1. Introduction

Glass is widely used in various fields including construction, daily life, art, medicine, chemical, electronics, instrumentation, nuclear engineering, and so on. Data shows that the global glass industry grew at a rate of 5.2% between 2016 and 2021, and the global glass industry is expected to grow at a rate of 4.1% to 5.3% between 2022 and 2030 [1]. Quartz sand is a major raw material in glass production and contains various metal oxides. These metal elements play a role in regulating glass properties. For example, the iron content is a crucial factor influencing glass quality. Ferrous ions have a strong coloring ability, significantly affecting the whiteness of glass. Ferrous ions can also influence the radiation heat transfer in glass, affecting the temperature distribution in glass melt in the furnace. Additionally, the ratio of ferrous ions to ferric ions in glass reflects the oxidative-reductive state of the glass melt. Furthermore, the addition of sodium oxide can lower the melting point of glass, making the melting process easier; calcium oxide can increase the compressive strength and heat resistance of glass; aluminum oxide can enhance the hardness and abrasion resistance of glass, and so on. Therefore, monitoring and controlling the content of major elements in glass is a key factor in optimizing glass production processes and plays a significant role for improving glass quality.

Determining the elemental contents of quartz sand before it enters the furnace allows reasonable measures to be taken to control the content of various elements in glass products. Traditional chemical analysis methods for determining the chemical composition of quartz sand are time-consuming and cumbersome, and the results are often influenced by the qualifications of the analysts and various reagent factors. When using inductively coupled plasma mass spectrometry (ICP-MS) to detect trace elements in quartz sand [2], the sample needs to be digested with hydrofluoric acid. The sample solution is atomized and sent into the ion source flame by the carrier gas after evaporation, dissociation, atomization, and ionization processes before entering the mass spectrometer through the collection system, making the operation complex. X-ray fluorescence spectroscopy (XRF) analysis [3] requires the use of high-energy X-rays to excite atoms in the substance to be tested. Since X-rays are harmful to the human body, additional protective measures need to be taken.

Laser-induced breakdown spectroscopy (LIBS) technology has gradually become an analytical tool capable of providing real-time measurements of almost any type of material composition [4]. LIBS, as an emission spectroscopic analysis technique, can generate plasma by interacting with the substance using high-energy pulse lasers. After detecting and analyzing characteristic spectral lines in the emitted radiation spectra, information about the composition of the substance to be tested can be obtained qualitatively and quantitatively. For quantitative analysis of samples using LIBS, a common method is to establish a calibration curve between the spectral intensity of standard samples and the content of the elements to be analyzed. This calibration curve is then used to predict the content of the elements to be analyzed, a method widely used [5–7]. In comparison, in 1999, Italian scientist A. Ciucci and colleagues proposed the calibration-free laser-induced breakdown spectroscopy (CF-LIBS) method [8,9], an analysis method that does not require standard samples. Based on the relationship between spectral intensity and atomic transition energy, plasma temperature, electron density, etc., CF-LIBS does not need to establish a calibration curve based on standard samples. It only requires the analysis of one sample to obtain the content of the elements to be analyzed, avoiding the effects of the sample matrix and system parameter fluctuations. Given the advantages of CF-LIBS technology, it has been widely applied in various fields [10–17]. Considering the complex situation of the lack of standard reference samples for quartz sand raw materials, this study attempts to investigate the feasibility of using CF-LIBS to calculate the elemental content in quartz sand, which would provide guidance for formulating corresponding treatment plans based on qualitative and semi-quantitative measurement results in the glass manufacturing.

2. CF-LIBS methodology

The calibration-free method is an analysis technique that does not require the use of standard samples. When conducting quantitative analysis using CF-LIBS technology, four conditions need to be met:

①Local Thermodynamic Equilibrium (LTE) of the Plasma: The plasma must be in local thermodynamic equilibrium, meaning that all processes in the plasma (excluding radiation) must be in balance at the same temperature. This ensures the stability of the plasma properties within a specific space-time range.

②Representation of Element Content in the Plasma: The elemental content in the plasma should accurately represent the relative elemental content in the sample (chemical stoichiometry). This condition ensures the accuracy of the analysis results.

③Uniform Spatial Distribution of the Plasma: The plasma's composition, temperature, and electron number density must be uniform throughout the plasma plume. This uniformity ensures consistent properties of the plasma within the observed space-time range, enhancing the reliability of the analysis.

④Optical Thinness of the Plasma: The plasma must satisfy the optical thinness condition, meaning that self-absorption can be neglected. This condition ensures that the observed spectral signals originate from the sample and not from the plasma itself.

Fulfilling these conditions guarantees the accuracy and reliability of quantitative analysis using CF-LIBS technology.

2.1 Calculating plasma temperature

Using the Boltzmann plot method to measure laser-induced plasma temperature. The intensity of spectral lines emitted when the plasma transitions from energy level ${E_i}$ to energy level ${E_j}$ satisfies

Organize Eq. (1) and take the logarithm on both sides, yielding

Letting $y = \ln \left( {\frac{{I_\lambda^{ij}}}{{{g_i}{A_{ij}}}}} \right)$, $m ={-} \frac{1}{{{k_B}T}}$, ${x_i} = {E_i}$, ${q_s} = \ln \left( {\frac{{F{C_s}}}{{{U_s}(T)}}} \right)$, the Eq. (2) can be rewritten as

Plotting the relationship curve between ${E_i}$ and $\ln ({{{I_\lambda^{ij}} / {{g_i}{A_{ij}}}}} )$ forms a two-dimensional Boltzmann plot represented by points $({{E_i}{,^{}}\ln ({{{I_\lambda^{ij}} / {{g_i}{A_{ij}}}}} )} )$. The slope m of the obtained curve reflects the plasma temperature, and the intercept ${q_s}$ indicates the content of the analyzed substance. By using experimental intensities and spectral parameters of multiple atomic (or ionic) lines of the same type, a straight line can be fitted with the energy level ${E_i}$ as the x-axis and $\ln ({{{I_\lambda^{ij}} / {{g_i}{A_{ij}}}}} )$ as the y-axis. The slope of this line can be used to determine the plasma temperature.

2.2 Determining the LTE condition

The premise of CF-LIBS quantitative analysis is the establishment of the local thermodynamic equilibrium (LTE) condition. Confirming whether the plasma is in LTE state is an essential step in CF-LIBS calculations. Typically, the McWhirter criterion [19] is used to determine the LTE status. It is considered that LTE condition is met when the electron number density ${n_e}$ ($c{m^{ - 3}}$) satisfies the following condition:

The estimation of electron number density is crucial to verify the validity of LTE state, and it is accomplished through the broadening of spectral lines (typically Stark broadening). The electron number density related to the half-width at half-maximum (HWHM) $\Delta {\lambda _{{1 / 2}}}$(nm) of the Stark broadened line is given by the following equation:

2.3 Calculating elemental content

Given ${q_s} = \ln \left( {\frac{{F{C_s}}}{{{U_s}(T)}}} \right)$, where ${C_s}$ represents the quantity of particles (atoms or ions of a specific element) undergoing a particular transition, F is the experimental parameter involving optical efficiency, plasma number density, and other factors, and ${U_s}(T)$ is the partition function of the transition particles. By using the Boltzmann plot, the temperature T of the laser-induced plasma can be obtained, and the partition function ${U_s}(T)$ can be expressed as follows:

The value of F is obtained through normalization, where the sum of the relative contents of all elements in the sample equals 1, resulting in

After obtaining the values of F, ${q_s}$, and ${U_s}(T)$, the content of each element in the sample can be calculated using the following formula:

2.4 Evaluation of the calculation results

To evaluate the accuracy and precision of the calculation results, the Relative Error (RE) was employed to assess the single-element errors in CF-LIBS quantitative analysis (where ${M_s}$ represents the measured value, and ${C_s}$ represents the actual value):

3. LIBS experiment

The experimental setup for obtaining LIBS spectral data is illustrated in Fig. 1(a). The laser light source used in the experiment is generated by a Q-switched Nd:YAG laser (Q-Smart 450, Quantel, France) with a laser wavelength of 1064 nm, a pulse width of 6 ns, a repetition rate of 8 Hz, and a laser energy of 100 mJ per pulse, with a delay time of 1.58 ms. To ensure that the laser energy irradiated onto the sample surface meets the requirements, a half-wave plate and a polarizing beam splitter are used in combination to achieve continuous adjustment of the laser energy. The half-wave plate can rotate the polarization direction of light, while the polarizing beam splitter can select the transmitted polarization direction. The combination of these two components enables continuous adjustment of light energy. Laser energy is monitored using a laser energy meter. If the laser energy is inappropriate, a variable beamsplitter can be achieved by rotating the half-wave plate. Subsequently, a quartz converging lens with a focal length of 100 mm focuses the laser beam on the sample surface to induce plasma generation. A 15 mm focal length collimating lens with a diameter of 10 mm collects the laser-induced plasma light, which is then transmitted to an 8-channel spectrometer (Avaspec-ULS2048, Avantes, Netherlands) coupled with a CCD detector through optical fibers. The spectrometer acquisition parameters include a delay time of 1.28 µs, an integration time of 1.05 ms, and a spectral range of 185 to 1070 nm. The resolutions of different channels vary slightly, ranging from 0.058 to 0.068 nm. Additionally, a three-dimensional displacement platform is used to control the scanning of the test position, and a laser rangefinder is employed to precisely control the focusing position. If the distance measured by the laser rangefinder exceeds the error limit, it prompts us to replace the sample or adjust its position on the three-dimensional displacement platform. To prevent contamination of the optical system or blockage of the laser beam, a small vacuum cleaner is used to collect the sample powder generated near the sample surface during the experimental process, and it is also helpful for the stabilization of plasma.

 

Fig. 1. (a) Schematic diagram of laser-induced breakdown spectroscopy data acquisition system. (b) The photograph of a quartz sand sample that has been pressed into a pie shape.

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Figure 1(b) shows the photograph of the quartz sand sample used in the experiment. The powder-like quartz sand was prepared into round cakes using the boron acid embedding and pressing method in advance, facilitating better excitation of LIBS spectra. The quartz sand sample was analyzed using our university's Analysis and Testing Center's X-ray Fluorescence Spectrometer (XRF, Rigaku, ZSX-100e model, Japan), and the content of various major elements obtained is shown in Table 1.

Table 1. XRF test results of quartz sand samples^a

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4. Experimental results and analysis

Considering the uncertainty of laser-induced plasma itself, the performance fluctuations of experimental instruments, and the influence of the experimental environment, LIBS spectra often exhibit significant fluctuations. To address this, the method of averaging multiple measurements is employed to determine the LIBS spectra. In our experiment, two samples from the same batch were selected. Six positions were chosen on sample one, and seven positions were selected on sample two. Each of these positions was measured nine times. At each position, we first calculated the average of the nine measurements, resulting in LIBS spectra curves at 13 positions on the test samples, as shown in Fig. 2(a). Then, we calculated the average data from all positions, obtaining the final LIBS spectra curve, as shown in Fig. 2(b).

 

Fig. 2. (a) The laser-induced breakdown spectra were measured at different locations on the sample. (b) Average data curve of laser-induced breakdown spectrum.

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To effectively eliminate or reduce the inherent and random errors in LIBS (laser-induced breakdown spectroscopy) spectral data, preprocessing of the LIBS spectral data is performed before qualitative and quantitative analysis. Firstly, the background spectrum is removed ($I = {I_{raw}} - {I_{background}}$), and a 5-point 3rd-order Savitzky-Golay smoothing method is applied. Subsequently, the spectrum is normalized to eliminate the dimensional influence (${I_{normalization}} = {{({I - {I_{\min }}} )} / {({{I_{\max }} - {I_{\min }}} )}}$), ensuring comparability between different data indices. Then, the adaptive iteratively reweighted penalized least squares method (airPLS) [21] is employed for baseline correction to minimize the impact of the baseline on subsequent quantitative analysis. For the parameters of airPLS, the integer indicating the order of the difference of penalties takes the value 2, the number of iterations is set to 20, the asymmetry parameter for the start and end is assigned the value 0.05, and the weight exception proportion at both the start and end is also assigned the value 0.05. The preprocessed data is illustrated in Fig. 3. Finally, an automatic peak-finding algorithm is utilized to identify various peaks in the spectral data. By comparing these peaks with the NIST Atomic Spectra Database [18], the types of elements contained in the quartz sand samples are determined.

 

Fig. 3. Spectrum after data preprocessing.

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Based on the comparison results, we have labeled the main characteristic spectral lines of some elements in the spectral chart (Fig. 3), such as Si (I) 251.6112 nm, Ca (I) 422.6727 nm, Na (I) 588.995 nm, and so on. Of course, spectral lines caused by molecular vibrations or rotations can also be observed in the spectrum (not labeled in Fig. 3), and these lines also contain information about the elemental content. The results indicate that the elements detected in the quartz sand samples using LIBS include oxygen (O), sodium (Na), aluminum (Al), silicon (Si), potassium (K), calcium (Ca), titanium (Ti), chromium (Cr), iron (Fe), cobalt (Co), nickel (Ni), zirconium (Zr), barium (Ba), tungsten (W), and so on. This is in good agreement with the results obtained from XRF detection, demonstrating the excellent qualitative analysis capability of LIBS. It should be noted that sulfur (S) and zinc (Zn) were not detected by LIBS, although they were shown in XRF results. Currently, measuring sulfur (S) faces significant challenges because the characteristic spectral lines of sulfur (S) elements in the visible light region, which we mainly observe, are generally weak. Hence, sulfur (S) elements were not detected. As for the absence of zinc (Zn) elements, the main reason might be the very low content of zinc (Zn) elements in the quartz sand samples used in the experiment, exceeding its detection limit.

To obtain the plasma temperature using LIBS, we selected characteristic spectral lines of certain elements (including Ba, Ca, Co, Fe, Si, Ti, W, O, etc.) for calculations. Based on Eqs. (2) and (3), and by consulting the NIST Atomic Spectra Database, we obtained the parameters corresponding to the upper energy levels ${E_i}$, degeneracy ${g_i}$, and transition probability ${A_{ij}}$ for the elemental characteristic spectral lines. With the obtained parameter data, using upper energy levels ${E_i}$ as the x-axis and $\ln \left( {\frac{{I_\lambda^{ij}}}{{{g_i}{A_{ij}}}}} \right)$ as the y-axis, we plotted the (${E_i}$, $\ln \left( {\frac{{I_\lambda^{ij}}}{{{g_i}{A_{ij}}}}} \right)$) relationship curve, i.e., the two-dimensional Boltzmann plane, as shown in Fig. 4. Based on the Boltzmann plane, the slope m of the Boltzmann straight line corresponding to each element can be determined. Then, by using the equation $T ={-} \frac{1}{{{k_B}m}}$ (${k_B}\textrm{ = 8}\textrm{.61733} \times {10^{ - 5}}\textrm{eV/K}$), the plasma temperature can be calculated. The calculated results are presented in Table 2. In this study, we took the average value as the final plasma temperature, T = 11677.51 K.

 

Fig. 4. Boltzmann plots of some elements in quartz sand sample.

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Table 2. Calculation results for plasma temperature

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After obtaining the plasma temperature, elemental content can be calculated based on it. Before calculating the elemental content using the plasma temperature, it is essential to confirm whether the plasma is in a local thermodynamic equilibrium (LTE) state. We randomly selected the Si (II) 637.1359 nm line as the basis for calculation and performed Lorentzian fitting on the line to obtain relevant parameters. The Si (II) 637.1359 nm line in the quartz sand sample, along with its Lorentzian fitting curve, is shown in Fig. 5.

 

Fig. 5. Lorentzian fit of spectral line intensity data of Si (II) 637.1359 nm for quartz sand samples.

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By consulting the NIST Atomic Spectra Database, the upper-level energy ${E_i}$ for Si (II) 637.1359 nm line is 10.066443 eV, and the lower-level energy ${E_j}$ is 8.121023 eV, resulting in an energy difference $\Delta {E_e}$ of 1.94542 eV. For the Si (II) 637.1359 nm line, assuming a plasma excitation temperature ${T_e} \approx T \approx 11677.51K$, the minimum electron density was calculated as ${n_{limit}} \approx 1.273 \times {10^{15}}c{m^{ - 3}}$ using the right side of Eq. (4). Referring to the literature [20], the electron collision width parameter was obtained as $\omega = {4.92^{ - 2}}$, the half-width at half-maximum (HWHM) of the Si (II) 637.1359 nm line obtained from the fitting curve is $\Delta {\lambda _{{1 / 2}}} \approx 0.27931nm$. Thus, according to Eq. (6), the electron density was calculated as ${n_e} \approx 3.38 \times {10^{16}}c{m^{ - 3}}$. Clearly, ${n_e} > {n_{limit}}$, confirming that the plasma is in an LTE state.

After confirming that the plasma was in a local thermodynamic equilibrium (LTE) state, we calculated the content of some elements. Based on the previously calculated plasma temperature, we computed the partition function according to Eq. (7). Considering the complexity of level transitions, direct calculations were challenging. In this study, the partition function was obtained from the NIST Atomic Spectra Database [18]. The intercept ${q_s}$ of the Boltzmann line was obtained from the Boltzmann plot shown in Fig. 4. Finally, utilizing Eqs. (9) and (10), we calculated the experimental parameter F and the content of some elements. The relevant data and results are presented in Table 3.

Table 3. Calculation results for some element concentration

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The results indicate that the free calibration method can be used for qualitative or semi-quantitative studies of quartz sand samples but exhibits significant errors in quantitative analysis. For major elements in quartz sand samples such as Si and O, the relative errors measured using CF-LIBS were within 15% (compared to XRF methods). However, for trace elements, the relative errors were considerably large, leading to serious inaccuracies. According to the classical CF-LIBS principle, assuming the sum of concentrations of all elements in the sample is 1, the experimental parameter F needs to be determined by ensuring the sum of concentrations of all elements in quartz sand samples equals 1. Therefore, the Boltzmann lines for each element in quartz sand samples need to be linearly fitted, obtaining the slope and intercept of the lines. However, due to the overlap of strong emission lines from different particles or the small energy gap between the transition levels corresponding to the selected emission lines (i.e., insufficient range along the x-axis), sometimes, it is challenging to find enough spectral lines from the same ionization state of an element. Consequently, accurate plasma temperature calculation becomes difficult. In this study, when calculating the experimental parameter F, only the categories of element spectral lines shown in Table 3 were used, and other elements had to be ignored, resulting in a less accurate measurement of the experimental parameter F. This ultimately affected the calculation results of the element content.

Furthermore, the CF-LIBS method requires the analysis of characteristic spectral information from all elements in the sample, using normalization for the direct derivation of the concentration percentages of each element. If there is any measurement error in the characteristic spectral lines of any element during the measurement process, it directly affects the calculation of the content of all other elements. Additionally, extensive research has shown that the intensity of elemental characteristic spectral lines is easily affected by various external factors and self-absorption effects. These factors also contribute significantly to measurement errors. In this study, these factors were not considered when using the traditional CF-LIBS method, which further impacted the measurement accuracy.

5. Conclusion

The calibration-free laser-induced breakdown spectroscopy (CF-LIBS) method directly performs compositional analysis based on the full spectrum information of the sample, avoiding the influence of matrix effects. In this study, we attempted to analyze and measure elemental compositions of incoming quartz sand raw materials using the traditional CF-LIBS method. The composition of quartz sand raw materials is highly complex containing metal oxides as impurities, making it challenging to establish standard sample data for reference. The use of the CF-LIBS method eliminates the need for standard samples for calibration.

The results showed that the CF-LIBS method enables simultaneous and rapid identification of multiple elements in samples without standard reference materials. For quantitative analysis of samples with complex elemental compositions, the CF-LIBS method falls short of ideal quantitative results with large measurement errors: almost 15% for main elements and even bigger for trace elements. This indicates that the CF-LIBS method can achieve qualitative or semi-quantitative analysis for samples with complex matrices, but complete quantitative analysis remains challenging. Nevertheless, utilizing the CF-LIBS for measuring complex quartz sand raw materials before entering the glass manufacturing workshop remains valuable. It provides guidance for formulating corresponding treatment plans based on qualitative and semi-quantitative measurement results in glass manufacturing.

Furthermore, in future studies, by mitigating the impact of adverse factors and improving the quantitative analysis performance of the CF-LIBS method, it can be used for rapid multielement analysis of complex samples and achieve real-time online detection of each component.