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Abstract
A novel self-absorption-free laser-induced breakdown spectroscopy (SAF-LIBS) technique is proposed to directly capture the optically thin spectral line by matching the measured doublet atomic lines intensity ratios with the theoretical one. To realize the experimental SAF-LIBS, the integration time, the fiber collection angle, and the delay time are optimized. The optically thin conditions are validated by comparing the linearity of Boltzmann plots with the traditional self-absorption (SA) correction method and evaluating the SA coefficients. The applicability and limitation of SAF-LIBS on element concentration and laser energy are also discussed. Univariate quantitative analysis results show that, compared with ordinary LIBS, the average absolute error of aluminum concentration has been reduced by an order of magnitude, which proves that this SAF-LIBS technique is qualified to realize accurate chemical composition measurements.
© 2017 Optical Society of America
1. Introduction
Laser-induced breakdown spectroscopy (LIBS) is a useful technique for elemental analysis, which is capable of providing remote, in situ, rapid measurement, and can be used in multi-elemental analysis of bulk and trace analytes in any phase (solid, liquid or gas), with no or minimal sample preparation. It has a variety of applications such as metal quantitative analysis, material processing, biomedical research, environmental monitoring, etc [1–9]. It refers to the analysis of radiation emitted from the laser-induced plasma (LIP) when the irradiance of the laser focused on the material exceeds the threshold for plasma ignition. The spectral analysis of the plasma plume produces the elemental compositions and relative abundance information. But in quantitative LIBS analysis, it is essential to account for the effect of self-absorption (SA) on the emission lines, which affects the spectral line shape, i.e., the line intensity decreases and its full width at half maximum (FWHM) increases [10–12]. With optically thin emission lines, it is capable of directly characterizing the plasma by using Boltzmann plot or Stark line broadening method and performing accurate quantitative analysis. So it is vital to obtain optically thin plasmas for specific elemental emission lines, in which case the SA effect in spectral emission could be neglected.
In recent years, various methods for SA effect elimination have been the subject of a number of papers. N. Omenetto et al. studied the SA phenomenon in inductively coupled plasma and discussed the main equations describing the SA process in a flame [13], the results were interpreted by means of curve of growth method [14]. D. Bulajic et al. developed a SA effect model to extend the calibration free LIBS to optically thick plasmas, and improved the accuracy of major elements by one order [15]. L. Sun et al. chose an internal reference line that the SA effect could be ignored to correct the aluminum line and obtain more regular Boltzmann plot [16]. A.M. El Sherbini et al. proposed a method for evaluating the SA coefficients of aluminum emission lines, which could be used for improving the precision in plasma temperature determination [17]. S.A.M. Mansour used the isolated optically thin hydrogen Hα-line to correct the optically thick spectral lines, and the corrected temperature varied from 1.28 to 0.89 eV instead of 1.40 to 1.25 eV as the delay time varied from 0 to 5 μs [18]. H.Y. Moon et al. characterized the degree of SA of atomic transitions by placing a spherical mirror behind the plasma and employed a SA correction factor to retrieve the optically thin line profile [19]. J.M. Li et al. proposed the laser-stimulated absorption assisted LIBS to make the ground-state atoms transit up to a highly excited state, the serious SA phenomena disappeared and the FWHM of K, Mn, and Al were reduced by 58%, 25%, and 52%, respectively [20]. All the above mentioned methods either rely on some modeling of the plasma parameters (including plasma size, temperature, electron density, etc.) to minimize the SA effect on some emission lines, or employ a complex device to eliminate the SA effect on a particular line. However, the complexity of the laser-target interaction mechanism and the fastness of the plasma evolution reduce the applicability of most of these models, in real situations, to quantitative analytical LIBS measurements [17]. In addition to the above methods, another straightforward technique for evaluating the SA effect is the method of checking doublet lines intensity ratio [21], which has already been used for plasma diagnostics and quantitative purposes [22].
In order to avoid introducing any extra modeling errors or experimental setups, a novel self-absorption-free LIBS (SAF-LIBS) technique that can directly obtain the optically thin spectral line by checking the doublet lines intensity ratio was proposed. The experimental parameters that corresponded to SAF-LIBS were optimized, and the optically thin condition of the induced plasma was validated. Meanwhile, the applicability and limitation of the technique were investigated. Quantitative analysis of aluminum in several homemade standard samples by SAF-LIBS was performed to evaluate the improvement in composition measurement accuracy.
2. Experimental and methodology
2.1 Experimental set-up and sample preparation
A Q-Switched Nd: YAG laser (Spectra Physics, INDI-HG-20S) operating at 532 nm was employed as the ablation source, with a pulse duration of 7 ns, a repetition rate of 20-Hz, and a fixed energy of 50 mJ/pulse. The laser was divided into two beams by a half-wave plate and a polarizing beam splitter. The energy of the reflected laser beam was monitored by an absolutely calibrated energy-meter (Newport, 2936-R). The transmitted laser beam was focused at the sample surface by a 200 mm focal length quartz lens to produce a focal spot diameter of about 700 μm. The emission from the plasma plume was recorded by a grating spectrograph (Princeton Instruments, SP-2750) that equipped with a time gated ICCD detector (Princeton Instruments, PI-MAX4-1024i) by means of an all-silica optical fiber. The fiber head that pointed to the center of the plasma was fixed to a 100 mm diameter circular arc sliding guide in order to collect the fluorescence of different radial parts of the plasma plume. Nine pressed tablet samples of finely powdered potassium bromide and aluminum oxide with aluminum concentration in the range of 5-19 wt% were prepared for experimental investigation.
2.2 SAF-LIBS method
Under local thermodynamic equilibrium (LTE) situation, the theoretical doublet intensity ratio of a specific element in the same ionization stage Z in an optically thin LIP spectrum can be expressed as [23]:
where I1 is the line intensity from the k-i transition and I2 is that from the n-m transition, λ is the transition wavelength, A is the transition probability, g is the degeneracy, E is the energy, kB is the Boltzmann constant, and T is the plasma temperature. If we consider the doublet lines having the same upper level or as close as possible, the temperature effect of the Boltzmann factor on the reproducibility of the line intensity ratio is minimized. Neglecting the exponential factor in that condition, the theoretical doublet intensity ratio can be calculated by using the atomic inherent parameters of the transitions, which is independent of the experimental parameters. Here, considering the inaccuracy level of A provided by the NIST atomic spectra database [24], it is suggested to choose appropriate doublet lines with low uncertainties for transition strength. Due to the doublet lines have the similar energy level structures and the close wavelengths, there exists a time interval that the doublet lines are mostly close to the optically thin condition. By matching this ratio with the measured values at different delay times, one can find out the time interval (at a delay time of tot with a certain integration time) where the plasma conditions are as close as possible to optical thinness for the lines investigated. Theoretically, once the delay time and the integration time are set to this time interval, the LIBS is converted into SAF-LIBS.3. Results and discussion
3.1 Realization of SAF-LIBS
The typical average spectrum of the tablet sample is shown in Fig. 1 (delay time of 600 ns, integration time of 400 ns, collection angle of 45°, 13 wt% aluminum pressed tablet), which covers a spectral region from 300 to 670 nm. The resonance neutral Al lines at 308.21 nm, 309.27 nm, 394.40 nm and 396.15 nm were selected for determining the plasma temperature T. The isolated optically thin hydrogen Hα line at 656.27 nm appeared in the spectrum was used to determine the plasma electron density ne and to correct the Al (I) lines which contained some optical thickness. The detailed spectroscopic parameters of the four Al (I) lines and Hα line are listed in Table 1. Combined them with Eq. (1), we studied temporal evolution of the intensity ratio of Al (I) doublet lines, 396.15 nm and 394.40 nm, with a theoretical ratio value of 1.97, in order to ignore the temperature effect of the Boltzmann factor. In our experiment, the time gate width was varied from 200 to 1000 ns and the fiber collection angle was varied from 10 to 80°. At each constant gate width and collection angle, the delay time after the laser pulse was varied from 300 to 2100 ns. The results of the temporal evolution of the intensity ratio under these corresponding conditions are shown in Fig. 2 and Fig. 3. In order to obtain enough reproducibility of the emission spectra from the LIP and compensate for sample inhomogeneity, 60 plasma spectra with background subtracted were averaged under identical experimental conditions.
Table 1. Spectroscopic parameters of the selected spectral lines.
Fig. 2 Temporal evolution of the intensity ratio of doublet Al (I) lines (a) and the tot values and spectral SNRs at different integration times (b).
Fig. 3 Temporal evolution of the intensity ratio of two Al (I) lines (a) and the tot values and spectral SNRs at different fiber collection angles (b).
Figure 2(a) gives the temporal evolution of Al (I) doublet lines intensity ratio as well as the theoretical value by using the 13 wt% pressed tablet with the integration time in the range of 200 to 1000 ns, while Fig. 2(b) shows the relationship between tot, the signal-to-noise ratio (SNR), and the integration time. In Fig. 2(a), the time on the x axis is delay time and time in the legend is integration time. It can be inferred that the tot was of 300-500 ns, and the optimal integration time was 400 ns. The behavior that the tot decreased with the increase of the integration time can be explained as follows: the evident declining trend of the temporal evolution of the doublet lines intensity ratio indicated that the line intensity of Al (I) 396.15 nm decreased faster than that of Al (I) 394.40 nm. At a fixed delay time, as the integration time increased, the line intensity of Al (I) 396.15 nm increased slower than that of Al (I) 394.40 nm, thus leading to a decrease in the spectral intensity ratio. Considering the rapid expansion features and changes in plasma temperature and density with time, it was preferable to have time resolved study with minimal integration time. However, small integration time would decrease the spectral SNR distinctly, it was essential to optimize the integration time. With the increase of the integration time, the SNR increased firstly and then decreased and reached its maximum at 400 ns.
Figure 3(a) shows the temporal evolution of Al (I) doublet lines intensity ratio with the integration time of 400 ns by using the 13 wt% pressed tablet at different fiber collection angles to the laser beam direction in the range of 10 to 80°, while Fig. 3(b) shows the relationship between tot, the SNR, and the collection angles. In Fig. 3(a), the inset shows the magnified section within 340-460 ns. In Fig. 3(b), the tot increased firstly and then decreased with the increase of the fiber collection angles. We considered that the SA effect was related to the characteristic parameters of plasma such as temperature, electron density, elemental composition, number density of neutral and singly ionized species, integrated plasma length, etc [25]. Therefore, for a given radial part of plasma, due to its unique characteristics, the integral spectra at different angles led to the differences in tot values. With the increase of the fiber collection angle, the SNR increased firstly and then decreased and reached its maximum at 45°.
Figure 4(a) shows the temporal evolution of Al (I) doublet lines intensity ratio at different aluminum concentrations in the range of 5-19 wt% and indicates that, except for the 19 wt% sample, the statistic tot value for the others was of 500 ± 70 ns. From Fig. 4(b), it is shown that the tot decreased with the increase of the aluminum concentration. Further discussion of this point is given in section 3.4.
Fig. 4 Temporal evolution of the intensity ratio of two Al (I) lines (a) and the tot values at different aluminum concentrations (b).
Thus, once the integration time, the fiber collection angle, and the delay time were set as 400 ns, 45°, and 500 ns, respectively, the experimental SAF-LIBS was realized. Note that these optimal parameters identified were specific to the present experimental setup and to the set of samples investigated.
In addition, we also calculated the limit for the electron density for a plasma exhibiting LTE by using the McWhirter criterion [26]. The measured ne was in the order of 1017 cm−3, which was greater than the calculated limit of 9.4 × 1015 cm−3 under the maximum T of 8274 K. Therefore, the condition for LTE was fulfilled for the laser-induced plasma in our experiment.
3.2 Validation of optically thin condition in SAF-LIBS
In order to validate the optically thin condition in SAF-LIBS, the SA coefficient was evaluated and the linearity of Boltzmann plot was compared with the traditional SA correction method.
SA coefficient is defined as the ratio of the actual intensity of the emission line at its maximum over the value obtained by extrapolating the curve of growth valid in the optically thin regime to the same emitters number density of the actual measurement [12, 15].The larger the SA coefficient is, the closer to the optically thin condition the line is, and SA is always ≤1. When the plasma electron density ne is known and in particular to lines whose Stark broadening parameter is available, the SA coefficient can be expressed as [17]:
with α = −0.54, where Δλ is the intrinsic FWHM of the Lorentzian components of the spectral line, wS is the half-width Stark parameter, ne is the electron density by measuring the Stark broadening of non-self-absorbed atomic or ionic emission lines. We can use the Hα line to get the ne for the analysis of spectra from metallic alloys, according to the relation:where ΔλH is the FWHM of the Hα line, α1/2 is the half-width of the reduced Stark profiles in Angstrom. Precise values of α1/2 for the Balmer series can be found in [27].The temporal evolution of SA coefficient for Al (I) 396.15 nm line calculated by Eq. (2) is shown in Fig. 5 (integration time of 400 ns, collection angle of 45°, the 13 wt% aluminum pressed tablet). The SA coefficient reached the maximum at 500 ns, namely at tot, the SA effect was minimized. After then, the declining trend indicated an increase of the optical depth of line with time. This is because, due to the expansion, the plasma became cooler while the population of the ground-state atoms became higher, there existed more absorption in the plasma.
For SA effect correction, the SA effect on the measured integral line intensity (Ī) can be numerically evaluated in terms of SA coefficient and of the non-self-absorbed integral intensity (Ī0) and then parameterized as [17]:
with β = 0.46.According to Eq. (2) and Eq. (4), the non-self-absorbed intensities of Al (I) lines at 308.21 nm, 309.27 nm, 394.40 nm, and 396.15 nm at 900 ns were obtained. Figure 6 gives a comparison of Boltzmann plots that before SA correction, after SA correction, and at tot by using the 13 wt% tablet. The points were very scattered before the SA correction and the linear correlation coefficient R2 was 0.95. However, in the cases of SA correction and the optically thin condition, the points tended to coincide with the corresponding straight fitting lines and show extremely good fits, with the same R2 of 0.99.
Fig. 6 Comparison of Boltzmann plots using Al (I) lines at 308.21 nm, 309.27 nm, 394.40 nm, and 396.15 nm before SA correction, after SA correction, and at tot.
3.3 Composition measurement using SAF-LIBS
To evaluate the composition measurement accuracy of SAF-LIBS, univariate quantitative analysis of aluminum in the homemade standard samples was performed. The 5 wt%, 6 wt%, 8 wt%, 10 wt% and 13 wt% tablets were selected as calibration samples and the other two tablets (marked as #1 and #2) with aluminum concentrations of 7 wt% and 9 wt% were selected for prediction. Figure 7(a) shows the calibration curves by using the Al (I) 396.15 nm line intensities at different delay times. As can be seen, at delay times of 300 ns, 900 ns, and 1300 ns, the curves displayed poor linearity, with the linear correlation coefficients R2 below 0.86. However, at delay time of tot = 500 ns, the calibration curve displayed satisfactory linearity (R2 = 0.98) in quite a wide range of weight percentages. Here, the different fitting ranges of intensity create an optical illusion that the linearity at 900 ns seems to be even better than that at 300 ns. The purple graphic symbols in the figure represent the prediction samples. Figure 7(b) shows a comparison of the SAF-LIBS and the ordinary LIBS (at other three different delay times) quantitative analysis results on aluminum concentrations. Each of the prediction samples was analyzed for six times. For SAF-LIBS, the absolute measurement errors were estimated to be 0.06% and 0.20%, respectively, with an average of 0.13%. For ordinary LIBS, however, the absolute errors were in the range of 0.32-2.52%, with an average of 1.20%. Evidently, the SAF-LIBS technique led to a more accurate determination of the elemental composition. In addition, the quantitative results also showed that the relative standard deviations (RSD) with shorter delay times seemed to be superior to those with longer delay times, and the RSDs were quite comparable at 300 ns and 500 ns, indicating that this technique did not improve the measurement repeatability.
Fig. 7 Calibration curves of aluminum (a) and comparison of the SAF-LIBS and the ordinary LIBS quantitative analysis results on aluminum concentrations (b).
3.4 Applicability and limitation of SAF-LIBS
In order to obtain the boundary conditions of the SAF-LIBS technique, the applicability and limitation on concentration and laser energy were investigated.
The relationship between tot and element concentration is shown in Fig. 4(b), where the red curve represents the exponential fitting line (R2 = 0.944). The tot decreased with the increase of the aluminum concentration. At the point tot = 0, the corresponding aluminum concentration was 20.8%, namely it was the optically thin threshold of concentration. If the aluminum concentration exceeded this value, it was impossible to generate optically thin spectral lines. Thus, the concentration limitation of SAF-LIBS was identified to be in the range of 0-20.8%. Moreover, due to the poor SNRs of plasma spectra that recorded at delay time less than 300 ns, the concentration of 15.9% at tot = 300 ns was defined as the SNR threshold. As a result, the applicable aluminum concentration that SAF-LIBS suited for performing accurate composition measurement was in the range of 0-15.9%. The dynamic range of applicable concentration can be further extended by using non-resonance doublet lines, because they are much less subject to self-absorption. Unfortunately, no other suitable non-resonance analytical line was found for aluminum in the observed spectral region.
The plot tot versus laser energy shown in Fig. 8 was also fitted by an exponential function, with a correlation coefficient R2 of 0.997. The tot values for laser energies of 30 mJ, 40 mJ, 50 mJ, 60 mJ, 70 mJ, 80 mJ, 90 mJ, and 100 mJ (the maximum output energy of our pulsed laser) were measured, with fixed fiber collection angle of 45° and integration time of 400 ns. It was observed that the tot increased with the increase of laser energy. The laser energies that correspond to the plasma ignition threshold, the optically thin threshold, and the SNR threshold were certified to be 3 mJ, 16.9 mJ, and 33.1 mJ, respectively. Thus, the laser energy limitation of SAF-LIBS was larger than 16.9 mJ, and the applicable laser energy that this technique suited for performing accurate composition measurement was larger than 33.1 mJ.
In Fig. 8, the tot fluctuations that calculated by considering the ± 2% laser energy fluctuation were also presented. With the increase of laser energy, the tot seemed to be more stable and had a maximum approximate value of 537.1 ns. For example, the tot fluctuations at 30 mJ and 100 mJ were estimated to be ± 8 ns and ± 1 ns, respectively. Generally, minor tot fluctuation at a fixed delay time implies that the negative effect caused by the laser energy fluctuation is relatively small and the induced plasmas have much possibility to become optically thin. Therefore, the laser energy was suggested to be appropriately larger to yield relatively stable optically thin plasmas.
4. Conclusions
In this work, we proposed a SAF-LIBS technique that can directly capture the optically thin spectral line by matching the measured doublet atomic lines intensity ratios with the theoretical one to infer the optimal time interval where the plasma conditions are as close as possible to optical thinness for the lines investigated. The technique is only appropriate for elements with doublet structures. By setting the integration time, the fiber collection angle, and the delay time as 400 ns, 45°, and 500 ns, respectively, the experimental SAF-LIBS was realized. Compared with the traditional SA correction method, the Boltzmann plot of SAF-LIBS displayed satisfactory linearity, with a relative high correlation coefficient R2 of 0.99, and the SA effect was validated to be minimal. Univariate quantitative analysis results showed that, compared with ordinary LIBS, the linearity of the calibration curve was improved from 0.86 to 0.98 and the average absolute error of composition measurement was reduced from 1.2% to 0.13%. For SAF-LIBS, the limitations of concentration and laser energy were certified to be 0-20.8% and larger than 16.9 mJ, while the applicable concentration range and laser energy were 0-15.9% and larger than 33.1 mJ. Moreover, large laser energy was suggested to yield relatively stable optically thin plasmas. This SAF-LIBS technique can provide accurate chemical composition measurements, and is expected to promote the practical processes of LIBS in industrial application.
Funding
National Key R&D Program of China (2017YFA0304203); Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (IRT13076); National Natural Science Foundation of China (NSFC) (61475093, 61378047, 61775125); Major Special Science and Technology Projects in Shanxi Province (MD2016-01).
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