Anal. Chem. 1999, 71, 5447-5449
Some Considerations on the Correlation between Signal and Background in Laser-Induced Breakdown Spectroscopy Using Single-Shot Analysis SIR: One of the most common problems in quantitative spectrochemical analysis is simulating the analytical signal and processing the data. This problem is particularly relevant for laser-induced breakdown spectroscopy (LIBS) because the expected linear relationship between the emission intensity and the concentration is often flawed due to the matrix dependence of the laser-material interaction and to fluctuations in the experimental parameters. The problems multiply when LIBS is applied to the direct analysis of complex matrices characterized by varying compositions and particle sizes. Each laser pulse produces a plasma which can vary in temperature and electron density. In addition, because of the small sampling volume and sample heterogeneity, each laser pulse does not always vaporize a mass which is representative of the bulk sample composition.1 There are several quantities which can be measured from the emission spectrum, including the peak intensity, the peak area, the background in the vicinity of the line, and the average background over a spectral window. The question arises as to which quantity or combination of quantities should be chosen as the analytical signal to obtain a correct calibration function. It is also generally important to somehow account for shot-toshot irreproducibility. Recently, a method for correction of variations in singleshot spectra obtained from soils and aerosols was proposed by Xu et al.2 Each single-shot spectrum was recorded, and spectral line intensities were found to correlate with the continuum plasma background. A simple algebraic model was proposed in which the background, Bi, for each laser shot i was given as the sum of a constant (b0) and a fluctuating term, (k1 fi)
Bi ) b0 + k1 fi
(1)
where “fi is a factor that is responsible for the signal and baseline fluctuations and k1 is a proportionality factor.”2 The (1) Schechter, I. Rev. Anal. Chem. 1997, 16, 173-298. (2) Xu, L.; Bulatov, V.; Gridin, V. V.; Schechter, I. Anal. Chem. 1997, 69, 21032108. 10.1021/ac990766l CCC: $18.00 Published on Web 10/27/1999
© 1999 American Chemical Society
same fluctuating factor fi, though with another proportionality factor (k2), was suggested to be present in the signal:
Pi ) Bi + Ck2 fi
(2)
Finally, after simple algebraic manipulations, the signal was expressed in the form
Pi ) Bi(1 + kC) - kCb0
(3)
According to eq 3, a correlation plot of the peak intensity versus the average background, constructed on a shot-to-shot basis, yielded a linear dependence, and the slope of this plot was found to be proportional to the analyte concentration. A new calibration function, the correlation plot slope (R) minus one (R - 1) versus concentration was then proposed and shown to give good results in the case of Zn in particulate materials.2 We applied this model to the LIBS analysis of iron, aluminum, phosphorus, silicon in phosphate rock, zinc in brass, and chromium in stainless steel. A typical example of our results is given in Figure 1. The first four graphs (box a) show a correlation of the peak intensity, Pi, of an aluminum line at 256.799 nm vs the background intensity, Bi, for 1000 laser shots on phosphate rock samples doped with Al2O3. Although a correlation exists, the slopes of the linear fit lines are somewhat uncertain due to the large scatter of the experimental points. Figure 1b shows the plots of the average peak intensity vs the concentration and the slope (R) minus one versus the concentration, respectively. It is clearly seen from Figure 1b that while a linear concentration dependence exists for the peak intensity (the average of 1000 laser shots), a linear relationship was not obtained for the slope minus one (R - 1) plot. We also applied the method to very homogeneous samples, such as NIST stainless steels (e.g., 1260 series). For these samples, the dependence of signal versus background was a cluster of points (Figure 2), from which no particular slope could be deduced. These results on one hand seem to indicate a lack of generality in the applicability of the model proposed by Xu et al.2 and on the other hand prompted us to take a closer look at the physical significance of eqs 1-3 used in the model. The discussion here can be focused on the following interpretations: (i) a purely analytical one, which takes into account the statistical meaning of the product k1 fi in eqs 1-3; and (ii) a physical one, in which the plasma parameters governing the emission of the analytical signal and the background are considered. First, we note that the expression for the background, in the form of b0+k1 fi, has a transparent physical sense if we think of b0 as a constant component of a dark current plus a constant (mean) emission signal from the plasma continuum, k1 as a maximum peak-to-peak background fluctuation taken over all laser shots, and fi as any random number between -1/2 and 1/2. If an unknown source of fluctuations Analytical Chemistry, Vol. 71, No. 23, December 1, 1999 5447
Figure 1. Determination of Al in phosphate rock sample (NIST 120c); box (a) signal plus background vs background correlation plots, R is the plot slope; box (b) the calibration based on the average peak intensity (left), and the calibration based on the correlation plot slope (right).
is considered to be the same for the background and for the analytical signal, it is logical to express the analytical signal in the same form as the background, i.e., s0 + k2 fi, where s0 is the mean signal (of course, concentration-dependent), k2 is the peak-to-peak signal fluctuation, and fi is the same random number. In the assumption of an ideal correlation, the correlation plot of the signal plus background vs background is therefore linear with a slope of 1 + k2/k1. The apparent concentration dependence arises from the signal statistics. It is obvious that the greater the signal, the greater the absolute signal noise, though the relative signal fluctuations may decrease. For example, for Poisson statistics, the noise (in our case, the peak-to-peak signal fluctuation k2) increases with the number of counts, N, measured in an experiment as N1/2. Assuming that the plasma background fluctuation (k1) remains the same for all concentrations (though correlates with k2), the 5448 Analytical Chemistry, Vol. 71, No. 23, December 1, 1999
Figure 2. Signal vs background for chromium in stainless steel (NIST 1262a).
(R - 1) will be proportional to N1/2. Indeed, in many experiments we observed a strongly nonlinear dependence of the Pi vs Bi slope upon the concentration (see Figure 1b). We, therefore, conclude that, on the basis of statistical considerations, the expression for the background-subtracted analytical signal given by Xu et. al2 in the form Ck2 fi (see eq 2) is incorrect. Besides, this expression implies that if fluctuations are negligibly small (k2 or fi ≈ 0) then no analytical signal can be observed, an obviously erroneous result. Regarding the second interpretation of the factors in eqs 1-3, it is instructive to consider the well-known expressions given in the pertinent literature (see, for example, Griem3 or Thorne4) relating the intensities of line and continuum emission, originating from a radiative plasma, as a function of fundamental plasma parameters. The resulting expression has several interesting implications for the single-shot analysis of different types of samples by LIBS.5 For the purpose of the present discussion, it can be shown that the line-to-continuum emission ratio, transformed algebraically into the formalism of the line-to-background emission ratio of Xu et. al,2 is given, for each laser shot, by the expression
Pi ) Bi[1 + ξCf(Te)]
(4)
In the above equation, the proportionality constant, ξ, is different from the constant k in eq 3, while the slope of the plot of Pi vs Bi is seen to depend on the analyte concentration, Ca, multiplied by a function of the electron plasma temperature, Te. Even before discussing this functional dependence, it can be immediately pointed out that the (slope - 1) of the plot is not simply proportional to the concentration, as predicted by Xu et. al.2 For an analyte element present as a trace constituent in a given matrix, it can be shown that the function f(Te) is expressed by the relationship
f(Te) )
exp[(Ei,m - Eu,a)/kTe] Zm(Te) Te Za(Te)Zi,m(Te)
(5)
upper excitation energy of the analyte element; k is the Boltzmann constant; and Zm, Za, and Zi,m are the partition functions of the matrix neutrals, the analyte, and the matrix ions, respectively. Only in the case in which f(Te) is constant from shot to shot and independent of analyte concentration does this physical interpretation of the factors ki fi of the equations used by Xu et. al2 lead to a simple, linear dependence of the (slope - 1) of the plot of Pi vs Bi with the concentration of the analyte. In conclusion, the method proposed by Xu et. al2 does not seem to be easily amenable to an underlying analytical or physical interpretation, thus detracting from its general applicability. Nevertheless, the idea of Xu et. al2 of working out a suitable analytical methodology for LIBS based on a shot-toshot procedure is indeed attractive. In addition, it has been shown to work in the case of the determination of Zn in particulate matter. On the basis of the considerations put forward in this discussion, it can be argued that the success of this application might be restricted to only a few particular matrixes or might even have been fortuitous. Work is now in progress in our laboratory to fully characterize the analytical feasibility of this approach with different types of samples, while at the same time making an effort to provide a general theoretical background upon which to justify or prevent its application. ACKNOWLEDGMENT This work was supported by a Grant from the Florida Institute for Phosphate Research and by the Engineering Research Center (ERC) for Particle Science and Technology at the University of Florida, the National Science Foundation (NSF) Grant no. EEC94-02989, and the Industrial Partners of the ERC.
I. B. Gornushkin,† B. W. Smith,† G. E. Potts,† N. Omenetto,‡ and J. D. Winefordner*,†
Department of Chemistry, University of Florida, Gainesville, Florida 32611, and European Commission, Joint Research Centre, Environment Institute, 21020 Ispra (VA), Italy
where Ei,m is the ionization energy of the matrix; Eu,a is the
AC990766L
(3) Griem, H. R. Plasma Spectroscopy; McGraw-Hill Book Co.: New York, 1964. (4) Thorne, A. P. Spectrophysics, 2nd ed.; Chapman and Hall: London, 1988. (5) Gornushkin, I. B.; Smith, B. W.; Potts, G. E.; Omenetto, N.; Winefordner, J. D., to be submitted for publication.
* Corresponding author. Tel.: 352-392-0556. Fax: 352-392-4651. E-mail:
[email protected]. † University of Florida. ‡ European Commission, Joint Research Centre, Environment Institute.
Analytical Chemistry, Vol. 71, No. 23, December 1, 1999
5449
