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Abstract
The single sample calibration laser-induced breakdown spectroscopy (SSC-LIBS) is quite suitable for the fields where the standard sample is hard to obtain, including space exploration, geology, archaeology, and jewelry identification. But in practice, the self-absorption effect of plasma destroys the linear relationship of spectral intensity and element concentration based on the Lomakin-Scherbe formula which is the guarantee of the high accuracy of the SSC-LIBS. Thus, the self-absorption effect limits the quantitative accuracy of SSC-LIBS greatly. In this work, an improved SSC-LIBS with self-absorption correction (SSC-LIBS with SAC) is proposed for the promotion of quantitative accuracy of SSC-LIBS. The SSC-LIBS with SAC can correct the intensity ratio of spectral lines in the calculation of SSC-LIBS through relative self-absorption coefficient K without complicated preparatory information. The alloy samples and pressed ore samples were used to verify the effect of the SSC-LIBS with SAC. Compared with SSC-LIBS, for alloy samples, the average RMSEP and average ARE of SSC-LIBS with SAC decreased from 0.83 wt.% and 13.75% to 0.40 wt.% and 4.06%, respectively. For the pressed ore samples, the average RMSEP and average ARE of SSC-LIBS with SAC decreased from 4.77 wt.% and 90.48% to 2.34 wt.% and 14.60%. The experimental result indicates that SSC-LIBS with SAC has a great improvement of quantitative accuracy and better universality compared with traditional SSC-LIBS, which is a mighty promotion of the wide application of SSC-LIBS.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser-induced breakdown spectroscopy (LIBS), as a new optical emission spectrometry, has many advantages, such as fast, real-time, in-situ, multi-element simultaneous detection, and no or simple sample preparation [1]. Thus, LIBS has been widely applied to many fields such as environmental monitoring [2], food safety [3], biomedicine [4], metallurgy [5], mining [6], and space exploration [7]. The quantitative analysis of LIBS depends on the calibration methods, including classical calibration [8], calibration-free (CF) [9], multi-energy calibration (MEC) [10], one-point and multi-line calibration (OP-MLC) proposed by our group in 2018 [11], and single-sample calibration (SSC) proposed by our group in 2019 [12]. Most of them are unsuitable for the major element quantification due to the self-absorption effect. CF-LIBS can overcome the matrix effect and quantify the major elements without standard samples. However, its accuracy is not high because the theory is quite ideal and far from reality. SSC-LIBS can achieve the total element determination using only one standard sample. It is quite suitable for the fields where standard samples are hard to obtain or prepare, such as geology [13], archaeology [14], jewelry identification [15], etc.
According to the Lomakin-Scherbe formula, SSC-LIBS must select one optically thin spectral line for each element to perform the quantitative procedure. However, the self-absorption effect always exists in the laser-induced plasma [16], which makes the spectral intensity obtained lower than the real intensity, resulting in a decrease in the accuracy of SSC-LIBS. Over the past few decades, the self-absorption effect has been investigated by many scholars. There are mainly three research directions of exploitation and compensation of self-absorption in the LIBS quantitative model. The first kind is to optimize the experimental parameters and experimental environment, such as laser parameters [17], ambient gas conditions [18], acquisition parameters [19], etc. which can make spectral lines as optical thin as possible to eliminate the effect of self-absorption on quantification. But most application situations limit the use of this method. The second kind is to add auxiliary devices, including a duplicating mirror [20], laser-stimulated absorption [21], microwave-assisted excitation [22], etc. The duplicating mirror method can be used in moderate self-absorption conditions and its sensitivity decreases if the line intensity is too low. The laser-stimulated absorption method needs an optical parametric oscillator (OPO) laser, whose cost is high. The microwave is harmful to the human body. The third kind is to correct self-absorption through the algorithm, including internal reference for self-absorption correction (IRSAC) [23], self-absorption correction algorithm based on blackbody radiation (BRR-SAC) [24], and the self-absorption coefficient (SA) method [25–27], which are substantially estimation of self-absorption parameter by different reference objects, There are also several untraditional self-absorption correction methods including the curve of growth (COG) [28,29], the columnar density formulation [30,31], the C-sigma method [32,33], which obtain the element concentration information from the optically thick lines directly [34]. The above methods about self-absorption correction are mainly suitable for CF-LIBS, however, the research about the self-absorption correction method for SSC-LIBS has not been reported yet.
In this work, an improved SSC-LIBS with self-absorption correction (SSC-LIBS with SAC) is proposed. This method is based on the improvement and simplification of the self-absorption coefficient (SA) calculation formula. The intensity ratio of spectral lines in the SSC-LIBS formula was corrected directly by this method without the calculation of a specific SA coefficient. We used the average relative error (ARE) and the root mean square error of prediction (RMSEP) to evaluate the effect of the SAC of the proposed method. The results proved that the proposed method can effectively reduce the influence of the self-absorption effect on SSC-LIBS and significantly improve the quantitative accuracy, which is conducive to the promotion of SSC-LIBS.
2. Self-absorption correction method
There are two common methods to calculate the SA coefficient. The first one is based on the ratio between measured and theoretical intensities or broadenings of the optically thick line [26]. The other is based on multiple standard samples to establish the calibration curve by exponential fitting [27] and the SA coefficient can be calculated through the exponential part of the curve equation. Only the first method can be chosen for SSC-LIBS which can only use single standard sample. Under the local thermodynamic equilibrium (LTE) condition and the plasma is homogeneous, the SA coefficient of the goal spectral line can be expressed as [26]:
where $\Delta \lambda$ is the measured line broadening, $\Delta {\lambda _0}$ is the theoretical line broadening without self-absorption. $\alpha$ is the numerical simulation constant, usually −0.54. In LIBS spectra, the collision broadening is caused by charged particles, also known as Stark broadening (Lorentz profile), which is usually dominant in the plasma [35]. If the effect of ions on Stark broadening is ignored and only the collision effect of electrons is considered, the theoretical full width at half maximum (FWHM) of the Lorentz line profile without self-absorption can be expressed as: where ${\omega _s}$ is the Stark half-width parameter, ${n_e}$ is the electron number density of plasma, ${n_e}^{ref}$ is the reference electron number density, usually 1016 or 1017 cm-3, which depends on the condition in the calculation of ${\omega _s}$ [36]. Thus, ${n_e}$ can be expressed through a reference line, which is optically thin, by: where $\Delta {\lambda _{SAF}}$ is FWHM of the reference line, ${\omega _{SAF}}$ is the Stark half-width parameter of reference spectral line. Equation (1) can be rewritten by simultaneous Eq. (1), (2), and (3) as:By defining the following quantities:
Equation (4) can be rewritten as:
In the absence of self-absorption effect, according to the formula of SSC-LIBS [12], the concentration of the element j in the test sample is:
According to Eq. (7) and (9), in the absence of self-absorption, the line intensity ratio of element j or oxide j in the test sample and the standard sample is:
The M value of the same spectral line is equal, and the Eq. (9) can be rewritten as:
Identically, the line intensity ratio of element i or oxide i in the test sample and the standard sample without self-absorption is:
According to Eq. (8), (11), and (12), the content of element j or oxide j in test sample after self-absorption correction is:
The K can be obtained directly by the FWHM ratio of the goal spectral line and the reference line of self-absorption free. However, the reference line without self-absorption is hard to obtain in the actual experiment. Since the hydrogen Balmer alpha (Hα) line is generated by the interaction between plasma and water vapor, it is usually regarded as the spectral line without self-absorption [37,38]. In this work, we selected the Hα line as the reference line. According to Sherbini’s method of calculating electron density based on the Hα line in 2006, formula (3) can be expressed as:
Defining the following quantities anew:
3. Experimental
3.1 Samples and sample preparation
To study the self-absorption correction effect of SSC-LIBS with SAC, alloy samples and ore pressed samples were used in the experiment, in which the alloy samples were aluminum bronze standard samples (BYG1916-1, Luoyang Copper Co., Ltd., China Aluminum Testing Center). To obtain ore samples with different oxide concentration distribution, we mixed dolomite (GBW03116, National Research Center of Testing Techniques for Building Materials) and potassium feldspar (GBW070160, Jinan Zhongbiao Technology Co., Ltd.) powder in the proportion of 5:0, 4:1, 3:2, 2:3, 1:4 respectively, and pressed them under high pressure to make five ore samples. The detailed fabrication process is shown in the following steps. Table 1 lists the element content of the alloy samples and Table 2 lists the oxide content of the pressed ore samples.
- (1) Mix dolomite and potash feldspar powders in five different proportions and mix them evenly in a high-speed oscillator for 10 min.
- (2) Transfer the mixed ore powder into a mortar for uniform grinding.
- (3) After mixing and grinding, take 1 g mixed ore powder on the substrate made with 9 g boric acid powder (GB/T 628-1993, Sinopharm Chemical Reagent Co., Ltd.). Press the mixed ore powder with boric acid substrate into pellets with a diameter of 40 mm under the pressure of 30Mpa.
Table 1. The certified concentration of the elements in aluminum bronze standard samples(wt.%)
Table 2. The certified concentration of the oxides in pressed ore samples(wt.%)
3.2 Experimental setup
The schematic diagram of the experimental system used in this work is shown in Fig. 2. The Q-switched Nd-YAG laser (wavelength: 532 nm, maximum power: 400 mJ, repetition rate: 1 Hz, pulse width: 8 ns, Beamtech Optronics, Nimma-400) was used to generate the laser. The horizontally emitted laser was reflected by a mirror and then focused on the sample surface through a focusing lens (f = 150 mm) to generate plasma. The spectrum emitted by the plasma was collected by the acquisition head and coupled to a six-channel fiber-optic spectrograph (Avantes B. V, AvaSpec-ULS4096CL-EVO, spectral ranges: 196–874 nm, minimum gate width: 9 μs). The photoelectric sensor in the spectrometer converted the spectral signal into the digital signal and transmitted it to the computer for subsequent processing and analysis. The time sequence between laser and spectrometer was controlled by a digital delay generator (Wuhan N & D Laser Engineering, LDG 3.0). The gate delay and width of the spectrograph were set to 2 μs and 9 μs respectively. To obtain a high spectral signal-to-noise ratio, the laser energy was optimized to 30 mJ and 70 mJ for aluminum bronze samples and ore pressed samples, respectively. In the experiment, the sample was placed on a 3D electric displacement platform (Beijing Jiangyun Juli Technology, DZY110TA-3Z) for generating a new excitation position for each pulse. To reduce the influence of laser energy on the stability of the spectral signal, 5 pulses were accumulated per spectrum and repeated 10 times.
3.3 Evaluation indexes
To study the improvement effect of SSC-LIBS with SAC on the quantitative accuracy of SSC-LIBS, one sample was selected as the standard sample each time, and the remaining sample was selected as the test sample. The standard sample was used for quantitative analysis of multiple test samples based on SSC-LIBS and SSC-LIBS with SAC, and the average relative error (ARE) and root mean square error of prediction (RMSEP) of the multiple quantitative analysis were calculated. The calculation formulas of ARE and RMSEP are as follows:
4. Results and discussion
4.1 Quantitative analysis of the alloy sample
According to formula (12), the single-sample calibration method needs to select one spectral line for each element in the sample. To avoid spectral interference and obtain high SNR (signal to noise ratio, SNR), four persistent lines (Cu II 204.38 nm, Fe I 382.04 nm, Al I 396.15 nm, and Mn I 404.14 nm) marked with red arrows in Fig. 3 were selected for the calculation of the SSC-LIBS. The four lines and Hα line (656.28 nm) were used for the fitting curve through Lorentz function. Taking aluminum bronze sample No.3 as an example, Fig. 4 shows the fitting curves of five spectral lines in the spectra of sample No.3. Table 3 lists the K values of selected spectral lines in each sample used in this experiment. According to the K value ratio of the same spectral line between the test sample and the standard sample, the spectral line intensity ratio was corrected in the quantitative process of the SSC-LIBS.
Fig. 4. The fitting curve of five spectral lines in the spectra of sample No.3: (a) – (e) for Cu II 204.38 nm, Fe I 382.04 nm, Al I 396.15 nm, Mn I 404.14 nm and H I 656.28 nm.
Table 3. The K value of element spectral lines of various sample
To study the effect of SSC-LIBS with SAC, we first selected the sample No.2 as the standard sample, the spectral line intensity in the calculation of SSC-LIBS was corrected through the K value obtained above. The corrected intensity was used to predict the element concentration of the remaining four samples and the prediction results were compared with the one without self-absorption correction and the certified concentration of elements. As shown in Fig. 5, the dotted line represents the certified concentrations, the blue dot and red dot represent the predicted concentrations without and with self-absorption correction, respectively (Fig. 5 (a) for Mn element, Fig. 5 (b) for Fe element). Obviously, after self-absorption correction, the element concentration predicted by the SSC-LIBS is closer to the certified concentration, which indicates that the method proposed in this paper has an obvious quantitative improvement effect for the SSC-LIBS.
Fig. 5. Comparison of the concentration calculated by SSC-LIBS with SAC (red) and by SSC-LIBS (blue) vs. the certified concentration in brass samples: (a) Mn and (b) Fe.
To further study the quantitative improvement effect of this method when using different samples as standard samples, we selected samples 1–5 as the standard sample respectively and predicted the element concentration of the remaining samples before and after the self-absorption correction. Finally, we obtained the average relative error (ARE) of the four elements before and after the self-absorption correction when using different samples as standard samples.
As is shown in Fig. 6, before self-absorption correction, the predicted concentration ARE of Mn is the largest relative to other elements. This may be due to the certified concentration of the four elements in the five aluminum bronze samples are basically more than 1%, which means that the spectral lines of these elements have strong self-absorption effect, and the certified concentration of Mn element is relatively low in the four elements. For the absolute error of similar level, relative error of elements with lower certified concentration may be larger.
Fig. 6. Comparison of the ARE calculated by SSC-LIBS before SAC and after SAC for aluminum bronze samples: (a) – (e) for No.1-5 sample as the calibration sample.
Besides, no matter which sample was used as the standard sample, ARE of elements in aluminum bronze overall decreased significantly compared with that before self-absorption correction, while the decrease of Cu was small. When sample 5 was used as the standard sample, the ARE even increased slightly. This may be because Cu is the matrix element in aluminum bronze, whose content is more than 80%. Furthermore, the content of Cu in five aluminum bronze samples is relatively close, and the self-absorption effect of the Cu spectrum is also relatively close, so the calculated K value of Cu is also relatively close. Thus, the fluctuation of the spectrum itself may exceed the influence of the self-absorption effect on the spectrum of Cu. After correction, the ARE of Cu cannot be reduced always. Even though, the method proposed in this paper still has a satisfactory effect on improving the accuracy of SSC-LIBS as a whole.
In addition, as shown in Fig. 7, the RMSEP of four elements when using different standard samples were calculated, whose trend is similar with the ARE. Table 4 lists the average RMSEP and average ARE when using different samples as standard samples before and after self-absorption correction. The results showed that the average RMSEP of Al, Fe, Mn and Cu decreased from 1.47, 0.52, 0.36, and 0.96 wt.% to 0.63, 0.18, 0.10, and 0.70 wt.%, respectively, and the average ARE decreased from 13.83%, 16.4%, 23.72%, and 1.03% to 5.98%, 4.96%, 4.53%, and 0.76%, respectively. Besides, four elements in five aluminum bronze samples were quantitatively analyzed by classical calibration method, the result showed that ARE of four elements were 3.40%, 2.93%, 9.34%, and 1.22%, which indicate that the method proposed in this work has a good effect on the self-absorption correction of alloy sample and achieve the quantitative accuracy close to the classical calibration method.
Fig. 7. Comparison of the RMSEP calculated by SSC-LIBS before SAC and after SAC for aluminum bronze samples: (a) – (e) for No.1-5 sample as the calibration sample.
Table 4. RMSEP (wt.%) and ARE (%) of elements in aluminum bronze samples through SSC-LIBS and SSC-LIBS with SAC
4.2 Quantitative analysis of the pressed ore sample
To further determine the universality of SSC-LIBS with SAC for different types of samples, we used five different oxide concentrations of ore pressed samples made with dolomite and potash feldspar. As shown in Fig. 8, To avoid spectral interference and obtain high SNR (signal to noise ratio, SNR), five persistent lines (Al I 237.31 nm, Si I 288.16 nm, Ca I 442.54 nm, Na I 589.00 nm, and K I 769.90 nm) marked by the red arrow were selected in the SSC-LIBS.
Similarly, we selected ore pressed samples from No. 1 to No. 5 as standard samples respectively, and the remaining four as test samples. Before and after self-absorption correction, the concentration of five oxides in the sample was quantified by SSC-LIBS, and the average RMSEP and average ARE using the different samples as standard samples were calculated. The results of Fig. 9 showed that the average RMSEP of SiO2, Al2O3, CaO, K2O, and Na2O decreased from 6.99, 2.05, 11.69, 2.11, and 0.99 wt.% to 5.37, 0.84, 4.33, 0.88, and 0.26 wt.%, respectively. The average ARE decreased from 25.62%, 34.40%, 31.14%, 212.80%, and 148.42% to 16.04%, 11.24%, 11.48%, 16.22%, and 18.04%, respectively, which indicate that SSC-LIBS with SAC proposed in this paper also has good correction effect for ore samples, and the quantitative accuracy of SSC-LIBS for ore samples is significantly improved.
Fig. 9. Comparison of the ARE and RMSEP calculated by SSC-LIBS before (black) SAC and after (red) SAC for pressed ore samples: (a) for ARE, (b) for (RMSEP)
The SSC-LIBS with SAC proposed in this paper is quite suitable for the samples with relatively large element concentration gradient distribution. Besides, the method has a good quantitative accuracy improvement effect for alloy samples and ore samples. It should be noted that SSC-LIBS with the SAC method requires that the Hα line can be observed clearly in the experiment or another reference line of self-absorption free can be obtained, only in this way can the K value be calculated. Therefore, the experiment parameters need to be optimized to obtain a clear Hα line and favorable signal-to-noise ratio. Besides the K value can be used to quantify the degree of self-absorption effect of the same spectral line under different experiment parameters, which is helpful to reduce self-absorption by optimizing experimental parameters.
5. Conclusions
In this work, The SSC-LIBS with SAC has been proposed for overcoming the self-absorption problem and improving the quantitative accuracy of SSC-LIBS. The SSC-LIBS with SAC is based on the improvement and simplification of the calculation formula of the SA coefficient and directly uses the relative SA coefficient K to correct the spectral line intensity ratio in the formula of SSC-LIBS. Alloy and ore pressed samples were used to study the self-absorption correction effect of the method. For alloy samples, after self-absorption correction, the ARE of Al, Fe, Mn, and Cu decreased from 13.83%, 16.4%, 23.72%, and 1.03% to 5.98%, 4.96%, 4.53%, and 0.76%, respectively. For the pressed ore samples, the ARE of SiO2, Al2O3, CaO, K2O, and Na2O decreased from 25.62%, 34.40%, 31.14%, 212.80%, and 148.42% to 16.04%, 11.24%, 11.48%, 16.22%, and 18.04%, respectively. These results showed that the SSC-LIBS with SAC had a good self-absorption correction effect in SSC-LIBS for various types of samples and the quantitative accuracy was significantly improved. The method also has the advantages of simple steps, good universality, and does not require preparatory information such as the Stark half-width parameter. It has great significance for the popularization and application of SSC-LIBS.
Funding
National Natural Science Foundation of China (61705064, 62075069); Natural Science Foundation of Hubei Province (2018CFB773).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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