## 3 Results and Discussion
### Quantitative Phase Analysis  
According to the results of qualitative analysis, the structure documents of CaO, BaSO\({}_{4}\), Ca\({}_{3}\)Al\({}_{2}\)O\({}_{6}\), CaAl\({}_{2}\)Al\({}_{14}\)O\({}_{33}\), BaAl\({}_{2}\)O\({}_{4}\), CaSO\({}_{4}\) and Ca\(\leftrightarrow\)Ba\(\leftrightarrow\)Al\(\leftrightarrow\)SO\({}_{16}\) were imported into TOPAS 4.2 software for quantitative analysis. All the phases and corresponding ICSD codes are listed in Table 2. Ca\({}_{4}\)\(\leftrightarrow\)Ba\(\leftrightarrow\)Al\({}_{6}\)SO\({}_{16}\) is derived from Ca\({}_{4}\)Al\({}_{6}\)SO\({}_{16}\) and there is only a little offset at the diffraction peaks compared with that of Ca\({}_{4}\)Al\({}_{6}\)SO\({}_{16}\). The ICSD code of Ca\({}_{4}\)Al\({}_{6}\)SO\({}_{16}\) was used to refine the structure of Ca\({}_{4}\)\(\leftrightarrow\)Ba\(\leftrightarrow\)Al\({}_{6}\)SO\({}_{16}\). In the replacement process, the probability that Ca\({}^{2+}\) at each position is replaced by Ba\({}^{2+}\) is the same. The R\({}_{\mathrm{wp}}\) values are all less than 15, which indicate the quantitative analysis results are reliable. The fitting effect of the sample sintered at 1400 \({}^{\circ}\)C for 180 min 1400 \({}^{\circ}\)C is presented in Figure 2. The result of raw data and fitting data has less error of fitting, it aligns nicely with the value of \(R_{\mathrm{wp}}\), which is 8.06. Unit cell parameters of CBSA samples sintered at 1200 \({}^{\circ}\)C, 1300 \({}^{\circ}\)C, 1350 \({}^{\circ}\)C, 1400 \({}^{\circ}\)C for 180 min \begin{table}
\begin{tabular}{c c c c} \hline
**Phase** & **ICSD code** & **Phase** & **ICSD code** \\ \hline Ca\({}_{4}\)Al\({}_{6}\)SO\({}_{16}\)-Cubic & 9560 & CaAl\({}_{4}\)O\({}_{7}\) & 16191 \\ Ca\({}_{4}\)Al\({}_{6}\)SO\({}_{16}\)-Orthorhombic & 80361 & Ca\({}_{12}\)Al\({}_{14}\)O\({}_{33}\) & 261586 \\ BaAl\({}_{2}\)O\({}_{4}\) & 246028 & CaSO\({}_{4}\) & 183919 \\ BaO & 186427 & CaO & 261847 \\ CaAl\({}_{2}\)O\({}_{4}\) & 180997 & - & - \\ \hline \end{tabular}
\end{table} 
Table 2: Phases and ICSD codes. Figure 1: XRD Patterns of calcium barium sulphoaluminate (CBSA) samples sintered at different temperature for 180 min. are presented in Table 3. As Table 3 shows, result of unit cell parameters indicated that the lattice constant increased with increasing sintering temperature. This phenomena can be attributed to the incorporation of Ba ions into the CSA crystal lattice because the atomic radius of barium is bigger than that of calcium. The same phenomena occurs when the soaking time of the same sintering temperature is increased. To illustrate the unit cell variation of different Ba incorporation, one pure CSA with full Ca content and a second one with half mole of Ba concentration were prepared. As Table 4 shows, \(d\) values of the main peak and the second peak were obtained. Phase analysis shows that the distance of crystal face of CBSA increase with the increasing of Ba ion implantation. The total amount of orthorhombic and cubic CBSA is marked as Ca\({}_{4-x}\)Ba\({}_{x}\)Al\({}_{6}\)SO\({}_{16}\) and the quantitative analysis results are presented in Figure 3.The total amount of Ca\({}_{4-x}\)Ba\({}_{x}\)Al\({}_{6}\)SO\({}_{16}\) is 40%-50% when the sintering temperature between 1200 \({}^{\circ}\)C and 1300 \({}^{\circ}\)C. With the increase of prolonged time, the amount of Ca\({}_{4-x}\)Ba\({}_{x}\)Al\({}_{6}\)SO\({}_{16}\) shows a negligible increase rate and the amounts of CaO, BaSO\({}_{4}\), Ca\({}_{3}\)Al\({}_{2}\)O\({}_{6}\), CaAl\({}_{2}\)O\({}_{4}\), Ca\({}_{12}\)Al\({}_{14}\)O\({}_{33}\), BaAl\({}_{2}\)O\({}_{4}\), CaSO\({}_{4}\) are relatively large with a total content of over 50%. Gypsum cannot react completely at 1200 \({}^{\circ}\)C and 1300 \({}^{\circ}\)C. When the sintering temperature is 1350 \({}^{\circ}\)C and 1400 \({}^{\circ}\)C, the proportion of Ca\({}_{4-x}\)Ba\({}_{x}\)Al\({}_{6}\)SO\({}_{16}\) is significantly increased; moreover, it increases with the