Extension of the dynamic range in Zeeman graphite furnace atomic absorption spectrometry

Spectrochimica Ac’4, Vol. 478. No 12. pp. 1411-1420, 1992 Printed in Great Bntain

0584-8547/92 $5.00 + .OO @I 1992 Pergamon Press Ltd

Extension of the dynamic range in Zeeman graphite furnace atomic absorption spectrometry B. V. L’vov, L. K. POLZIK and P. N. FEDOROV Department

of Analytical Chemistry, St. Petersburg Technical University, St. Petersburg 195251, Russia

and WALTERSLAVIN Bonaire Technologies,

Box 1089, Ridgefield, CT 06877, U.S.A.

(Received 26 February

1992; accepted 19 May 1992)

Ah&act--In order to extend the dynamic range of Zeeman graphite furnace atomic absorption spectrometry (GFAAS), we propose a method to restore the dip formed in the region of the absorption pulse maximum and resulting from the roll-over of the calibration curve. A previously proposed model (B. V. L’vov et al., Spectrochim. Actu 47B, 1187 (1992)) for the ascending part of the Zeeman calibration curve and one developed on the same basis for the descending part of the curve has made it possible to linearize the calibration graph over the entire range of absorption variation in terms of two parameters: roll-over absorbance, A,; and Zeeman sensitivity ratio, R. The use of the dip extends the dynamic range, on average, by an order of magnitude compared to a range restricted by the roil-over point. This makes the full dynamic range of Zeeman GFAAS 3-4 orders of magnitude higher than the characteristic mass, ma. The method has been tested on three elements (Be, Bi and Cd) having different A, and R parameters. The measurement error in the determination of analyte mass for large signals in the dip region does not exceed that for signals of average magnitude. The correction of spectral interference in the dip region is approximately equivalent to the continuum background correction with a single light source.

1. INTRODUCTION THE RELATIVELY narrow dynamic range of Zeeman graphite furnace atomic absorption spectrometry (GFAAS) is one of the obstacles to the development of instruments for simultaneous multi-element analysis. There are several approaches to solve this problem. A three-field method proposed by DE LOOS-VOLLEBREGT and coworkers [l-3] is the most interesting. Its idea is to measure the signal in three magnetic fields differing in strength; zero, maximum (8 kG) and intermediate (6 kG). The additional analytical curve corresponding to the difference in the absorption signals, A6-As, with a reduced sensitivity compared to the main curve, A,,-A,, enables the extension of the dynamic range by 5-10 times on the average [2]. The use of this technique calls, however, for the modification of the instrument and somewhat deteriorates the conditions for measurement of small signals due to a 1.5 times increase in the number of independent measurements: A,,, A8 and A6 instead of the usual A0 and A8 [3]. Besides, the nonlinearity of the calibration graph requires standardization over the entire analytical range, thereby limiting the application of the concept of characteristic mass as a single, simple, calibration parameter. Another approach is based on the use of complete information concerning the pulse shape, e.g. its duration for the given absorbance or the absorbance for the given signal duration, or on the measurement of part of the pulse area (either over the ascending or the descending slope) within the linearity range [4,5]. All these methods are applicable provided the shape and position of the pulse are kept constant irrespective of the possible variation in the matrix composition of the samples and variations of other uncontrollable factors, e.g. deteriorations of the pyrocoating in the process of the tube firing. This condition is evidently far from reality. Still another approach to extend the dynamic range is based on the use of an analytical curve for the uncorrectable value of absorption by the u-components of the 1411

1412

B. V. L’vov et

al.

line, A,, in the maximum field [6]. The application of the method presumes absence of spectral interferences, which practically excludes its use with GFAAS. The present study proposes to extend the dynamic range of Zeeman GFAAS by correcting the dip being formed at the pulse. maximum as a result of the roll-over effect of the calibration curve. Following the methods of linearization of calibration curves as developed in Refs [7-lo], we applied a technique which was successfully used for correction of pulses without a dip [lo]. It may be assumed that the lack of interest shown among scientists in this possibility is connected with a number of obvious limitations of the method. These include the impossibility to use a Zeeman-effect corrector in the dip region, the increased noise in this region, as well as the roll-over of the calibration function at the maxima of a double-hump pulse, thus making automatic processing of the signals more difficult. Below, we shall discuss these limitations and ways of overcoming them. 2. THEORY 2.1. Correction of spectral interferences in the dip region The absorption value at the pulse dip is determined by a relationship a.c. Zeeman GFAAS: AZ = A(SB) - A(BG)

common for (1)

where A(SB) and A(BG) are absorption signals for “single-beam” (SB) and “background” (BG) channels when the magnetic field is switched off and switched on, respectively. The functions of these channels at the roll-over point of the calibration curve interchange: the sensitivity of the BG channel to variation in analyte atom concentration appears to be higher than that of the SB channel. The measurement of the analytical signal is carried out due to the absorption of the o-components in the BG channel, while the spectral interference is determined by the SB channel. At the point where the dip occurs, the main portion of radiation in the SB channel attributed to the analytical line appears to be absorbed completely and the spectral distribution of the remaining portion is determined by the distribution of non-absorbed radiation within the light source spectrum near the analytical line. We assume the contribution of stray light to the residual non-absorbed radiation to be insignificant, i.e. the spectral distribution of non-absorbed radiation is confined to the instrument spectral band pass (SBP). Under these conditions, the SB channel functions in a manner similar to a Dzlamp channel in the conventional continuum background corrector. It is to be noted that unlike the usual D,-corrector optical schemes with two light sources, this arrangement preserves the advantage of having a single light source (just as in a Zeeman-effect corrector), which ensures full coincidence of the optical paths for both measuring channels. Thus, the measurement, in the dip region, of the differential signal [Eqn (l)], in contrast to the measurement of the uncorrected signal A, [6], functions as an ideally adjusted D2-corrector. 2.2. Signal-to-noise ratio in the dip region A reduced light flux resulting from complete or almost complete absorption of the analytical line within the SB channel must lead to a deterioration of the signal-to-noise ratio (S/N) when measuring the differential signal [Eqn (l)] within the dip. However, the extent of such deterioration is determined by the magnitude of the residual nonabsorbed light and in most cases may be controlled by a proper choice of the instrument SBP and/or the type of light source. Hollow cathode lamps (HCL) with a richer spectrum as compared to electrodeless discharge lamps (EDL) are probably preferable for this purpose. If the quantity of the residual non-absorbed light is 5-10% of the total light flux, the decrease of the S/N ratio while operating in the dip region must not exceed S-4.5 times. If we take into account the increase of the total light flux for the enlarged SBP, it becomes evident that this restriction may not be critical.

1413

Dynamic range extension in Zeeman GFAAS

Af&---&?T? 0

I

2

3

4

2

3

4

5

6

7

a

9

IO

5

6

7

a

9

IO

A:; 0

I

A 0.n

Fig. 1. (a) Forming of a real Zeeman calibration curve, A, = A(SB) - A(BG), and (b) its model description, AZ = A, - A(BG’), at A, = 1.5 and R = 0.7.

2.3. A model for dip correction While modelling the descending part of the calibration curve beyond the roll-over point, we used the same model that was successfully used for the ascending portion of the Zeeman calibration curve [lo]. This model connects the quantity AZ being measured with a normalized, as to its sensitivity, quantity Ao,, for a linearized curve through a single parameter, the roll-over absorbance, A,. Introducing “a” and “d” designations to denote the quantities in the ascending and descending parts of the calibration curve and taking account of an additional condition A: = A, + 0.01 used in Ref. [lo] for better correlation of calculation and experiment, we can write the basic equation for the correction of the ascending part of the curve in the form: A& = (1 - 10-A;) log lo;;“;A;

! I .

The same principle has been chosen to correct the values of AZ for the descending part of the calibration curve. While doing so, we assumed that the real curve AZ = A(SB) - A(BG) (Fig. l(a)) is equivalent to the curve AZ = A, - A (BG’) approximating it (Fig. l(b)). Here, A(BG’) is a hypothetical curve close in shape and slope to the real one A(BG) having the origin on the x-axis at a point corresponding to the roll-over and having the roll-over absorbance, A,, as its limiting value. To restore the values of AZ in the dip region, it is necessary to add to the constant value of Ao,, determined by the quantity A,, a value dependent on the depth of the dip, A, - AZ, i.e. Ad,,, = A,,,(A,)

+ A&A,

- A,) .

(3)

Considering the reversed scale of variation for quantities AZ on the descending slope of the curve and a R/(1-R) times difference in the initial slope of the curves A(BG’) and AZ, we obtain a complete equation to correct the values of AZ in the dip region:

Analysis of the proposed model for dip correction makes it possible to draw some practical conclusions. (1) The use of Eqn (4) for the correction in the dip region requires a preliminary location of the dip region. This can be done only after recording the entire pulse. In the present study, this work was done manually on a computer monitor. We suppose, however, that modern computer technology will permit the definition of the boundaries of the dip region automatically, e.g. by finding the positions of two resolved maxima

B. V. L'vovetal.

1414

having height about A,. In this case, the whole correction procedure can be made fully automatic. (2) In order to correct quantities AZ at the dip, it is necessary to know not only the parameter A, but also the parameter R. Finding the parameter R does not require any additional measurements while working with modern Zeeman spectrometers. However, one must not overlook the fact that because of the curvature of the curve A BG, the initial slopes of curves A(BG) and A(BG’) (see Fig. 1) may differ from each other and the actual value of R in Eqn (4) may exceed the value measured by a conventional method (at AZ eA,). (3) The upper limit of the measurement including the dip is defined by the value of AZ = 0. In this case, the analytical line appears to be fully absorbed in both channels and the Zeeman spectrometer becomes insensitive to further increase in the concentration of analyte atoms. According to Eqn (4), condition AZ = 0 corresponds to a maximum (A&),,

= ’ ; t”iA’

log ‘;;2;31

,

(5)

The upper limit of a linearized graph, according to Eqn (5), at mean parameter values (A, = 1 and R = 0.8) is about 10 and at values close to the maximum ones (A, = 1.5 and R = 0.98) would reach 150 absorbance units. (4) From Eqn (4) it follows that the use of the dip must ensure an extension of the dynamic range, as compared to one confined to the roll-over point, equal to: (Ado,Jmax~(A&,),,, = l/(1 - R).

(6)

Though the relative magnitude of the extension of the range does not depend on A,, and, consequently, also the absolute value of it does affect the value of (A&,),, (A:,,),,.

3. EXPERIMENTAL 3.1. Instrumentation The experiments were conducted on a Perkin-Elmer model Zeeman/SOOOspectrometer with an HGAJOO atomizer and an AS-40 autosampler. The absorption signals were recorded by a 3600 Data Station provided with a graphics plotter. The light sources for Be and Cd were HCLs of the LSP-1 type manufactured in Russia. For Bi, an EDL was used. Standard pyrocoated graphite tubes and conventional platforms of anisotropic pyrolitic graphite were used. Argon containing no more than 10e3% of O2 and N2 served as a sheath gas. 3.2. Calibration solutions The stock solutions with a concentration of 0.1 g/l were prepared by dissolving pure metals. The working solutions were prepared by diluting the stock solution with distilled water containing 0.5% HN03. The solution of NaCl used in experiments for the correction of spectral interference was prepared by dissolving a portion of salt in distilled water. 3.3. Measurement conditions

Measurement conditions as listed in Table 1 are typical for the stabilized temperature platform furnace (STPF). Matrix modification was not used except for the Cd determination in the presence of excess NaCl, where 5 pg of Pd was used to delay evaporation of Cd and thus attain a coincidence of NaCl and Cd peaks. The analyte mass used for the examination of the dynamic range was varied by the volume of the solution injected into the furnace within 5-50 ~1. To cover all the mass region to be investigated, we used for Be three solutions differing in concentration 10 times from each other, and four solutions with a Xl-fold difference in concentration from one another for Bi and Cd. 3.4. Peak restoration procedure The measurement of the roll-over level, A,, was carried out by the peak height method for a pulse whose dip dropped up to about 0.5 A,. The peak height was estimated automatically by

1415

Dynamic range extension in Zeeman GFAAS Table 1. Experimental Element and wavelength (nm)

Light source

Lamp current (mA)

Be Be Bi Cd

LSP-1 LSP-1 EDL LSP-1

30 (T3!YV)

234.9 234.9 306.8 228.8

15

conditions

Spectral band pass (nm)

Atomization temperature (“C)

2.0 0.7 2.0 2.0

2500 2500 1900 1600

Integration time (s)

5 5 3 4

the maximum count on a computer. In those cases where the counts within the pulse peak were accompanied by considerable noise, digital smoothing [ll] of the pulse was done before starting to look for the pulse maximum. Probably, application of the noise filtration technique of SAVITZKYand GOLAY[12] will be more efficient for this purpose. The Zeeman sensitivity ratio, R, which enters the algorithm of Eqn (2) was determined by a method of successive approximations, restoring the same pulse with a dip. A value of R measured for small signals in the linear region was used as the first approximation. Then in the process of iterative calculations of the pulse area, this value was varied in order to achieve the best agreement between the value of the characteristic mass obtained and its value for a pulse without a dip. The correction program for a 3600 Data Station microcomputer was written in BASIC. It includes the following steps: choosing

(i) readout of the signal AZ = f(t) from the floppy disc and plotting it on the monitor; (ii) visual analysis, by the operator, of the pulse shape and establishing by marks on the screen the pulse dip region; (iii) correction of each pulse point (50 points/s) according to the algorithm of Eqn (4) within the dip and to the algorithm of Eqn (2) outside the dip, i.e. finding the function Ao., = f(t); and (iv) finding

the area of the corrected

pulse,

i.e. determining

the integral,

JA,,“dt.

While using Eqn (2) as an algorithm, we introduced into the correction program a restricting condition excluding the denominator from becoming equal to 0 or a negative quantity at AZ >A,. For this purpose, all the values of the signal AZ exceeding A, were assumed to be equal to A,. Similarly, in using Eqn (4), all the values of signal AZ smaller than 0.01 were taken to be equal to 0.01.

4. RESULTS AND DISCUSSION 4.1. Linearization of calibration curves Figures 2-4 are illustrations of the potential of the proposed method for restoration of the absorption signal. They present absorption pulses for Be, Bi and Cd with dips of differing depths and the corresponding restored signals. Our attention is drawn by sharp discontinuities in the profile of the restored pulses (see the descending pulses in Fig. 3(b), as well as by the sharp spikes of the signal (see the descending pulses in Fig. 4(b)) at the time corresponding to the transition from one algorithm to another. The first feature is caused by inaccuracies in the approximation of the change of the analytical curve near the maximum (see Fig. 1) where the smooth curvature at the roll-over level is modelled by a sharp discontinuity. The second feature (spikes) is a result of differences in the maxima on both sides of the dip on the pulse. The cause of these differences is that the analyte evaporation occurs in the process of heating the platform and, consequently, of increasing the gas temperature near the platform. Increased temperature causes changes in the parameters of the absorption line profile: increase of the Doppler and reduction of the Lorentz width. As a result, the roll-over level is continuously changing. This is explicitly seen in Figs 2(a)+a). In the model used by us, this circumstance has not been taken into account. It is quite possible that these imperfections in the theoretical model lead to a larger error than implied here.

B. V. L’vov et al.

1416 04

E

! x

B 8 2 a

8 9

,-

0

C

. 0

, 0

4

5

Time k4

Time k.) 1000

I (cl

3

E

2

b :: a

B

100

Fig. 2. (a) Absorption pulses for 0.1, 0.2 and 0.4 ng of Be (at SBP = 2 nm), (b) corresponding restored pulses and (c) calibration graphs plotted over all initial (0) and corrected (0) values of the integrated absorbance.

The height of the restored pulses reach as much as 11 and 32 absorbance units for Bi and Cd (Figs. 3(b) and 4(b)). These are unthinkable values for the conventional non-Zeeman measurement scheme because, in the case of a monochromatic light source, they must correspond to a decrease in the light intensity by the same number of orders of magnitude. In this case, the S/N ratio should have increased by about 6 and 16 orders of magnitude, respectively. In our case, as seen from Figs 2(a)-4(a), the increase of noise does not exceed an order of magnitude, which enables us to carry out measurements with sufficient precision. Figures 2(c)-4(c) and Table 2 provide the results of calibration curve linearization for the three elements. Their relevant parameters A, and R differ widely covering practically the entire range of their possible variation. However, linearization has proved to be efficient for all three elements, including pulses whose dips reach the Xaxis. As expected, the values of R within the dip region entering into Eqn (4), proved to be higher than those of R measured at small signals. For Bi, the value of R remains practically constant, which indicates that the function A(BG) = f(A& is close to linear. The widening of the dynamic ranges by using a dip determined by the ratio m2/m1, where ml and m2 are analyte masses characterized by the appearance of a dip and by the dip reaching the x-axis, was: 2.5 and 2.7-fold for Be; 4-fold for Bi; and 12.5fold for Cd. These results are in good agreement with the expected values calculated by the ratio given in Eqn (6): 2.9 and 3.2-fold for Be; 3%fold for Bi and 14.3-fold for Cd. It follows from Table 2 that the full linearized range of measurement extends for

1417

Dynamic range extension in Zeeman GFAAS

Time (s)

Time (s)

I

100

I

I

I

1000 Mass(pg)

10000

100000

Fig. 3. (a) Absorption pulses for 10, 15 and 30 ng of Bi, (b) corresponding restored pulses and (c) calibration graphs plotted over all initial (0) and corrected (0) values of the integrated absorbance.

Table 2. Parameters used in the correction program and some results of that program Element

Be* Bet Bi Cd

A,

0.4 0.7 1.2 1.0

R AaA, 0.53 0.56 0.735 0.87

R in dip 0.66 0.69 0.74 0.93

UAo.Nm,x (s) 3.4 5.0 7.6 20.0

U-Ao.ndOmax 0.0044 s 780 1140 1700 4500

(Z)

(Z)

0.2 0.3 10.0 0.4

0.5 0.8 40.0 5.0

n

RSD W)

26 17 43 18

4.4 7.3 5.6 4.4

* SBP = 2.0 nm. t SBP = 0.7 nm.

3-4 decades above the values of mo: up to 1140 m. for Be; 1700 m. for Bi and 4500

m. for Cd. Linearization error was characterized as before [lo] by the relative standard deviation (RSD) of the experimental points around the linearized graph. In the calculation, we used all (n) experimental points on the graph, taking into account a number of parallel measurements with each mass of analyte. This error includes not only linearization error but also errors resulting from sampling of different volumes of solution and from signal measurement as well. Comparison of RSD values presented in Table 2 with the error of repeated measurements of one and the same mass of analyte without using linearization has shown that the error of the linearization procedure should not exceed 2-3%. This is a surprising result considering the approximations of the model.

B. V. L’vov et al.

1418

0'5

2;

I

I

05

25

Time (s)

0.01

Time (s)

’

I

I

I

I

I

IO

loa

loo0

10000

Mass tpg) Fig. 4. (a) Absorption pulses for 0.5, 1, 2 and 4 ng of Cd, (b) corresponding restored pulses and (c) calibration graphs plotted over all initial (0) and corrected (0) values of the integrated absorbance.

4.2.

Correction of spectral interferences

The efficiency of correcting for spectral interference in the dip region was examined by determining varying amounts of Cd in the presence of a large excess of NaCl. Figure 5, as an illustration, shows pulses for 0.5 and 2.5 ng of Cd in the absence and

l-

E ..

E .... d u

01 l

I

I

4

Time (sl

I

0

I

4 Time k.)

Fig. 5. Absorption pulses for (a) 0.5 ng and (b) 2.5 ng of Cd in the absence and presence of 13.5 p,g of NaCI. The dotted line indicates the absorption pulse for 13.5 pg of NaCl in the SB mode.

Dynamic range extension in Zeeman GFAAS

1419

Table 3. Correction of molecular absorptionof 13.5 pg NaCl in the case of Cd determination for the peaks with dips I&.&

(s)

Mass of Cd (ng)

no NaCl

with NaCl

Signal difference (s)

0.5 1.0 2.5 3.0

1.92 3.95 10.58 12.12

1.95 3.94 10.68 12.62

0.03 -0.01 0.10 0.50

presence of 13.5 pg of NaCl, and Table 3 lists the results of correction for different masses of Cd. As clearly seen from the results listed, the overlap of intense molecular absorption, reaching at the maximum as high as 1.2, had very little affect on either the shape of the analytical signals, or their integrated absorbance value. This is an indication that the main portion of non-absorbed radiation of the HCL entering the detector is absorbed by a rather selective NaCl molecular band, just as the analytical line radiation is. This is possible only in that case when the non-absorbed radiation is confined to a narrow region of the spectrum near the analytical line (within SBP), and the contribution of stray light with broad distribution over the spectrum is insignificant. Indeed, if the main portion of non-absorbed radiation entering the detector were determined by stray light with a spectral distribution outside the SBP of the monochromator, a reliable correction of spectral interference in the region of the analytical line would be impossible. This would manifest itself in dramatic changes of the pulse shape and would be especially visible for Cd pulses with a slight dip (see Fig. 5(a)). We consider the conclusion about the homology of the non-absorbed portion of radiation and the analytical line radiation with respect to spectral interferences to be valid not only for Cd but also for other elements. This is confirmed, judging by many publications, by successful application of Zeeman spectrometers in situations when the absorption intensity of the spectral interferant exceeded the roll-over value and where the presence of radiation non-homological with respect to spectral interference might lead to incorrect results even at small and medium absorption signals. This conclusion is in agreement with the comprehensive investigation by DE LOOS-VOLLEBREGT and DE GALAN [13] who concluded from their experimental results “that the stray radiation is located close to the resonance wavelength of the analyte”. Nevertheless, on the whole, the problem requires further careful study.

5. CONCLUSIONS Let us sum up the advantages and drawbacks of the method proposed. As to the advantages over the 3-field method [l-3], they are listed below. First, the method permits the extension of the measurement range without introducing any changes in the instrument design and it may be used with the currently employed spectrometers. Second, it provides a two-fold increase in the dynamic range on account of a dl.5 fold improvement in performance of the SIN ratio at small signals and 1.6-1.8-fold widening of the upper limit of analytical range. For example, for Be and Cd, according to data from Ref. [3], the extension of the range is equal to 1.4 and 7.9. In our case (see Table 2) it is 2.5 and 12.5. Third, the calibration graph for the proposed method is linear and, consequently, does not require a large number of solutions and measurements. To find the three parameters needed for work with a linearized graph (m,,,A, and R), only two measurements with two solutions were necessary. Fourth, the method provides constancy of the analytical signal irrespective of possible variations in the shape of peaks for different matrices. Among the drawbacks of the method vs the 3-field method are the transition in the

B. V. L’vov et al.

1420

dip region from the Zeeman-effect background correction to the less efficient continuum background correction and the necessity (we hope, removable in the future) of having to define visually the boundaries of the dip region. We are aware of the fact that the present study is only a first step, but the prospects appear promising. The problems to be solved include: defining the dip region boundaries automatically; improvements in the theoretical model; and application of the method to other elements, particularly in routine conditions. Both this paper and that by DE LOOS-VOLLEBREGTand DE GALAN [13] emphasize the importance of understanding the spectral distribution of the radiation that is used for correcting background in the Zeeman correction system, especially in the presence of large background signals. The source and spectral distribution of this radiation remains unclear. With these problems solved, the method developed might significantly increase the potential of the Zeeman GFAAS and, in particular, bring us closer to the solution of the problem of simultaneous multi-element analysis. In view of the latest achievements [14] in the field of the application of spatially isothermal furnaces for simultaneous atomization of elements covering a wide range of volatilities, the prospect of the development of the necessary instrumentation seems to be more and more realistic. An equally important opportunity offered by this method is to move GFAAS much closer to absolute analysis, largely independent of instrumental parameters as well as matrix effects. REFERENCES [l] M. T. C. de Loos-Vollebregtand L. de Galan, Appl. Spectrosc. 38, 141 (1984). (21 M. T. C. de Loos-Vollebregt, L. de Galan and J. W. M. van Uffelen, Spectrochim. Acta 41B, 825 (1986). [3] M. T. C. de Loos-Vollebregt, J. P. Koot and J. Padmos, J. Anal. At. Spectrom. 4, 387 (1989). [4] M. S. Hashimoto, H. Yamada, K. Ohishi and K. Yasuda, Anal. Sci. 2, 109 (1986). [S] T. W. Brueggemeyer and F. L Fricke, Pittsburgh Conf, Abstract book, Paper No. 1254. New York (5-9 March 1990). [6] H. Koizumi, H. Yamada, K. Yasuda, K. Uchino and K. Oishi, Spectrochim. Acta XiB, 603 (1981). [7] P. A. Bayunov and B. V. L.‘vov, Zh. Anal. Khim. 42, 621 (1987). [8] B. V. L’vov, J. Anal. At. Spectrom. 3, 9 (1988). [9] B. V. L’vov, L. K. PoLzik and N. V. Kocharova, Spectrochim. Acta 47B, 889 (1992). [lo] B. V. L.‘vov, L. K. Polzik, N. V. Kocharova, Yu. A. Nemets and A. V. Novichikhin, Spectrochim. Acta 47B, 1187 (1992).

[ll] V. P. D’yakonov, Handbook on Algorithms and Programs for Personal Computers. (1987). [12] A. Savitzky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964). [13] M. T. C. de Loos-Vollebregt and L. de Galan, Spectrochim. Acta 41B, 597 (1986). [14] M. Berglund, W. Frech and D. C. Baxter, Spectrochim. Acta 46B, 1767 (1991).

Nauka, Moscow