The influence of line profiles upon analytical curves for copper and silver in atomic absorption spectroscopy

SpectrochimicsActa, vol. 30B,pp. 361 to 381. PergamonPress,1975.Printed In NorthernIreland

The infiuence of line profiles upon analytical curves for copper and silver in atomic absorptionspectroscopy H. C. WAQENAAR Laboratorium

and L. DE GALAN

voor Instrumentele Analyse, Technische Delft, The Netherlands (Received

12 May

1976.

Hogeschool

Delft,

Revised 26 June 1975)

Abstract-Analytical curves for copper (324 and 327 run) and silver (328 and 338 nm) have been calculated by using experimental hollow cathode lamp proties and profiles of the absorption coefficient in the air-acetylene flame. Lamp line profiles were recorded with a Fabry-Perot interferometer and corrected for instrumental distortion by an iterative pseudo-deconvolution technique. Gas-temperatures in the hollow cathode between 410 and 450 K were calculated from profiles recorded at low lamp current. An analysis was made of the changes of the lamp line profile when the lamp radiation is partly absorbed by metal atoms in the flame. It was found that the asymmetry in the transmitted profile caused by absorption in the flame, can yield accurate values of the flame line shift, particularly when the lamp line is self-reversed. The influence of hollow cathode lamp current upon sensitivity and linearity of analytical curves was studied. It was calculated that a tunable dye laser emitting narrow lines and used as a primary source, can raise sensitivity relative to a low current operated lamp by 35% at maximum in the case of copper and 10% in the case of silver. If such a laser line is simulated by reducing the source line width with an interferometer, the results are found to agree with calculations. At low lamp current the curves for silver appear to be straight whereas the curves for copper are bent due to hyperiine structure. Self-reversal at high current enhances curvature, so that at 25 mA the curves deviate by 15 % from a straight line at absorbance one. Straightforward atomic absorption measurements yield experimental curvatures that agree with the calculated values within the experimental error.

1. INTRODUCTION IT IS well-known that in atomic absorption spectroscopy analytical curves for the elements copper and silver are bent towards the concentration axis. As a,consequence the analyst either has to restrict his concentration range or must subject his data to some polynomial fitting procedure. The factors contributing to the shape of the analytical curve mity include nonabsorbed radiation from the primary source, poor optics and shapes of lamp and flame line profiles. In previous investigations [l-3] it has been shown that the shapes and positions of the profiles involved can introduce curvature and loss of sensitivity. However, for the elements studied (Ca, Al, Mn, Ga, In) the effects appeared to be relatively small and would have hardly withheld an analyst from fitting a straight line through the measured absorbance values. In the determination of other elements the influence of line profiles is easily demonstrated by the dependence of the slope of the analytical curve on the hollow [l] H. C. WAQENAAR, I. NOVOTN~ and L. DE GALAN, Spectrochim. Actu $9B, 301 (1974). [2] C. F. BRUCE and P. HANNAFORD, S~ectrochina. Acta 26B, 207 (1971). [3] I. RTJBE~KA and V. SVOBODA, Anal. Chim. Actu a, 253 (1965). 1

361

362

H. C. WA~ENAAR

and L. DE GALAN

cathode lamp (HCL) current ; copper and silver are notorious examples [P’71. It was therefore decided to examine the analytical curves of these elements in more detail. The profiles of the absorption coefficient (absorption profiles) in a nonshielded air-acetylene flame have been measured before [8]. In addition to these, information about HCL line profiles and flame line shifts is required. However, the interferometric determination of Cu and Ag HCL profiles and shifts involves two problems. First the influence of the interferometer instrument function should be considered. The filter action of a Fabry-Perot interferometer is characterized by two quantities [9], namely the free spectral range between two successive interference orders Ad (cm-l) and the finesse, being the ratio of free spectral range and the width of the instrument profile da P = Au/de. (I) Under proper conditions (exact parallelism of the interferometer plates), P reaches an acceptable value only within a preselected wavelength region of about 30 nm. The free spectral range, however, can be freely chosen by selecting the distance between the plates. A lower limit to Au is dictated by the full width (at the line base) of the proille to be recorded in order to prevent overlap with the profile in the adjacent order. The Cu lines at 324 and 327 nm consist of twelve and eight hyperfine components respectively [S, IO], collected in two regions each 0.05 cm-l wide and O-4 cm-l apart. In the HCL profile, the individual profiles within one region are not resolved and the envelope of such a composite profile component* is at least 0.06 cm-l wide (see Table 3). The free spectral range must therefore be at least 0.6 cm-1 at low lamp currents and O-8 cm-l at high lamp currents. With a finesse of 25 (cf. Table 1) the instrument width will then be equal to about half the width of an individual profile component. The silver lines at 328 and 338 nm contain four closely spaced hyperfine components and for low current HCL profiles a free spectral range of 0.3 cm-l can be used [8, 111. However, the high sputtering rate in the cathode causes selfreversal already at moderate currents. At high current very little is left from the original profile and the line has changed into two separated components, each about 0.04 cm-l wide (Fig. 2). This is only three times the width of the instrument function at a finesse of 24 (Table 1). It is clear that under such conditions neither the silver nor the copper line profiles can be recorded without distortion by the interferometer. To use these profiles * To simplify the text, the term profile components will be used from now on. These profile components shouldbe distinguishedfrom hyper@e components; in fact each profile component is a composition of several hyperfine components (cf. Ref. 7). [4] [6] [6] [7] [8] [9] [lo] [ll]

K. YASUDA, Japan AnaZyst1’7, 289 (1968). H. G. C. HUMAN,Ph.D.Thesis, Univ. of South Africct,Pretorie (1970). C. S. RANN, Spectrochim. Acta 2sB, 827 (1968). D. KENNETH DAVIES, J. Appl. Phy8.88,4713 (1967). H. C. WAQENAAR, C. J. PICEFORD and L. DE GALAN, Speotrochim. Acta 29B, 211 (1974). P. JAQUINOT, Rep. Progr. Phya. a8, 268 (1960). P. Bnrx snd W. HUMBACH, 2. Phy8ik lQ8,606 (1960). P. Bnrx, H. KOPFERMAN, R. MARTIN and W. WALCHER, 2. Physik 130, 88 (1951).

363

Analytical curves for copper and silver in atomic absorption spectroscopy

Table 1. Absorption profiles of Cu and Ag in the air-acetylene flame and experimental values of the interferometer instrument profile (Voigt function) at the wavelengths of the Cu and Ag transitions [8]

* a-value

Flame absorption profile AaD* - AC;? (cm-l) (cm-l)

Transition Ag Ag Cu Cu

328 338 324 327

nm nm nm nm

* Half-intensity t Half-intensity

0.73 0.56 0.56 0.57

0.102 0.099 0.135 0.134

0.089 0.067 0.093 0.091

Total width (cm-l)

Instrument

profile

a-value

Finesse

0.174 0.160 0.530 0.555

0.8 1.0 0.7 0.8

24 22 25 24

Doppler width collisional width

directly in the calculation of analytical curves will introduce errors so that the aid of a deconvolution technique has to be invoked to correct for these distortions. In the second place the displacement of the flame absorption profile relative to the HCL emission profile has to be measured. Flame line profiles above 350 nm can be measured in emission and the flame line shift can then be obtained by recording lamp and flame lines in alternate orders [l] or in some cases with the aid of a low pressure absorption tube as a reference [12]. However, below 350 nm the fraction of excited atoms in the air-acetylene flame becomes too low for an acceptable emission S-N ratio and flame line profiles must be measured in absorption [8, 13, 141. The set-up we used to measure the Cu and Ag flame line profiles consists of a continuum background source, a flame interferometer and a high-resolution monochromator. Profile measurements were performed by simultaneous scanning of the monochromator and the interferometer, but this method does not allow shift measurements. If, on the other hand, the wavelength setting of the monochromator is fixed, the necessary narrow entrance slit (4 pm instead of 400 pm, see Ref. [S]) causes a severe deterioration of the HCL line S-N ratio. Since, moreover the lamp current and hence the intensity of the HCL line must be kept low to avoid self-absorption, the precision in determining the positions of the hyperfine components inside the profile becomes too poor to warrant accurate shift measurements. Another possibility is the use of a beam splitter behind the interferometer and two separate monochromators with different bandwidths. To our experience, however, the beam adjustment is very critical and can easily introduce systematic errors in the shift values. The Zeeman scanning technique, introduced by HOLLANDER et al. [13], yields absorption line profiles and shifts but is not easily applicable in this case, because the lines of Cu and Ag do not show a simple Zeeman triplet. Therefore we decided to study the influence of atomic absorption in the flame upon the HCL profile. YASUDA [15] has demonstrated that the change in profile shape contains information about the displacement of the flame absorption profile [12] W. BEHMENBURG, J. Quant. Spectrosc. Radiative Transfer 4, 177 (1964). [13] TJ. HOLLANDER, B. J. JANSEN, J. J. PLAAT and C. TH. J. ALKEMADE,J. Quant.Spectrosc. Radiative Transfer 10, 1301 (1970). [14] G.F. KIRKBRIGHT and O.E.T~~~~~~~,Speclrochirn.Actu28B, 33 (1973). [la] K. YASUDA, Anal. Chem. 38, 692 (1966).

H. C. WAOENAARand L. DE GALAN

364

relative to the lamp line. It will be shown here that when self-reversed lamp line profiles are used, the deformation by flame absorption can yield accurate shift values. In the final part of the paper the experimental profile data are used to calculate analytical curves under various conditions, and the results are compared with experimentally observed analytical curves. 2. EXPERIMENTAL Table 2 shows the items used for the measurement of line profiles. The external optics consisted of a lens (50 mm dia., 120 mm focal length) to focus the lamp on the Table 2. Instrumental components * Apparatus

Description

interferometer

pressure scanned system; plates (Halle, Berlin) for region 300-340 nm; used area 10 mm dia. unshielded laminar acetylene-air flame ; gas temperature 2380 K, total gas flow 10.4 l./min, solution uptake 4 ml/mm, nebulizer efficiency 10 %. 67 mm slot burner (Varian Techtron). d.c.-operated HCL’s for Cu and Ag [Varian Techtron (VT) or Perkin-Elmer (PE)] 0.5 m Ebert mounting (Jarrell-Ash); f/8.6 aperture; first order dispersion 0.6 mm/run; slits for atomic absorption 60 pm; slits for interferometry 400 and 600 pm, entrance and exit respectively.

flame

burner lamps monochromator

read-out

EM1 6256 S photomultiplier; PAR model 122 lock-in amplifier; recorder or paper-tape punch.

* The reader should consult previous publications for detailed information about the operating principle of the interferometer [18], the fine adjustment and the instrument profile [8] or the recording of lamp line profiles and the calculation of analytical curves [l]. flame, a similar lens to project a parallel beam through the interferometer and a

final lens (60 mm dia., 300 mm focal length) to image the interference pattern onto a circular diaphragm (0.6 mm) attached to the entrance slit. 3. CORRECTIONFOR INSTRUMENT BROADENING The shape and width of the instrument profile at the wavelengths of the Cu and Ag lines has been determined previously by recording several mercury isotope lines in the region 300-350 nm with an interferometer plate distance of 1 mm [8]. To correct the experimental HCL profiles for instrument broadening a method designated by JONES et al. [16] as pseudo-deconvolution was selected from several deconvolution techniques [17], because it is simple to use and independent of the profile shapes involved. Here the observed profile P(u) is first convoluted once more with the instrument profile B(G) to give a convolution product C(a). A first approximation of the true [lS] R. N. JONES,R. VxNgATARAarrAv.4x and J. W. HOPKINS, Spectrochiwa. Acta 23& 926,941 (1967). [17] A. DEN HARDER and L. DE GALAN, And. Chem. 46, 1464 (1974).

Analytical cnrves for copper and silver in atomic absorption spectroscopy

365

profile is then calculated as II(u) = P(a)z/C(a). The iteration procedure tends to converge if the width of the instrument profile is less than the width of the true profile P(o), provided thst the S-N ratio is sufficiently high to avoid oscillations in the wings. To improve the performance, the digitized profiles (at least thirty 4-digit points over the full width) are smoothed by a 7-point least square quadratic function after each iteration step. The convolution product of each iteration Ii(c) x B(o), is compared with the original experimental profile P(a). As soon as a root mean square deviation of all data points of less than O-lo/o is reached, the iteration stops. In practice this limit was reached in 5-7 iterations for profiles showing little noise (lamp currents above 5 mA). At low lamp currents convergence appeared to be slow, taking 7-10iterations, but except in the case of silver 328 nm, 2 mA, the test criterion was met and the maximum deviation between the experimental profile and the convolution product Ii(c) x B(a) was found to be less than 0.5%. Nevertheless, in some cases at low current (Ag 338 nm, 2 and 5 mA; Cu 327 nm, 2 mA) the deconvoluted profile did show oscillations in the wings. Clearly the test criterion is of no help here because the oscillations are smoothed away by the convolution, I$( a) x B(c), required for the comparison with the original experimental profile. It was therefore decided not to use the oscillating profiles in the calculation of analytical curves. In the next paragraph it will be shown that the 2 mA profiles are not broadened by self-absorption. In the calculstion of analytical curves, the deconvoluted experimental profiles could therefore be replaced by calculated profiles, composed of pure gaussian hyperfine components. The onset of oscillations can just be detected in Fig. 1 which shows the deconvolution effect upon the Ag 328 nm st 15 mA after six iterations. The experimental

convoluted profile perimental

profile

0.1

0.2

0.3

Wavenumber,cm-’

Fig. 1. Smoothed experimental profle of the Ag 328 nm hollow cathode lamp line at 15 mA and same profile after deconvolution for instrument broadening effect (six iterations).

366

H. C. WAUENAARand L. DE GALAN

profile is almost completely smooth (preliminary smoothing has already been effected, see Ref. [l]), but the almost invisible irregularities in the low intensity region (selfreversal minimum), are enlarged by deconvolution. It will be clear that the noisy low current profiles are much more seriously affected in this way. It should be pointed out that the instrument function needed for the deconvolution, B(o), is measured once and used in all later calculations. Consequently, the stability of the instrument profile from one measurement to the other is a questionable point. Although the direct measurement of the profile is more realistic than the calculation from several instrument parameters, it should be emphasized that there is no direct way to control the instrument before each measurement. The use of a library with best profiles ever recorded of a spectral line showing hypehe structure (such as T1323 nm) and the measurement of this profile before and after each run is probably one of the best checks on proper instrument setting [18]. The day to day finesse may however still vary, although the agreement that will be shown to exist between calculated and experimental values indicates that finesse variations are small. 4. THE DOPPLER TEMPERATURE IN THE HOLLOW CATHODE LAMT In order to calculate the temperature of the atomic vapour from the width of a lamp line profile, this profile should be undistorted by self-absorption or instrument broadening. The absence of self-absorption was tested by measuring the integrated intensity ratio of the two silver and the two copper resonance lines at decreasing values of the lamp current. It was found that the Ag line intensity ratio approaches the theoretical ratio within 10% (1.85 instead of 2.0) at 2 mA. Some self-absorption may still be present here but further current reduction would diminish the S-N ratio too much (compare Fig. 2). The Cu lines 324 nm and 327 nm showed the theoretical intensity ratio of 2.0 below 3 mA. Doppler temperatures were calculated in the following way: the width of an experimental profile (recorded at a lamp current where self-absorption is absent), is compared with the width of profiles calculated for different temperatures. Gaussian shaped hyperfine components are used and the overall profile is convoluted with the instrument function. Thus, contributions of natural broadening and collision broadening were assumed to be negligible [2]. By interpolation temperature values of 415 K and 410 K were found from 2 mA profiles of Cu 324 nm and Cu 327 nm respectively, while from the profiles of Ag 328 nm (2 mA) and Ag 338 nm (2.5 mA) values of 420 K and 450 K were calculated. Noise limits the precision of these values to f30 K. The mean temperatures are in good agreement with values we calculated from profiles emitted by a potassium (420 K) and an aluminium lamp (460 K) [18]. A somewhat lower value of 340 K was found by BRUCE and HANNAFORD[2] in a Ca lamp at 5 mA and by JANSEN etal. [19] in a Sr lamp at 4 mA. GOFMEISTERand KA~AN [20] calculated a value of 370 K from neon lines in a lamp at 20 mA. Although a few [18] H. C. WA~ENAAR and L. DE GALAN, Spectrochim. Acta 28B, 157 (1973). [19] B. J. JANSEN, TJ. HOLLANDER and L. P. L. FRANKEN, Spectrochim. A& [20] V. P. GOFMEISTER and Yu. M. KAQAN, Opt. Spectry25, 185 (1968).

29B, 37 (1974).

367

Analytical curves for copper and silver in atomic absorption spectroscopy

authors [7,2 l-231 have recorded HCL profiles of copper and/or silver, no temperatures have been reported. It seems that in most cases the instrumental distortion or the self-absorption broadening was too high. 5. THE INFLUENCE OF LAMF CURRENT UPON THE Lm

LINE PROFILE

A change in the applied HCL current does not only affect the lamp line intensity and hence the influence of shot-noise upon the S-N ratio, but it will also influence the shape and width of the profiles through changes in the excitation energy and in the number of emitting and absorbing atoms inside the hollow cathode. Changes in stray-light level (continuous background or non-absorbed lines) will not be considered here and the current region to be discussed extends to the maximum current advised by the manufacturer. Table 3 shows the influence of HCL current upon the profile width (that means in the case of Cu the width of the stronger one of the two components in each profile). Table 3. Experimental half-intensity widths in 1W3 cm-l for Varian Techtron hollow-cathode lamps except where stated PE (Perkin-Elmer) lamp. Audec indicates the experimental line width Auexp after deconvolution for instrument broadening. For Cu, Au is the width of the stronger of the two profile components; in the case of self-reversal Aa extends over both side maxima of the profile Lamp current +A) 2.0 2.6 6 10 16 20 26 30 40

Cu 324 nm Aeexr 73 76 62 112 149 176 196

AS, 60 64 71 106 140 166 187

P,“~P 73 76 87 106 126 142 166 176

Cu 327 nm Auexr Audec 81 86 89 104 129 166 176

68 73 79 96 123 148 168

Ag 323 nm Alex,, Auaec 49

66 -

-

99 167 187 208 224

94 164 182 201 217

Ag 338 nm A~,xp Au,,, -

-

67 63 141 169 192 204

48 66 136 161 180 188

Looking at the data for the VT lamp we find that the profiles of the 324 and 327 nm lines increase in width by a factor of 3-l and 2.5 respectively if the current is raised from 2-O to 25 mA. Moreover, the shape of the profiles changes from a collection of purely gaussian hyperflne components to profiles showing strong self-reversal (Fig. 2). At the same direct current (the voltages across the electrodes differ for the two lamps by less than 5%), the PE-lamp emits narrower lines than the VT-lamp. A closer examination of the data in Table 3 shows that the PE-lamp requires about twice the current of the VT-lamp to reach an equal profile width (e.g., VT-15 mA: O-149 cm-l, PE-30 mA: O-155 cm-l and VT-20 mA: O-175 cm-l, PE-40 mA: O-176 cm-l). [21] C. VEILLON md P. MERCHANT,AppZ. Spectry 97,361 (1973). [22] D. KENNETH DAVIES, J. AppZ. Phya. 88,4713 (1967). [23] G. J. DE JONG and E. H. PIEPZSEIER, Spectrochim. Acta MB, 169 (1974).

IX C. WAUENAAR and L. DE GAUN

368

By comparing the wavelength integrated line intensities we found however, that at equal currents also the intensities differ; the narrower PE-lamp lines are also lower in intensity by again about a factor of two. To compare the two lamps in more detail some characteristics of the experimental profiles areplotted vs the wavelength integrated intensity of the lines (Fig. 3). The ta)

0.4

Wavenumber

*cm-’

Fig. 2(a)

/ 0.6

0.4

Wavenumber

Fig. 2(b)

( cm-’

I

0.8

Analytical curves for copper and silver in atomic absorption spectroscopy

369

c

Cd)

I

0

I

I

0.2 Wavenumber,

Fig. 2(c)

0.4

cm-’

0

0.2 Wavenumber,

0.4

cm-’

Fig. 2(d)

Fig. 2. Experimental hollow cathode lamp line profiles of copper and silver at low current (2 or 4 mA) and high current (25 mA). Relative intensities are not interrelated. relation between the intensity and the necessary current has also been indicated for the two lamps. Apparently, the shapes of the emitted profiles are much more related to the intensity than to the applied current. At low current the intensity ratio of the two proflle components is 1.86 and this represents the situation where self-absorption is absent. We checked this value by calculation of the HCL profile at a temperature of 415 K followed by convolution with the instrument function and found a ratio of 1.87. Self-absorption reduces this ratio as soon as the lamp current is raised. Above an intensity of 2 (a.u.) the ratio becomes smaller than one due to self-reversal (the component intensities are measured at the centres of the profile components). The close fit of the experimental values of the two lamps to the single curve indicates the surprising resemblance of the profiles. At an intensity of 2 (a.u.) self-reversal becomes noticeable by a dip in the centre of the strong profle component. The amount of self-reversal can be expressed by the intensity ratio of the side maximum of the prolYe to that at the centre of the component; as long as self-reversal is absent the positions and values of maximum and minimum intensity coincide and the ratio is one. Figure 3 shows that self-reversal in the lamps starts at equal intensity but that at higher currents the self-reversal in the VT-lamp is somewhat stronger than in the PE-lamp, although the component intensity ratios do not differ. This might indicate that the distributions of emitting and absorbing atoms differ. It should also be noticed that self-reversal in the two lamps first becomes visible when the two profile components have just reached equal intensity.

H. C. WA~ENAAR

370

B

0

Integrated line

and L. DE GALAN

intensity,arbltrary

units

Fig. 3. Characteristicsof Cu 324 nm line profiles emitted by P&in-Elmer (PE) and Varian Techtron (VT) hollow cathode lamps. O-component intensity ratio PE-lamp, momponent intensity ratio VT-lamp, ~--self-reversal ratio PElamp, m-self-reversal ratio VT-lamp. The component intensity ratio is the ratio of the intensitiesof the two Cu-profilecomponents at the centres [q/r in Fig. 2(a)], while the self-reversalratio indicates the ratio of the maximum intensity and the centre intensity of the stronger of the two profile components [p/q in Fig. 2(a)].

The results of this comparison between lamps of clearly different design support a previous conclusion [l] based on the resemblance of profiles emitted by VT and PE Ca HCL’s, that the performance of different lamps should be compared at equal integral intensity, rather than at equal current. 6. COLLISIONAL SHIFT IN THE AIR-ACETYLENE

FUME

Jf in an atomic absorption set up a metal solution is aspirated into the flame, the HCL emission profile will be reduced in intensity by absorption of radiation. Figure 4 shows the lamp profile of Cu 324 nm before and during aspiration of a 10 mg/l. Cu solution. At a lamp current of 26 mA the two components are self-reversed and the profile contains four side-peaks. The different amount of absorption at each of these side-peaks reflects the wavelength dependence of the absorption coefficient in the flame. The hyperhne structure in the flame (see Ref. [S]) will be responsible for the fact that the two profIle components are not equally absorbed; the absorption coefficient at the position of the weak lamp profile component (the one that shows less self-reversal) is smaller than at the position of the strong lamp line component (Fig. 4). However, the two self-reversal side-peaks of a single component should still be reduced by almost the same amount as long as the hyperfine components in the two profiles coincide. The asymmetry in the recorded profile therefore reflects a shift of the flame line towards higher wavelengths.

Analytical

curves for copper and silver in atomic absorption spectroscopy

371

without absorption

Wavenumber,

cm-’

Fig. 4. Experimental protiles of the lamp line Cu 324 nm at 25 mA recorded before and after absorption by copper atoms in an air-acetylene flame (solid curves). The shape and position of the flame absorption profile is indicated by a dotted line. Aspirated solution concentration 10 mg/l.

In principle this provides a simple way to obtain the shape of the absorption coefficient and its position relative to the HCL line from a point by point calculation of the absorbance A(b) while

= log

CWPb)l

It(a) = A(a)/(0*43

Zc)

(24 (2b)

indicate the lamp line intensity before and after absorption in the flame at wavenumber b. Because we are only interested in the shape of k(o), the flamelength 1 and the concentration c can be ignored. One important drawback of this method is the limited accuracy of the ratio 1&~)/l(c), in regions where lo(b) is very small, for instance between the lamp line components and in the profile wings. The flame line shift makes it especially difficult to obtain accurate 1,,(b)/l(b) values for the red side of the flame profile. However, the method can be used to obtain half-intensity width values if a primary source is available that emits sufficiently wide lines. We tried it out for two cases and found agreement within 10% with previous width values [8, 181, namely: Ga 403 nm in an acetylene-N,0 flame using an EM1 electrodeless discharge tube at high power (50 W), and Ag 328 nm in an acetylen+air flame using a HCL at 15 mA. Obviously the method can not yield information about the far-wings of the flame profile, where lo(u) is zero. Our present requirements are less demanding, however, because the profile of the absorption coefficient of Cu and Ag in the flame is known and the shift value remains to be found. This is easily done by comparing the experimental, partly absorbed

Ic( o) and I(u)

H.

372

C. WACJENAAR

and L. DE GALAN

HCL profiles with profiles calculated using the known shape and varying shift values for the flame absorption line. One elegant way to make this comparison is to take the absorbance ratio for the two side-peaks of a self-reversed line (Fig. 4). If these side-peaks are situated at wavenumbers ol en G,, Equation 2 predicts:

The left hand side of this equation is derived from the experimental profiles and the right hand side is easily calculated for various shift values. The advantage of this procedure is that the proposed absorbance ratio is independant of the concentration. In practice this is not exactly observed. For example, for Cu 324 nm the absorbance ratio of the weaker profile component changes from l-55 at 10 mg/l. Cu to l-63 at 20 mg/l. Cu. A careful examination of Fig. 4 will reveal the cause of this effect: The maxima of the self-reversed components move outwards when the concentration of the aspirated Cu solution increases, because the absorption coefficient is not constant over the width of one self-reversal side-peak. Consequently, in order to apply Equation 3 to the easily measured absorbance ratio of the sidepeaks, it is necessary to compare the experimental profile with calculated profiles that are absorbed to about the same extent. In the case of Cu the experiment yields two values, one for each component. Figure 5 shows the calculated relation between the shift and the absorbance ratio for the two profile components of the Cu 327 nm line. The calculated mean shift value is stated in Table 4. The differences between the values for each profile component are assumed to be due to random errors. For copper the same procedure can be used at low lamp current, without selfreversal, by using the two profile component centres as points of fixed wavenumber. For the Ag lines, the proposed procedure is only possible at high current. At low

‘L

0

0.6

2 8

0.6

f

f

0.4

SI 2

0.2

0

10

Flame

30

20

line

red

40

50

shift ,10-3cm-’

Fig. 6. Determination of the flame line shift of Cu 327 nm in an air-acetylene ,flame. Curves show absorbance ratios calculrtted from partly ‘absorbed lamp line protie as a function of flame line shift.

Analytical curves for copper and silver in atomic absorption spectroscopy

373

Table 4. Air-acetylene flame line shifts

Experimental ratio * Transition A(al)/A(a2) Cu Cu Ag Ag

324 nm 327 nm 328 nm 338 nm

Calculated Experimental red shift ratio * (1W3 cm-l) A(bl)/A(bS)

1.64 1.67 163 1.82

30.3 33.1 32.8 35.1

Calculated red shift (10m3cm-l)

1.52 1.52 -

Mean red shift 49

(10e3 cm-l)

30.5 35.3

30 34 33 35

-

& & + f

3 3 3 3

Shift devided by AQ 0.32 0.37 0.37 0.52

* See Fig. 6 for the wavenumber positions in the Cu profiles.

currents, the profile is only distorted asymmetrically by absorption and the calculation of the flame line shift becomes less accurate. Figure 6 shows the behaviour of the Ag 338 nm HCL line profile at 15 mA during absorption by various Ag concentrations. Here too, the presence of a flame absorption profile that is shifted to the red is demonstrated by the dependance of the side-peak intensities on the concentation. One problem faced during calculation of partly absorbed HCL profiles is to match the positions of flame and lamp line for zero shift. Matching is exact if the corresponding hyperflne components in the two profiles coincide. In the case of Cu the minimum in the partly resolved flame absorption profile was positioned at the minimum between the two lamp profile components, causing the flame line maxima to coincide with the minimum in the self-reversed components within one encoding interval (0.003 cm-l). In the case of Ag we measured lamp lines alternately et a low (3 mA) and a high (15 mA) current in successive orders. At low current the profile is almost gaussian shaped and the exact positions of the hyperflne components are known. By comparing the order distance with the distance between the low current peak position and the high current self-reversal minimum the position of this minimum relative to the hyperllne components could be calculated. In the subsequent calculation the maximum of the absorption coefficient was made to concide with this self-reversal minimum to create a starting position called “zero shift.” The true zero shift position was calculated to differ 0.004 cm-l from this starting position. A second problem is the elimination of profile distortion due to the instrument function. Both the unabsorbed and the partly absorbed experimental HCL profiles are distorted and a direct comparison of these profiles with calculated ones may introduce errors.

2

c~2mg/l

c=O me/l 0

ce

5mgp

~~:.i 0

0.2

0

Wavenumber.

a2

0

a2

cm-’

Fig. 6. Profile of the lamp line Ag 338 nm at 15 mA before and after absorption by Ag atoms in the air-acetylene flame.

H. C. WAGENAARand L. DE GALAN

374

Therefore the unabsorbed HCL profile was put on paper tape, smoothed and deeonvoluted for the instrument function. A partly absorbed profile was calculated using the deconvoluted HCL profile and the profile of the absorption coefficient. For the latter known a-value, flame temperature and hyperfine data were used. Starting with the prosles in a non-shifted position calculations were repeated for a number of incree&ng shift values. Each calculation was completed by convolution of the profile with the instrument fun&ion. For each shift four absorbance ratios (according to Equation 2) were found. The true flame profile shift was calculated from the experimental ratio by graphical interpolation (Table 4).

If pure Van der Waals interaction is assumed to exist between absorbing atoms and perturbing particles, the red shift is predicted by LINDHOLM’Simpact theory [24] to be equal to 0.36 times the collisional (Lorentz) width AbL of the flame line. However, the experimental collisional width A@, is the sum of various conl&butions. Among these, A#, due to adiabatic collisions and Aa, due to quenching collisions may be important. The latter contribution is unknown [13] but does not affect the relation as long as the shift due to quenching collisions also amounts to O-36 times the quenching width AG, [24]. Table 4 shows that except in the case of Ag 338 nm, the experimental ratio of shift over oollisional width is indeed close to the theoretical value of O-36. However, it should be pointed out that the ratio of 0.36 for quenching collisions is not generally accepted to be correct [25]; it is even not yet understood whether quenching collisions introduce any line shift at all. To our knowledge no experimental shift values for Cu or Ag have been published so far. Recently L’Vov [26] found ratios of shift over AC, for Ca, Sr and Ba in an airacetylene flame to agree with the theoretical value of 0.36 within 20%. BEHM~~BUR~ [12] reported ratios of shift over AU, for Na in an acetylene-oxygen flame with heavy peturbers Nz, CO, and Ar which exceed the value O-36 by 20-30%. A low ratio in the case of He as the perturbing atom could be explained by taking also a

repulsive force into account. A Lennard-Jones potential was also used by HOLLANDER et al. [ 131 to explain Ghe ratios for Ca (O-29), Sr (O-20) and Ba (O-23) in air-acetylene measured by the Zeeman scanning technique. 7. ANALYTICAL CURVES FOR COPPER AND SILVER The method used to calculate analytical curves from experimental profiles and shifts has been described before [l]. Deconvoluted HCL proties I(b) were used together with normalized Voigt-shaped absorption proties IE(d) calculated from the experimental data in Table 1. The profiles were matched in the way just described after which the absorption profile was shifted to the red. The accuracy of the

relative positions is limited by the encoding interval to 0*00.2cm-l. By solving Equation 4 for stepwise increasing values of /c(o), analytical curves can be generated ITo(@)exp T-W41 d@ A = - log f (4) &(b) do s [24] E. LINDHOLM, Dk~ertaliolz,Uppsala (1942). [ 251 TJ. HOLLANDER, personal communication.

[263 B. V. L’Vov, L. P. KRUULIKOVA, L. K. POLZIKand D. A. KATSKOV,Spe&o&&m. Acta SOB, submitted (1975).

Analytical curves for copper and silver in atomic absorption spectroscopy

375

The reader is referred to [l] for details about the relation between absorption coefficient and aspirated metal solution concentration. Previous results have indicated [l] that analytical curves may be described by a quadratic equation when line profiles and shift are the causes of curvature ; A = SC -

Bc2

(5)

Therefore we tested the curves for Cu and Ag by polynomial least squares regression, using 7 data points up to absorbance 1.2. It was found that the calculated curves are best described by a cubic polynomial, but that a quadratic function is sufficiently accurate. In all cases the maximum deviation between the calculated curve and a quadratic polynomial is less than 0.3% of the calculated absorbance. The coefficients in Equation 6 were used to calculate the ratio B/S2 that expresses the deviation of the analytical curve from a straight line through the origin, with slope S. The results of these calculations, presented in Figs. 7 and 8 and in Table 5, reflect two phenomena : hyperflne structure and source line distortion by selfabsorption and self-reversal. The hyperfine components of the silver resonance lines are only detectable by the presence of a shoulder in the low current HCL profile (see Fig. 2). The linewidth is then only 0.05 cm-l and can be regarded aa narrow in comparison with the absorption profile width of 0.17 cm-l. As long as the source line profile is narrow, the BeerLambert law should be obeyed to a great extent. However, the flame shift will cause some reduction of the sensitivity. This is confirmed by the values in Table 5. If the

1 00 1

Silver concentration, mg/l

Fig. 7. Plots of Ag absorbance at 328 nm divided by oonoentrationvs concentration, calculf&edfor vsrioua type8 of primary source line profiles: experimental profilesfrom a hollow cathode lamp ueed at different (indicated) currents; profile with hype&e components of zero width (To = 0) ; single component emission line of zero width positioned at maximum absorption coefficient (laser).

H. C. WAOENAU and L. DE GALAN

370

To=0 25rnA 5mA 1OmA 15mA 20mA 25mA

Copper

concentration

, mg/l

Fig. 8. Plots of Cu absorbance at 324 nm divided by concentrationvs ooncentration, calculatedfor various types of primary source line profiles. See caption to Fig. 7 for explanation.

coefficients for the laser line are compared with those for the hypothetical HCL line at TD = 0 (see also Fig. 7), we find a 10% decrease in sensitivity but no significant curvature (B/S2 close to zero). In these calculations the laser line represents a hypothetic dye laser emitting an infinitely narrow line, tuned at the maximum of the absorption profile. The source line at To = 0 supposes real shift and hyperfine structure to be present at a Doppler temperature of 0 K. Natural broadening and collisional broadening are assumed to Table 6. Calculated coefficients of the analytical curve A = So - Bcs [S in (mg/l.)-1, B in (mg/l.)-2] and ratio B/S2 (no units), calculated from experimental line profiles emitted by a VT-lamp Lampcurrent @A)

105B

102s

B/S2

Laser* 0 2.6 5 10 16 20 25

0 13.3 13.2 13.8 14.1 14.2 14.6 14.2

6.6 4.4 4.2 4.2 4.0 3.7 3.6 3.4

0 0.07 0.07 0.08 0.09 0.10 0.12 o-13

Cu 324 nm

Ag 328 nm

Ag 338 nm

Cu 327 nm 105B lo25 B/S2

105B

102S

B/S2

105B

lo25

B/S2

0 0.07 0.08 0.09 0.10 0.11 0.12 0.13

0 1-l 7.7 13.6 23.3 28.4 25.9 2.10

7.5 6.9 6.7 6.4 6.0 6.2 4.4 3.9

0 0.00 0.02 0.03 0.07 0.10 0.13 0.16

0 1.1 3.0 -

4.2 3.9 3.7 -

0 0.0 0.02 -

6.9 9.1 10.9 10.3

3.4 3.2 3.0 2.6

0.06 0.09 0.13 0.16

0 3.1 3.4 3.6 3.7 3.8 3.9 4.0

2.7 2.1 2.0 2.0 1.9 1.9 1.8 1.7

* Values calculated under assumption of infinitely narrow source line.

Analytical curves for copper and silver in atomic absorption spectroscopy

377

be absent. A real Ag HCL line at 2 mA creates only slight curvature; instead of 1.00 an absorbance value of 0.98 would be found. By contrast, the absorption coefficients of the Cu lines in the flame are far from constant over the lamp linewidth. Consequently sensitivity is raised by 30% if the low current HCL line could be replaced by a dye laser line. The exclusive presence of hyperfine structure and shift causes the analytical curve to deviate already by 7% from a straight line at A = 1. When the extreme current values are compared (about 2 and 25 mA), the Cu 324 nm curve shows a reduction in sensitivity of 20% and an increase of the B coefficient of 7%. Both values cumulate in the ratio B/A!? causing an absorbance value of l-00 to reduce to 0.87 by curvature at 25 mA. The HCL profile components become three times wider (from 0.060 cm-l to 0.187 cm-l) but relative to the absorption profile width (the flame profile components are only partly resolved) the increase Reduction of sensitivity is probably predominantly due to is only about 25%. reduction of lamp line intensity at the positions of maximum absorption coefficient by self-reversal. The Ag 328 nm curve, at the contrary, shows a reduction of sensitivity of 40% whereas the B coefficient increases by a factor of almost three over the same current range. The straight line observed for 2 mA is severely bent at 25 mA, where B/S2 is O-15. In other words, the concentration that should give A = 1 under the assumption of a straight line would actually give a value of only O-85. This influence upon the Ag curves is caused by an extreme widening of the HCL profile and strong selfreversal. At 25 mA the lamp lines are almost four times wider than at low current (O-220 and 0.060 cm-l respectively) and even exceed the width of the flame line at half height. Moreover, the originally single profile is split into two peaks, so narrow that the absorption coefficient is almost constant over the width of each. If flame line shift were absent a straight analytical curve would be approached again. The different absorption coefficients at the positions of the self-reversal side peaks, however, still create curvature just as the Cu components do at low current. A closer examination of the data in Table 5 reveals this tendency. Although sensitivity gradually decreases when the current is raised, the B coefficient of the Ag 328 nm curve shows a maximum at 15 mA. The increase in the ratio B/i32 is consequently slowed down. Due to a lower-degree of self-reversal this phenomenom is less pronounced for the Ag 338 nm line, although a maximum B-value is still observed at a current of 20 mA. The Cu curves show the same phenomenom, but to a lesser extent; only the Cu 324 nm curve has a maximum in the B-value. If in Figs. 7 and 8 a vertical line is drawn e.g. through c = 10 mg/l. the consecutive intersection points of this line with the A/c vs c curves describe the influence of the lamp current upon the absorbance for that concentration. As an example, Fig. 9 presents such plots for two spectral lines, with experimental measurements included for comparison (the data point at 10 mA current was used as the point of reference). For Cu 324 as well as for Cu 347 and Ag 338 (not shown in Fig. 9) the calculated curves describe the experimental data points within 3%. For the Ag 328 line the actually measured absorbance seems to decrease a little more rapidly with increasing current than would be expected from the theoretical curve, although the difference is 2

378

H. C. WAOENAARand L. DE GALAN

0o Lampcurrent, mA Fig. 9. Relation between lamp current and absorbance. Solid lines indicate the relationcalculatedfrom experimentalline profiles; dots show the results of atomic absorption measurements.

still only 7%. In the literature, a few investigations have been reported that partly deal with the analytical curves of copper and silver. VEILLON and MERCHANT [21] measured analytical curves for Cu and Ag using a Fabry-Perot interferometer and a continuum source and observed for the two Cu resonance lines and the Ag 338 nm line exactly the same sensitivities as those obtained with conventional atomic absorption using HCL lamps. We, therefore, decided to simulate the narrow laser line by positioning the interferometer in the atomic absorption set-up between the flame and the monochromator. At a finesse of, say, 22 the interferometer selects a portion of the HCL profile that is O-038 cm-l wide in the case of Cu (plate distance 6 mm) and O-016 cm-l wide in the case of Ag (plate distance 14 mm). These values are less than 10% of the corresponding absorption profile widths. Moreover, the transmission band of the interferometer can be positioned exactly at the maximum of the absorption profile, so that the influence of flame line shift is eliminated. The results should, therefore, be comparable to the data labeled ‘laser line’ in Fig. 8. Absorbance values have been compared from measurements with and without interferometer in the light path. The interferometer transmission band was first positioned at the self-reversal minimum of a high current HCL line (for Cu the stronger component). The maximum of the flame line, however, is positioned at a slightly higher wavelength so that the absorbance measurement was repeated after moving the transmission band over a small wavelength region (by raising the pressure between the plates) until a maximum in the A-value was reached. A 500 mg/l. solution was used to determine the 0% transmission baseline. Table 6 shows that good agreement was found between the expected and the measured improvement.

Analytical

curves for copper and silver in atomic absorption spectroscopy

Table 6. Absorbance interferometer (FPI),

improvement realised by placing a Fabry-Perot in front of the HCL at 15 mA (Ag) or 25 mA (Cu)

A

A

Transition

with FPI

without FPI

Cu Cu Ag Ag

0.722 0.359 0.802 0.460

0.411 0.203 0.532 0.321

324 327 328 338

mn nm nm nm

* Compare and 10 mg/l.

Fig.

379

8:

calculated

Experimental ratio 1.76 1.77 1.51 1.43

ratio = A(laser)/A(HCL)

Calculated ratio 1.75* 1.69 1.54 1.36 at 25 mA

Clearly the finite width of the source line window no longer influences the absorbance and suggests a perfect abeyance of the Beer-Lambert law. VEILLON and MERCHANT, however, used a plate distance of only 2.2 mm at a finesse of about 18 resulting in an interferometer transmittance band of 0.13 cm-l wide. Consequently, the assumption of a narrow source line is not valid although for Cu an exact positioning of the band may still result in improved sensitivity. In a paper concerning atomization efficiency, WILLIS [27] thoroughly evaluated the different methods underlying the determination of the degree of atomization in flames. To account for discrepancies between results based on measurements with continuum sources and HCL’s a correction factor y was calculated and found to be 2.1 for Cu 324 nm and 1.2 for Ag 328 nm. Here y is the factor by which the HCL absorbance would be improved if the actual situation is replaced by a laser line positioned at the maximum of a single component flame line. HCL-temperatures of 350 K and flame line shifts according to LINDHOLM’S impact theory [24] of about O-03 cm-l were used in these calculations (and justified by the present results). Before a comparison is made with the data in Table 5, it should be reminded that all present calculations take the hyperfine structure of the flame line into account. Therefore, the absorbance improves only by a factor of 5.6l4.2 = I.3 if the Cu-HCL is replaced by a laser. However, if we also eliminate the structure in the flame line (thus replacing the two profile components with intensity ratio of about two, by one single profile) this factor has to be multiplied by 312 to give 2, which closely agrees with WILLIS’ 2.1. In the case of Ag 328 nm a laser line will improve the absorbance by a factor 7.5/6.7 = l-12. The influence of the flame line structure can be roughly estimated from the flame line width to raise this factor to 1.3. The agreement with WILLIS’ value of 1.2 improves even more if the differences in the u-values used by WILLIS are taken into account. 8. CURVATURE MEASUREMENTS In order to verify experimentally curves, all other causes of curvature [27] J. B. WILLIS,&&~OC~~~.

Acta

the influence of line profiles upon analytical should be eliminated. A 500 mg/l. standard

26B, 177 (1971).

380

H. C. WAUENAAR and L. DE GALAN

solution was used to adjust the O%T level in order to eliminate interference straylight and non-absorbed lamp lines. Close to the first lens an aperture stop of 8 x 4 mm was placed to improve the beam geometry in the flame. In this way a beam of 1 x 2 mm at the flame ends was obtained. Further reduction of this cross-section rapidly deteriorated the S-N ratio with only slight improvement (2%) of the absorbance. Linearity of the read-out system (amplifier, detector, recorder) was checked with a series of calibrated density filters. Other causes of curvature such as non-atomic absorption were assumed to be absent. With these provisions only the lamp line profile remains to affect the shape of the analytical curve. When this influence is eliminated by placing an interferometer in front of the lamp, the analytical curve should be straight. To minimize the influence of drift in the uptake-nebulizer system, only three solutions were used to measure the analytical curve at various lamp currents, namely a blank cO,and two solutions with metal concentrations c1 and c2. According to Equation 5 the following values should be found: A, = SC, -

Bc,~

(9

A, = SC, -

Bc,~

(6b)

If we assume c1 = pcz, curvature is present as soon as AA=A,--A,#0

Substituting Equations 6a and 6b we find: AA = Bc,~(~ - p”) which reaches a maximum value for p = 0.5. In that case the ratio B/S2 is related to the experimental absorbance values by B/,.9 = (4A, -

2A,)/(4A,

-

A,)8

(10)

The low concentration c1was prepared by putting equal amounts of c0 and c, together. Mean values B/P and standard deviations were calculated from the results of six independent groups of 5 measurements each. For each group new standard solutions were prepared. The 95% confidence limits of the mean values (Table 7) turned out to be &O-O3B/&P units up to 15 mA and better than fO.02 at 25 mA. The accuracy of the method is limited by the fact that the calculation of B/P involves the subtraction of two almost equal quantities and is mainly influenced by the shot noise due to the lamp light reducing effect of the aperture stop. Table 7 shows that the difference between the experimental values B/S2 and the calculated values are within the confidence limits of f0.03 units. We noticed before (compare Fig. 9) that the experimental sensitivity of Ag 328 nm at 25 mA was found to be lower than the calculated one. However, this does not cause the experimental value of B/S2 to exceed the calculated value significantly. If the interferometer is positioned in front of the HCL a B/Sa value of O-0 was found indicating that this procedure results in a straight analytical curve and that other curvature effects than those corrected for, are absent. In our previous investigation [l] it was shown that for many elements the values B/S2 may be well below O-1 even when lamp currents of 25 mA are used. It is clear that in these cases the accuracy of the present B/S*

Analytical curves for copper and silver in atomic absorption spectroscopy

381

Table 7. Calculated and experimental curvature values Experimental ratiot B/S2

Calculated ratio

Transition

Lamp current (mA)

Cu 324 nm

1 0-FPI*

5 15 2&i

0.01 0.06 0.10 0.13

0.00 0.08 0.10 0.12

Ag 328 nm

lo-FPI* 2.5 10 25

0.00 0.00 0.06 0.17

0.00 0.02 0.07 0.15

Ag 338 nm

lo-FPI* 4 10 25

0.00 0.00 0.09 0.17

0.00 0.02 0.06 0.16

B/S

* Interferometer used to select part of lamp line profile. t 95 % confidencelimits &O-03.

measurement is insufficient to detect curvature significantly. On the other hand, such slight deviations from the straight line will hardly worry the analyst because the shape of his analytical curve may well be dominated by more serious curvature effects. 9. CONCLUSION In conclusion it can be stated that the analytical curves of Cu and Ag are appreciably bent due to the influence of the HCL line profiles even in the absence of other curvature effects. An analyst aspirating a low concentration and extrapolating from the observed absorbance linearly to the concentration that should give him an absorbance of l-00, would for this higher concentration actually observe an absorbance of only 0.90at a HCL current of 15 mA and of only 0.85at 25 mA. In the case of silver limitation of the current to 5 mA would help him, but for copper his problem is only slightly reduced. For copper only a very narrow source line would help him to remove curvature completely, thereby improving the sensitivity by about a factor of two.