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Abstract
Calibration-free laser-induced breakdown spectroscopy (CF-LIBS) is a very useful elemental analysis technique. However, it requires knowledge of transition probabilities of the analytical lines. To solve this problem, a variant one-point calibration (OPC) LIBS method was proposed. Quantitative elemental analysis on Cu-Zn-Ag-Au alloys was realized with this method capable of using zinc analytical lines with unknown transition probabilities. The relative error was demonstrated to be less than 3.3%. This variant OPC method will be helpful for quantitative elemental analysis of different samples using CF-LIBS, no matter whether the transition probabilities of the observed lines are known or unknown.
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1. Introduction
Since it was first proposed by Ciucci et al. in 1999 [1], calibration-free laser-induced breakdown spectroscopy (CF-LIBS) has been becoming a very important and useful technique to give quantitative elemental analysis of different samples. CF-LIBS is based on three assumptions: the plasma is in local thermodynamic equilibrium (LTE); the plasma is homogeneous and optically thin; and laser-ablation process is stoichiometric. Thus, the elemental concentrations can be determined according Boltzmann plots of all elements contained in the samples. CF-LIBS does not require standard samples; for this reason, it has been successfully applied as an elemental analysis tool in different fields of modern sciences and engineering, such as material science [2,3], metallurgy [4,5], astronomy [6], environment monitoring [7], food science [8], medical science [9,10] and so on.
Three factors will affect the analytical accuracy of CF-LIBS. The first one is self-absorption effect. For major or minor elements, the laser-induced plasma can’t be considered as optically thin for resonant lines or even other lines with low-lying lower electronic states. Self-absorption of these lines should be corrected if one wishes to put them in the calculations. Different methods have been proposed to correct self-absorption and improve the analytical accuracy of CF-LIBS, such as curve of growth (COG) [11], internal reference [12], blackbody radiation reference [13] and columnar density and standard reference line (CD-SRL) methods [14].
The second one is the uncertainty of the determined plasma temperature. The accuracy of the determined plasma temperature directly affects the accuracy the quantitative analytical results of CF-LIBS. A reversed CF-LIBS procedure was proposed by Gaudiuso et al. to determine plasma temperature more accurately based on analyzing one standard sample [15,16]. Dong et al. optimized plasma temperature by genetic algorithm (GA) method, which also required one standard sample [17]. Yang et al. optimized plasma temperature using the particle swarm optimization (PSO) algorithm without requiring any standard samples [18]. After temperature optimization, the analytical accuracy could be improved obviously.
The third one is the uncertainty of transition probability or spontaneous emission coefficient of the analytical line. Sometimes, the uncertainty of the spectral response of the spectrometer, especially in ultra-violet (UV) region will also affect the analytical accuracy of CF-LIBS. To solve this problem, one-point calibration (OPC) method has been proposed by Cavalcanti et al. in 2013 [19]. In OPC-LIBS, one standard sample with certified elemental concentrations was used to calibrate the intensity of the analytical lines. This is very helpful to improve the analytical accuracy of traditional CF-LIBS. Since it was proposed, OPC-LIBS technique has been widely applied on the elemental analysis of different samples, including emeralds [20], hydroxyapatite [21], meteorite [22], alloys [23,24] and Al-W-Mo materials coated on magnetic confined fusion devices [25]. Borduchi et al. analyzed carbon in different matrices by combining OPC method with Saha-Boltzmann plot. Both the accuracy and precision of quantitative analysis of carbon have been improved obviously in comparison with those obtained by combining OPC method with Boltzmann plot [26]. Quantitative elemental analysis of aluminum alloys with OPC high repetition rate laser-ablation spark-induced breakdown spectroscopy (HRR LA-SIBS) has also been reported [27]. Besides, one-point and multi-line calibration method and single-sample calibration method have also been reported to realize quantitative elemental analysis [28,29]. In these two methods, one standard sample was also required, but it was not necessarily to use Boltzmann plots of the elements.
In traditional CF-LIBS or OPC-LIBS, the transition probabilities of the analytical lines are required to build Boltzmann plots. However, in real cases, not all transition probabilities of the experimentally observed lines are available. For example, Zn I 468.014 nm, Zn I 472.216 nm and Zn I 481.053 nm analytical lines show moderate line intensities in LIBS spectra of samples contained zinc element, however, these lines have unknown transition probabilities thus can’t be selected as analytical lines when taking quantitative elemental analysis by CF-LIBS. To our best knowledge, when zinc contained samples were quantitatively analyzed with CF-LIBS, these lines have not been included to build Boltzmann plot of zinc in the articles already published. If there are no sufficient usable analytical lines, it will be difficult or even impossible to realize accurate elemental analysis of zinc contained samples by CF-LIBS. This is possibly happened for other elements, not only limited to zinc.
To solve this problem, a variant OPC-LIBS method was proposed in this article. Cu-Zn-Ag-Au alloys will be quantitatively analyzed using this method. The quantitative analytical results will be presented and discussed.
2. Experimental
The LIBS experimental setup of this work is schematically shown in Fig. 1. An electro-optically Q-switched Nd:YAG laser (Joyee Technologies Co., Ltd., China, Model: Turbolite) was used to ablate the sample and produce sample plasma. The wavelength, pulse width and repetition rate of the output laser was 1064 nm, 12 ns and 5 Hz, respectively. Typical laser pulse energies selected here was lower than 50 mJ. The laser beam was focused on the sample surface by a glass spherical lens L1 with 80 mm focal length. The sample was placed on a two-dimensional moveable platform. During the experiments, the platform was linearly moved at a speed of 1.0 mm /s, thus each laser pulse could be shot on a fresh place on the sample surface. The optical emission of the laser-induced plasma was collected on to the fiber entrance of a compact three-channel spectrometer (Avantes, AvaSpec-ULS2048-3-USB2) by a set of quartz lens, L2 and L3. The diameter and focal length of L2 and L3 was 50 mm, 50 mm, 100 mm and 150 mm, respectively. The spectrometer was operated under LIBS mode with 1.5 µs gate delay and 2.0 ms gate width. The covering wavelength range of this spectrometer was 200-550 nm, and the spectral resolution was about 0.11 nm in 300-550 nm wavelength regions, which was determined using a low-pressure mercury lamp. In 200-300 nm wavelength regions, the spectral resolution was slightly better than 0.11 nm. The spectral response of this spectrometer has been calibrated using a standard lamp (Avantes, AvaLight-DH-BAL- CAL). Both the Nd:YAG laser and the spectrometer were externally synchronized with a pulse delay generator (SRS, DG 535). The spectral data were finally transferred to a personal computer for further process.
Three pieces of Cu-Zn-Ag-Au alloy samples were analyzed in this work. The samples were purchased from different sellers and the dimension of the samples was 40 × 20 × 0.5 mm3. The elemental concentrations (in atom number) of copper, zinc, silver and gold in the samples were determined with Scanning Electron Microscope-Energy Dispersive Spectrometer (SEM-EDS) (Zeiss, Merlin SEM and Oxford, X-MaxN 20 EDS). Each sample was analyzed for five times and the averaged results were considered as the certified results which were listed in Table 1. The relative error of the measurement was better than 2% for copper and zinc and better than 3% for silver and gold. In this work, Sample #1 was selected as the standard sample to take one-point calibration. Sample #2 and #3 were selected as verification samples.
Table 1. List of elemental concentrations (in atom number) of the analyzed samples determined with SEM-EDS technique
3. One-point calibration method
CF-LIBS algorithm and one-point calibration (OPC) method have been reported in two original articles [1,19]. In this section, a variant OPC method will be described. Supposing the plasma is optically thin, homogeneous and in an LTE state; and the laser-ablation is stoichiometric, the observed intensity of an atomic line Is can be expressed as:
where, Is is the integral intensity of the atomic line calibrated by the spectral response of the spectrometer;$C_s^I$ is the concentration (in atom number) of neutral atoms of one element in the plasma; Aki is the transition probability; gk and Ek is the degeneracy and energy of the upper level, respectively; F is an experimental factor; kB is the Boltzmann constant;$U_s^I(T)$ is the partition function of neutral atoms at temperature T (in K).If a calibration factor µ is used to correct the observed line intensity, Eq. (1) can be rewritten as:
To define
Then Eq. (2) can be rewritten as:
Taking a natural logarithm on both sides of Eq. (4), then,
Here, qs represents the vertical intercept of the fitted straight line of a Boltzmann plot. Since the elemental concentrations of the standard sample are known, once the electron density and temperature of the plasma have been determined, $C_s^I$ can be calculated out according on the following equations [30]:
When analyzing the standard sample (Sample #1) by LIBS, it’s impossible to build a Boltzmann plot for zinc under current experimental condition, because the transition probabilities of some observed zinc lines are unknown. So, it’s impossible to determine F factor according to well-known closure function in CF-LIBS algorithm [1]. However, qs for copper, silver and gold can be determined from their Boltzmann plots; their F factors can be determined according to Eq. (6) separately. Considering the consistency of F factor between each element, the averaged F value can be considered as the final F factor under optimized plasma temperature T. Then the ideal intercept qs0 of each element for the standard sample can be calculated according to Eq. (6). Therefore, the equation of an ideal straight line of a Boltzmann plot for one element can be established as:
After taking OPC procedures, all experimental data points of one element should be moved onto the ideal straight line of the Boltzmann plot of this element, therefore, P value for each analytical line can be deduced according to,
The advantage of using P instead of µ in this work is, no matter whether Aki of the analytical line is known or unknown, quantitative elemental analysis will be possible using CF-LIBS. To realize quantitative elemental analysis of other matrix-matched samples, it is only required to replace Akigk in Eq. (1) with P and calculate elemental concentrations using traditional CF-LIBS algorithm.
4. Results and discussion
4.1. Spectra observation
Figure 2 shows a typical plasma emission spectrum of Sample #1 in the wavelength region of 450-540 nm. This spectrum was an averaged result for five laser shots. The laser pulse energy was 27 mJ in the experiment. In this spectrum, atomic lines of copper, zinc, silver and gold can be observed, including three strong zinc lines with unknown transition probabilities, Zn I 468.014 nm, Zn I 472.216 nm and Zn I 481.053. If one wishes to analyze this sample with traditional CF-LIBS, these lines can’t be selected. Although the transition probabilities of seven zinc lines (213.857 nm, 307.590 nm, 330.258 nm, 330.294 nm, 334.501 nm, 334.557 nm and 334.594 nm) in the wavelength region 200-550 nm are known, these lines can’t be selected as analytical lines due to either spectral congestions or weak intensities. Therefore, it’s impossible to realize quantitative elemental analysis of Cu-Zn-Ag-Au alloys with traditional CF-LIBS algorithm under current experimental conditions. This will be solved using our proposed OPC method.
Fig. 2. Plasma emission spectrum in the wavelength region of 450-540 nm. Sample #1 was analyzed and the laser pulse energy was 27 mJ, corresponding to a fluency of 1.38 J/cm2, approximately.
4.2. Electron density determination
To calculate the concentration of first ionized atoms for each element in the laser-induced plasma, electron density of the plasma has to be determined at first. Usually, the electron density of laser-induced plasma can be determined according to the Stark broadening of a selected line with known Stark broadening coefficient. However, in the observed LIBS spectra of Cu-Zn-Ag-Au alloy samples, without any suitable line can be selected to directly determine the electron density of the plasma due to lacking of the Stark broadening coefficients. Although Zmerli et al. have calculated Stark broadening coefficient of Cu I 510.554 nm [31], the observed line broadening of this line was close to the instrument broadening of the spectrometer, 0.11 nm, therefore it would give large determination error on finding real Stark broadening of this line.
In order to determine the electron density of the laser-induced plasma of Cu-Zn-Ag-Au alloy, a comparison method was adopted in this work. The basic ideal of this method is to establish a calibration between the plasma electron density determined according to hydrogen Hβ line and the line broadening of a suitable line observable in LIBS spectra of Cu-Zn-Ag-Au alloy samples. This line should have large Stark broadening effect, which means the observed line broadening is obviously wider than the instrument broadening. Secondly, this line can’t be affected by self-absorption and intensity saturation effects. Thirdly, this line should not be overlapped by other lines. Cu I 520.292 nm line satisfies all these requirements.
Experimentally, 10% (in weight) copper powder was mixed with KHCO3 grains; then about 6 g mixtures were pressed to a pellet under 21.4 MPa pressures. The diameter of the pellet is 30 mm. The LIBS spectra of this prepared pellet were then recorded under the excitations by the laser pulses with different pulse energies. Figure 3(a) shows a LIBS spectrum of this pellet, in which, both hydrogen Hβ line centered at 486.135 nm and multiple copper lines, including Cu I 520.292 nm, can be observed. The plasma electron density can be determined according to the following equation based on the Stark broadening of hydrogen Hβ line [32]
where, ${w_{{H_\beta }}}$ is the Stark broadening (full width at half maximum, FWHM) of the hydrogen Hβ line.Fig. 3. Determination of electron density of the plasma using a comparison method. (a) Partial LIBS spectrum of copper doped KHCO3 pellet showing both hydrogen Hβ line and Cu I lines. (b) Plot of plasma electron density determined according to Stark broadening of hydrogen Hβ line versus the observed broadening of Cu I 529.252 nm analytical line. (c) Lorentzian fit of Cu I 529.252 nm analytical line observed for the standard sample, the laser pulse energy was 27 mJ.
Figure 3(b) shows a plot of plasma electron density versus the observed line broadening of Cu I 520.292 nm line. Error bar indicates deviations in three repeated measurements under the same experimental condition. The laser pulse energy was selected in the range of 15-60 mJ. These five data points can be approximated fitted with a straight line within a narrow line-broadening range. This fitted line represents the expected calibration between the plasma electron density and the observed line broadening of Cu I 520.292 nm line. The electron density of laser-induced Cu-Zn-Ag-Au plasma can be determined based on this calibration and the observed line broadening of Cu I 520.292 nm line in the LIBS spectrum of the studied sample. Figure 3(c) shows a Lorentzian fit of Cu I 520.292 nm line in the LIBS spectrum of Sample #1, the observed line broadening (FWHM) is 0.155 nm. Thus the electron density of laser-induced Cu-Zn-Ag-Au plasma excited under current condition was determined to be approximately 1.45 × 1017 cm-3.
The calibration shown in Fig. 3(b) may be different if using different matrix instead of KHCO3 at the same excitation laser pulse energy because the electron density of the plasma is matrix-dependent. This can be solved by adjusting the laser pulse energy to have a close line-broadening for Cu I 529.252 nm line as that observed in LIBS analysis of Cu-Zn-Ag-Au alloy samples. The observed line-broadening of Cu I 529.252 nm line (0.155 nm) was not sufficiently large in comparison with the instrumental broadening (0.11 nm), this would introduce slightly large determination error on the real Stark broadening. Considering also the error of the electron density determined using Hβ line, the overall determination error on the electron density of alloy plasma in this work was estimated to be about 10-15%. Fortunately, the influence of this error on the accuracy of quantitative elemental analysis was much weaker than the error of plasma temperature.
4.3. Plasma temperature determination
The plasma temperature could be primarily determined according to the Boltzmann plots of copper. Eight emission lines of copper atoms, including 282.437 nm, 306.341 nm, 427.511 nm, 458.697 nm, 465.112 nm, 510.554 nm, 515.324 nm and 521.820 nm were selected to build this Boltzmann plot. The required transition parameters, Ek, Aki and gk of these selected lines could be found from NIST atomic spectra database. The plasma temperature was primarily determined to be 8810 ± 480 K according to this Boltzmann plot.
In order to find more accurate plasma temperature, a new optimization method was introduced in this work. This was based on the consistency of F factor between different elements in the same experiment. The procedures of temperature optimization using this method can be described: First, building Boltzmann plots of copper, silver and gold based on experimental data points; second, supposing a plasma temperature and determining qs for each element under this temperature assumption; third, calculating F factor for each element according to the following equation,
Finally, calculating the relative total error for F value (ΔF) according to the following definition:
To run this temperature optimization, analytical lines not affected by self-absorption should be selected. Therefore, resonant lines and other lines with low-lying lower states should be avoided. Table 2 lists the selected analytical lines of copper, silver and gold and the energies of their lower states, Ei. The optimization result on the plasma temperature is shown in Fig. 4. The optimized temperature was 8950 K. At the same time; the F factor was determined to be 5.83.
Fig. 4. Optimization of the plasma temperature using consistency of F factor of copper, silver and gold.
Table 2. List of the lower-level energies of the transitions corresponding to the analytical lines selected for plasma temperature optimization
4.4. P values determination
Once the temperature and electron density of the plasma, and the F factor have been successfully determined, ideal Boltzmann plots of four elements in the standard samples can be established. Figure 5 shows ideal Boltzmann plots of copper, zinc, silver and gold of the standard sample analyzed under current experimental condition. The experimental data points of the selected analytical lines of copper, silver and gold have also been shown in this figure. No experimental data points of zinc could be shown in this figure due to previously-mentioned reasons. Based on these ideal Boltzmann plots, the P values for each selected analytical lines of copper, zinc, silver and gold can be obtained and the results are listed in Table 3.
Table 3. List of the transition parameters as well as determined P values of the selected analytical lines
4.5. CF-LIBS elemental analysis using P values
By replacing Akigk in Eq. (1) with previously determined P value for each select line, quantitative elemental analysis for Sample #2 and Sample #3 were carried out using traditional CF-LIBS algorithm. A different recorded spectrum of Sample #1 was also used to take CF-LIBS elemental analysis of Sample #1 itself. The plasma temperatures were obtained by free linear fitting of the Boltzmann plots of copper. Since P values have already been calibrated, all data points located very closely to the fitted straight lines, indicating well-determined plasma temperatures. Actually, the plasma temperatures for three samples were all close to 8950 K. Then data points of zinc, silver and gold were linearly fitted using a fixed slope which was determined by the plasma temperature. Figures 6(a)-(c) show the Boltzmann plots of copper, zinc, silver and gold for Sample #1-3, respectively. Now, the experimental data points of the selected zinc lines can be shown in the figures. The electron densities of the plasma were taken as 1.45 × 1017 cm-3 according the line broadening of Cu 529.252 nm. Then the quantitative analytical results could be obtained according to CF-LIBS algorithm. The results were listed in Table 4 and compared with those determined with SEM-EDS technology. The absolute values of the relative errors are all less than 3.3%, demonstrating reliable quantitative elemental analysis results for Cu-Zn-Ag-Au alloy samples using this variant OPC method.
Fig. 6. Boltzmann plots of copper, zinc, silver and gold for Sample #1-3 using the determined P values.
Table 4. Comparison of the elemental concentrations analyzed by CF-LIBS in this work with those analyzed by EDS technique
The quantitative analytical accuracy of this method was affected by the accuracy of the determined P value for each selected line. As P value was determined with an OPC method, the accuracy was affected by the accuracy of the elemental concentration of the standard sample, and the accuracy of the determined electron density and temperature of the plasma. Improving the accuracy of them in the future will be helpful to improve the analytical accuracy of this proposed method.
The major advantage of this variant OPC-LIBS method is, no matter whether the transition probabilities of the analytical lines are known or unknown, quantitative elemental analysis of a sample is possible by using CF-LIBS algorithm, where only one standard sample is required to provide a calibration. The application of this method is not limited to zinc-contained samples; it is also applicable for elemental analysis of other samples containing special elements, whose part or all emission lines lack transition probabilities. Even for those samples capable of analyzing with CF-LIBS, this method is still helpful to improve its accuracy by adding additional analytical lines with unknown transition probabilities in the calculations.
The limitation of this variant OPC-LIBS method is, due to the plasma temperature and F factor are determined based on other species having emission lines with known transition probabilities; this method will not be applicable if the sample only contained the special elements having emission lines with unknown transition probabilities. However, this is seldom happened in real practices.
5. Conclusions
In conclusion, a variant OPC-LIBS method was proposed and successfully applied to realize quantitative elemental analysis of Cu-Zn-Ag-Au alloy samples for the first time. Reliable analytical accuracy has been demonstrated. The plasma electron density can be determined with a comparison method and the plasma temperature can be optimized according to the consistence of F factors between different elements. It is believed that this variant OPC-LIBS method will be helpful for quantitative elemental analysis of different samples containing special elements, when the transition probabilities of their selected analytical lines are unknown.
Funding
National Natural Science Foundation of China (12174117, 61875055).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. Ciucci, M. Corsi, V. Palleschi, S. Rastelli, A. Salvetti, and E. Tognoni, “New procedure for quantitative elemental analysis by laser-induced plasma spectroscopy,” Appl. Spectrosc. 53(8), 960–964 (1999). [CrossRef]
2. J. Hermann, E. Axente, F. Pelascini, and V. Craciun, “Analysis of multi-elemental thin films via calibration-free laser-induced breakdown spectroscopy,” Anal. Chem. 91(3), 2544–2550 (2019). [CrossRef]
3. C. Gerhard, A. Taleb, F. Pelascini, and J. Hermann, “Quantification of surface contamination on optical glass via sensitivity improved calibration-free laser-induced breakdown spectroscopy,” Appl. Surf. Sci. 537, 147984 (2021). [CrossRef]
4. A. Jabbar, Z. Y. Hou, J. C. Liu, R. Ahmed, S. Mahmood, and Z. Wang, “Calibration-free analysis of immersed metal alloys using long-pulse-duration laser-induced breakdown spectroscopy,” Spectrochim. Acta, Part B 157, 84–90 (2019). [CrossRef]
5. M. Hafeez, S. A. Abbasi, M. Rafique, R. Hayder, M. Sajid, J. Iqbal, N. Ahmad, and S. Shahida, “Calibration-free laser-induced breakdown spectroscopic analysis of copper-rich mineral collected from the Gilgit-Baltistan region of Pakistan,” Appl. Opt. 59(1), 68–76 (2020). [CrossRef]
6. M. Ferus, J. Koukal, L. Lenža, J. Srba, P. Kubelík, V. Laitl, E. M. Zanozina, P. Váňa, T. Kaiserová, A. Knížek, P. Rimmer, E. Chatzitheodoridis, and S. Civiš, “Calibration-free quantitative elemental analysis of meteor plasma using reference laser-induced breakdown spectroscopy of meteorite samples,” Astron. Astrophys. 610, A73 (2018). [CrossRef]
7. J. M. Anzano, A. Cruz-Conesa, R. J. Lasheras, C. Marina-Montes, L. V. Pérez-Arribas, J. O. Cáceres, A. I. Velásquez, and V. Palleschi, “Multielemental analysis of Antarctic soils using calibration free laser-induced breakdown spectroscopy,” Spectrochim. Acta, Part B 180, 106191 (2021). [CrossRef]
8. C. T. Chen, D. Banaru, T. Sarnet, and J. Hermann, “Two-step procedure for trace element analysis in food via calibration-free laser-induced breakdown spectroscopy,” Spectrochim. Acta, Part B 150, 77–85 (2018). [CrossRef]
9. M. Al-Salihi, R. X. Yi, S. Q. Wang, Q. Wu, F. R. Lin, J. L. Qu, and L. W. Liu, “Quantitative laser-induced breakdown spectroscopy for discriminating neoplastic tissues from non-neoplastic ones,” Opt. Express 29(3), 4159–4173 (2021). [CrossRef]
10. J. Iqbal, H. Asghar, S. K. H. Shah, M. Naeem, S. A. Abbasi, and R. Ali, “Elemental analysis of sage (herb) using calibration-free laser-induced breakdown spectroscopy,” Appl. Opt. 59(16), 4927–4932 (2020). [CrossRef]
11. D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 57(2), 339–353 (2002). [CrossRef]
12. L. X. Sun and H. B. Yu, “Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy by an internal reference method,” Talanta 79(2), 388–395 (2009). [CrossRef]
13. T. Q. Li, Z. Y. Hou, Y. T. Fu, J. L. Yu, W. L. Gu, and Z. Wang, “Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy (CF-LIBS) with blackbody radiation reference,” Anal. Chim. Acta 1058, 39–47 (2019). [CrossRef]
14. Z. L. Hu, F. Chen, D. Zhang, Y. W. Chu, W. L. Wang, Y. Tang, and L. B. Guo, “A method for improving the accuracy of calibration-free laser-induced breakdown spectroscopy by exploiting self-absorption,” Anal. Chim. Acta 1183, 339008 (2021). [CrossRef]
15. R. Gaudiuso, M. Dell’Aglio, O. De Pascale, A. Santagata, and A. De Giacomo, “Laser-induced plasma analysis of copper alloys based on local thermodynamic equilibrium: An alternative approach to plasma temperature determination and archeometric applications,” Spectrochim. Acta, Part B 74-75, 38–45 (2012). [CrossRef]
16. R. Gaudiuso, M. Dell’Aglio, O. De Pascale, S. Loperfido, A. Mangone, and A. De Giacomo, “Laser-induced breakdown spectroscopy of archaeological findings with calibration-free inverse method: Comparison with classical laser-induced breakdown spectroscopy and conventional techniques,” Anal. Chim. Acta 813, 15–24 (2014). [CrossRef]
17. J. Dong, L. Liang, J. Wei, H. S. Tang, T. L. Zhang, X. F. Yang, K. Wang, and H. Li, “A method for improving the accuracy of calibration-free laser-induced breakdown spectroscopy (CF-LIBS) using determined plasma temperature by genetic algorithm (GA),” J. Anal. At. Spectrom. 30(6), 1336–1344 (2015). [CrossRef]
18. J. H. Yang, X. M. Li, J. W. Xu, and X. H. Ma, “A calibration-free laser-induced breakdown spectroscopy (CF-LIBS) quantitative analysis method based on the auto-selection of an internal reference line and optimized estimation of plasma temperature,” Appl. Spectrosc. 72(1), 129–140 (2018). [CrossRef]
19. G. H. Cavalcanti, D. V. Teixeira, S. Legnaioli, G. Lorenzetti, L. Pardini, and V. Palleschi, “One-point calibration for calibration-free laser-induced breakdown spectroscopy quantitative analysis,” Spectrochim. Acta, Part B 87, 51–56 (2013). [CrossRef]
20. G. Agrosì, G. Tempesta, E. Scandale, S. Legnaioli, G. Lorenzetti, S. Pagnotta, V. Palleschi, A. Mangone, and M. Lezzerini, “Application of laser induced breakdown spectroscopy to the identification of emeralds from different synthetic processes,” Spectrochim. Acta, Part B 102, 48–51 (2014). [CrossRef]
21. G. C. Gomes, F. O. Borges, F. F. Borghi, G. H. Cavalcanti, C. M. S. Martins, V. Palleschi, and A. Mello, “Rapid stoichiometric analysis of calcium-phosphorus ratio on hydroxyapatite targets by one-point calibration laser-induced breakdown spectroscopy,” Spectrochim. Acta, Part B 184, 106250 (2021). [CrossRef]
22. G. S. Senesi, G. Tempesta, P. Manzari, and G. Agrosi, “An innovative approach to meteorite analysis by laser-induced breakdown spectroscopy,” Geostand. Geoanal. Res. 40(4), 533–541 (2016). [CrossRef]
23. H. B. Fu, H. D. Wang, J. W. Jia, Z. B. Ni, and F. Z. Dong, “Standard reference line combined with one-point calibration-free laser-induced breakdown spectroscopy (CF-LIBS) to quantitatively analyze stainless and heat resistant steel,” Appl. Spectrosc. 72(8), 1183–1188 (2018). [CrossRef]
24. R. Hai, W. N. Tong, D. Wu, Z. L. He, H. Sattar, C. Li, and H. B. Ding, “Quantitative analysis of titanium alloys using one-point calibration laser-induced breakdown spectroscopy,” Appl. Phys. B 127(3), 37 (2021). [CrossRef]
25. X. Bai, R. Hai, Z. L. He, X. Y. Wang, D. Wu, C. Li, W. N. Tong, H. C. Wu, G. L. Xu, D. D. Dong, Z. H. Hu, and H. B. Ding, “One-point calibration laser-induced breakdown spectroscopy for the quantitative analysis of EAST-like plasma-facing materials,” J. Anal. At. Spectrom. 37(2), 289–295 (2022). [CrossRef]
26. L. C. L. Borduchi, D. M. B. P. Milori, and P. R. Villas-Boas, “One-point calibration of Saha-Boltzmann plot to improve accuracy and precision of quantitative analysis using laser-induced breakdown spectroscopy,” Spectrochim. Acta, Part B 160, 105692 (2019). [CrossRef]
27. Y. R. Wang, Y. Q. Chen, R. H. Li, J. Kang, and J. K. Gao, “Quantitative elemental analysis of aluminum alloys with one-point calibration high repetition rate laser-ablation spark-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 36(2), 314–321 (2021). [CrossRef]
28. Z. Q. Hao, L. Liu, R. Zhou, Y. W. Ma, X. Y. Li, L. B. Guo, Y. F. Lu, and X. Y. Zeng, “One-point and multi-line calibration method in laser-induced breakdown spectroscopy,” Opt. Express 26(18), 22926–22933 (2018). [CrossRef]
29. R. Yuan, Y. Tang, Z. H. Zhu, Z. Q. Hao, J. M. Li, H. Y. Yu, Y. X. Yu, L. B. Guo, X. Y. Zeng, and Y. F. Lu, “Accuracy improvement of quantitative analysis for major elements in laser-induced breakdown spectroscopy using single-sample calibration,” Anal. Chim. Acta 1064, 11–16 (2019). [CrossRef]
30. E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta, Part B 62(12), 1287–1302 (2007). [CrossRef]
31. B. Zmerli, N. Ben Nessib, M. S. Dimitrijevic, and S. Sahal-Bréchot, “Stark broadening calculations of neutral copper spectral lines and temperature dependence,” Phys. Scr. 82(5), 055301 (2010). [CrossRef]
32. M. A. Gigosos, M. A. Gonzalez, and V. Cardenoso, “Computer simulated Balmer-alpha, -beta and -gamma Stark line profiles for non-equilibrium plasmas diagnostics,” Spectrochim. Acta, Part B 58(8), 1489–1504 (2003). [CrossRef]
