JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2 513 Inductively Coupled Plasmas: Line Widths and Shapes, Detection Limits and Spectral Interferences. An Integrated Picture* Plenary Lecture P. W. J. M. Boumans and J. J. A. M. Vrakking Philips Research Laboratories, P.O. Box 80.000, 5600 JA Eindhoven, The Netherlands This paper discusses the significance of the basic knowledge of atomic spectra for the interpretation of detection limits, the optimisation of line selection and the design of interference libraries for universal application in inductively coupled plasma atomic emission spectrometry (ICP-AES). Specifically, the paper reviews (i) the measurement of the physical widths and shapes of 350 prominent ICP lines of 65 elements, (ii) the use of these results for the breakdown of detection limits in general and the assessment and comparison of three comprehensive sets of detection limits in particular, (iii) the development and application of a new rational criterion for line selection in dependence on sample composition and spectral resolution and (iv)the prospects of using physically resolved spectral data in future compilations of spectral information for ICP-AES. Although the topic is treated with reference to ICP-AES, many aspects of the discussion are of general interest in AES. Keywords : Inductively coupled plasma; atomic emission spectrometry; line widths and shapes; spectral band width; spectral interferences The availability of basic spectroscopic data, such as transition probabilities, excitation and ionisation energies, cross-sections for a variety of processes and line widths, is indispensable in plasma diagnostics to describe the processes and mechanisms that govern the generation of the signals used for analytical purposes. Insight into these processes and mechanisms, in turn, helps clarify observations made under analytical conditions and, more importantly, may be used to rationalise analytical procedures. One of the areas where such a rationalisation is still badly needed is the part of atomic emission spectroscopy concerned with line selection and spectral interferences. In a recent review, “A century of spectral interferences in atomic emission spectroscopy-Can we master them with modern apparatus and approaches?,”’ it was indicated that, in spite of various recent attempts to produce new data compila- tions, the real progress is still rather meagre, because the capabilities of computers and modern spectroscopic instru- ments have not yet been sufficiently exploited. This situation can be expected to change rapidly in the forthcoming years. In this light the present text discusses (i) some recent measure- ments of basic spectroscopic data, (ii) the direct application of these data to analytical atomic emission spectroscopy and (iii) the perspectives of extending the data base and using it in a rational way to face the problem of line selection and spectral interferences in inductively coupled plasma atomic emission spectrometry (ICP-AES) . Specifically, the following topics will be addressed: (a) The measurement of the effective shapes and physical widths of about 350 prominent lines, including lines with hyperfine structure (HFS), of 65 elements emitted from an ICP. (b) The use of the results of the line width measurements (a) in a breakdown of three extensive sets of AES detection limits for argon ICPs compiled with three different ICP sources and spectrometers in three laboratories. (c) The development of a novel analytizal figure merit as a rational criterion for line selection, that is, the “true detection limit” for real samples, formulated in such a way that both the selectivity and the “conventional detection limit” for smooth background are taken into account. * Presented at the 1987 Winter Conference on Plasma and Laser Spectrochemistry, Lyon, France, 12th-16th January, 1987. (d) The interference library of the 1990s: a library in the software domain based on physically resolved spectral data, from which the effective data relevant to a particular spectroscopic apparatus can be derived by convolution with the instrumental function. Physical Widths of Lines Emitted from an ICP Data Available up to the End of 1986 In the textbook “Inductively Coupled Plasma Emission Spectroscopy”2 Boumans summarises the literature con- cerned with determinations of physical line widths in ICPs, as follows. (a) Human and Scott3 found a width of 3.6 pm for Ca 1422.673 nm using a Fabry - Perot interferometer. (b) Also using interferometry Kawaguchi et al.4 measured the widths of 15 lines of 10 elements. Their results are based on the assumption of a Lorentzian instrumental profile and Gaussian profiles for both hollow-cathode and ICP lines, yielding a Voigt profile as experimental profile. For the de-convolution Kawaguchi et al. used an approximation proposed by Posener,s but Boumans and Vrakking6 recalcu- lated their results using a more accurate formula. (c) Hasegawa and Haraguchi7 reported widths for 34 lines of 19 elements obtained with an echelle monochromator with crossed dispersion incorporating a refractor plate for wavelength scanning. Their results are based on the assump- tion that the experimental profile is a Voigt profile of which the Gauss (or Doppler) component of the half-width and the a parameter can be determined with a curve-fitting procedure. The Gauss and Lorentz components are then split separately, into an instrumental and a physical part, using quadratic de-convolution for the Gauss components and linear de- convolution for the Lorentz components. (d) Batal and Mermetg calculated line widths for nine atomic or ionic lines of Ca, Mg and Sr on the basis of Doppler broadening (T = 5000 K) and van der Waals interaction. (e) Broekaert et al.9 determined the widths of 18 lines of 16 rare earths using a spectrograph provided with an order sorter. They used the same method and equipment as had been used previously by Laqua et ~1.10 for the measurements of the widths of 67 lines of 40 elements emitted from four types of d.c. arc and a soft spark.
Transcript
JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2 513
Inductively Coupled Plasmas: Line Widths and Shapes, Detection Limits and Spectral Interferences. An Integrated Picture* Plenary Lecture
P. W. J. M. Boumans and J. J. A. M. Vrakking Philips Research Laboratories, P.O. Box 80.000, 5600 JA Eindhoven, The Netherlands
This paper discusses the significance of the basic knowledge of atomic spectra for the interpretation of detection limits, the optimisation of line selection and the design of interference libraries for universal application in inductively coupled plasma atomic emission spectrometry (ICP-AES). Specifically, the paper reviews (i) the measurement of the physical widths and shapes of 350 prominent ICP lines of 65 elements, (ii) the use of these results for the breakdown of detection limits in general and the assessment and comparison of three comprehensive sets of detection limits in particular, (iii) the development and application of a new rational criterion for line selection in dependence on sample composition and spectral resolution and (iv) the prospects of using physically resolved spectral data in future compilations of spectral information for ICP-AES. Although the topic is treated with reference to ICP-AES, many aspects of the discussion are of general interest in AES. Keywords : Inductively coupled plasma; atomic emission spectrometry; line widths and shapes; spectral band width; spectral interferences
The availability of basic spectroscopic data, such as transition probabilities, excitation and ionisation energies, cross-sections for a variety of processes and line widths, is indispensable in plasma diagnostics to describe the processes and mechanisms that govern the generation of the signals used for analytical purposes. Insight into these processes and mechanisms, in turn, helps clarify observations made under analytical conditions and, more importantly, may be used to rationalise analytical procedures. One of the areas where such a rationalisation is still badly needed is the part of atomic emission spectroscopy concerned with line selection and spectral interferences.
In a recent review, “A century of spectral interferences in atomic emission spectroscopy-Can we master them with modern apparatus and approaches?,”’ it was indicated that, in spite of various recent attempts to produce new data compila- tions, the real progress is still rather meagre, because the capabilities of computers and modern spectroscopic instru- ments have not yet been sufficiently exploited. This situation can be expected to change rapidly in the forthcoming years. In this light the present text discusses (i) some recent measure- ments of basic spectroscopic data, (ii) the direct application of these data to analytical atomic emission spectroscopy and (iii) the perspectives of extending the data base and using it in a rational way to face the problem of line selection and spectral interferences in inductively coupled plasma atomic emission spectrometry (ICP-AES) . Specifically, the following topics will be addressed:
(a) The measurement of the effective shapes and physical widths of about 350 prominent lines, including lines with hyperfine structure (HFS), of 65 elements emitted from an ICP.
(b) The use of the results of the line width measurements (a) in a breakdown of three extensive sets of AES detection limits for argon ICPs compiled with three different ICP sources and spectrometers in three laboratories.
(c) The development of a novel analytizal figure merit as a rational criterion for line selection, that is, the “true detection limit” for real samples, formulated in such a way that both the selectivity and the “conventional detection limit” for smooth background are taken into account.
* Presented at the 1987 Winter Conference on Plasma and Laser Spectrochemistry, Lyon, France, 12th-16th January, 1987.
(d) The interference library of the 1990s: a library in the software domain based on physically resolved spectral data, from which the effective data relevant to a particular spectroscopic apparatus can be derived by convolution with the instrumental function.
Physical Widths of Lines Emitted from an ICP Data Available up to the End of 1986
In the textbook “Inductively Coupled Plasma Emission Spectroscopy”2 Boumans summarises the literature con- cerned with determinations of physical line widths in ICPs, as follows.
(a) Human and Scott3 found a width of 3.6 pm for Ca 1422.673 nm using a Fabry - Perot interferometer.
(b) Also using interferometry Kawaguchi et al.4 measured the widths of 15 lines of 10 elements. Their results are based on the assumption of a Lorentzian instrumental profile and Gaussian profiles for both hollow-cathode and ICP lines, yielding a Voigt profile as experimental profile. For the de-convolution Kawaguchi et al. used an approximation proposed by Posener,s but Boumans and Vrakking6 recalcu- lated their results using a more accurate formula.
(c) Hasegawa and Haraguchi7 reported widths for 34 lines of 19 elements obtained with an echelle monochromator with crossed dispersion incorporating a refractor plate for wavelength scanning. Their results are based on the assump- tion that the experimental profile is a Voigt profile of which the Gauss (or Doppler) component of the half-width and the a parameter can be determined with a curve-fitting procedure. The Gauss and Lorentz components are then split separately, into an instrumental and a physical part, using quadratic de-convolution for the Gauss components and linear de- convolution for the Lorentz components.
(d) Batal and Mermetg calculated line widths for nine atomic or ionic lines of Ca, Mg and Sr on the basis of Doppler broadening ( T = 5000 K) and van der Waals interaction.
(e) Broekaert et al.9 determined the widths of 18 lines of 16 rare earths using a spectrograph provided with an order sorter. They used the same method and equipment as had been used previously by Laqua et ~ 1 . 1 0 for the measurements of the widths of 67 lines of 40 elements emitted from four types of d.c. arc and a soft spark.
514 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
(f) Using high-resolution Fourier transform spectrometry (FTS) Faires et af.11 determined the widths and shapes of 81 Fe I lines in the spectral range 290-390 nm.
(8) Boumans and Vrakking6 determined line widths with a 1.5-m echelle monochromator with pre-disperser. They covered 16 Fe I lines (364-384 nm) for comparison with the results of Faires et al. 11 and subsequently 13 lines of nine other elements.
Recently, Boumans and Vrakking12 extended the latter approach to ca. 350 prominent lines of 65 elements. This work will be considered more extensively in the next section.
New Data Published at the End of 1986 As in the initial approach6 for the line-width measurements Boumans and Vrakking used a 1.5-m echelle monochromator with pre-disperser, the characteristics of which have been described previously.6.13 If such an instrument is used for line-width measurements, two conditions must be fulfilled: (i) it should be possible to adjust the spectral band width so that it matches the physical line widths, and (ii) the band width should be accurately known.
Generally, the practical spectral band width of a dispersive spectrometer consists of three components: resultant spectral slit, diffraction width and a contribution from aberrations. The resultant spectral slit is the product of the largest slit width and the reciprocal linear dispersion. The latter quantity can be calculated according to the procedure reviewed in recent literature. 6,1&16
At the slit widths used with the echelle monochromator,h the diffraction width is negligible, but the contribution from aberrations is large, which appears to be a feature of all dispersive spectroscopic instruments.14
Initially Boumans and Vrakking6 determined the contribution from aberrations by measuring the widths of hollow-cathode lines, but experienced the problem that the value of the aberration correction varied with the kchelle angle. This difficulty could be solved by avoiding small echelle angles and using the echelle then at off-blaze settings at the opposite angle in the next high order.12 The contribution from aberrations then enters the formula for the band width as a constant correction of the slit width. The value of the correction was finally adjusted so that the results of line width measurements for iron lines were, on average, identical with those of Faires et ~1.11 who used high-resolution FTS with negligible instrumental broadening. The widths subsequently measured for the lines covered by Hasegawa and Haraguchi’ and Kawaguchi et af.4 were found to be intermediate between the results reported by the latter two groups of authors. In view of these agreements the approach was considered to be reliable enough to be extended to about 350 prominent lines of 65 elements, of which the four to five “most” prominent lines were usually covered. More lines were included for Au, Cr, Eu, Hf, Ho, Lu, Mo, Nb, Ni, Pd, Ru, V and W.
The measurements were made in the analytical zone (12-mm observation height) of a conventional 50-MHz argon ICP, operated at 1.15 kW. The spectral band width varied between 1.3 and 3.8 pm, depending on wavelength, and was almost always smaller than 1.5 times the found physical line widths.
Each measurement comprised a computer-controlled step- wise scan of the effective line profile. The data were stored on disks and subsequently plotted using a five-point, second- order Savitzky - Golay fit.17 Examples are shown in Figs. 1-3. The effective line width (EFW) was determined “manually” in the plot. The physical line width (PHW) was calculated from
PHW = d ( E F W * - B W 2 ) . . . . (1) where BW is the practical band width.
The Doppler width was computed for a temperature of 6300 K, that is, the temperature which, according to the measure- ments by Faires et al.,11 is likely to prevail under the
Wavelength
Fig. 1. Examples of effective line profiles with virtually Gaussian shapes for which the physical width found is close to the Doppler width if a Doppler temperature of 6300 K is assumed.12 Spectral band width, 2.35 pm. ( a ) Tm I1 313.126 nm, PHW = 1.4 pm; (b ) Be I1 313.042 nm, PHW = 6.4 Dm. (ReDroduced with Dermission from Boumans, P. W. J. M., andbrakkini, J. J. A. M., Sp’ectrochirn. Acta, Part B , 1986,41, 1235)
Wavelength
Fig. 2. Effective profile of Co I1 238.892 nm as an example of a line with unresolved HFS.12 The Co line has an apparent physical width of 5.7 pm (a = 2.4) and is compared with a simple Fe line of about the same wavelength having a physical width of 2.1 pm. Spectral window is 16.7 pm. (Reproduced with permission from Boumans, P. W. J . M., and Vrakking, J. J. A. M., Spectrochim. Acta, Part B , 1986,41, 1235)
c
Ho379.675 I
Wavelength
Fig. 3. Effective profiles of four lines for which complex HFS is evident. Horizontal lines indicate the apparent physical widths. a-f refer to the peaks of HFS components which were identified and whose wavelengths are included in the “atlas of spectral scans” in reference 12. (ReproducedwithpermissionfromBoumans, P. W. J. M., and Vrakking, J . J. A. M., Spectrochim. Acta, Part B , 1986,41,1235)
JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2 515
experimental conditions used. The calculation of the a parameter from the measured physical line width and the Doppler width then provided, in principle, an estimate of the contribution from Lorentz broadening. Actually, however, the values of the a parameter served as an indication of the presence or absence of HFS. It was known from previous w0rk4~63~Jl that the lines emitted from an argon ICP generally show little Lorentz broadening, H and Ar lines being the exceptions. This was confirmed by the present measurements in that, for the majority of the lines, the values of the a parameter varied between 0 and 0.5. Therefore, an a value of 0.5 was chosen as a criterion for assessing the plausibility of HFS. Evidently this is a reasonable, but not rigorous, criterion. HFS became just discernible when a was larger than ca. 2 and was clearly revealed when a exceeded a value of 3, as is illustrated in Fig. 3. In these instances the components of the HFS composites were identified using the tabulated wavelengths18 of narrow lines of other elements as references.
The main results are presented12 in the following forms: (a) A table with wavelengths, physical line widths, Doppler
widths and a values, of which a sample page is reproduced as Table 1.
(b) An atlas of some 90 effective profiles of HFS compo- sites, of which Fig. 3 provides examples. The last column of Table 1 refers to the figure numbers of the profiles in the atlas.
(c) A tabulation of the wavelengths of HFS components which are of potential interest in spectrochemical analysis as separate prominent analyses and/or interfering lines.
The entirety of the results can be basically summarised as follows:
(i) Many prominent ICP lines show chiefly Doppler broadening (a < 0.5). The physical widths of these lines lie between 0.9 and 1.2 pm for heavy elements and between 4 and 8 pm for light elements. Fig. 1 provides two examples; the narrow profile of Tm I1 313.126 nm, for which PHW = 1.4 pm (a = 0.05), and the broad profile of Be I1 313.042 nm, for
Table 1. Sample page from the complete table in reference 12 listing the measured physical widths (Ahphys), the Doppler widths (Ah,) calculated for T = 6300 K, and the corresponding a values for the 350 prominent lines covered. Column 2 states the concentration at which the measurement was made, while the last column refers to the figure if included in the atlas of spectral scans. (Reproduced with permission from Boumans, P. W. J. M., and Vrakking, J. J. A . M., Spectrochirn. Acta, Part B , 1986,41, 1235)
Spectral line/ nm
Ag I1 224.641 Ag I1 243.779 Ag I 328.068 Ag I 338.289 A1 I 237.312 A1 I 308.215 A1 I 309.271 A1 I 396.152 Ar I 415.859 As I 193.696 As I 197.197 As I 200.334 As I 228.812 Au I 197.745 Au I1 200.081 Au I1 208.209 Au I1 211.068 Au I 242.795 Au I 267.595 B I 208.893 B I 208.959 B I 249.678 B I 249.773 Ba I1 230.424 Ba I1 233.527 Ba I1 455.403 Ba I1 493.409 Be I 234.861 Be I 249.473 Be I1 313.042 Be I1 313.107 Bi I 206.170t$
* HFS is perceptible if a > 2; otherwise the line only appears broadened or asymmetrically distorted. 1- Partly or completely resolved HFS: the wavelengths and widths of completely resolved components are listed here; the wavelengths of all
$ Wavelength of the centre of the quintet structure (Fig. 3 in this paper) determined to be 206.155 nm using Cr 206.149 as reference. identifiable components are stated in the relevant figure caption and in Table 6 of the original paper.
516 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
which PHW = 6.4 pm (a = 0.15). The Be line can be used to measure changes in Doppler temperature because the absolute change in line width with temperature is relatively large, owing to the small atomic mass of Be. Thus it was found, for example, that the Doppler temperature in the. ICP increased from the assumed 6300 K to 7400 K when the power was increased from 1.15 to 1.65 kW.
(ii) Substantial broadening, most probably resulting from unresolved HFS, was found for lines of Co, Mn, Pb, Pt, Sb and V. As an example, Fig. 2 contrasts Co I1 238.892 nm (PHW = 5.7 pm, a = 2.4) and Fe I1 239.562 nm (PHW = 2.1 pm, a =
(iii) Very broad structures with partly or wholly resolved HFS were found for Bi, Eu, Ho, In, La, Lu, Nb, Pr, Re, Ta and Tb. The separate components of these structures showed mainly Doppler broadening. A complete analysis of the complex structures is possible with curve-fitting techniques.19
Fig. 3 shows four examples. The horizontal line in each frame represents the “apparent line width,” that is, the width of the line when the structure is unresolved. Analytically this width is of interest with regard to the behaviour of the signal to background ratio (SBR) of the line, as is discussed below.
0.20).
Two main conclusions were drawn from this work: (1) The knowledge of the physical widths of a great number
of prominent lines will permit an accurate calculation of the effect of spectral band width on “conventional” detection limits (smooth background) and thus allow unambiguous comparisons of detection limits in real situations.
(2) It appears possible to set up an interference library (software) for ICPs based on physically resolved spectra from which, for any spectroscopic instrument, the effective spectra can be computed to assess the interferences and to select the best analysis lines a priori or a posteriori for any specified sample type, if an appropriate criterion is specified. These points will be elaborated on in the following sections.
Breakdown of Detection Limits Rigorous Comparison of Detection Limits
The knowledge of the physical widths of a great number of prominent lines permitted (i) a rigorous comparison20 of three extensive sets of detection limits reported for different argon ICPs and (ii) the establishment of “standard” values for a 50-MHz ICP and 15 pm spectral band width. These values may be considered as being representative of the performance of the conventional argon ICP. The principle of this approach originates from the work of Laqua and co-workers.10.21 Recently, Boumans and Vrakking applied this approach to ICP detection limits, first tentatively, using empirical approxi- mations,22 then rigorously,20 using the values of the physical line widths discussed above.
The approach implies the breakdown of detection limits into the factors contributed by the SBR characteristics of the source, the spectral band width of the spectroscopic apparatus and the noise characteristics of the complete system (source and spectroscopic apparatus). The following sections discuss the relationships involved and their application to an assess- ment and comparison of detection limits reported by Winge and co-workers,23.24 Wohlers2S and Boumans and Vrakking.20
Relationships 10,13,20,21,2628
For a smooth, featureless background the detection limit (q) can be formulated as
cL = 2 V 2 (0.01 RSDB) c@BR . . (2)*
* For fundamental reason^,*^^^* equation (2) is written with the factor 2 ~ 2 instead of the commonly used factor 3; numerically the difference is immaterial.
SBR is the signal to background ratio for an analyte concentration cO:
SBR=XA/XB . . . . * (3) where xA is the net analyte signal and xB the background signal.
RSDB is the relative standard deviation of the background signal (“/o), which can be written as
RSDB = (G + P / x B + Y/X;)’” . . . . (4)
where the terms in parentheses account for flicker noise, shot noise and detector noise, respectively. In ICP-AES, the flicker noise coefficient (aB) is usually 0.5-1%. The value of the shot noise coefficient (P) depends on the units in which XB is expressed.26 In the case of photon counting P = lo4 if RSDB is expressed as a percentage.13 For a good photomultiplier, detector noise is negligible ( y = 0).
A measured SBR can be written as the product of two factors:
(SBR)meas = fopt(SBR)source * - * * ( 5 ) where (SBR),ource is the SBR at infinite resolution (BW = 0) andfop, is the factor by which this “source SBR” is modified by the spectroscopic apparatus (BW > 0).
In view of equations (2) and ( 5 ) , a ratio R(I/JI) of two detection limits obtained with methods I and I1 can be written as the product of three factors:
R(I/II) = FnoiseFoptFsource * - . - (6) where
Fnoise = RSDB(I)/RSDB(II) . . . . (7)
Fopt = fopt(IIYfopt(1) * . . . * . (8) and
Fsource = SBRso”rc,(II>/SBR,ou~c~(I) * (9) Equation (6) was applied to data sets for which R(I/II) and
Fnoise are known and Fop, can be computed from the known spectral band widths and physical line widths. The latter calculation is based on the following, experimentally established dependence of fop, on BW and PHW:
fopt = 1 if PHW > BW . . . . (10)
. . (11)
. . (12)
fop, a l/m if PHW < BW < 2 PHW
fopt a 1/EFW if BW > 2 PHW where EFW is the effective line width [cf., equation (l)]:
EFW = d(PHW2+BW2) . . . . (13) The significance of equations (10)-(12) is illustrated by the
data in Table 2 and Fig. 4 (see also the Appendix). Table 2 shows in a self-explanatory way the calculated effect of a change in spectral band width from 20 to 3 pm in terms of the ratio of the effective line widths and the ratio of the corresponding values of fopt for spectral lines with different physical widths. Fig. 4 depicts the profiles of the narrow Mo line at 317.0 nm and the broad Nb line at 309.4 nm, measured at two spectral band widths. For the Mo line, an increase in band width by a factor of ca. 3 results in a reduction of the SBR by a factor of 2.6, whereas for the Nb line hardly any change in SBR is observed. The results for the Nb line clearly demonstrate that a line behaves as a continuum when the spectral band width is smaller than the physical line width.
Comparison of Three Sets of Detection Limits20 The experiment involving the line-width measurements12 discussed above also covered the measurement of the SBRs and background signals for the 350 prominent lines emitted by the 50-MHz ICP. The latter measurements were not made at
JOURNAL O F ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2 517
Table 2. Effect of a change in spectral band width from 3 to 20 pm on the effective width (EFW) and fopt for prominent lines with different physical widths (PHW). The effect is expressed in terms of the ratios EFW(20)/EFW(3) and f0pt(3)/f0pt(20). [Reproduced with permission from Boumans, P. W. J. M., Labstract, 1986, No. 3, 8 (Philips Nederland, Eindhoven)]
Spectral line nm
Au I1 200.081 U I1 263.553 Mo I1 202.030 Nb I1 269.706 Ag I 328.068 Lu TI 261.542 V I1 311.071 La I1 408.672 B I 249.773 Be I1 313.107 Co I1 237.862 V I1 290.882 Co I 345.350 Lu I1 307.760 La I1 398.852 Nb I1 309.418 Ho I1 347.426
Fig. 4. Examples illustrating the effect of an increase in spectral band width (BW) by a factor of about three on the SBRs of two lines with widely differing physical widths (PHW). They include the values of the effective line width (EFW) and SBR. All line widths are expressed in pm. The SBR of the Nb line has been measured with respect to a blank, because a back round measurement within the narrow spectral window would inclufe a substantial contribution from the line wing
the spectral resolution used in the line-width measurements, so-called “physical high resolution” (PHR), but at a resolution level compatible with analytical measurements, for conven- ience designated “analytical high resolution’’ (AHR) . This is the resolution achieved at the optimised slit width, thus the resolution at which the best compromise is found between the effect of the spectral band width on the shot noise contribution to RSDB and its effect on the SBR, as has been discussed previously. 1328 The practical spectral band width correspond- ing to AHR ranges from 4 to 12 pm, depending on wavelength. 13.27
The availability of numerical values of SBR and background signal for the 350 lines implies the availability of numerical values of the detection limits, because for the ICP spec- trometer used, RSDB is a unique function of the background signal (XB)13:
RSDB = 10.52 + 104/~B]1’2 . . . . (14) where RSDB is expressed in % and XB in counts [cf. , equation
Detection limits determined thus for the 50-MHz ICP and AHR are listed in column 2 of Table 3, which is a sample page from the complete data set.20
These detection limits were compared with those reported by Wohlers25 for a 27-MHz ICP, measured at a 24-pm band width, and those of Winge and co -worke r~23~~~ for another 27-MHz ICP, determined at a 17-pm band width. Columns 4 and 5 of Table 3 list these detection limits, while columns 6 and 7 show the ratios RWoH and RWIN with respect to the detection limits in column 2 for the 50-MHz ICP and AHR, thus for a band width between 4 and 12 pm. Obviously, both sets of detection limits for 27-MHz ICPs lag substantially behind those for the 50-MHz ICP.
To what extent are the differences attributable to a difference between the sources?
This question can be rigorously answered by application of the breakdown approach outlined in the previous section. In practice this involves the calculation of Fsou,c- from equation ( 6 ) , explicitly:
(411.
. . . . . R( 1/11) Fsource =
r noiseropt
where for R(I/II) the experimental values of RWoH or RWrN (Table 3) must be substituted and the values of Fnoisc and Fopt are found from equations (6) and (7), as follows.
(a) For both the Wohlers25 and Winge and co-workers23J4 data sets RSDB has been assumed to be 1%; therefore, in equation (6), RSDB(1) = 1%. The value of RSDB for the 50-MHz ICP, thus RSDB(I1) is calculated from equation (14) from the measured values of xB.
(b) Fopt is calculated from the known values of the band widths and the physical line widths, as discussed in the previous section. The results are listed as FWoH and FWrN ( “ F factors” or “source SBR ratios”) in columns 8 and 9 of Table 3.
From the complete results20 it was concluded that the 50-MHz ICP gave a SBR advantage of a factor of 3-15 with respect to the ICP used by Winge and co-workers and a factor of 2-6 with respect to the ICP used by Wohlers, on average factors of 6.5 and 3, respectively,
Interestingly, the scatter of the source SBR ratios ( F factors) among the elements was found to be reasonably small in the comparisons considered, namely a factor of 1.5 on the basis of one standard deviation for a log-normal distribution. This indicates that, aside from a constant factor, SBRs can be transferred from the one ICP to another, if all SBRs are measured under ICP compromise conditions, as happened in the considered situations.
“Standard” Detection Limits for the Conventional ICP
To facilitate comparisons between detection limits the results for the 50-MHz ICP and AHR were also converted into values that apply at medium resolution, defined by a spectral band width of 15 pm. These normalised values are listed in italics in column 3 of Table 3. They may be considered as standard values for the conventional argon ICP.
The consideratioin of these detection limits may throw a different light on results that have been published in recent years for high-efficiency ICPs29 or ICPs generated with novel types of torches.30 Authors have gladly used the data of Winge and co-workers for comparison, either as they appeared in the publications from Iowa State University23.24 o r in the form
518 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
Table 3. Sample page from the complete table in reference 20 listing detection limits (c,), ratios of detection limits (R) and ratios of source SBRs ( F factors), as detailed in the text. The detection limits are defined on the basis of 2 f i I e q u a t i o n (2)]. (Reproduced with permission from Boumans, P. W. J. M . , and Vrakking, J . J. A . M., Spectrochim. Acta, Part B, 1987, 42, 553)
Detection limit/ng ml-I
Spectral line/ nm
Ag I 328.068 Ag I 338.289 Ag I 243.779 Ag I1 224.641 A1 I 309.278 A1 I 396.152 A1 I 308.215 A1 I 237.312 As I 193.696 As I 197.i97 As I 228.812 As I 200.334 Au I 242.795 Au I 267.595 Au I1 208.209 Au I 197.745 Au I1 211.068 Au I1 200.081 B I 249.773 B I 249.678 B I 208.959 B I 208.893 Ba I1 455.403
Ba I1 233.527 Ba I1 230.424 Be II 313.042 Be f 234.861 Be I1 313.107 Be I 249.473
stated in Boumans' line coincidence tables31 or a related publication.32 The latter detectim limits were directly based on the measurements of Winge and co-workers and therefore do not differ essentially from their results. Doubtless, it is encouraging to use rather poor data as standards of compari- son, but it may put innovations into a biased perspective.
We have shown on various occasions that a conventional argon ICP can yield detection limits that are much better than those of Winge and co-workers and not only in combination with high-resolution apparatus. 13&%,28,33 The fact that we have used such apparatus in the past few years may have confused the situation to some extent, but in reality, the profit of high resolution (HR) compared with medium resolution (MR) is less than a factor of 3 for detection limits in pure aqueous solution.1-13,27,28 The detection limits at HR may be even worse than at MR, as c>n be seen in Table 3 for lines of low wavelengths. This is due to increased shot noise.lJ3.28
The publication of the extensive set of new data20 aims at putting this point into the correct perspective, also in comparisons of detection limits obtained with either disper- sive spectrometry or FTS.3"36 Here, too, the use of rather poor data as being representative for dispersive spectrometry and a conventional ICP may easily bias the appreciation.
Alternatively, the availability of data on line widths12 and the description of how these can be used to account for the contribution of the spectrometer to the detection limits20 may be helpful towards interpreting experimental values of detec- tion limits more rigorously. As a further aid, the Appendix in
this paper gives a simple algorithm for the band width conversion of SBRs (and detection limits).
Generally, a rigorous interpretation of detection limits requires the availability of more information than the mere values of these detection limits. Either the SBRs of the lines or the RSDs of the background signals should also be known, in addition to an accurate value of the practical spectral band width, not just the dispersion and the slit width, or the theoretical spectral band width (= spectral slit). Aberrations or trivial and unnoticed optical misalignments tend to make an important contribution to the practical spectral band width. In fact, the latter can be easily determined with the aid of relatively narrow lines emitted from the ICP. Therefore, one measures the effective line width and calculates the band width according to
BW=d(EFW2-PHW2) . . . . (16)
The use of narrow lines minimises the error, but generally it will not be necessary to use a hollow-cathode lamp. Lines emitted from an ICP by elements such as Ni, Mo or W are narrow enough12 to be used for reliable band width measure- ments. In addition, these elements provide lines over an extended wavelength range so that the variation of the band width with wavelength, common to kchelle spectrometers, but also inherent in MR to HR grating instruments,6J416 can be conveniently covered.
519 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
Detection Limit Including Selectivity as a Criterion for Line Selection
Quantification of the Effect of Line Overlap on the Detection Limit
Detection limits for pure water are indispensable figures of merit, but do not necessarily apply to real-sample analysis. I t is well known that the concomitants of a sample can drastically worsen the detection limits, in particular, as a result of line overlap. This section concerns the quantification of this effect. 37
Fig. 5 serves as the starting-point and shows two spectral scans. The lower scan represents the profile of an interfering line as obtained on a blank solution of the interferent. The upper scan represents the profile for the solution of the interferent spiked with analyte.
At the wavelength h, of the analysis line we have three signals: the background signal xg, the net interfering signal x I and the analyte signal xA. (i) The background signal XB is the signal that can be rationally considered as the smooth background level in that wavelength region so that its magnitude can be unambiguously determined by a measure- ment outside the structure. (ii) The net interfering signal XI is that part of the signal contributed by the interferent at the wavelength h, of the analysis line which cannot be covered by the measurement of xB, but must be derived from an additional measurement. The latter may be either a measure- ment at h, during the aspiration of a blank solution or a measurement at a wavelength of another line of the interferent during the aspiration of the sample (cf. Fig. 2 in reference 37). In the former instance it must be ensured that the blank solution yields a spectrum identical with that of the sample blank; in the latter, the ratio of the two signals of the interferent must be constant.
The equations for the detection limit, the SBR and the RSD of the background signal can now be written as
(SBR)BI = xA/xBI . . . . . . (18)
RSDBl = (a: + + ([j/xBI + Y/X;,)’” . . (19)
These equations differ from equations (2)-(4) in two respects: (a) XB has been replaced by xBI (B1 = blank); and (b) the expression for the RSD of the background signal [equation (19)] contains an additional flicker noise term a:, associated with the determination of the net interfering signal. It is this term which introduces an essential difference between the situation of smooth background and the case of line overlap.
To appreciate the effect of a: on the detection limit one must distinguish between the two approaches for measuring XI
xB I I A -
Wavelength
Fig. 5 . Profile of an interfering line (blank) and resultant profile of interfering and analysis lines (spiked) to illustrate the meaning of the quantities: net analyte signal xA, net interfering signal x I and background signal xB.3’ The arrow marks the peak wavelength of the analysisline. (ReproducedwithpermissionfromBoumans, P. W. J . M., and Vrakking, J . J . A . M.. Spectrochim. Acta, Part B , 1987,42,819)
referred to above: the direct determination using a blank solution and the indirect determination using a reference signal of the interferent.
(i) In the direct determination the blank is measured with a fixed wavelength setting of the spectrometer (“static measure- ment”). Under these idealised conditions, the additional flicker noise term will be small; moreover, its contribution to RSDBI will be partly compensated for by a reduction of the shot noise term. Therefore, a series of successive intensity measurements based on 10-s integrations, for instance, will generally yield a value of RSDBI that is only slightly higher than the value of RSDB found for the pure solvent.13 Hence the chief effect of the line interference on the detection limit would be a marginal effect from a decreased SBR. We have called this the “Conventional detection limit.” I Although it can be measured by an unambiguous procedure, it is in general an unrealistic quantity, because its determination underlies the postulate that the blank of all samples is exactly the same as the separately measured blank. This situation will hardly ever be found in real sample analysis. Commonly the concentrations of the concomitants vary for each sample, which necessitates a separate indirect determination of the interfering signal in each sample.
(ii) The indirect determination of the net interfering signal requires measurements at various wavelength positions for each sample separately. This “dynamic measurement” will yield a substantially higher value of at than the “static measurement,” since ( ~ f will now reflect the effects of variations in sample composition, variations in the excitation conditions between samples and instabilities in the wavelength setting such as those occurring in slew-scan spectrometers. It is the latter value of at which dictates RSDBl and thus the “true detection limit” in the case of line overlap. Unfortunately, this realistic value of a: cannot be measured simply in daily practice and actually can only be approximately determined via model experiments.
Using the latter approach, Boumans and Vrakking27-3s arrived at an approximation, which makes it reasonably possible to take the effect of a: into account and at the same time can be used in common practice. The starting-point of this approach is the limit of determination, cD, which, as usual, was defined as the concentration which can be determined with an RSD of 10%. The concentration CD is a function of the errors in the background and the net interfering signals. Boumans and Vrakking made it plausible that with line overlap cD can be approximated by
. . .
where SA is the sensitivity of the analyte signal. The first term in equation (20) is twice the analyte
concentration equivalent of xI. The value of 2 for the coefficient is not based on a rigorous treatment, but is merely an estimate,27,28 which, however, links up well with practical experience.lJ9 The first term in equation (20) links the limit of determination with the selectivity, the quotient SA/xI being proportional to the “line selectivity,” that is, the ratio of the net line signal and the net interfering signal, or generally the sum of the interfering signals.27 The selectivity term in equation (20) replaces a complex expression which, in a rigorous treatment, would be necessary to account for the various error sources in the case of line overlap.
The second term in equation (20) is five times the conventional detection limit, that is, the detection limit defined by equations (2)-(4) but conventionally determined by static measurements on a blank solution. This second term has been introduced for reasons of continuity: when the net interfering signal decreases to zero, the equation should yield the classical relationship between the limit of determination and the limit of detection.’.2”40.4’
As it is customary to look primarily at limits of detection rather than limits of determination, Boumans and Vrakking37
c3n JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
finally defined the “true limit of detection” with line overlap to be
where cD is given by equation (20). Substitution then yields
In the event that more than one component contributes an interfering signal, xI should be understood as the sum of the various net interfering signals.
To conclude, equation (22) takes into account both the selectivity and the detection limit that is classically reached when the selectivity becomes infinite. This approach clarified two points:
(i) It brings a quantitative understanding of the effect of spectral resolution on analytical performance.l.2J7-38-42343
(ii) It provides a quantitative criterion for line selection for any sample composition and spectral resolution.37
The use of equation (22) for line selection will be illustrated in the next section for the determination of traces of indium in binary mixtures of tungsten and molybdenum. The prime target of that discussion is to show how the problem of line selection can be quantified, what data are required and how these data can be derived from spectral scans. The complete treatment of the problem in the original paper37 also covers the effects of the spectral resolution, the solid concentration in the solution and the ICP operating conditions.
Line Selection for the Determination of Traces of In in a Binary Mixture of W and Mo: Classical Table
The analyst is asked to choose the best In line(s) for the determination of In traces in binary mixtures of W and Mo, the composition of which may vary from pure W to pure Mo. Consultation of lists of prominent ICP lines2”-25Jl will primarily lead to the four In lines listed in Table 4, which includes the conventional detection limits and the spectral band widths for HR and MR. Unfortunately, none of the present wavelength tables contains sufficient information on the ICP spectra of W and Mo to select a line which is “free from interference.” If such data were available in the form of a classical table, they would look as shown in Table 5 , which lists the wavelengths and ICP sensitivities of all relevant lines as derived from HR spectral scans for pure In, W and Mo solutions. The reader may attempt, as we did, to select optimum analysis lines on the basis of the data in Tables 4 and 5. Doubtless the reader will then experience the uneasy feeling that, in spite of the abundance of relevant data, he or she cannot make a rigorous decision.
We state the problem in this form because it clearly reveals that with the classical approach there is no firm basis for line selection even if the available data are entirely complete and relevant. It is only by rigorous calculations that line selection can be lifted from the qualitative “yesho domain” to the domain of unambiguous quantification, which not only tells whether an analysis “goes” or “does not go,” but also indicates accurately what is analytically still possible under the circumstances given.
Actually, to quantify the problem, data different from those in Tables 4 and 5 should be derived from the spectral scans.
* A critical examination of the approach made by Boumans and Vrakkingz’ indicates that they could also have adopted a different starting-point to arrive at essentially the same results. They chose the limit of determination (10% error) as the prime figure of merit to assess the adverse effects of line overlap on analytical performance under realistic, dynamic measurement conditions. Alternatively, they could have adopted the “true limit of detection” ( c ~ , ~ ~ ~ ~ ) as a starting-point, defining it as the concentration which can be determined with an RSD of 50”/0.~O Afterwards, it appears that this starting-point was avoided for “psychological reasons.” Whatever i t was, the results would have been entirely the same.
Table 4. Detection limits of In lines in pure aqueous solutions for the “soft” conditions specified37 at high (HR) and medium resolution (MR), as defined by the spectral band widths stated. The detection limit is defined by equation (2) and refers to a 10-s integration time. (Reproduced with permission from Boumans, P. W. J . M., and Vrakking, J . J . A. M., Spectrochim. Actu, Part B , 1987, 42, 819)
Spectral line/ nm
In I1 230.559 In I1 230.606 In I1 230.612 In I 325.609 In I 303.936 In I 451.131
Detection limit/ Spectral ng ml- band widthlpm
H R MR H R MR 21 24 13 3.6 10.9 29 4 7 5.0 14.9 8 10 5.1 14.7
11 30 7.3 22.1
- - -
- - -
Table 5. Classical table of data relevant to the selection of the best In line for the determination of traces of In in a binary mixture of W and Mo.” The table lists the peak wavelengths h (in nm) of the lines, the distance Ah (in pm) of potentially interfering lines to the respective In lines and the peak sensitivities S (in counts per 10 s per kg ml-1) for “soft” ICP conditions and HR. (Reproduced with permission from Boumans, P. W. J . M. , andvrakking, J . J. A. M., Spectrochim. Acta, Part B , 1987,42, 819)
h Ah S MO 230.585 -21 130 W 230.590 -16 8.4 W 230.596 -10 4.5 MO 230.596 -10 4.7 MO 230.600 - 6 3 .O In 230.606* 0 2400 W 230.614 + 8 1.1 W 230.626 +20 1.1 MO 303.906 -30 640 W 303.933 - 5 500 In 303.936* 0 37000 W 303.958 +22 390 Ar 451.073 -58 -
In 451.131* 0 37000 W 451.122 - 9 45
* Analysis lines.
h Ah MO 230.585 -27 W 230.590 -22 W 230.596 -16 MO 230.596 -16 MO 230.600 -12 In 230.612* 0 W 230.614 + 2 W 230.626 +14
In 325.609* 0 Mo 325.622 +13 W 325.623 +14
W 325.596 -13
S 130
8.4 4.5 4.7 3.0
1.1 1.1
2000
210 90 000 2 600 360
Line Selection for the Determination of Traces of In in a Binary Mixture of W and Mo: Equation (22)
As an example, Fig. 6 shows spectral scans of In I1 230.606 nm; a detailed explanation of the figure is given in the legend.
At HR the In line is a resolved triplet: 230.598,230.606 and 230.612 nm. 12,13,18 In 230.606 nm does not experience line interference from W, while In 230.612 nm is free from line interference from Mo. At MR, both W and Mo contribute net line signals at the peak (230.606 nm) of the unresolved In line. From the printouts of the scans it followed that W and Mo each produce, at both HR and MR, background enhancements due to line wings.44
We now consider how the data implied in these scans can be quantitatively used, where “quantitative use” means the calculation of the true detection limit as a function of the sample composition according to equation (22):
The net interfering signal x I can be written as
XI = c ~ S I , ~ + C Z S ~ , ~ . . . . . . (23)
where c is concentration and SI the sensitivity of the net interfering signal with subscript 1 for W and 2 for Mo. In agreement with experimental evidence,44 all signals are assumed to be additive.
JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2 521
Wavelength
Fig. 6. Spectral scans in the vicinity of In 230.606 nm. Spectral window 0.050 nm.37 Each frame contains two scans: the lower ones are for the pure matrix, the upper ones for the matrix spiked with the analyte. (a)-(d) The W matrix and (e)-(h) the Mo matrix. The matrix concentration is 1 mg ml-I. Analyte concentration c is expressed in pg ml- l . Where appropriate, an arrow marks the wavelength position of the analysis line. The scans are for "soft" excitation conditions. (Reproduced with permission from Bournans, P. W. J. M., and Vrakking, J . J. A. M., Spectrochim. Acta, Part B , 1987, 42, 819)
The measurement of the three sensitivities SA, SI,l and SI,2 for the pure solutions of the analyte and the two interferents permits the calculation of the first term in equation (22) for any composition of the binary mixture.*
For the calculation of the second term we proceed as follows. We write for the conventional detection limit
CL,BI = ~ ~ ~ ( O . O ~ R S D B ~ ) X B I / S A . . . . (24) This is essentially equation (17) in which C~I(SBR)BI has been replaced by the equivalent expression xBI/SA.
The total background signal xB1 is made up of three contributions :
xBI = x B + XW + X I . . . . . . (25)
where xB is the background signal for the pure solvent and xw the background contributed by the two interferents as continua and/or line wings. This contribution can be built up additively from the separate contributions44:
where Sw.l and SW,* are the corresponding sensitivities, which can also be determined for pure solutions of the interferents. Thus xB1 in equation (25) can be calculated for any sample composition.
There remains the last quantity, RSDBI. Generally it may be calculated using an equation of the form of equation (4) and not equation (19) because the first term in equation (22) accounts for the additional noise from the interfering signal. Therefore, for the system used in this work:
RSDBl = (0.52 + lO4/xBI)li2 . . . . (27) in analogy with equation (14).
In summary, the experimental measurement of the solvent background xB, the analyte sensitivity SA and the sensitivities SI.], S1.2, Sw,l and Sw.z of the interfering signals provides all the essential data needed for the calculation of the true limit of detection for any composition of the binary mixture. These data can be derived from spectral scans.
Table 6 lists such data for the four In lines as derived from MR spectral scans. The sensitivities and the background signal
XW = c ~ S W , ~ + C ~ S W , ~ . . . . (26)
* The original paper37 also covers possible contributions from the pure solvent plasma (Ar lines and band components).
Table 6. Experimental values of the sensitivities (S) of the analytc signals, net interfering line signals, and wing signals and thc background contribution ( x B ) from the pure solvent p l a ~ r n a . 3 ~ The sensitivities and background signal refer to MR and are stated in counts per 10 s. (Reproduced with permission from Bournans, P. W. J . M., and Vrakking, J . J. A . M., Spectrochim. Acta, Part B , 1987,42, 819)
are stated in counts per 10 s, with the understanding that the eventual analysis is based on 10-s integrations at fixed wavelength positions rather than on scans. Clearly, the integration time is relevant only in the calculation of RSDBI.
Fig. 7 shows the detection limit of In for the four In lines as a function of the Mo concentration, whereby the total concen- tration of W and Mo has been assumed to be 1 mg ml-1. The curves have been calculated with the aid of equations(22-27) using the data in Table 6. Evidently, up to about 0.2 mg ml-1 Mo, In 325.6 nm is the best line, while for higher Mo concentrations In 451.1 nm is optimum. Note the position of the curve for In 303.9 nm high in the diagram. This line cannot compete because it suffers a severe overlap from a W line, as is illustrated by the scans in Fig. 8. The effect of this coincidence is unambiguously revealed and quantitatively expressed in a diagram of the type shown in Fig. 7.
As a further illustration of the approach we consider what happens if the spectral resolution is changed from MR to HR. Qualitatively the effect of this change is seen in the spectral scans (Figs. 6 and 8 and the corresponding figures for In 325.6 and In 450.1 nm in reference 37). Quantitatively the effect is expressed in terms of a diagram similar to that of Fig. 7. Such a diagram is included and discussed in reference 37. Here we confine discussion to the final result, shown in Fig. 9, which contrasts the curves for the best lines (In 325.6 and In 450.1 nm) at MR and HR. The detection limit is expressed here in
522 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
MR
1000 r
I Y
lob 1 0 0.2 0.4 0.6 0.8 1.0
Molybdenum concentrationimg ml-
10
1 I I I I 0 0.2 0.4 0.6 0.8 1.0 Molybdenum concentrationimg ml-
Fig. 7. Dependence of detection limit of indium (ng ml-1) on the composition of a binary mixture of W and Mo with a total metal concentration of 1 mg ml-l for four lines: A, In I , 303.9; B, In I, 325.6; C, In 11, 230.6; and D, In I, 451.1 nm. The detection results refer to medium resolution and “soft” excitation conditions.37 (Reproduced with permission from Boumans, P. W. J . M., and Vrakking, J. J. A. M., Spectrochim. Acta, Part B , 1987,42, 819)
pg g-1 with respect to the dissolved solid for a 1 mg ml-1. metal concentration in solution. *
Fig. 9 demonstrates (i) a drastic effect of the resolution on the optimum line choice and (ii) an appreciable difference in detection power associated with the difference in spectral resolution.
In summary, the application of the true detection limit [equation (22)] as the criterion for line selection implies the quantitative and realistic evaluation of a basic analytical figure of merit for real samples. Therefore the approach permits the calculation, of what is analytically possible with each analysis line of interest, given the composition of the sample and the spectral band width of the spectroscopic apparatus. The result of this calculation then provides a quantitative basis for decisions on line selection. Thus the approach transfers line selection from the nebulous domain of “interferencelno interference” to a domain in which the seriousness of an interference is quantified on a continuous scale and is numerically expressed in terms of an analytical figure of merit with a well defined meaning. Suitable software permits application of the criterion to multi-component samples of whatever degree of complexity.
Although the present discussion covers only the application of the criterion to a priori line selection, it is implicit that the same criterion can be used in a posteriori line selection, and thus in “multiple line analysis,” as used in d.c.-arc methods for general survey analysisl.45 and proposed for It appears reasonable to determine the concentration of an element as the weighted mean of the concentrations found with the various analysis lines, where the weighting factor for each line could be rationally defined as the ratio of the pertinent concentration and the “true detection limit” for that line. As this “true detection limit” depends primarily on the selectivity, such an approach automatically implies the rejection of lines with poor selectivity, i . e . , lines suffering severe line overlap from concomitants.
~~
* The reasons for changing from ng ml-1 to pg g-1 are given in the original paper.37 The change is irrelevant in this context because for a 1 mg ml-1 metal concentration, the two detection limits are numerically equal.
The approach should also be of interest in comparisons of dispersive and Fourier transform spectrometry. It has been shown34,48 that the detection limit in FTS worsens in the presence of concomitants as a result of both an increase in the flicker noise due to strong lines of concomitants and a decrease in analyte sensitivity. In dispersive spectrometry, concomitants may also produce an increase in flicker noise due to line overlap. However, this point is hardly ever quantified. The proposed approach may be helpful towards treating the problem more rigorously and easing comparisons between the two types of spectroscopy.
The Interference Library of the 1990s The criterion for line selection [equation (22)] discussed in the preceding section also indicates how the ideal interference library should look: (i) it must contain the sensitivities of interfering lines and line wings at the wavelength positions of the analysis lines, and (ii) be in such a form that the data can be universally applied to any spectroscopic equipment.
Data such as those presented in Table 6 fulfil condition (i) but lack universality, in that they carry the seal of the spectral instrumental function of the apparatus with which they were collected. Obviously, interference data in the form of a classical table, as shown in Table 5 , are still further remote from the ideal.
The principle of the approach used in Boumans’ line coincidence tables31 meets the conditions for an ideal tabula- tion, as is discussed in references 2 and 37, but the result was not ideal because the line coincidence model and the data base were not entirely adequate.1.2
Recent developments indicate that the ideal interference library is coming within reach, that is, an interference library in the software domain which contains information about analysis and interfering lines in the form of physically resolved spectral data so that the computer can reconstruct actual spectra for any spectroscopic apparatus by convoluting physically resolved spectra with the instrumental func-
It was concluded from the measurement of physical line widths in ICP spectral2 that the physical profiles of all simple lines can be approximated by Doppler profiles, if necessary, extended to Voigt profiles with a d 0.5. This approximation can also be used for complex structures if the wavelengths and relative intensities of the separate components are known. Both simple lines and the separate components of HFS composites can be convoluted with the instrumental function to yield effective line profiles. The total effective profile of complex structures can then be found by superposition of the effective profiles of the components. In this way, the basic data primarily required for the characterisation of ICP spectra can be reduced to peak wavelengths, peak sensitivities, atomic masses and a values. It must be investigated whether a single a value for all lines or separate values for the individual lines are required. Additional data on line wings and recombination continua may also be needed.
Either of two approaches can be adopted for collecting the necessary data: (i) registration of the complete ICP spectra of the elements, or (ii) registration of spectral data in narrow spectral windows centred about prominent ICP lines.
Considering the satisfactory results obtained hitherto with the 1.5-m kchelle monochromator referred to earlier, the present authors are investigating the application of this instrument to approach (ii). 1 9 3 ) For approach (i), high- resolution FTS appears the most promising.sl The future will have to show to what extent these efforts will eventually lead to interference libraries that can be universally applied in ICP-AES. In view of the large amount of work involved in the acquisition, testing and handling of the data, it seems realistic
tion.l,l2,43.49
JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2 523
Wavelength
Fig. 8. with permission from Boumans, P. W. J . M., and Vrakking, J . J. A. M., Spectrochim. Acra, Part B , 1987, 42, 819)
Spectral scans in the vicinity of In 303.936 nm.37 Spectral window 0.067 nm. See legend to Fig. 6 for further explanations. (Reproduced
r
L l E u, 5 . c .- E .- - c 0
a a
.- 4-
c
n I
1 0 20 40 60 80 100
M o l y bde n u m concentration , ‘10
Fig. 9. Dependence of detection limit of indium (pg g-1) with the best available lines, (A, In 1325.6 and B, In 1451.1 nm) on the composition of a binary alloy of W and Mo at high (HR) and medium (MR) res0lution.3~ Total metal concentration in the solution is 1 mg ml-I. (Reproduced with permission from Boumans, P. W. J. M . , and Vrakking, J. J. A . M . , Spectrochim. Acta, Part B, 1987,42,819)
to refer to these data bases as “the interference library of the 1990s. l7
Conclusions The conventional detection limit for smooth background can be formulated as a function of (i) the relative standard deviation (RSDB) of the background signal, (ii) the signal to background ratio (SBR) in the source and (iii) an optical factor v) by which the source SBR is modified by the spectroscopic apparatus. Factor f is a function of the physical width of the line and the practical spectral band width of the spectrometer.
The availability of numerical values for the physical widths of some 350 prominent ICP lines permits the calculation off for these lines and therefore allows a rigorous comparison of detection limits measured with different spectrometers in
different ICPs if, in addition, the values of RSDB and the practical spectral band width are known.
Owing to possible contributions from aberrations andlor optical misalignment, the practical spectral band width does not necessarily equal the resultant spectral slit as calculated from the slit width and the reciprocal linear dispersion. However, the practical spectral band width can be easily measured with the aid of narrow lines emitted from the ICP, e . g . , Ni, Mo or W lines.
Reliable and conservative values of RSDB can be conve- niently determined if RSDB is recognised as a function of flicker noise, shot noise and detector noise.
It has been definitely shown that the source SBRs for the 27-MHz argon ICP used by Winge and co-~orkers*3,24 are a factor of 3-15 poorer than those of a conventional 50-MHz argon ICP. The use of the values produced by Winge and co- workers as standards of comparison thus tends to introduce optimistic bias in assessments of the detection capabilities of novel ICP sources. Detection limits recently determined for a 50-MHz ICP and normalised to a spectral band width of 15 pm are therefore recommended as standard values for the conventional argon ICP.
The effect of line overlap on the detection power can be quantitatively expressed in terms of the “true detection limit,” defined as the sum of the conventional detection limit for smooth background and a selectivity term. The “true detec- tion limit” is dictated by the sample composition and the spectral resolution; therefore, it is an adequate and effective criterion for line selection.
Prominent ICP lines, including the separate components of hyperfine structure composites but excluding Ar and H lines, show chiefly Doppler broadening with a small contribution from Lorentz broadening (a < 0.5). If this feature applies generally, then the data required for an efficient storage of physically resolved ICP spectra can be limited to peak wavelengths, peak sensitivities, atomic masses and u values. Recombination continua must be separately accounted for, while line wings may be described by a single function.44
Modern spectroscopic instruments, such as high-resolution Cchelle spectrometers or high-resolution Fourier transform spectrometers, permit the measurement of physically resolved spectra. The further application of such instruments for data acquisition brings the ideal universal interference library within reach, that is, a compilation of physically resolved spectra, which can be convoluted with the spectral instrumen- tal function of whatever spectroscopic apparatus. A new data base of this type is the only adequate way to solve an old basic problem of atomic emission spectrometry: dealing with spectral interferences.
524 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY, SEPTEMBER 1987, VOL. 2
Appendix Band Width Conversion of SBRs in Practice
For converting SBR values obtained at a particular spectral band width BW1 to another band width BW2 the following practical procedure is recommended.
One calculates, for each of the two band widths, the factorf by which the SBR increases when the band width is reduced to the value where it equals the physical line width. If we denote the two SBRs as SBRl and SBR2 and the factors asfl andf2, respectively, then
F = f l / f 2 . . . . . . (Al)
is the factor by which SBRl has to be multiplied to obtain SBR2:
S B R 2 = F x SBRl . . . . (A2)
As the same procedure is followed for the calculation offl and f2, we formulate this procedure in terms of the single factorf.
(a) The effective line width is calculated from the known band width BW and the listed12 value of the physical line width PHW:
E F W = d P H W 2 + B W 2 . . . . (A3)
(b) To formulate the algorithm we define the transition
E F W L = P H W a . . . . . . (A4) points:
and E F W H = P H W f i . . . . . . (A4)
(c) The algorithm then takes the following form:
If BW d PHW, then f = 1 . . . . . . . . (A5)
and no further calculation is required. If BW d 2PHW, then
f = ~EFWIEFWL
or f = d E F W / ( P H W f i ) . . . . (A6)
else
f = (EFW/EFWH) dEFWWEFWL
f = E F W / ( P H W a ) . . . . (A7)
(d) Procedure: calculate EFW for situations 1 and 2 [equation (A3)]; apply the algorithm to calculate fr and f2 [equations (A5)-(A7)]; calculate F [equation (Al)]; and calculate SBR2 [equation (A2)].
(e) For example, for Mn I1 257.610 nm SBRl was measured to be 100 for BW1 = 5.0 pm. What is SBR 2 if BW2 = 15 pm?
From reference 12 we find PHW = 3.7 pm. The procedure yields F = 0.46 and therefore SBR2 = 46. If the RSD of the background signal is the same for both situations, then the detection limit at 15 pm band width will be a factor of 100/46 = 2.17 higher than at 5 pm band width.
For hypothetical lines with physical widths of 1, 2, 4 , 6 and 10 pm, one calculates F to be 0.34, 0.36, 0.49, 0.66 and 0.89, respectively. For other examples refer to Table 2 in reference 20.
or
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