Self-absorption in Quantitative Glow Discharge Emission Spectrometry ZDENE¡ K WEISS L ECO Corporation, 3000 L akeview Avenue, St. Joseph,MI 49085–2396, USA The emission intensities of five resonance atomic lines affected GD-OES for situations in which self-absorption lines with non-linear intensity responses are used. by self-absorption were investigated as a function of analyte concentration in a sample for a Grimm-type atomization/ excitation source operated in the dc mode in argon.Based on considerations of radiative transfer within the source, and THEORETICAL CONSIDERATIONS using the two-layer model and other approximations, the equation The model of matrix-independent emission yields used4,5 is based on two basic assumptions: (i ) the analyte atom density I E M=R E0 qMc E M exp (-bE qMc E M) in the discharge is proportional to the flux cEMqM of analyte atoms sputtered from the sample (cathode); and (ii) excitation was derived, linking the emission intensity I E M, the sputter rate conditions are independent of the sample (cathode) material, qM and the analyte concentration c E M in the matrix, where E provided that the discharge voltage and discharge current are is a particular element in a matrix M.The R E0 and bE both kept constant. constants resulting from fitting the experimental data to this For a description of intensity of a self-absorbed emission relationship were investigated as functions of GD operating line as a function of the concentration of the particular element conditions.It was shown that R E0 can be regarded as the in the sample, a simple two-layer model was used, as suggested (generalized ) emission yield. Dependence of the R E0 and bE by West and Human6 in their early investigations of line parameters on discharge operating conditions suggests that shapes originating from the Grimm-type GD source. In this they could reflect more fundamental processes occurring in the model, the light source is assumed to consist of a layer discharge.Comparison of bE factors for different lines, containing emitting as well as absorbing atoms close to the however, leads to results that are not explicable within the cathode (layer I), followed by a layer of absorbing atoms only adopted model. Methodology of quantitative GD-OES analysis (layer II). In Fig. 1, the geometry of this model is shown, was generalized to be applicable also to self-absorption lines where z and r are cylindrical coordinates, z=0 on the sample with non-linear intensity responses.surface and z=z0 on the plane separating both layers. Keywords: Glow discharge; emission spectrometry; self- Proportionality between the flux of the sputtered atoms W and absorption; excitation; emission yield; sputtering rate; multi- the atom density n(z,r) of the particular element in the discharge element calibration can be written as n(z,r)=g(z,r)W (2) Glow discharge optical emission spectrometry (GD-OES)1,2 with a conventional dc Grimm-type atomization/excitation The intensity of a specific emission line at the entrance slit source has been used extensively for bulk as well as depth of the spectrometer can be obtained by solving the equation profile analysis of conductive materials. Depth profiling appli- of radiative transfer: cations, in which very different matrices (i.e.the substrate and the coating) have to be analysed in a single analysis, have led dIv dz =evkvIv(z,r) (3) to a significant effort aimed at developing GD-OES as a quantitative multi-matrix method of analysis.3,4 Such a task requires a reliable model of the response of where v is the angular frequency, Iv(z,r) is the spectral density emission intensity as a function of sample composition.In of the beam at a distance z from the cathode and a distance r previous papers4,5 a quantification scheme based on the con- from the axis, with propagation parallel to the axis.The terms cept of matrix-independent emission yields has been described. ev, kv are the Einstein emission and absorption coefficients, In this approximation, emission intensities were believed to be linear functions of the quantity cEMqM, where cEM is the concentration of the particular element E in the matrix M, and qM is the sputtering rate of that matrix. The product cEMqM represents the flux of atoms of that element, entering the discharge: W=cEMqM (1) As mentioned in ref. 4, emission line intensity is a linear function of the atom flux cEMqM only for certain emission lines. For some frequently used resonance atomic lines, selfabsorption causes deviations from a linear intensity response. In the present paper, a theoretical description is given of the effect of self-absorption on the emission intensity of several analytically important AE lines and a model of matrixindependent emission yields is generalized accordingly, to give Fig. 1 Geometry of the two-layer model of the discharge.a methodological basis for multi-matrix analyses by dc Journal of Analytical Atomic Spectrometry, February 1997, Vol. 12 (159–164) 159respectively, defined by reciprocal atom flux and can be used as a measure of selfabsorption, i.e., for no self-absorption, b=0, and the more severe the self-absorption, the higher the value of b can be ev=hv 4p Akink(z,r)g(v, z,r) (4) expected to be. The pre-exponential factor in eqn. (10) is proportional to the line intensity at the end of the excitation kv=hv 4p Bikni(z,r)g(v, z,r) (5) zone (of layer I in the two-layer model) and, consequently, to the flux.This, together with eqn. (1), leads to the following Here Aki and Bik are Einstein A and B coefficients associated equation: with the transition k�i, ni(z,r) and nk(z,r) are the populations IEM=RE0qMcEM exp(-bEqMcEM) (11) of the levels k and i, g(v,z,r) is the line profile and h is the The proportionality constant RE0 corresponds to what was Planck constant/2p.Eqn. (5) holds for situations in which called the emission yield RE in refs. 4 and 5 for emission lines stimulated emission can be neglected, which is the case here. with linear intensity response: for bE=0, eqn. (11) will express According to the two-layer model, for the layer II the the direct proportionality between the intensity and the flux following can be written: cEMqM with the proportionality factor of RE0. Therefore, the nk(z,r)=0, ni (z,r)=n(z,r) for z>z0 (6) constant RE0 can be termed the emission yield and this definition will hold for both the ‘linear’ and the ‘self-absorption Substituting eqns.(2), (4), (5) and (6) into eqn. (3), eqn. (7) is affected’ lines. obtained: Eqn. (11) is used as a basic relationship, to describe the observed signal intensity of self-absorption lines in the present dIv dz =-hv 4p BikWg(z,r)g(v, z,r)Iv(z,r) (7) paper. A similar equation was suggested by Payling et al.,9 based on the assumption that the line has a Gaussian profile.Integrating this equation gives PIv(r) Iv(z0,r) dIv Iv =-hv 4p BikWP2 z0 g(z,r)g(v, z,r)dz (8) EXPERIMENTAL Relationship (11) was tested for five analytically important and emission lines listed below. All of the measurements were made on the LECO SA-2000 spectrometer. The LECO SA-2000 is a Iv(r)=Iv(z0,r) exp C-hv 4p BikWf (r,v)D (9) GD-OES system based on a 40 cm Paschen–Runge vacuum polychromator with a 2400 lines mm-1 holographic grating.A Grimm-type atomization/excitation source with a 4 mm where Iv(r) is the spectral density of the line in the light leaving the lamp and propagating along a distance r from the optical internal anode diameter, operating in the dc mode and using argon (99.995%) as a working gas was used for all experiments. axis. It is assumed that the focal distance of the lens or mirror imaging the source onto the spectrometer entrance slit is much The discharge voltage was stabilized electronically.The preset discharge current was maintained by changing the argon longer than the size of the area where absorption takes place. The term f (r,v) is the integral on the right-hand side of eqn. pressure, based on the feedback loop with the PID valve as a pressure control device. (8). Further integration of the spectral density in eqn. (9) is not possible because of the unknown functions f (r,v) a In each series of experiments, the intensity of the investigated emission line was recorded for a set of different samples, while Iv(z0,r).However, as functionsof v, these functions are strongly localized close to the line centre v0. As functions of the radial keeping the discharge voltage and discharge current constant. The samples were selected to give different values for the flux coordinate r, they both have maxima on the axis (r=0) because the ‘normalized’ atom density of the sputtered atoms g(r,z) of analyte atoms entering the discharge.To check the validity of eqn. (11), ln(IEM/qMcEM) was plotted against qMcEM and the also has its maximum there7,8. Moreover, contributions from larger r are suppressed by imaging a circular source onto the constants RE0 and bE were calculated as the best linear regression fits. straight entrance slit. Consequently, substantial contributions to the total intensity can be expected from a narrow range of For investigations of Fe I 371.99, Ni I 341.48 and Cr I 425.43 nm lines, the samples listed in Table 1 were used.The both r and v. This is the basis for another approximation, assuming that the exponential dependence of Iv(r) on the flux emission intensities of the atomic lines of all certified elements were recorded. Together with these samples, NIST SRMs W will lead to an exponential dependence of the total intensity I on the flux W, for a certain range of actual line profiles (k is 1761–1768 Low Alloy Steels were measured under the same conditions. From the resulting data, relative sputtering rates a constant): of the samples from Table 1 with respect to pure iron were I=kI(z0) exp(-bW) (10) determined, using the multi-element calibration algorithm5 with the Cr II 267.716, Mn I 403.449, C I 165.701 nm and The constant b, defined by eqn.(10), has a dimension of Table 1 Samples used for investigations of Fe I 371.994, Ni I 341.477 and Cr I 425.433 nm lines (concentrations in % m/m) Sample Supplier* Al C Co Cr Cu Fe Mn Mo Ni Si Ti W BS-690 1 0.26 0.025 0.076 30.1 0.28 9.49 0.2 0.16 58.5 0.39 0.32 — JK-8F 2 — 0.0389 0.125 16.91 0.0523 67.1 1.55 2.775 11.01 0.424 — — 37A 3 0.03 0.13 0.015 4.27 0.13 94.1 0.46 0.46 0.1 0.25 0.004 0.015 38A 3 0.009 0.13 0.029 8.67 0.15 88.9 0.41 0.96 0.24 0.38 0.003 0.023 53A 3 0.12 0.063 0.11 15.14 0.02 7.62 0.32 0.05 76.12 0.15 0.25 0.01 58A 3 0.53 0.076 0.1 20.71 0.03 44.9 0.65 0.17 32.01 0.26 0.49 — 59A 3 0.05 0.02 0.25 22.12 1.71 30.8 0.33 2.68 40.91 0.1 0.83 0.13 6A 3 0.023 0.046 0.19 17.41 0.18 68.5 1.95 0.37 10.16 0.57 0.36 0.03 4A 3 0.01 0.068 0.1 25.48 0.3 51.3 1.69 0.15 20.05 0.53 0.006 0.05 * 1, Brammer Standard, Houston, TX, USA; 2, Swedish Institute for Metals Research, Stockholm, Sweden; and 3, Analytical Reference Materials International, Evergreen, CO, USA. 160 Journal of Analytical Atomic Spectrometry, February 1997, Vol. 12Mo I 386.411 nm lines as reference signals and NIST SRMs The experiments described above were repeated for different 1761–1768 as the calibration basis.5 Multi-element calibration discharge conditions (voltages of 700 and 1200 V and currents is a non-linear regression algorithm for calculation of sputter of 10, 20 and 50 mA).Similar experiments were carried out to rate-corrected calibrations. Sputtering rate for a given sample evaluate the intensity response of the Al I 396.15 nm (Table 3) is calculated as a common multiplicative factor to concen- and Cu I 327.39 nm lines (Table 4). Instead of low-alloy steels, trations of certain elements within the sample, which makes Zn–Al and Cu matrix samples with known sputtering rates the intensity- and sputter rate-corrected concentration data relative to an iron matrix were used as reference samples in corresponding to that sample compatible with calibration the multi-element calibration (the calibration basis approach5 ).curves of all reference elements.Actual sputtering rates were The sensitivity of the photomultiplier detectors was kept calculated by multiplying the resulting values by the actual constant for the intensity measurements made under different sputtering rate of pure iron under the same operating con- discharge operating conditions for all the lines investigated, to ditions. To determine the sputtering rate of iron, an elec- be able to compare intensities under these different discharge trodeposited Fe-on-steel (Fe-3209) thickness standard conditions.(KOCOUR, Chicago, IL, USA) was depth profiled using the same discharge operating conditions as in the measurements above. Sputtering rate was calculated based on the time needed to reach the interface (see Fig. 2). The resulting sputtering rates RESULTS AND DISCUSSION are summarized in Table 2. In this way, it was possible to calculate the constants RE0 and bE for all the three lines (Fe I The resulting ln(IEM/qMcEM) versus qMcEM plots are in Figs. 371.994, Ni I 341.477 and Cr I 425.433 nm) from one series of 3–7. From these graphs, it can be concluded that eqn. (11) is measurements. a good approximation of the intensity response over a fairly wide range of GD operating conditions for all five lines examined. Deviations exist for the highest current and voltage (50 mA, 1200 V) for the Ni I 341.48, Al I 396.15 and the Cu I 327.39 nm lines. For the Cu I 327.39 nm line, deviation from the linear dependence was also found for 700 V, 50 mA (see Fig. 7). Values of RE0 and bE constants resulting from a linear regression are summarized in Tables 5 and 6. First, the emission yield will be discussed. No absolute intensity measurements were carried out, therefore only emission yields for each line separately can be compared. Emission yield as function of discharge conditions exhibits a similar pattern for all the lines investigated: it increases with discharge current and decreases with discharge voltage.For comparison, the emission yield of the Cr II 267.716 nm line, resulting from the same series of Fig. 2 Depth profile of minor elements in the Fe-3209 thickness experiments, was added to Table 5. Similar behaviour of the standard (9.9 mm thick electrodeposited layer of iron on steel), 700 V, emission yield for all the lines suggests that emission yield 20 mA. The position of the Cu peak at the interface was used to could possibly be related to more fundamental quantities determine the sputter rate of iron at different operating conditions.describing excitation, e.g., to the electron density in the This profile corresponds to a sputter rate of 3.0 mg s-1. excitation zone. As far as the parameter bE in the exponential term of eqn. Table 2 Sputtering rates of the samples from Table 1 (mg s-1) (11) is concerned, bE is significantly higher at 700 V than at 700 V 1200 V 1200 V for all lines investigated. One possible explanation within the two-layer model could be a possible voltage-related Sample 10 mA 20 mA 50 mA 10 mA 20 mA 50 mA change in the thickness of the excitation zone [layer I, par- BS-690 2.09 4.10 8.66 4.61 7.75 18.42 ameter z0 , see eqn.(8)]. Changes of bE with discharge current JK-8F 1.80 3.36 7.82 3.53 6.19 16.22 are far less pronounced. Because of the limited accuracy of 37A 1.47 2.98 6.33 3.23 5.55 13.33 the determination of bE , its dependence on current is not 38A 1.54 3.07 6.53 3.60 5.90 13.88 discussed here. 53A 2.09 4.10 9.37 4.51 — 18.56 58A 1.83 3.60 7.82 4.07 7.17 16.36 What can be done, however, is a comparison of the bE 59A 2.10 4.07 8.98 4.67 7.75 19.52 factors for different lines. Eqn. (9) together with the subsequent 6A 1.69 3.27 7.36 3.67 6.24 15.40 assumptions suggests that bE should be proportional to Bikv0. 4A 1.79 3.54 7.62 4.00 — 15.95 Designating the corresponding proportionality constant as k, Table 3 Samples used for investigations of the Al I 396.152 nm line (concentrations in % m/m) Sample Supplier* Si Al Ni Fe Mn Cu Pb Zn Mg Sn 629 4 0.078 5.15 0.008 0.017 0.0017 1.5 0.0135 93.1 0.094 0.012 631 4 0.001 0.5 0.0005 0.005 0.0002 0.0013 0.001 99.49 0.0005 0.001 1256A-7 4 9.16 84.2 0.41 0.91 0.38 3.51 0.11 1.02 0.063 0.1 NZA-5 5 — 10.85 — 0.016 — 1.04 0.0012 88.1 0.021 0.0017 NZA-7 5 — 13.17 — 0.016 — 0.212 0.0136 86.5 0.052 0.0116 NZA-1 5 — 28.7 — 0.046 — 1.51 0.003 69.7 0.02 0.0069 43XZ3D 6 — 3.6 0.002 0.08 0.03 1.36 0.012 94.7 0.12 0.02 41X0336Zn2 6 — 1.42 — 0.015 0.02 0.25 0.51 97.4 0.11 0.06 41X0336Zn3 6 — 0.54 — 0.05 0.01 0.33 0.042 98.6 0.09 0.11 * 4, National Institute of Standards and Technology, Gaithersburg, MD, USA; 5, CANMET, Ottawa, Ontario, Canada; and 6, MBH Analytical, Barnet, UK.Journal of Analytical Atomic Spectrometry, February 1997, Vol. 12 161Table 4 Samples used for investigations of the Cu I 327.396 nm line (concentrations in % m/m) Sample Supplier* Si Al Ni Fe Mn C Pb Zn Sn Cu 17868T 6 0.014 0.081 0.025 0.02 0.019 — 0.014 0.022 0.029 99.54 73A 3 0.003 0.01 0.06 0.3 0.01 0.009 2.94 34.78 0.2 61.7 78A 3 0.005 0.01 0.038 0.083 0.01 0.009 4.26 3.68 4.35 87.5 80A 3 0.022 9.89 4.85 4.01 0.23 0.013 0.007 0.18 0.02 80.8 87A 3 0.01 0.42 0.33 0.23 0.008 0.008 0.92 37.49 0.55 60.00 92A 3 0.005 0.01 0.36 0.01 0.01 0.012 9.58 0.27 9.75 79.6 93A 3 0.11 10.39 1.15 3.77 0.37 0.016 0.06 0.18 0.05 83.9 309B 7 0.13 12.65 1.71 0.86 1.02 — 0.05 0.22 0.53 82.6 52A 3 0.01 2.99 64.3 0.04 0.74 0.17 — — 0.0005 31.16 51A 3 0.26 0.05 66.0 2.07 1.49 0.13 0.001 — — 29.87 * 7, C¡ KD Research Institute, Prague, Czech Republic. 3, 6, see Tables 1 and 3. Fig. 3 Plots of ln(IEM/qMcEM) versus qMcEM for the Fe I 371.99 nm line under different GD operating conditions (samples from Table 1). Fig. 6 Plots of ln(IEM/qMcEM) versus qMcEM for the Al I 396.15 nm line under different GD operating conditions (samples from Table 3). Fig. 4 Plots of ln(IEM/qMcEM) versus qMcEM for the Ni I 341.48 nm line under different GD operating conditions (samples from Table 1).Fig. 7 Plots of ln(IEM/qMcEM) versus qMcEM for the Cu I 327.39 nm line under different GD operating conditions (samples from Table 4). Table 5 Emission yields resulting from the described experiments. For each line, ratios of RE0/RE0 (700 V, 20 mA) are displayed. For comparison, emission yields of the Cr II 267.716 nm line are presented in the last row 700 V 1200 V Line Wavelength/ nm 10 mA 20 mA 50 mA 10 mA 20 mA 50 mA Cr I 425.43 0.54 1.00 2.39 0.29 0.57 1.61 Ni I 341.48 — 1.00 1.71 — 0.83 1.27 Fe I 371.99 0.64 1.00 2.08 — 0.69 1.00 Cu I 327.39 — 1.00 2.29 0.21 0.55 1.36 Al I 396.15 — 1.00 3.03 — 0.51 1.44 Fig. 5 Plots of ln(IEM/qMcEM) versus qMcEM for the Cr I 425.43 nm Cr II 267.72 0.62 1.00 2.08 0.28 0.61 1.32 line under different GD operating conditions (samples from Table 1). 162 Journal of Analytical Atomic Spectrometry, February 1997, Vol. 12Table 6 bE factors resulting from the described experiments (s mg-1) relationship, which is the basis of the methodology described in refs. 4 and 5: 700 V 1200 V Line Wavelength/ IEM=REqMcEM+BE+.F aEFIFM (15) nm 10 mA 20 mA 50 mA 10 mA 20 mA 50 mA where BE is the background and aEF is the inter-element Cr I 425.43 0.54 0.56 0.45 0.28 0.27 0.24 Ni I 341.48 — 0.10 0.08 — 0.07 (0.04) correction coefficient used for corrections of spectral inter- Fe I 371.99 0.16 0.14 0.09 — 0.05 0.04 ferences and other possible effects causing different back- Cu I 327.39 — 0.10 (0.06) 0.05 0.05 (0.03) grounds in different matrices.An analogous relationship for Al I 396.15 — 0.36 0.29 — 0.19 0.14 self-absorption lines would be IEM=RE0qMcEM exp(-bEqMcEM)+BE+. F aEFIFM . (16) eqn. (12) can be written: As opposed to what was suggested in ref. 4, eqn. (16) itself does not seem to be a suitable basis for calibration. The reason bE=k v0Bik ME (12) is that for an unknown sample, a non-linear algebraic equation would have to be solved to obtain qMcEM.Instead, calibration where ME is the relative atomic mass of the element E, and it can be based on the inverse relationship to eqn. (16). In corrects for the fact that the flux W in the above presented practical work, it is convenient to use a quadratic approxi- experimental data is expressed as mass sputtered per second, mation of the type instead of the number of atoms sputtered per second. Considering the relationship between the A and B coefficients10 qMcEM=IEM-BE RE0 +jE(IEM-BE)2+.F aEFIFM (17) Bik=p2c3 hv03 gk gi Aki (13) where jE is another constant to be obtained by calibration. To keep the quantification scheme as described in refs. 4 where gi and gk are the statistical weights of both levels, and 5 consistent, the lines with a non-linear intensity response should not be used as a basis for additive spectral interference bE=k¾ gk gi Akil02 ME (14) corrections.In the linearized version of the multi-element calibration scheme employing the calibration basis approach,5 is obtained where k¾ is another proportionality constant and self-absorption lines should not be used for sputter-rate deter- l0=2pc/v0 which is the wavelength of the line. Comparison minations, unless the range of qMcEM is small enough to make of experimental values of bE at 700 V and 20 mA with the the deviations from linear relationship negligible. Finally, it is corresponding quantity from the right-hand side of eqn.(14) worth mentioning that even for self-absorption lines, linear is in Table 7. Transition probabilities Aij and statistical weights calibrations are satisfactory for methods designed to cover gk and gi for the transitions discussed were taken from ref. 11. only a limited range of qMcEM for the particular element. This From Table 7, it is evident that there is no agreement with happens either if this element has to be determined only in eqn.(14). A more exact method of integration of eqns. (8) and low concentrations or if the only matrix to be analysed consists (9) should be used. One possible way would be to take the mostly of this element. An example of the second case is the atom densities n(z,r) resulting from computer simulations8 and analysis of nitrided or nitrocarburized steels. For such types to calculate the f (r,v) functions from eqn. (9). Line profiles in of analyses, satisfactory results can be obtained even if the Fe I the excitation zone g(v,z0,r) needed for these calculations could 371.99 nm line is used with linear calibration.possibly be measured using a side-viewed source similar to Previous papers4,5 together with the above suggestions that described in ref. 7. Recently, anomalous line profiles have describe a complete GD-OES quantification scheme, the most been reported for certain Fe I lines excited in the dc Grimm- important features of which are as follows. 1. In calibrations, type discharge.12 Clearly, line shape and width, including any intensities are considered to be functions of the product qMcEM. hyperfine structure, will affect the amount of self-absorption. 2. For the sputtering rate-corrected calibration to be con- Another question is adequacy of the two-layer model itself. It structed, it is not necessary to know a` priori sputtering rates is implicitly assumed that the line intensity leaving the first of all the standards used. 3. This approach does not support layer is proportional to the atomic flux, although some self- voltage- and current-intensity corrections. In the case of a absorption also occurs within the first layer. The above changing matrix, this scheme relies on the dynamic pressure reported inconsistencies indicate limitations of the proposed control, making it possible to keep the discharge current and self-absorption model. voltage constant and equal to the values used for calibration.The above reported results for bE and RE are not used for developing alternative intensity corrections. However, it is CONSEQUENCES FOR THE GD-OES interesting to discuss the correspondence of the present results METHODOLOGY with the model of Bengtson and co-workers.3,13 Assuming that The consequences of the above presented results to the method- the sputtering rate is directly proportional to discharge current ology of quantitative GD-OES analysis remains to be dis- and considering only the situations in which the exponential cussed.The matrix-independent emission yield concept leads, term in eqn. (16) can be neglected (low sputtering rates, low for lines with a linear intensity response, to the following concentrations), the emission yield ratio RE0/RE0(700 V, 20 mA) from Table 5 can be expressed as (i/i0)A(m)-1 in Bengtson’s notation, where i is the discharge current, i0 is the Table 7 Comparison of bE factors for different lines (see the text) reference current of 20 mA and A(m) is the parameter defined l0/ Aik/ bE (700V, 20mA)/ l02 gkAik/(giME )/ in ref. 13. Comparing the data from Table 5 with corresponding Line nm gi gk 108 s-1ME s mg-1 109 cm2 s-1 values predicted by the Bengtson formula, it can be concluded Cu I 327.396 2 2 1.37 63.54 0.10 2.31 that the agreement is very good (see Table 8). On the other Al I 396.152 4 2 0.98 26.98 0.36 2.85 hand, self-absorption seems to be violating the validity of Cr I 425.433 7 9 0.315 51.99 0.56 1.41 Bengtson’s corrections in some cases.As an example, the Fe I 371.994 9 11 0.162 55.85 0.14 0.49 emission intensity of the Cu I 327.39 nm line was measured as Ni I 341.477 7 9 0.55 58.71 0.10 1.40 a function of discharge current for two samples with a different Journal of Analytical Atomic Spectrometry, February 1997, Vol. 12 163Table 8 Comparison of emission yields with a discharge voltage of 700 V from Table 5 with the corresponding values predicted by the model of Bengtson et al.3, 13 (see the text) RE(10mA)/RE(20 mA) RE(10 mA)/RE(20 mA) A(m) Literature Literature Literature Line value* This work value* This work value* Cr I 425.43 nm 2.1±0.2 0.54 0.47±0.06 2.39 2.74±0.5 Ni I 341.48 nm 1.6±0.1 — — 1.71 1.73±0.17 Fe I 371.99 nm 1.8±0.2 0.64 0.62±0.08 2.08 1.90±0.4 Cu I 327.39 nm 2.0±0.2 — — 2.29 2.50±0.5 Al I 396.15 nm 2.2±0.2 — — 3.03 3.00±0.6 Cr II 267.72 nm 1.6±0.2 0.62 0.66± 0.09 2.08 1.73±0.35 * From refs. 3 and 13. Jones,14 who suggested that argon pressure is the key parameter controlling the excitation of sputtered atoms. It was shown that RE0 can be regarded as the (generalized) emission yield. Emission yield as a function of discharge conditions increases with discharge current and decreases with discharge voltage. The parameter bE in the exponential term of eqn. (11), characterizing self-absorption, is significantly higher at 700 V than at 1200 V for all lines investigated.The observed dependence of the RE0 and bE parameters on discharge operating conditions suggests that they could possibly be used for comparison of the above presented theoretical description of the discharge to more sophisticated microscopic models. Limitations of the proposed simplified self-absorption Fig. 8 Ratio of emission intensities I (74A)/I(102A) produced by model are apparent from the inconsistency found when samples 74A and 102A for the Cu I 327.39 nm line as a function of comparing the bE factors for different lines.the discharge current i (4 mm anode diameter, 700 V). Sample 74A is The methodology of quantitative GD-OES analysis was CuZn38 brass with 61.3% m/m Cu and sample 102A is AlCu4.5 alloy generalized, so that it could also be applicable to self- with 4.5% m/m Cu in an Al matrix with minor concentrations of Fe, absorption lines with non-linear intensity responses. Mn and Si (all below 1% m/m). Correspondence with the traditional approach as proposed by Bengtson and co-workers3,13 was discussed briefly.matrix and the ratio of the intensities produced by both samples was plotted as a function of the discharge current The author thanks the LECO Corporation for permission to (Fig. 8). If the intensity–current relationship were matrix- publish this paper and Dr. Arne Bengtson, Swedish Institute independent, the intensity ratio would be constant (a straight for Metals Research, Stockholm, Sweden, for his comments.line parallel to the abscissa in Fig. 8). The observed decrease in this ratio with current can be explained by a stronger self-absorption for sample 74A because it has a higher Cu REFERENCES concentration and a higher sputtering rate than sample 102A. 1 Grimm, W., Spectrochim. Acta, Part B, 1968, 23, 443. 2 Boumans, P. W. J. M., Anal. Chem., 1972, 44, 1219. 3 Bengtson, A., Spectrochim. Acta, Part B, 1994, 49, 411. CONCLUSIONS 4 Weiss, Z., J. Anal. At. Spectrom., 1995, 10, 891. 5 Weiss, Z., J. Anal. At. Spectrom., 1994, 9, 351. The emission intensities of five resonance atomic lines affected 6 West, C. D., Human, H. G. C., Spectrochim. Acta, Part B, 1976, by self-absorption were investigated as a function of analyte 31, 81. concentration in the sample for the Grimm-type atomization/ 7 Ferreira, N. P., Strauss, J. A., and Human, H. G. C., Spectrochim. excitation source operated in the dc mode in argon. Based on Acta, Part B, 1983, 38, 899. simplified considerations of radiative transfer within the source 8 Hoffmann, V., and Ehrlich, G., Spectrochim. Acta, Part B, 1995, 50, 607. and using the two-layer model and other approximations, an 9 Payling, R., Marychurch, M., Jones, D. G., and Dixon, A., paper equation [eqn. (11)] was derived, linking the emission intensity presented at the CSI Post-Symposium on GDS, Dresden, IEM, the sputter rate qM and the analyte concentration cEM in Germany, September 1–4, 1995. the matrix. The RE0 and bE constants resulting from fitting the 10 Thorne, A., Spectrophysics, Chapman and Hall, London, 1974. experimental data to this relationship were investigated as 11 Fuhr, J. R., and Wiese, W. L., in CRC Handbook of Chemistry functions of GD operating conditions. All series of experiments and Physics, ed. Lide, D. R., and Frederikse, H. P. R., CRC Press, Boca Raton, FL, 75th edn., 1995. were carried out with the discharge current and discharge 12 Steers, E. B. M., and Thorne, A., Fresenius’ J. Anal. Chem., 1996, voltage constant while changing the matrix being analysed. 355, 868. The fact that the results obtained in this way show a consistent 13 Bengtson, A., Eklund, A., Lundholm, M., and Saric, A., J. Anal. pattern, suggests that the discharge voltage and the discharge At. Spectrom., 1990, 5, 563. current are good parameters to characterize the discharge if 14 Payling, R., and Jones, D. G., Surf. Interface Anal., 1993, 20, 787. the analysed matrix is changing, i.e., it is likely that more fundamental quantities controlling the excitation are primarily Paper 6/03151J dependent on the current (current density) and the voltage. ReceivedMay 7, 1996 This finding is in disagreement with the work of Payling and Accepted July 17, 1996 164 Journal of Analytical Atomic Spectrometry, February 1997, Vol. 12