07 & 0.82 & 8.97 & 17.04 & 0.08 \\ \hline \end{tabular}
\end{table}
Table 7: Evaluation of the coefficient of determination (R\({}^{2}\)) and mean absolute error (MAE) for the prediction and validation between the phase content and relative intensity of the Raman peaks and phase content for C3A-CaS.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & & \multicolumn{3}{c}{**Training Data**} & \multicolumn{3}{c}{**Validation**} \\ \cline{3-8}
**Phases** & **Relative Intensity** & **Mean (R\({}^{2}\))** & **Mean (MAE)** & **Mean (R\({}^{2}\))** & **Mean (MAE)** & **Sum MAE** & **Relative Stability** \\ \hline CaS–Al\({}_{2}\)O\({}_{3}\) & 157/420 & 0.94 & 5.65 & 0.95 & 6.23 & 11.88 & 0.46 \\ CaS–Al\({}_{2}\)O\({}_{3}\) & 157/386 & 0.58 & 14.68 & 0.59 & 15.49 & 30.17 & 0.06 \\ CaS–Al\({}_{2}\)O\({}_{3}\) & 157/760 & 0.82 & 9.72 & 0.83 & 10.86 & 20.58 & 0.17 \\ CaS–Al\({}_{2}\)O\({}_{3}\) & 198/420 & 0.91 & 5.49 & 0.90 & 5.84 & 11.33 & 0.14 \\ CaS–Al\({}_{2}\)O\({}_{3}\) & 198/386 & 0.38 & 18.50 & 0.40 & 19.99 & 38.49 & 0.03 \\ CaS–Al\({}_{2}\)O\({}_{3}\) & 198/760 & 0.80 & 9.88 & 0.82 & 11.10 & 20.98 & 0.14 \\ \hline \end{tabular}
\end{table}
Table 8: Evaluation of the coefficient of determination (R\({}^{2}\)) and mean absolute error (MAE) for the prediction and validation between the phase content and relative intensity of the Raman peaks and phase content for CaS- Al\({}_{2}\)O\({}_{3}\).