**2. Experiments**

The experimental setup is depicted in Figure 1. The LIBS system consisted of a Q-switched laser (Beamtech Nimma-900), where the laser pulse duration was 10ns, shot-to-shot energy variation (RMS) ≤1%. We used an Avantes optical fiber spectrometer (190 nm to 650 nm) with 6 channels, the spectral resolution was 0.05nm, and a Stanford Research System Delay Generator SRS DG645. The laser was focused on the surface of the sample by a lens with a focal length of 100 mm. It was ablated operating at a wavelength of 1024 nm. The laser energy of the Nimma-900 could be adjusted from 1 J to 900 J. Laser fluence was determined at 1.9 J/cm<sup>2</sup> for 38 mJ, 3.8 J/cm<sup>2</sup> for 76 mJ, and 6.4 J/cm<sup>2</sup> for 128 mJ.

**Figure 1.** Laser-induced breakdown spectroscopy (LIBS) experimental setup.

All chemicals used in the experiments were acquired from Aladdin and were of analytical reagen<sup>t</sup> grade. Mixed samples of Na2CO3 and NaHCO3 were prepared with a series of Na concentration gradients. The total mass of each sample remained constant, and the mass of Na2CO3 and NaHCO3 to be mixed was calculated separately according to the total concentration of Na set by the concentration gradient and the various mixing ratios of Na in Na2CO3 and NaHCO3. The total concentration of Na for each sample varied from 27.4% to 43.4% because the mass percentage of Na in Na2CO3 was 43.4%, and that in NaHCO3 was 27.4%. Similarly, the quantity of CaSO4 and CaCO3 to be mixed in each sample was obtained using the above method, and the Ca mass fraction of the mixtures ranged from 29.4% to 40%, corresponding to the mass percentages of Ca in CaSO4 and CaCO3, respectively. Varying ratios of Na2CO3, NaHCO3 and CaSO4, CaCO3 were prepared and mixed, as shown in Table 1. The ratios of the Na and Ca mass fractions of Na2CO3:NaHCO3 and CaSO4:CaCO3 are also shown in Tables 1 and 2. Pellets were formed from each sample by using a circle pellet forming press with a diameter of 8 mm under 5 tons of force, which improved the LIBS ablation of the sample.


**Table 1.** Di fferent ratios of Na2CO3 and NaHCO3, CaSO4, and CaCO3.

**Table 2.** Wavelength of typical spectral lines for sample by LIBS.


For the LIBS analysis, the pellets were placed on an optical platform. The vertical distance between the optical platform and convex lens was adjusted, so the laser spot was focused on the sample surface. The delay time of the LIBS system was 3 μs, and the diameter of the laser spot was 0.8 mm. The dark spectrum captured by the spectrometer was acquired 50 times without laser ablation. Then, 5 points were selected randomly for each sample, and the spectral data for each point were obtained after 10

rounds of 10 Hz continuous ablation. The averaged background spectrum was subtracted from the processed spectral data, and the resulting spectra were averaged. The NIST database was used to determine spectral intensities for Ca, C, Na, etc. [19]. The above analyses were repeated for the two groups of samples, #1-1 through #1-6 and #2-1 through #2-6, at a laser fluence of 3.8 J/cm<sup>2</sup> and 6.4 J/cm2, respectively. Due to the influence of Na matrix effects, LIBS analysis at 1.9 J/cm<sup>2</sup> was added for the analysis of samples #1-1 through #1-6. The elements were measured, as shown in Table 2.

#### **3. Results and Discussion**

#### *3.1. Spectral Characteristics for Na2CO3 and NaHCO3*

Figure 2 shows the whole spectra for samples #1-1 to #1-6 at an energy intensity of 3.8 J/cm2. The intensity of the spectra increased with increasing concentrations of Na. The Na content in Na2CO3 was higher than that in NaHCO3 when the sample had the same amount of substance. Therefore, the spectral intensity of Na2CO3 was higher than that of NaHCO3, which was demonstrated in the range of 588 nm to 589 nm. As Na2CO3 and NaHCO3 were similar in element composition, except for H, the characteristic spectral wavelengths were very similar in these samples, i.e., either they were pure compounds (#1-1 and #1-6) or a mixture of two compounds (#1-2 through #1-5).

**Figure 2.** Spectra intensity of samples #1-1 to #1-6 at an energy intensity of 3.8 J/cm<sup>2</sup> shown in black, red, navy blue, green, light blue, and purple, respectively.

In Figure 3, the spectral resonance lines (588.995 nm, 589.592 nm) and nonresonant lines (568.297 nm, 568.859 nm) for Na were selected from Figure 2. Self-absorption was found in the resonance lines (588.995 nm, 589.592 nm) at a laser fluence of 3.8 J/cm2, as shown by a significant decrease in signal intensity. The variation in the Na concentration in different samples contributed to the self-absorption phenomenon, i.e., the higher the concentration, the more notable the self-absorption. This susceptibility existed because the laser ablated the target surface, and plasma was generated by the trailing edge of the laser pulse and disappeared during condensation. Moreover, the temperature of the entire

illuminant was not uniform. After Na atoms are excited by the emission wavelength, the generated photons were absorbed by other Na atoms when passing through the low-temperature region of the plasma, resulting in changes in the intensity and profile of the Na spectrum. The influence of Na concentration on the self-absorption effect could be determined by comparing the contours of the Na resonance lines.

**Figure 3.** Emission intensity of Na in samples #1-1 through #1-6 measured at different wavelengths at an energy intensity of 3.8 J/cm2. Spectra show the resonance lines (588.995 nm, 589.592 nm) and nonresonant lines (568.263 nm, 568.859 nm).

The relationship between the Na content, according to the atomic lines (Na I 588.995 nm, Na I 568.859 nm), and the average relative spectral intensity as a function of laser energy intensity is shown in Figure 4. As the laser energy density increased, the spectral intensity corresponding to each spectral line was enhanced significantly. At a laser fluence of 6.4 J/cm2, as the concentration increased, the intensity first increased and then decreased, which was due to the strong self-absorption effect. This result demonstrated that the range of Na content was limited when using calibration curves to analyze the linear relationship between Na concentration and laser fluence.

However, reducing the laser energy density per pulse and selecting the ion line reduced the atomic emission intensity because of the weak self-absorption effect. It prolonged the dynamic range of the concentration measurements, which allowed the Na atomic lines (Na I 588.995 nm, Na I 568.859 nm) to maintain a good linear relationship at a laser energy of 1.9 J/cm2. Therefore, when the concentration was held constant, reducing the laser energy, and selecting the proper Na ion line would extend the linear analysis range and improve the accuracy of Na determination using linear calibration curves. For the elements tested, a good linear relationship was the basis of the artificial data methods used to process the LIBS spectral data. This method could also be used as a preprocessing method when employing the artificial intelligence algorithm to determine the relationship between the concentration of other elements and spectral intensity.

The intensity and variation trends of spectral lines were considered to analyze the influence of the Na salt mixture on the calibration results. The linear calibration coefficient (R2) for Na was obtained with a laser fluence of 3.8 J/cm2. The R<sup>2</sup> value was greater than 0.7, as shown in Figure 5. Although the middle data point was higher in the spectrum corresponding to 588.995 nm and 589.592 nm, the spectral intensity and concentration corresponding to these data points also had linear relationships. The spectral data presented here represented the original data after subtracting the dark spectrum. The ratio of Na in samples #1-1 through #1-6 varied, but the calibration curves were similar to that of the pure compound. The mixing of various proportions of Na had minimal effects on the linear calibration model, which also indicated that the results of other complex artificial intelligence methods would not be affected. These results provided a convenient LIBS method for the on-line detection of elemental composition from multi-compound mixing.

**Figure 4.** Emission intensity under varying concentrations of Na as a function of laser energy. Signals obtained from the Na I 588.995 nm, Na I 568.859 nm are shown.

**Figure 5.** LIBS signal intensity of Na vs. Na concentration at a laser fluence of 3.8 J/cm2.

PLSR (partial least squares regression) was applied in the LIBS spectroscopy analysis to obtain the calibration model through MATLAB. There were five standard samples in the experiment, four of which were used as the calibration sample set, and their spectral data were used to train the prediction model. Meanwhile, the remaining one is used to predict and verify the model.

To compare the prediction results of the model, we used the Pearson correlation coefficient(R) to measure the calibration effect of the model. The root mean square error (RMSE) was used to describe the prediction accuracy of the model. The closer the R was to 1, the better fitting effect of the calibration curve: the smaller the RMSE, the more accurate the quantitative effect of the model.

As shown in Figure 6, The red diamond data point indicates the predicted value. The degree of fit of the regression line to the observed values was higher than that of the univariate regression model.

**Figure 6.** Results of Na data for Partial least squares regression (PLSR) (2 components).

#### *3.2. Characteristic Spectra of CaCO3 and CaSO4*

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:

$$\ln\left(\frac{\lambda\_{\text{mm}}I\_{\text{mm}}}{\ln\mathfrak{g}\_{\text{m}}A\_{\text{mm}}}\right) = -\frac{\mathbf{E}\_{\text{m}}}{k\_{B}T\_{c}} + \ln\frac{N(T)}{\mathcal{U}(T)}\tag{1}$$

where m and *n* are the upper and lower energy levels of the spectral line transition, λ 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 × 10<sup>4</sup> K at a laser fluence of 3.8 J/cm<sup>2</sup> and 1.52 × 10<sup>4</sup> K at a laser fluence of 6.4 J/cm2.

**Species Wavelength**/**nm Em**/**cm**−**<sup>1</sup> Amn**/**107s**−**<sup>1</sup> gm** Ca II 392.065 148515 3.3 9 504.133 135910 1.6 5 534.516 156767 1.1 13 &D,,'DWD /LQHDU)LW OQλΙ/KFJ\$ ODVHUIOXHQFH-FP N7H 7H î . \_5\_ ODVHUIOXHQFH-FP N7H 7H î . \_5\_ HQHUJ\FP

**Table 3.** Parameters of calcium atomic emission line.

**Figure 7.** Boltzmann diagram of plasma electron temperature (obtained by 3 calcium atomic lines).

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 di fferent wavelengths, linear calibration curves for spectral intensity and concentration were generated, and R<sup>2</sup> values were determined.

The results showed that in the Ca linear calibration curves, at a laser energy fluence of 3.8 J/cm2, four spectral lines had R<sup>2</sup> values greater than 0.8, and 24 lines had R<sup>2</sup> values greater than 0.9. The maximum R<sup>2</sup> value was 0.972. Furthermore, there were ten calibration curves at the laser fluence of 6.4 J/cm<sup>2</sup> that led to an R<sup>2</sup> value greater than 0.9. The maximum R<sup>2</sup> value was 0.951. In general, the linearity of the laser energy intensity of 3.8 J/cm<sup>2</sup> had better linearity and a better di fferent degree

of increase in R<sup>2</sup> at 6.4 J/cm2. The lines with R<sup>2</sup> values greater than 0.9 at 3.8 J/cm<sup>2</sup> and 6.4 J/cm<sup>2</sup> correspond to the linear calibration curves shown in Figure 8. The distribution of R<sup>2</sup> values greater than 0.9 as they relate to the wavelength at a laser fluence of 3.8 J/cm<sup>2</sup> and 6.4 J/cm2, respectively, are also shown in Figure 8. The result of the PLSR model is shown in Figure 9. The R<sup>2</sup> values were 0.9813 and 0.9688, which were close to the maximum R<sup>2</sup> value in the Ca linear calibration curves.

(**a**) R2 of linear calibration curves at 3.8 J/cm2.

(**b**) R2 of linear calibration curves at 6.4 J/cm2.

**Figure 8.** R<sup>2</sup> values greater than 0.9 at various Ca spectral lines as a function of laser energy intensity. The two laser fluences are drawn in black (3.8 J/cm2) and red (6.4 J/cm2).
