Sample diagnosis using indicator elements and non-analyte signals for inductively coupled plasma mass spectrometry

Spectrochimica Acta Part B 58 (2003) 837–850

Sample diagnosis using indicator elements and non-analyte signals for inductively coupled plasma mass spectrometry Margaret Antler, Hai Ying, David H. Burns, Eric D. Salin* Department of Chemistry, McGill University, 801 Sherbrooke St. W, Montreal, Quebec, Canada H3A 2K6 Received 12 December 2002; accepted 13 February 2003

Abstract A sample diagnosis procedure that uses both non-analyte and analyte signals to estimate matrix effects in inductively coupled plasma-mass spectrometry is presented. Non-analyte signals are those of background species in the plasma (e.g. Nq, ArOq), and changes in these signals can indicate changes in plasma conditions. Matrix effects of Al, Ba, Cs, K and Na on 19 non-analyte signals and 15 element signals were monitored. Multiple linear regression was used to build the prediction models, using a genetic algorithm for objective feature selection. Non-analyte elemental signals and non-analyte signals were compared for diagnosing matrix effects, and both were found to be suitable for estimating matrix effects. Individual analyte matrix effect estimation was compared with the overall matrix effect prediction, and models used to diagnose overall matrix effects were more accurate than individual analyte models. In previous work wSpectrochim. Acta Part B 57 (2002) 277x, we tested models for analytical decision making. The current models were tested in the same way, and were able to successfully diagnose matrix effects with at least an 80% success rate. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Inductively coupled plasma mass spectrometry; Sample diagnosis; Non-analyte signals; Autonomous instrument

1. Introduction Inductively coupled plasma mass spectrometry (ICP-MS) is a powerful technique for trace metal analysis; however, ICP-MS can suffer from severe matrix effects, making it difficult to use in practice w2–5x. Analyte signals can change significantly with moderate concentrations (0.1–0.5%) of matrix species w6x. Several groups have investigated new methods to minimize or correct for these *Corresponding author. Fax: q1-514-398-3797. E-mail address: [email protected] (E.D. Salin).

matrix effects, such as concomitantsymatrices separation w7,8x, mathematical correction procedures w9–11x, alternate operating conditions w12x and high resolution MS w13x. More traditional calibration methods, such as matrix matching, standard additions, isotope dilution, internal standards, or simple dilution, may also be used to correct for matrix effects. Alternative calibration methods have also been described w14,15x. Choosing the correct methodology to analyze a complex sample can be difficult even for experienced users, thus there is a need to establish an intelligent system to help users make the correct choice of analytical

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methodology and to ensure the quality of the final result w16x. For the past decade, our laboratory has been investigating the automation of analytical instrumentation. The Autonomous Instrument Project aims to develop software that allows independent operation of ICP-AES w17,18x and ICP-MS w1,6,14,16,19,21x. In the present design, when analyzing a new sample the system first obtains semi-quantitative data from a full mass scan. This information is then used to calculate the severity of the matrix effects. If the calculated matrix effects are lower than a threshold value, the default calibration method, external standards, is used. If the calculated matrix effect is high, the instrument must then choose a more rigorous calibration method. Several branches of the software have already been reported, including a technique for the selection of internal standards, optimization of operating conditions, sample diagnostics and sample recognition w1,6,14,16,19,21x. This work focuses on diagnosing matrix effects for use in the Autonomous Instrument. Non-analyte signals have been of concern because of their potential to cause spectroscopic interferences. Olivares and Houk w20x noted that Arq and ArHq signals were suppressed by the presence of a matrix in an early paper. More recent papers have investigated the use of non-analyte signals for instrument diagnostics and signal calibration. In particular, non-analyte signals have been utilized as internal standards to compensate for matrix effects. Beauchemin et al. w22,23x used 12 q C and 80Arq as internal standards in the analysis of marine sediments. These species accurately corrected for matrix effects in most cases, with the exception of the heavier elements Cd and Pb. Chen and Houk w24x used various other polyatomic q q signals (Naq and MOq) as internal 2 , ArO , ClO standards. We reported a simple diagnostic procedure for ICP-MS w16x that warns of instrumental malfunction using non-analyte signals monitored while measuring blank solutions (i.e. water or 0.5% HNO3). In a previous paper w1x, we investigated nonanalyte signals to estimate overall absolute matrix effects. This work showed that non-analyte signals vary significantly in the presence of matrix inter-

ferents, and that these non-analyte signals could be used to calculate the overall absolute matrix effect. A linear model was constructed using the non-analyte signals, and the model was tested in the context of the Autonomous Instrument, i.e. to estimate whether the sample could be accurately analyzed with a ‘simple’ calibration method, such as external standardization, or if a more powerful calibration methodology would be necessary. Although this model was quite successful at estimating the overall absolute matrix effects, it is known that matrix effects can vary widely from element to element w1x. Also, the overall absolute matrix effect is an average of matrix effects for each analyte in the sample. It would seem reasonable that models for individual analytes would perform better than models to estimate the overall matrix effect. This work explores the utility of non-analyte signals to estimate matrix effects for individual analytes in ICP-MS. In addition, element signals are compared with non-analyte signals for their utility as estimators of matrix effects. Matrix specific models are also considered in this work. 2. Algorithms Models were constructed from spectral information using multiple linear regression (MLR); however, not all of the spectral myz values contain useful information. Therefore, some of these data can be discarded to reduce the computational complexity and provide simple models which may provide insight into the chemical processes. To appreciate the need, consider a model that uses three myz values (independent variables) to estimate the dependent variable, i.e. ysm1x1qm2x2q m3x3qb. If there are 256 myz values to choose from, then there are approximately 2563 possible models. Therefore, an efficient method is needed to search for the optimal combination of variables to include in the model. Several techniques exist including stepwise linear regression and the genetic algorithm. A genetic algorithm was used in this work. The main advantage of genetic algorithms over other search methods is that they resist the tendency to get caught in local minima. Excellent

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Table 1 ICP-MS operating conditions and experimental parameters Instrument: Skimmer cones: Nebulizer: ICP RF power: Auxiliary gas flow: Sample liquid uptake: Nebulizer gas flow rate:

PE-SCIEX Elan 6000 ICP-MS Nickel Cross-flow with Scott-type spray chamber 1.0 kW 15 lymin 1.0 mlymin 0.825 lymin

Mass spectrometer Detector: Ion lens voltage: Auto lens: Peak scan parameters: Basic mass range: Scan mode: Replicates: Dwell time: Resolution: Sweeps per reading: Reading per replicate:

Dual 7.5 V Off 2–15, 17–39, 42–250 (amu)a Peak hopping 3 25 ms 0.1 (amu) 15 1

a The real mass range for data collection was determined with different matrices as well. When doing experiments for a specific matrix element, all isotopes of this element were avoided.

tutorials on genetic algorithms can be found in the literature w25,26x. In order to search for the optimal model, the data are first encoded into a bit string. In this work, each myz value was represented by a bit string. If there are 256 (28) myz values, then eight bits are necessary to encode the values. Mass number 1 is represented by 00000000, mass number 2 is represented by 00000001, and mass number 256 is represented by 11111111. If three independent variables are used to build the model, then a bit string 24 bits long is necessary to represent the model. For example, the model Ysm1wmass 1xqm2wmass 2xqm3wmass 256xqb would be encoded by the following bit string (spaces are added for clarity). 00000000

00000001

11111111

The genetic algorithm searches for the optimal model by first generating an initial random population of individuals, i.e. possible models. Each individual is evaluated using a fitness function. In

this work, the fitness function evaluated the standard error of the estimate for each individual model. The individuals that had the smallest standard error were the best, or most fit individuals. The best individuals were selected for breeding and mutation to create a new population, or generation, of individuals. Breeding, or cross-over, creates a new individual from two parent individuals by combining the first x bits of one parent with the last (24-x) bits of the second parent. Mutation creates a new individual by toggling one randomly selected bit in the bit string. These new individuals are then evaluated using the fitness function, and the process is repeated for N generations to ensure convergence. 3. Experimental All analyses were performed on a PE-SCIEX Elan 6000 ICP-MS with a cross-flow nebulizer and a Scott-type spray chamber. The nebulizer gas flow rate and ion lens voltage were determined using the standard daily optimization procedure outlined by the manufacturer. In order to minimize experimental variables, the Auto Lens function was turned off, and the ion lens voltage was fixed

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at the value that maximized the 103Rhq signal. The operating conditions and experimental parameters are outlined in Table 1. The detector was set in dual mode. For the calculations, the analyte signals were processed in pulse mode, and the non-analyte signals were processed in analog mode, since they are generally of higher intensity, and can saturate in pulse mode. Full scan spectra were collected in peak hopping mode, skipping myz values 16Oq and 40Arq. In addition, when experiments for specific ‘matrix elements’ (elements present in high concentration to induce matrix effects) were performed, all isotopes of the matrix element were skipped in the data acquisition. All samples were prepared in distilled deionized water (Milli-Q water system, Millipore Corp., Bedford, MA, USA) by sequential dilution of multi-element standards (SCP Science, St. Laurent, Quebec, Canada) and trace metal grade acids (Baker Instr-Analyzed, J.T. Baker, Phillipsburg, NJ, USA). There were 15 analytes, spanning a range of myz values and ionization potentials: Cu, Fe, Mg, Ni, Pb, Pt, Y, Zn, Be, La, Li, Mo, P, Sb and Sr. Based on previous work w6x, five matrix elements were selected for this study, Na, K, Al, Cs and Ba. Single matrix element solutions were made from solid nitrates (Alfa Aesar, Ward Hill, MA, USA). Matrix effects depend on the absolute amount of the matrix element rather than on the molar ratio of matrix element to analyte w3x, so the concentrations of matrices in mgyml are used. Five solutions without matrices (i.e. without high concentrations of an interfering matrix species) were used: water, 0.5% HNO3 and three multielement standard solutions: 5 ngyml, 10 ngyml and 20 ngyml. For each matrix, except for Cs, there were six different matrix concentrations: 10 mgyml, 30 mgyml, 100 mgyml, 300 mgyml, 400 mgyml and 1000 mgyml. Matrix blanks were necessary for blank subtraction in case trace amounts of any analyte were present, but the matrix blanks were generally not significant. For each matrix concentration, a matrix blank and 10 ngyml multi-element standards were prepared. Because Cs is known to cause more serious matrix effects than the other matrix elements w6x, five

concentrations were used: 10 mgyml, 30 mgyml, 100 mgyml, 200 mgyml and 500 mgyml. Different matrix solutions were run on different days. The experiments during a day were performed in the following sequence, Milli-Q water, 0.5% HNO3, matrix-free standard solutions (5, 10 and 20 ngyml), lower matrix blank, lower matrix solution with standards, higher matrix blank, and higher matrix solution with standards. The washout time was selected to ensure that there was no residual contamination in the instrument from the matrices. Full scan spectra of Milli-Q water were used to monitor the background for drift before and after experiments each day. Furthermore, to minimize effects from day to day changes in instrument performance, all spectra were normalized to the Milli-Q blank spectrum obtained for that day w1x. 4. Model building and verification The data were split into two sets, the first set for model building (or training) and cross-validation, and the second set for model testing. The first set of data consisted of water, 0.5% HNO3, the three multi-element standard solutions (5, 10, and 20 ngyml), and blank-subtracted matrix standards of four concentrations, 10, 100, 200 and 500 mgyml (Cs) or 1000 mgyml (Na, K, Al and Ba). The second data set consisted of the 30 and 200 or 400 mgyml matrices and was used for blind testing. The first data set was further subdivided into two parts. For the training set, 70% of the data were randomly chosen. The model coefficients for each individual in the population were calculated using the training set. The standard error of the estimate was evaluated using the remaining 30% of the data, the cross-validation set. A flow chart of the model development process is shown in Fig. 1. There were 250 individuals in each population, and 500 generations. This process was repeated for models containing two to sixteen independent variables. A Visual Basic subroutine was compiled to read and convert the Elan 6000 report files to the desired format for processing. The programs for data processing and model building were written

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Fig. 1. Flow chart of the model development process. Models were generated using 250 individuals (M) in the population, and 500 generations (N).

in MATLAB, and the genetic algorithm was based on an algorithm written by Roger Jang w27x.

NA

5. Matrix effects calculations

OMEs8ZMEiZ yNA

Matrix effects are defined as matrix-induced signal variations, suppression or enhancement w4x. In this work, the matrix effect for an analyte was calculated as the variation of the net intensities using the following formula: MEs

IMyIMBl IyIBl

of the matrix effect for each analyte, calculated using the following formula:

(1)

where IBl and IMBl represent the blank with no matrix and the matrix blank respectively, while I and IM represent the signal intensity with no matrix and with a matrix for a specific analyte at the same concentration. The absolute overall matrix effect (OME) is the average of the absolute value

(2)

i

where NA is the number of analytes measured. Because both signal enhancements and suppressions were observed due to the matrix effect, information is lost when the average OME is calculated. Most element signals were suppressed due to the matrices, but Pt and Fe signals were enhanced. Further information is available in Ying et al. w1x. The true matrix effect for each analyte in each matrix was calculated using Eq. (1). Models to estimate the matrix effect for each analyte were constructed using coefficients calculated by MLR with features selected by the genetic algorithm. The models were then compared with the true

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matrix effect to evaluate the performance of the model. Fifteen analytes were studied, so there were 14 ‘indicator elements’ to choose from for each analyte. The matrix effect was predicted as a linear combination of the selected element signals. An example of a model using element signals is: MEsm1Sw63Cuxqm2Sw208Pbxqb where S indicates the name and myz ratio of the indicator element signal, and m1, m2 and b represent the model coefficients. Previous work showed that ratios of non-analyte signals (NAS) were better indicators of matrix effects than raw nonanalyte signals w1x. Nineteen non-analyte signals were observed, so there were 171 different nonanalyte signal ratios. The matrix effect is estimated as a combination of non-analyte signal ratios. An example of a model using NAS ratios is: MEsm1Swy17ŽOH.z~ ySw12Cx x

|

qm2Swy76ŽAr2.z~ ySw15Nxqb x

|

Finally, the total data set consists of all element signals and non-analyte signal ratios, and so the model could have terms as in either of the above examples. For example MEsm1Swy17ŽOH.z~ ySw12Cxqm2Sw63Cuxqb x

|

Note that because each spectrum was normalized to the Milli-Q spectrum, for non-analyte signals, the above example is almost mathematically equivalent to the Common Analyte Internal Standardization formula found in the work of Al-Ammar and colleagues w11x. Table 2 lists all the myz ratios used in the present work in bold font. Information about all mass species was extracted from a useful ICP-MS database-MS Interview software w28x for a nitric acid environment. Several non-analyte species, 56ArO, 76Ar2, 78Ar2 and 80Ar2, overlapped with isobarics of other analytes. However, since they originate from the major component of the plasma, Ar, we assume that their signals are much stronger than those of the analytes, which were present in very low concentrations, if at all.

6. Results and discussion 6.1. Overall matrix effect estimation The models were evaluated using the following definitions w6,21x. The threshold is the desired accuracy bound; if the threshold is 5%, then the operator has specified that the accuracy of the analysis should be within 5% or another calibration methodology should be selected. There are four possibilities for classification. True positives occur when the model estimates a matrix effect greater than the threshold, and the actual matrix effect is also greater than the threshold. True negatives occur when the true matrix effect is less than the threshold, and the model estimates a matrix effect less than the threshold. Both cases are defined as ‘GOOD,’ because the model classifies the sample properly. If the matrix effect is greater than the threshold, then a higher calibration methodology, such as standard additions, is recommended. If the matrix effect is below the threshold, then the default calibration strategy, external standards, is used. A false positive occurs if the model estimates a matrix effect greater than the threshold, when in fact the matrix effect is less than the threshold. This is called ‘OK,’ since the autonomous instrument would recommend a better calibration methodology than is necessary, and the accuracy of the analysis would be maintained. Finally, a false negative occurs when the model estimates a matrix effect less than the threshold, when the actual matrix effect is greater than the threshold. This is ‘BAD,’ since the default calibration strategy would be used, leading to an inaccurate analysis. All models perform equally well for classification of the blind test set. Previous work w1x showed that the average overall matrix effect could be estimated from NAS ratios. In the present work, models constructed using NAS ratios and elemental signals are compared. Three models to estimate the average overall matrix effect (OME) were constructed. The first was constructed using only element signals (e.g. Li, Mg, Pb). The second was constructed using only non-analyte signal ratios (e.g. ArOyN, Cy OH). The third was constructed using both element

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Table 2 All myz values used in the current study (in nitric acid environment) Mass Analyte signals 7 9 24 31 54 58 63 64 88 89 98 121 139 195 208 Non-analyte signals 2 3 4 12 13 14 15 17 18 19 20 21 36 37 38 56 76 78 80 a

Background species (non-analyte signals)

Isobarics

Doubly charged ions

Matrix dependent or oxidesyhydrides

Ca, Ti

C2 (organics)

Li Be

N2H, NOH, NO, CO ArN, ArO ArO, ArOH ClN2

H2, H H3 C C N N OH, NH3, O O, OH, H2O, NH4 OH, H2O, H3O H2O, H3O HsO Ar ArH, H3O (H2O) Ar, ClH ArO, ArNH Ar2 Ar2 Ar2

Mg P Fe, Cra Ni, Fea Cu Zn, Nia Sr Y Mo, Rua Sb La Pt Pb

Cd Cd

Lu, Yb

NaCl, CaO PO2, NaAr, MgCl HPO2, CaO, TiO, Na2O GeO, MnO2H GeO NiAr, CuCl SbO HfO

H He C C N N O O F Ne Ne S, Ar Cl Ar Fe Cd CaO Ge, Se Se, Kr Se, Kr

Mg Mg

CH (organics) CH (org.), CH2 (org.) NH (org.)

Ca Ca

Eu, Sm, Gd Gd, Dy Tb, Gd, Dy

AsH, NiO NiO, TiO2 NiO, TiO2

These isobarics were regarded as spectral interferences here.

signals and non-analyte signal ratios. Fig. 2 illustrates how well the model works as a test for the presence of matrix effects with a 20% threshold using the OME (absolute overall matrix effect). The model constructed from element signals appears to have fewer ‘BAD’ classifications, but this is not statistically significant compared to the other models. In theory, the model constructed from both indicator elements and non-analyte signals should do no worse than either the NAS

model or the indicator element model, since the best combination of either of the individual sets will be available in the data set containing both data sets. The results indicate that non-analyte signal ratios are adequate markers for the presence of matrix effects, even when compared to element signals, and they imply that the information available in the sample itself (NASs) is sufficient to predict matrix effects and that an additional indicator element is not needed. For the remainder of

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Fig. 2. Comparison of prediction accuracy of three models to estimate absolute overall matrix effects constructed using three different data sets; element lines only (Element), non-analyte signal ratios only (NAS ratio), and both element and NAS ratios (Both).

the model building processes, both indicator elements and non- analyte signals are included in the data set. 6.2. Overall matrix effects vs. individual analyte matrix effects Some analyte signals may be severely suppressed in the presence of the matrix, while others may minimally affected. By calculating the OME (absolute overall matrix effect) this information is lost. For example, if one analyte is suppressed 20% in the presence of the matrix, while a second analyte is suppressed 3%, then one might consider different remedies for each analyte. A prediction model for each analyte was constructed and tested in order to determine if calibration for each analyte gave useful results. The model was constructed with both element signals and NAS ratios available for the genetic algorithm to select. The results are shown in Fig. 3. The model is extremely conservative at the 5% threshold, recommending a better calibration methodology more often than is necessary in many cases. The figure also illustrates that performance is particularly poor at approximately the 10% threshold. This suggests that the models are underestimating the matrix effect at high matrix concentrations. 6.3. Individual matrix calibration The previous models were all calculated from

data sets with all five of the matrix effect inducing elements present at high concentrations. It would seem reasonable that one might do better if one developed a model specifically for a specific matrix. The data were then split into five smaller sets, one for each matrix element (Al, Ba, Cs, K and Na). A model to estimate average overall matrix effects (of all analytes) was constructed for each matrix. The models were then tested as a flag for matrix effects, and the results are shown in Fig. 4. The models were able to classify the samples correctly most of the time, however, there are still a significant number of false negative (BAD) results. The highest bar (All) illustrates the results that were obtained when using the model developed with all matrix elements included in the data set. The large number of false negative results compared to the number of false positive results indicates that the models tend to underestimate the matrix effect. In all cases, the genetic algorithm selected a combination of non-analyte signal ratios to build the models. Matrix effects for individual analytes were then determined in each matrix, in order to determine if this type of calibration would improve the predictive abilities of the models. Fig. 5 shows how well the models were able to estimate matrix effects at 10% threshold for the Ba, Cs and K matrices, and 20% threshold for the Al and Na matrices. These thresholds were selected because they had the poorest results for the average overall matrix effect (Fig. 4). The sodium, barium and cesium matrices all showed an improvement in the prediction accuracy with the individual analyte calibration models compared to the overall matrix effect. The cesium models were conservative, with a large number of false positive (OK) results, but for the sodium, barium and cesium matrices, there were no false negative (BAD) results. The aluminum matrix models showed approximately the same prediction accuracy for the individual and overall matrix effect models, while the individual potassium models performed poorer than the overall matrix effect model. Again, in all cases, the genetic algorithm selected a combination of nonanalyte signal ratios to build the models.

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Fig. 3. Prediction accuracy of models for individual analyte matrix effects within 5%, 10%, 20% and 30% accuracy bounds. ‘Good’ indicates the correctly classified samples, ‘Ok’ indicates a false positive identification of matrix effects, and ‘Bad’ indicates a false negative classification of matrix effects.

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Fig. 4. Prediction accuracy of models for absolute overall matrix effects calibrated using individual matrices. ‘All’ indicates the results of the pooled data set, as shown in Fig. 2.

From a practical standpoint, it would be desirable to develop a model with the collection of a minimum of data. This would require a minimum number of calibration solutions. To test the viability of using one matrix species to develop a model sufficiently general that it could be used for another matrix, several computations were done. A model was constructed with the sodium matrix data and was used to predict matrix effects for the potassium matrix samples. Sodium and potassium are chemically similar, and the potassium data were used as a blind test of the sodium model. The results are illustrated in Fig. 6. The prediction results are over 90% accurate (GOOD or OK). Similarly, a model constructed with cesium matrix data was used to estimate the matrix effects for the barium matrix. The results are shown in Fig. 7, The model is conservative at the 20% threshold, with approximately 25% of samples yielding an OK result (false positive identification of matrix

effects). However, the model has no BAD (false negative) results. The results are accurate (GOOD or OK) 100% of the time. The data from both experiments indicate that for similar matrix elements, only one matrix element is necessary for calibrating the model. 7. Conclusions The diagnosis procedures described above were designed to predict when a calibration methodology more powerful than external standardization would be needed in an automated system. When models were developed using a variety of matrix effect inducing species, the results showed that non-analyte signal ratios are useful for estimating matrix effects in ICP-MS. Models developed for specific matrices were more successful in estimating matrix effects than models developed from a

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Fig. 5. Prediction accuracy for individual analyte matrix effects calibrated using single matrix element data. Ba, Cs and K-10% accuracy bound, K and Na-20% accuracy bound.

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Fig. 6. Prediction accuracy for model calibrated using sodium matrix data, and blind tested with potassium matrix data. The accuracy threshold (e.g. 5%) is indicated in the bottom left corner.

pooled data set of many different matrices. The average overall matrix effect is useful for making calibration decisions with respect to the entire suite

of analytes, but it does not perform as well as models developed for individual analytes in specific matrices. The OME model may still be useful

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Fig. 7. Prediction accuracy for model calibrated using cesium matrix data, and blind tested with barium matrix data. The accuracy threshold (e.g. 5%) is indicated in the bottom left comer.

because the calibration of the OME model takes much less time than for the individual models, and the improvement in performance over the individ-

ual models is not dramatic. Models developed with a matrix chemically similar to the sample matrix are also useful for estimating the matrix effect and

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may also reduce the amount of data required to develop a model. Acknowledgments The authors would like to thank the Natural Sciences and Engineering Research Council of Canada for financial support, and Amila De Silva and Claudia Gributs for valuable discussions. References w1x H. Ying, J.W. Tromp, M. Antler, E.D. Salin, Spectrochim. Acta Part B 57 (2002) 277–290. w2x A. Montaser, Inductively Coupled Plasma Mass Spectrometry, Wiley-VCH, New York, 1998. w3x E.H. Evans, J.J. Giglio, J. Anal. At. Spectrom. 8 (1993) 1–18. w4x R.F.J. Dams, J. Goossens, L. Moens, Mikrochim. Acta 119 (1995) 277–286. w5x N. Jakubowski, D. Stuewer, New instrumental developments and analytical applications in ICP-MS, in: G. Holland, S.D. Tanner (Eds.), Plasma Source Mass Spectrometry: Developments and Applications, The Royal Society of Chemistry, Cambridge, 1999, pp. 298–312. w6x J.W. Tromp, R.T. Tremblay, H. Ying, E.D. Salin, J. Anal. At. Spectrom. 15 (2000) 617–625. w7x J.W. McLaren, A.P. Mykytiuk, S.N. Willie, S.S. Berman, Anal. Chem. 57 (1985) 2907–2911. w8x D. Beauchemin, S.S. Berman, Anal. Chem. 61 (1989) 1857–1862. w9x W. Zhu, E.W.B. De Leer, M. Kennedy, P. Kelderman, J.F.R. Alaerts, J. Anal. At. Spectrom. 12 (1997) 661–665. w10x M.A. Vaughan, D.M. Templeton, Appl. Spectrosc. 44 (1990) 1685–1689.

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