1. Introduction

Laser-induced breakdown spectroscopy (LIBS) is an emerging analytical technique due to its unique advantages such as fast multi-elemental analysis, real-time and in situ detection, remote sensing capability, and direct analysis of any type of materials [1]. The method has been successfully used in industrial and agricultural production [2, 3], biological and medical testing [4, 5], environmental protection [6], geological and resource exploration [7], sea and space exploration [8, 9], artifacts and jewelry identification [10], etc. However, quantitative aspects have generally been considered a shortcoming of LIBS, which greatly limits its application and also weakens its positive features [1].

Several ways have been proposed to obtain quantitative information from LIBS measurements. The most commonly used quantitative analysis methods are universal calibration curves, which describing the relationship of line intensity against the known concentrations of elements in standard samples. To reduce the effect of uncontrolled random fluctuations of emission intensity, the normalization approaches, such as internal standard method, are commonly used for simplicity and effectiveness. Furthermore, to overcome matrix effect [11], self-absorption effect [12] and spectral interference in quantitation, the use of chemometric approaches to improving the accuracy and precision have proliferated in recent years [13, 14]. These above-discussed approaches require many reference samples with the same matrices as the analyte and are long time consuming. Therefore, it’s inconvenient in field analyses for unknown samples. Ciucci et al. have developed a calibration-free LIBS (CF-LIBS) for quantitative elemental analysis of a given sample [15], and the technology has been applied to solid materials, ambient air, and aqueous solution [16]. CF-LIBS is based on several simplifying assumptions of plasma conditions such as in local thermodynamic equilibrium (LTE), stoichiometric ablation, homogeneous, and optically thin. Actually, the above assumptions are beyond control in most LIBS practice, in which the plasma temperature would not be accurately determined. Thus, CF-LIBS can only provide a highly accurate quantitative estimation for major elements, but difficult for minor and trace ones.

In the past ten years, some variations of CF-LIBS method were proposed with the aim of improving the trueness of the analysis. Gaudiuso et al. proposed a calibration-free inverse method (CF-IM) [17], in which the plasma temperature is determined by using the known composition of one certified standard. Cavalcanti et al. presented a one-point calibration LIBS (OPC-LIBS) method, which is a variation of CF-LIBS with only one standard sample for empirical determination of essential experimental and spectroscopic parameter [18]. The technique could definitely improve the trueness of traditional CF-LIBS, but it requires wide-wavelength LIBS spectra and the efficiency of the spectral detection system can affect the analysis accuracy of all elements to be measured. Aragón et al. proposed a CSigma LIBS (Cσ-LIBS) method base on the calculation of a line cross section for each of the experimental data [19]. The Cσ-LIBS method has been proven to perform well on quantitative analysis of rocks and aluminum alloys [20, 21]. Although the accuracy of quantitative analysis can be improved greatly by above variations of CF-LIBS, their algorithms are complex and time consuming.

The objective of the present work is proposing a new one-point and multi-line calibration (OP-MLC) method, which is based on a single matrix-matched standard sample and multiple lines of the analyzed element. The technique does not require calculation of plasma temperature, electron number density, and other experimental parameters, and each elemental content can be independently estimated. After introducing the methodology of the OP-MLC, the reliability of this method was validated by analyzing several trace elements in low-alloy steel standard samples.

2. One-point and multi-line calibration method

Under the assuming of the plasma is optically thin and in local thermodynamic equilibrium (LTE) in the temporal window of signal acquisition, according the Boltzmann equation, the measured integral line intensity can be expressed as [22]:

According to Eq. (1), for two emission lines ${\lambda }_1$ and ${\lambda }_2$ from same plasma and same element, their intensity ratio can be described as follows:

In addition, for the two emission lines ${\lambda }_1$ and ${\lambda }_2$ emitted from same element but different samples, their intensity ratio can be described as follows:

3. Experimental

The experimental setup is schematically shown in Fig. 1. The plasma was generated by a second harmonics of a Nd: YAG laser (Quantel Brilliant B, maximum energy: 400 mJ per pulse, pulse width: 5 ns) operating at 532 nm, 60 mJ and 10 Hz. The laser beam was reflected by a mirror and focused by a plano-convex lens (f = 150 mm) with a focal point of 3 mm onto the target surface. The target was mounted onto a motorized 3D translation stage. The sample was moved to provide a fresh surface for each laser shot. The plasma emission was collected using a two-lens light collector, which coupled light into an echelle spectrometer (Andor Tech., Mechelle 5000, 200-950 nm, spectral resolution: λ/Δλ = 5000) through an optical fiber. The spectrograph equipped with an intensified charge coupled device (ICCD; Andor Technology, DH320T, 1024 × 1024 pixel) in this study. A digital delay generator (DG535, Stanford Research System, 5 ps delay resolution) was adopted to trigger the laser pulses and control gate delays of the ICCD. The time-integrated LIBS spectra from each sample were measured with a time delay of 4 μs after the laser pulse and a gate width of 20 μs, which are optimized in order to achieve low background intensity and sufficient signal intensities. To reduce the influence of laser energy fluctuation on spectral intensities, each spectrum was accumulated for 30 shots per spectrum. To weaken the effects of sample surface characteristics and height fluctuations, every measurement was repeated ten times at different locations on a sample, and the average data was used for quantitative analyses.

 

Fig. 1 Schematic diagram of the experimental setup.

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Seven standard low-alloy steel samples (serial number: GSB 03-2453-2008, NCS Testing Technology Co. Ltd, Beijing, China) were used in this study. Table 1 lists the certified concentrations of Mn, Cr, Ni, Ti and Fe elements in the samples, which were determined using at least two kinds of reference techniques, such as spectrophotometry and inductively coupled plasma atomic emission spectroscopy. As shown in Table 1, one sample for each element was selected as the calibration sample (marked with the superscript), in which the concentration of the detected element is moderate relative to other samples. Other six samples were used as test samples to validate the accuracy of OP-MLC method.

Table 1. Certified concentrations of the elements in low-alloy steel samples (wt.%)

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The spectral lines of the elements Mn, Cr, Ni, and Ti used for multi-line calibration are listed in Table 2. Since the OP-MLC-LIBS method is based on the assumption of optical thinness, the spectral lines used for the calibration do not select resonance lines that are prone to self-absorption. In addition, low-alloy steel sample contains many metallic and non-metallic elements that result in very large spectral lines in the LIBS spectrum. Spectral interference is difficult to avoid, so the spectral lines interfered by other lines from coexisting elements cannot be used in OP-MLC-LIBS method. Due to the difference in quantum efficiency of the spectrograph-detector combination for different wavelengths, spectral line intensities need to be corrected before calibration. To minimize the shot-to-shot variations of LIBS emission signals, the internal standardization method based on the intensity ratios of analyte and reference lines were adopted, in which the weak lines of the matrix element iron were used as reference lines. Because iron is the major element of the low-alloy steel samples (see Table 1), the intensities of iron lines approximately remain constant for all standard samples. For these reasons, spectral lines of the elements Mn, Cr, Ni, Ti and Fe used for multi-line calibration were selected as listed in Table 2.

Table 2. Spectral lines of the elements Mn, Cr, Ni, and Ti used for multi-line calibration (nm)

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4. Results and discussion

According to Eq. (4), the intensity ratio can be obtained by linear fitting the measured integral line intensities emitting from analyzed and calibration samples. Based on the lines listed in Table 2, Fig. 2 shows the relationship between the multi-line normalized intensities of the analyzed element in an ‘unknown’ sample and in a standard sample. The sample No. 3, 1, 5 and 2 were chosen as the standard sample for Mn, Cr, Ni and Ti, respectively. The linear fitting function of the standard sample is y = x. Other six samples were taken as ‘unknown’ test samples, in which the element concentrations were predicted based on the single standard sample. The normalized intensity ratios of the lines can be obtained from the slope of each linear fitting function in Fig. 2. Substituting these slope values and the elemental content of the standard sample (Table 1) into Eq. (4), the contents of the specified element in the ‘unknown’ samples can be predicted. It is worth mentioning that the intercept of the linear fitting function is generated from the continuous background of the spectrum, which can be ignored because only the slopes of the linear fitting function were used for analysis result calculation.

 

Fig. 2 Normalized intensity of the analyzed element in an unknown sample as a function of that in a standard sample: (a) Mn; (b) Cr; (c) Ni; and (d) Ti.

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The comparison of certified concentrations of Mn, Cr, Ni and Ti and predicted concentrations by OP-MLC-LIBS method, and relative errors of the predicted concentrations in OP-MLC-LIBS were given in Fig. 3. It was shown that, the concentrations calculated on the test samples basically close to the nominal concentrations, and their relative errors (REs) vary from 2% to 79% while their content change in the range from 0.030 to 2.000 wt.%. Relatively, the Mn element has the highest accuracy of quantitative analysis among these four elements. This is because the content of Mn is high, and its spectral line is not easily affected by spectral interference. The average relative errors (AREs) of six test samples are 9%. But the AREs are 22, 21 and 36% for Cr, Ni and Ti, respectively. As can be seen from Fig. 3(b) ~3(d), the AREs of the detected elements in a few test samples are unacceptable for those concentrations are lower than 0.1 wt.%., such as Cr in No. 7, Ni in No. 6, and Ti in No. 3 and 5. From Fig. 2, it can also be found that the values of R² correspond to above samples for the analyzed elements are lower than that of other samples. Therefore, a possible explanation for this might be that their spectral line intensities too weak due to their low element content, and could be easily affected by spectral interference and continuous background [23].

 

Fig. 3 Comparison of the certified concentrations (see Table 1) and predicted concentrations by OP-MLC-LIBS method: (a) Mn; (b) Cr; (c) Ni; and (d) Ti.

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To more clearly demonstrate the quantitative analysis capabilities of OP-MLC-LIBS, Fig. 4 shows the comparison of the predicted concentrations by OP-MLC-LIBS and the certified concentrations listed in Table 1. The concentrations calculated on the ‘unknown’ samples result are very close to the certified concentrations. However, as shown in Fig. 4, a small number of points are farther from the dotted line, which corresponds to the ideal correspondence between determined concentration and nominal concentration. That is because this technology is based on ideal LIBS spectra without self-absorption and no spectral interference. To overcome these drawbacks and improve the accuracy of analysis, it’s necessary to solve the problem of self-absorption of spectral lines when detecting high-content elements, and to solve spectral interference problems form coexisting elements. There have been a large number of studies and reports on correction methods for self-absorption [12, 24–26] and spectral interference [27–29], and combining these methods with OP-MLC may improve the accuracy and precision of the quantitative analysis.

 

Fig. 4 Comparison of predicted concentrations by OP-MLC-LIBS and certified concentrations for Mn, Cr, Ni, and Ti elements. The short dot line corresponds to the ideal correspondence between determined concentration and nominal concentration.

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5. Conclusions

A new LIBS quantitative analysis method based on a single standard sample and multi-line intensities of the detected element is presented. The reliability of quantitative analysis with OP-MLC-LIBS was verified by detecting the trace elements Mn, Cr, Ti and Ni in low-alloy steel. The AREs of Mn, Cr, Ni and Ti elements determination in six test samples are 9, 22, 21 and 36%, respectively. The results showed that OP-MLC-LIBS has the advantage of no requiring large number of standard samples and no complicated calculations. Although quantitative analysis of OP-MLC faces the challenge of self-absorption effect and spectral interference, this study still provides a new way for rapid quantitative analysis of unknown samples using LIBS. This simple and low cost approach may contribute to the development and application of LIBS in future.