# An Integrated Software for Computing Mechanical Properties of Crystalline Material by Means of XRD
## 3 Results and Discussion
### Analysis of Phase Compositions  
The phase compositions of multi-phase materials (triple-phase carbide in this study) can be analyzed simply using XPro 2.0. Figure 8 is diffraction peaks in accordance with the diffraction planes for various phases. A formula for calculating the phase component was proposed in the previous studies [6,7] as the following. \[q_{x}=\frac{\sum\limits_{a=1}^{n}E_{(hkl)_{i}^{a}\lambda_{j}}^{a}}{\sum E_{( hkl)_{i}^{a}\lambda_{j}}^{a}+\ldots+\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}} \tag{25}\]  
Figure 9 represents the diffraction line from a three-phase material. The areas under a peak of a phase are the diffracted energy portion of that phase. Therefore, the phase composition is determined from the energy portion \(q_{x}\), \(q_{\beta}\), and \(q_{\gamma}\) diffracted from phases \(\alpha\), \(\beta\), and \(\gamma\) with the total diffracted energy of material as:  
\[q_{a}=\frac{\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}}{\sum E_{( hkl)_{i}^{a}\lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a} \lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{\beta}} \tag{26}\] \[q_{\beta}=\frac{\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}}{\sum E_{( hkl)_{i}^{a}\lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a} \lambda_{j}}^{\beta}}\] \[q_{\gamma}=\frac{\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}}{\sum E_{( hkl)_{i}^{a}\lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a}\lambda_{j}}^{a}+\sum E_{(hkl)_{i}^{a} \lambda_{j}}^{\beta}}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Zones**} & \multicolumn{3}{c}{**XPert 2.0**} & **Origin 3.0** \\ \cline{2-4}  & **Gaussian** & **Parabola** & **Half-Width** & **Centroid** & **Gaussian** \\ \hline
1 & \(-17.3\pm 2.8\) & \(-17.3\pm 0.2\) & \(5.4\pm 19.7\) & \(7.5\pm 9.4\) & \(-25.3\) \\
2 & \(-26.0\pm 8.9\) & \(26.0\pm 0.4\) & \(-3.2\pm 18.3\) & \(-2.4\pm 7.2\) & \(-30.4\) \\
3 & \(13.2\pm 3.1\) & \(13.2\pm 0.4\) & \(11.6\pm 42.8\) & \(8.7\pm 8.5\) & \(10.1\) \\
4 & \(-29.5\pm 6.0\) & \(-29.4\pm 0.6\) & \(-19.8\pm 27.7\) & \(-23\pm 9.6\) & \(-28.3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Residual stresses of alumina alloy 1060 (MPa). \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Diffraction Method**} & \multicolumn{1}{c}{\(\Omega\)**-Type, Fixed-\(\eta\)**} \\ \hline Diffraction plane & (422) of hexagonal \\ Bragg angle & \(82.3^{\circ}\) \\ Scanning range & \(132\)–\(142^{\circ}\) \\ Step size & \(0.04^{\circ}\) \\ Preset time & \(5\) s \\ Voltage and current & \(20\) kV and \(10\) mA \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The experimental conditions for stress measurement using XRD. where \(E^{a}_{(hkl)_{i}^{\lambda}\lambda_{j}}\);\(E^{\beta}_{(hkl)_{j}^{\beta}\lambda_{j}}\);\(E^{\gamma}_{(hkl)_{i}^{\gamma}\lambda_{j}}\) are the energy portion diffracted from phase \(\alpha\), \(\beta\), \(\gamma\) from the \(i\)th plane \((hkl)_{i}\) for wavelength \(\lambda_{j}\). Five samples of commercial triple-phase ceramic T15K6, containing three phases WC-TiC-Co, were prepared with dimensions of 15 \(\times\) 15 \(\times\) 20 (mm). The average chemical compositions of the phases WC, TiC, and Co, respectively, were 78.63%, 14.17%, and 6.79%, together with their 95% confidence limits. Table 3 lists the XRD experimental conditions for analyzing phase compositions of carbide T15K6. Table 4 compares the phase composition determined from the XRD method and chemical analysis method, which is known as a traditional and accurate technique for determining compositions. The results show good agreement between the methods, confirming the validity of proposed Equations (25) and (26) using the XRD technique. \begin{table}
\begin{tabular}{c c} \hline \hline
**Measurement Method** & \(\boldsymbol{\Omega}\)**Type, Fixed-\(\boldsymbol{\eta}\)** \\ \hline \hline \
\begin{tabular}{c} Preset time \\ Step size \\ Voltage and current \\ \end{tabular} &
\begin{tabular}{c} 5 s \\ 0.02\({}^{\circ}\) \\ 20 kV and 10 mA \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}