One-point calibration for calibration-free laser-induced breakdown spectroscopy quantitative analysis
Introduction
The calibration-free laser-induced breakdown spectroscopy (CF-LIBS) technique has been widely applied, after its introduction in 1999 [1], for the quantitative analysis of metallic alloys [2], [3], [4], [5], [6], biological materials [7], [8], [9], coal and combustion products [10], [11], geological samples [12], [13], [14], extraterrestrial objects [15], [16], cultural heritage [17], [18], [19], [20], etc. The basic assumptions and the procedures of CF-LIBS have been discussed in several articles [21], [22], [23], [24] and review papers [25], [26], [27], [28]; however, despite of the number of successful applications, CF-LIBS analysis has not yet reached the diffusion that a standard-less LIBS technique could potentially obtain, especially in industrial applications.
CF-LIBS analysis is based on the fundamental hypothesis of having the laser-induced plasma in LTE conditions [29]. Moreover, the stoichiometric condition must be fulfilled (i.e., the plasma chemical composition must be the same of the sample) [30] and the plasma must be optically thin, although this last condition can be somewhat relaxed applying suitable corrections to the LIBS line intensities [31], [32]. Besides these “fundamental” constraints, there are a number of practical issues to be considered: for example, for the determination of the plasma electron temperature (an information which is usually obtained through the Boltzmann [33] or Saha–Boltzmann [34] plot method) one must know the spectral parameters of each emission line considered and the efficiency of the spectral detection system at the line wavelengths. These parameters contribute multiplicatively to the measured line intensity which, according to the Boltzmann equation, is:where Cs is the number density of the species considered, l is the central wavelength of the transition, Ek is energy of the upper level, gi is the degeneration of the lower level, Aki is the transition probability between the two levels, Us(T) is the partition function of the species considered, KB is the Boltzmann constant and T is the plasma electron temperature. It is well known that the transition probabilities Aki of some lines have uncertainties of the order of 50% or more [35]. Similarly, the precise determination of the efficiency of the spectral detection system F(l) is very difficult, especially in the near-UV/blue region of the spectrum, where most of the lines of interest for the analysis lay. There are many other effects that can introduce errors in Eq. (1), as for example the possibility of having two or more lines of the same species at very close wavelengths; with a spectral detection system at low resolution, these superimposed lines will be seen as a single line with an “effective” giAki product which is a linear combination of the same parameters for all the emission lines under study. As a result of the indetermination on the above mentioned parameters, the linear fitting of the points in the Boltzmann or Saha–Boltzmann plot would be affected by a large uncertainty and, correspondingly, the trueness of the results of the CF-LIBS approach would be compromised. Note that the indetermination on F(l) has the same effect on the measurement as the indetermination of the giAki product, so that Eq. (1) can be rewritten as:where P(λ) = F(λ)giAki.
In fact, the concentration of the species present in the sample is obtained by the best fitting of the points vs. Ek in the Boltzmann plot with the linear function:
In particular, the plasma temperature kBT = -1/b and the concentration of each species is proportional by a constant factor H (to be determined by the closure relation ∑ sCs = 100%) to the intercept of the best fitting curve at Ek = 0, i.e.
It is therefore crucial, for obtaining good results with the CF-LIBS method, to construct an accurate Boltzmann plot from where the electron temperature (the same for all the species, according to the LTE conditions) and the species' concentrations could be precisely determined.
The strict dependence of the trueness of the CF-LIBS results on the quality of the Boltzmann plot has pushed several researchers to propose variations of the method that would guarantee a more accurate determination of the plasma electron temperature and the intercept of the best fitting curve. As discussed in Ref. [25], Aguilera et al. [36] proposed the use of the Saha–Boltzmann plot instead of the usual Boltzmann plot, for obtaining a more accurate determination of the plasma temperature and the element concentration from the intercept. A different approach was recently developed by Gaudiuso et al. [37], which proposed a method based on the same principles of CF-LIBS, in which the plasma temperature would not be calculated from the Boltzmann or Saha–Boltzmann plot but instead evaluated as the one that minimizes the discrepancy between the certified composition of a single matrix-matched standard and the concentrations determined by CF-LIBS at that temperature. This optimum temperature would be then used for the CF-LIBS analysis of the other unknown samples.
Section snippets
One-point calibration method
The method that we propose is conceptually similar to the one proposed by Gaudiuso, in the sense that it implies the use of a single matrix-matched calibration standard for the determination of some experimental parameters that are not easy to know in other ways. However, contrarily to the Gaudiuso approach, ours preserves the calibration-free main capability of self-adapting to the variations of plasma parameters (electron temperature and number density) which are unavoidable when dealing with
Experimental setup
All the samples were analyzed using the Modì instrument by Marwan Technology [40] in the “Smart” configuration. The instrument delivers two collinear laser pulses at Nd:YAG fundamental wavelength (1064 nm) with an energy of 50 mJ per pulse with a FWHM of about 10 ns. The interpulse delay was set at 1 µs. The focusing lens had a focal length of 10 mm.
The spectral acquisition was performed using an AvaSpec Dual-Channel Fiber-optic Spectrometer by Avantes equipped with two gratings which allowed the
Experimental results
The test of the OPC-LIBS procedure was performed using five bronze samples whose elemental composition was measured by X-ray fluorescence as reported in Table 1.
The samples used were standards previously used for other LIBS tests. They are not certified, but the uncertainties of the XRF measurements are well within the expected trueness of the CF-LIBS analysis; therefore for the demonstration of the OPC-LIBS method, we considered their characterization by XRF sufficient. We tested the OPC-LIBS
Conclusion
The results on the application of the one-point calibration LIBS method show that the procedure, basically simple and as fast as the usual CF-LIBS approach, maintains all the advantages of the calibration-free method in terms of independence on the matrix effect while offering the possibility of compensating for the lack of precise information on crucial parameters which are essential for the application of the CF-LIBS analysis, and in particular the knowledge of the response curve of the
Acknowledgement
Lorenzo Pardini acknowledges the support of the European Commission, of the Italian Ministero del Lavoro, della Salute e delle Politiche Sociali and of Regione Toscana, through the POR FSE 2007–2013 “MONDI” grant. Gildo de Holanda Cavalcanti acknowledges the support of CAPES (Coordenadoria de Aperfeiçoamento de Pessoal do Ensino Superior) proc. 3877-11-6.
References (41)
- et al.
Calibration analysis of bronze samples by nanosecond laser induced breakdown spectroscopy: a theoretical and experimental approach
Spectrochim. Acta Part B
(2005) - et al.
Effect of target composition on the emission enhancement observed in Double-Pulse Laser-Induced Breakdown Spectroscopy
Spectrochim. Acta Part B
(2008) - et al.
Calibration free laser-induced breakdown spectroscopy of oxide materials
Spectrochim. Acta Part B
(2010) - et al.
Double pulse, calibration-free laser-induced breakdown spectroscopy: a new technique for in situ standard-less analysis of polluted soils
Appl. Geochem.
(2006) - et al.
Laser induced breakdown spectroscopy on meteorites
Spectrochim. Acta Part B
(2007) - et al.
Investigation of LIBS feasibility for in situ planetary exploration: an analysis on Martian rock analogues
Planet. Space Sci.
(2004) - et al.
Non-equilibrium and equilibrium problems in laser-induced plasmas
Spectrochim. Acta Part B
(2000) - et al.
A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma
Spectrochim. Acta Part B
(2007) A novel approach to elemental analysis by laser induced breakdown spectroscopy based on direct correlation between the electron impact excitation cross section and the optical emission intensity
Spectrochim. Acta Part B
(2011)- et al.
Methodologies for laboratory laser induced breakdown spectroscopy semi-quantitative and quantitative analysis-a review
Spectrochim. Acta Part B
(2008)
Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: beyond the McWhirter criterion
Spectrochim. Acta Part B
A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy
Spectrochim. Acta Part B
Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements
Spectrochim. Acta Part B
Quantitative micro-analysis by laser-induced breakdown spectroscopy: a review of the experimental approaches
Spectrochim. Acta Part B
Application of calibration-free laser-induced breakdown spectroscopy to radially resolved spectra from a copper-based alloy laser-induced plasma
Spectrochim. Acta Part B
Laser-induced plasma analysis of copper alloys based on local thermodynamic equilibrium: an alternative approach to plasma temperature determination and archeometric applications
Spectrochim. Acta Part B
Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements
Spectrochim. Acta Part B
Measurement of electron density utilizing the H α-line from laser produced plasma in air
Spectrochim. Acta Part B
New procedure for quantitative elemental analysis by laser-induced plasma spectroscopy
Appl. Spectrosc.
Comparative study of two standard-free approaches in laser-induced breakdown spectroscopy as applied to the quantitative analysis of aluminum alloy standards under vacuum conditions
J. Anal. At. Spectrom.
Cited by (87)
A strategy to reduce spectral intensity uncertainty and predicted content uncertainty of low and medium alloy steel elements
2024, Spectrochimica Acta - Part B Atomic SpectroscopyLaser-induced breakdown spectroscopy of biological tissues: Plasma diagnostics and a comparison of quantification approaches
2024, Spectrochimica Acta - Part B Atomic SpectroscopyExtension of the Boltzmann plot method for multiplet emission lines
2023, Journal of Quantitative Spectroscopy and Radiative TransferQuantitative analysis of tungsten in steel by one-point calibration laser-induced breakdown spectroscopy in vacuum
2023, Spectrochimica Acta - Part B Atomic SpectroscopyA statistical definition of limit of detection for calibration-free laser-induced breakdown spectroscopy
2023, Spectrochimica Acta - Part B Atomic Spectroscopy