Standard Reference Line Combined with One-Point Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) to Quantitatively Analyze Stainless and Heat Resistant Steel

Abstract

Due to the influence of self-absorption of major elements, scarce observable spectral lines of trace elements, and relative efficiency correction of experimental system, accurate quantitative analysis with calibration-free laser-induced breakdown spectroscopy (CF-LIBS) is in fact not easy. In order to overcome these difficulties, standard reference line (SRL) combined with one-point calibration (OPC) is used to analyze six elements in three stainless-steel and five heat-resistant steel samples. The Stark broadening and Saha-Boltzmann plot of Fe are used to calculate the electron density and the plasma temperature, respectively. In the present work, we tested the original SRL method, the SRL with the OPC method, and intercept with the OPC method. The final calculation results show that the latter two methods can effectively improve the overall accuracy of quantitative analysis and the detection limits of trace elements.

Keywords

Calibration-free laser-induced breakdown spectroscopy CF-LIBS Saha–Boltzmann plot Stark broadening standard reference line one-point calibration OPC

Introduction

Laser-induced breakdown spectroscopy (LIBS) employs a pulsed laser and a focusing lens to generate a plasma. By analyzing the plasma emission spectra, the samples can be qualitatively and quantitatively analyzed. The usual technique for quantitative measurements of plasma composition is the univariate or multivariate regression model. However, they require calibration samples and standards investigated with identical matrices and identical experimental parameters (e.g., laser energy, spot diameter) to establish a calibration curve. Laser-induced breakdown spectroscopy calibration curves are also strongly dependent on the physical and chemical properties of the analytical materials, known as the matrix effect. Calibration-free LIBS (CF-LIBS) takes the matrix into account as part of the analytical problem which analyzes the matrix together with the analyte instead of looking at the matrix as an external disturbing interference.¹ Due to the unique advantages, it has inspired many researchers’ enthusiasm since it was first proposed by Ciucci et al.² in 1999. Up to now, CF-LIBS has been widely used for various samples and different research fields, e.g., all kinds of alloys^2–5 and their oxides,^6–9 aqueous solution,¹⁰ and soils and rocks.^11–14 In practice, CF-LIBS quantitative analysis still faces many difficulties. This is mainly because laser-induced plasma does not fully meet the basic assumptions of CF-LIBS requirements.¹

Several research groups have devoted their efforts to modify or improve the CF-LIBS algorithm from the experimental or theoretical aspects. Tognoni et al.³ used the Saha–Boltzmann plot to replace the Boltzmann plot to calculate the plasma temperature when the plasma is assumed as an ideal homogeneous source. Since more spectral lines are used for calculations, the temperature obtained by the Saha-Boltzmann plot is expected to be more accurate. Bulajic et al.⁵ proposed a self-absorption correction algorithm based on the curve of growth (COG) from which the quantitative results show a significant improvement with respect to those obtained without self-absorption correction. However, this method is complicated and time-consuming. Taking this into account, Sun et al.⁴ proposed a simplified procedure for correcting self-absorption effects in calibration-free analysis which they named internal reference for self-absorption correction (IRSAC). The IRSAC procedure greatly reduces analytical time, but the choice of an internal reference line is strongly dependent on the operator’s experience. The spectral lines of different species are affected differently by self-absorption, which leads to inconsistent plasma temperatures in the use of IRSAC. Based on IRSAC, Dong et al.¹⁵ proposed an internal reference-external standard with iteration correction (IRESIC) method to obtain a more accurate plasma temperature. This needs one standard sample to simulate the accurate plasma temperature of the unknown samples using a genetic algorithm (GA). In recent years, several hybrid approaches which need standard samples have been put forward. For example, Cavalcanti et al.¹⁶ presented one-point calibration (OPC) CF-LIBS, which improved the accuracy of quantitative analysis by modifying the relative efficiency correction factor and theoretical parameters.

In view of the significant potential of CF-LIBS in the field of in situ and online analytics, improving its accuracy is still an important task. It is hard to construct a reasonable Boltzmann plot for trace elements because their spectral lines are commonly scarce or hardly observable. In our previous work,¹⁷ a standard reference line (SRL) method was presented and applied to a stainless-steel sample. It does not seek to construct the Boltzmann plot of trace elements like classic CF-LIBS. Therefore, the detection limit of trace elements is improved. However, the selection of the SRL for the main element is still a difficulty. In the present work, we attempted to solve this problem and improve the accuracy of CF-LIBS by combining SRL with OPC.

Experimental

The experimental set-up is similar to the one used in previous work.¹⁷ The experimental procedure is briefly recalled here. A Q-switched neodymium-doped yttrium aluminum garnet (Nd:YAG) laser (Beamtech Dawa-100) is operated at the fundamental wavelength of 1064 nm. The laser pulse energy is fixed at 80 mJ, pulse width is 9 ns. The laser is reflected by a 45° mirror first and focused on the sample surface by an optical lens with a 100 mm focal length. In order to avoid a breakdown in air and increase the signal strength, the sample surface is positioned approximately 2 mm above the focal plane. The plasma emission spectrum is gathered by a lens, transmitted through a fiber (Ocean Optics 0.22 NA and 200 µm) and guided into an echelle spectrograph (Andor Mechelle ME 5000) providing an instant record of a wide wavelength range of 200–850 nm in one acquisition. Before the experiment, the correction of wavelength and relative efficiency is performed. For the actual measurement, which is carried out under atmospheric pressure, the experimental sample is placed upon an xyz-translation stage. In order to overcome the laser energy fluctuations, a signal-pulse analysis is utilized. Ten spectra were collected from each sample. In the process of our experiment, the gate pulse delay and the gate pulse width are fixed at 5 μs and 0.3 μs, respectively. Three stainless-steel (samples 1682∼1684) and five heat-resistant steel (samples 1685∼1689) standard samples (Shandong Metallurgical and Science Research Institute) are employed for analysis. The relative abundance of six elements in all samples are given in Table I.

Table I.

The relative abundance of six elements in eight steel samples.

Sample	Al	Cr	Fe	Mn	Ni	Si
1682	0.0516	9.2406	88.5111	0.8411	0.1404	1.2152
1683	0.0095	12.7629	83.4881	0.4377	2.5168	0.7850
1684	0.0725	20.5501	71.0304	0.4913	6.0809	1.7748
1685	0.0090	10.6813	83.8458	0.5090	0.2316	4.7233
1686	0.0772	16.1953	69.2070	0.3336	13.3066	0.8802
1687	0.1492	14.6148	69.2024	0.8314	13.5211	1.6812
1688	0.0086	18.2755	78.4095	0.3699	1.2447	1.6917
1689	0.1004	24.1577	57.0220	2.3861	15.2664	1.0674

Results and Discussion

Standard Reference Line

The SRL method has been reported in detail in the previous work¹⁷ and here we are simply reviewing the basic idea of the method. Since the Stark effect is the dominant mechanism of spectral line broadening compared with Doppler broadening or collisional broadening, it can be used to calculate the electron density.^18–21 The experimental samples are three stainless-steel and five heat-resistant steels in which the major element is iron (Fe). Due to the rich lines of Fe, it is selected for calculating the electron density and plasma temperature. In this work, w = 0.014 nm for Fe(I) 381.584nm²² is chosen for analysis. Under the assumption of local thermodynamic equilibrium (LTE), the Saha–Boltzmann plot²³ can give a more reliable plasma temperature relative to the Boltzmann plot. In order to determine the plasma temperature with minimal relative errors and partially overcome the effects of self-absorption, a pre-selection procedure presented by Aydin et al.²⁴ is employed. For the spectral lines of Fe(I) and Fe(II), > 400 lines are chosen to constitute a spectral database²⁵ for which the minimum accuracy of transition probability is B+ ( $\leq 7 %$ ) and minimum relative intensity is 10⁴. After finding, identifying, and fitting, the integral intensity of all Fe lines is brought into the pre-selection procedure. The iteration calculation will be performed until the goodness of fit is > 0.98 ( $R^{2} > 0.98$ ). The mean and standard deviations of plasma temperature (T) and electron density (N_e) are shown in Fig. 1. For eight steel samples, the plasma temperature and electron density are relatively stable.

Figure 1.

The mean and standard deviations (error bar) of plasma temperature (T) and electron density (N_e) for eight steel samples.

Based on LTE, the fitting area intensity I corresponding to the transition between lower level E_l and upper level E_u of an atomic species α can be expressed as:

I = {FN}_{α}^{I} A_{ul} \frac{g_{u}}{U_{α}^{I} (T)} exp (- \frac{E_{u}}{k_{B} T})

(1)

where F is the experimental parameter,

N_{α}^{I}

is the atomic number density, A_ul is the transition probability, g_u is the upper level degeneracy, and

U_{α}^{I} (T)

is the partition function at the temperature T. Once T is known, each atomic spectral line can be used to derive a corresponding concentration from Eq. 1. For each element, the strongest atomic spectral line is chosen as the SRL (Table II) to calculate the concentration. The atomic number density calculated with the reference line serves as the reference concentration. Meanwhile, the atomic number density calculated with the remaining lines of the element can then be compared with the reference concentration. If the relative error is > 30% for one line, then this line will be abandoned. The ion number density of different elements can be derived via the Saha equation. Finally, one can get the relative content of each element by the closed equation:

\sum_{α = 1}^{m} \sum_{z = 0}^{n} C_{α}^{z} = 1

(2)

Where

C_{α}^{z} = N_{α}^{z} / \sum_{α = 1}^{m} \sum_{z = 0}^{n} N_{α}^{z}

C_{α}^{z}

and

N_{α}^{z}

is the concentration and density of the emitting species, respectively. Subscript α represents different elements and superscript z represents different ionization states.

Table II.

The lines which are chosen as the SRL and their related parameters.

Species	$λ (nm)$	$A_{ul} (s^{- 1})$	$E_{l} ({cm}^{- 1})$	$E_{u} ({cm}^{- 1})$	g_l	g_u
Al	396.152	9.80E + 07	112.06	25347.76	4	2
Cr	357.8704	1.48E + 08	0	27935.24	7	9
Fe	404.581	8.62E + 07	11976.24	36686.18	9	9
Mn	279.482	3.70E + 08	0	35769.97	6	8
Ni	352.454	1.00E + 08	204.787	28569.2	7	5
Si	288.1579	2.17E + 08	6298.85	40991.88	5	3

Tognoniet et al.¹ introduced a measure of the overall accuracy of the CF-LIBS results. The C and V are the calculated concentration by CF-LIBS and the verified concentration, respectively. The distance (dist) between two vectors represents the sum of absolute errors and can be expressed as:

dist = \sum_{α = 1}^{m} abs | C_{α} - V_{α} |

(3)

The mean and standard deviations of dist from SRL for eight steel samples are shown in Fig. 2. It shows that the results obtained using the SRL method are very poor. On the one hand, Fe is the major element and Fe(I) 404.581 nm has a clear self-absorption which led to the underestimation of C_Fe. On the other hand, inaccuracy of relative efficiency corrections also plays a crucial role. Even if the intensity calibration has been performed using a Deuterium-Halogen calibration light source (Ocean Optics, DH-3plus-CAL), the accuracy of the relative efficiency correction coefficient is still not high. There may be two reasons. First, the true intensity of the standard light source is not consistent with the recorded intensity. Second, the fiber is directly docked to the light source without considering the transmission efficiency of air and a converging lens.

Figure 2.

The mean and standard deviations (error bar) of dist from SRL for eight steel samples.

Standard Reference Line with One-Point Calibration

In the previous work,¹⁷ we re-selected a SRL in order to overcome self-absorption of the main element line. Like IRSAC, the choice of this line is difficult. Further, if the main element concentration is different, then the SRL should also be different. To correct self-absorption and spectral efficiency coefficient, the OPC method presented by Cavalcanti et al.¹⁶ is employed. We define the correction factors obtained from the standard intensity light source and OPC as cf and $cf'$ , respectively. The integral intensity of the experimental measurements has been corrected by the standard intensity light source, i.e., $I = cf \times I_{0}$ , where I₀ is the true intensity of the plasma emission spectrum. $cf'$ for the SRL of each element used in Table II is defined as:

cf'_{α} \times I \propto cf'_{α} \times C_{α} = V_{α}

(4)

Sample 1682 is chosen as the calibration sample. The mean of

cf'

for ten measurements is shown in Table III. It can be seen that

cf'

increases with the increase of wavelength except Al(I) 396.152 nm. This is caused by the absorption of air; and the obstruction of converging lenses to short wavelength lines is stronger. Another possible reason is that the drifts of the deuterium lamp used for the relative efficiency correction of ultraviolet band is much worse than the tungsten halogen lamp, and it has not been recalibrated recently. Because V_Al is very low, the continuous spectrum inevitably increases its integrated intensity. Because of the self-absorption of Fe(I) 404.581 nm,

cf'_{Fe}

is relatively larger.

Table III.

The correction factor of SRL.

SRL	Al	Cr	Fe	Mn	Ni	Si
SRL	396.152	357.8704	404.581	279.482	352.454	288.1579
$cf'$	0.1143	0.8341	1.3742	0.0451	0.7795	0.0637

The mean and standard deviations of dist from SRL with OPC and V_Fe for eight steel samples are shown in Fig. 3. One can see that the accuracy has been significantly improved compared to the original SRL results and all the means of dist are < 10. The closer the sample to the calibration sample, the better the calculated result. Although this trend is not obvious, it still can be seen. This is due to $cf'_{Fe}$ being obtained from sample 1682. However, V_Fe of the remaining seven steel samples has a certain gap with sample 1682 (especially sample 1689) which makes C_Fe deviate from V_Fe. Since the concentration of Al is very low, only one line of Al(I) 396.15 nm can be detected from the experimental spectrum. The Boltzmann plot of Al cannot be constructed as in the classical CF-LBS.² However, the SRL method can calculate its relative content, even if its relative error is very large (Electronic Supplementary Material). For trace elements (e.g., Al) with very low concentration, the closed equation (Eq. 2) may be the main limitation.

Figure 3.

The mean and standard deviations (error bar) of dist from SRL with OPC and V_Fe for eight steel samples.

Standard Reference Line or Intercept with One-Point Calibration

When calculating temperatures, we assume that the plasma temperature obtained by the pre-selection procedure²⁴ is accurate. If this assumption is true, then C_Fe can also be obtained by the intercept of the Saha-Boltzmann plot. In fact, the good calculation of the temperature in Fig. 3 has shown that it is accurate.

cf'

of SRLs or intercept is recalculated and reported in Table IV. One can see that the

cf'

of the intercept is very close to 1. It indicates that the plasma temperature is accurate. Except for Fe, the mean and standard deviations of the ratios (Table IV is divided by Table III) are 1.5642 and 0.0917, respectively. Their relative values are analogous.

Table IV.

The correction factor of SRL or interceptor.

SRL or intercept	Al	Cr	Fe	Mn	Ni	Si
SRL or intercept	396.152	357.8704	Intercept	279.482	352.454	288.1579
$cf'$	0.1920	1.1973	0.9913	0.0629	1.2437	0.1093

The mean and standard deviations of dist from SRL or intercept with OPC for eight steel samples are shown in Fig. 4. One can see that all the means are < 9. By comparing Figs. 3 and 4, the mean of dist from samples 1682 and 1689 is less than the value obtained by SRL with OPC, but other samples showed opposite results. Overall, the accuracy of the two methods is not so different. Calculating C_Fe by intercept does not make the calculation results more accurate. The change of self-absorption coefficient of Fe(I) 404.581 nm is not significant relative to the change of V_Fe in all samples, as shown in Fig. 3. It also demonstrates that the plasma temperature, which is obtained by the pre-selection procedure, is accurate. To further improve the accuracy of CF-LIBS quantitative analysis, it is possible to carry out further work from two aspects of closed equation and stoichiometry ablation.

Figure 4.

The mean and standard deviations (error bar) of dist from SRL or intercept with OPC for eight steel samples.

Conclusion

The main factors that limit the accuracy of CF-LIBS include the rare lines of trace elements, self-absorption of major element lines, and relative efficiency correction of the experiment system. The spectrum of major elements is used to calculate the electron density and plasma temperature, taking advantage of its strong signal and rich spectral lines. For three stainless-steel and five heat-resistant steel samples, the plasma temperature and electron density are relatively stable. Because of self-absorption and relative efficiency corrections, the results obtained by the original SRL method are very poor. In order to overcome the effects, the OPC method is used in the present work. Meanwhile, in order to verify the accuracy of the plasma temperature obtained by the pre-selection procedure, the Fe concentration from the intercept of the Saha–Boltzmann plot is also calculated. The calculated results show that the plasma temperature calculated by the pre-selection procedure is accurate. The sum of absolute errors from the latter two methods with OPC shows a distinct decrease relative to the original SRL method, but the difference between them is not obvious. The two methods allow us to use trace elements’ single spectra to calculate the concentration, without the need to construct their Boltzmann plot.

Supplemental Material

Supplemental material for Standard Reference Line Combined with One-Point Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) to Quantitatively Analyze Stainless and Heat Resistant Steel

Supplemental material for Standard Reference Line Combined with One-Point Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) to Quantitatively Analyze Stainless and Heat Resistant Steel by Hongbo Fu, Huadong Wang, Junwei Jia, Zhibo Ni and Fengzhong Dong in Applied Spectroscopy

Footnotes

Conflict of Interest

The authors report there are no conflicts of interest.

Funding

This work has been supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant no. 61505223).

Supplemental Material

All supplemental material mentioned in the text is available in the online version of the journal.

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