# Analysis of Salt Mixture Contamination on Insulators via Laser-Induced Breakdown Spectroscopy
## 3 Results and Discussion
### Characteristic Spectra of CaCO\({}_{3}\) and CaCO\({}_{4}\)  
Under local thermal equilibrium conditions, the common method to calculate the plasma electron temperature is the Boltzmann method. The layout number on the atomic bound energy level satisfies the Boltzmann distribution, as shown in the following equation:  
\[\ln(\frac{\lambda_{\text{mn}}I_{mn}}{hcg_{m}A_{mn}})=-\frac{\text{E}_{\text{m}}} {k_{B}T_{e}}+\ln\frac{N(T)}{U(T)} \tag{1}\]  
where m and \(n\) are the upper and lower energy levels of the spectral line transition, \(\lambda\) is transition wavelengths, \(A\) is spontaneous transition probability, \(I\) is the relative strength of the measured spectral line, \(Em\) and gm are the excitation energy and statistical weight of the m level, respectively. h, c, and kB are the Planck constant, the speed of light, and the constant number of Boltzmann, respectively. The electron temperature of the plasma can be derived from the slope of linear fitting [20; 21]. In this experiment, three calcium atomic lines were selected. The relevant parameters of these lines are listed in Table 3. Figure 7 shows that as the laser energy fluence increases, the electron temperature increases. The electron temperature of the plasma was \(1.38\times 10^{4}\) K at a laser fluence of 3.8 J/cm\({}^{2}\) and \(1.52\times 10^{4}\) K at a laser fluence of 6.4 J/cm\({}^{2}\). The characteristic spectral wavelengths of Ca in samples #2-1 through #2-6 were searched in the NIST database. According to the average relative spectral intensity of Ca at different wavelengths, linear calibration curves for spectral intensity and concentration were generated, and R\({}^{2}\) values were determined. The results showed that in the Ca linear calibration curves, at a laser energy fluence of 3.8 J/cm\({}^{2}\), four spectral lines had R\({}^{2}\) values greater than 0.8, and 24 lines had R\({}^{2}\) values greater than 0.9. The maximum R\({}^{2}\) value was 0.972. Furthermore, there were ten calibration curves at the laser fluence of 6.4 J/cm\({}^{2}\) that led to an R\({}^{2}\) value greater than 0.9. The maximum R\({}^{2}\) value was 0.951. In general, the linearity of the laser energy intensity of 3.8 J/cm\({}^{2}\) had better linearity and a better different degree  
Figure 7: Boltzmann diagram of plasma electron temperature (obtained by 3 calcium atomic lines). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Species** & **Wavelength/nm** & **E\({}_{\text{m}}\)/cm\({}^{-1}\)** & **A\({}_{\text{mn}}\)/10\({}^{7}\)s\({}^{-1}\)** & **g\({}_{\text{m}}\)** \\ \hline \multirow{2}{*}{Ca II} & 392.065 & 148515 & 3.3 & 9 \\  & 504.133 & 135910 & 1.6 & 5 \\  & 534.516 & 156767 & 1.1 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of calcium atomic emission line. of increase in R\({}^{2}\) at 6.4 J/cm\({}^{2}\). The lines with R\({}^{2}\) values greater than 0.9 at 3.8 J/cm\({}^{2}\) and 6.4 J/cm\({}^{2}\) correspond to the linear calibration curves shown in Figure 8. The distribution of R\({}^{2}\) values greater than 0.9 as they relate to the wavelength at a laser fluence of 3.8 J/cm\({}^{2}\) and 6.4 J/cm\({}^{2}\), respectively, are also shown in Figure 8. The result of the PLRS model is shown in Figure 9. The R\({}^{2}\) values were 0.9813 and 0.9688, which were close to the maximum R\({}^{2}\) value in the Ca linear calibration curves. By comparing the linear relationship between the laser energy of 3.8 J/cm\({}^{2}\) and 6.4 J/cm\({}^{2}\), increasing the output energy was not determined to result in a higher number of spectral lines with good linearity. The appropriate laser energy should be selected according to the experimental results. As shown in Table 1, the mixing ratio of the two Ca ion compounds in samples #2-1 through #2-6 was different, but the linear relationship between the concentration and the intensity was not affected. Increasing the number of compounds containing the same cation did not influence the concentration relationship in the LIBS analysis of Ca.