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Application of line width measurements in spectrographic analysis
38B.No
4.p~ 54-547. 1983.
Application of line width measurements in spectrographic analysis A. M. KABIEL, A. M. SHOAEB, M. M. MOSSAAD, and M. K. NASRA Medical Research Institute and Faculty of Sciences, Alexandria University, Alexandria, Egypt (Receioed 14 April 1982) Abstract-Investigations Based on theoretical assumptions and experimental results were carried out for usmg the line width as a concentration index in spectrographic analysis of complex materials.
1. INTR~DUCH~N IT IS well known that the spectrum lines have an observable width that results from a combination of both physical and instrumental factors [l-3]. Several investigators [4,5] have developed spectrographic methods based on so-called “effective line widths”. KABIELer al. [6] have recently pointed out that the line width factor is precisely proportional to the apparent intensity. Although their proposal is the best one to represent and fit the instrumental profile, yet the determination of the line width factor is too lengthy and becomes tedius when applied in practical spectrographic analysis of complex material. The aim of this article is to discuss some aspects about the line width and report its application to attain in a simple way precise spectrographic results. 2. PRELIMINARYINVESTIGATIONS The line profile of the emission line was considered to be Lorentzian [2,3,7-91. Taking into consideration the assumption given in [6], the Lorentz equation can have the form: 1,
cm
1
1 +/?x2
where I,,, is the apparent maximum intensity, I, the apparent intensity at a profile width x and /.I a constant to be determined. Others [2,3, lo] found that it is convenient and probably reasonable to assume that the profile of the emission line is Gaussian. We can bring the Gauss equation in the form: I, = I, exp ( - yx’)
(2)
where y is a constant. Using the experimentally determined minimum slit width [6], verification of the above two equations are shown in Figs. 1 and 2, where it was found that Eqn (1) is only valid for small x values while Eqn (2) is only valid for large x values. Since both Lorentzian and Gaussian forms are statistically independent, the combined treatment of both leads to the form: [l] P. COHEUR,J. Opt. Sot. Am. 36,498 (1946). [Z] H. E. WHITE,Introduction to Atomic Specrra. McGraw-Hill, New York (1963). [3] I. I. SOBEL'MAN, An Introduction to the Theory of the Atomic Spectra, Academy of Sciences of the U.S.S.R (1972). [4] W. GERLACH and W. ROLLWAGEN, Met. Wirfschaff 16. 1083 (1937). [S] E. J. EASTMOND and B. E. WILLIAMS, J. Opt. Sot. Am. 38, 800 (1948). [6] A. M. KABIEL,A. M. SHOAEB.F. I. NASRand Y. M. ALI, Specrrochim.Ada 36B, 129 (1981). [7] G. V. MARR,Plasma Spectroscopy. Elsevier, Amsterdam (1968). [S] H. G. KUHN, Atomic Spectra, Longman. London (1971). [9] C. S. WILLIAMS and A. BECKLUND, Oprics. Wiley-Interscience, New York (1972). [lo] S. BRODERSEN, J. Opt. Sot. Am. 44, 22 (1954). [l I] IUPAC, Spectrochim. Acta 33B, 228 (1978).
A. M.
544
KABIEL ef al.
1 zo.14 lm
1.0 -
$= slope of straight
portion
p zo.030
I 50
0.0'
I 100
I 150
I 200
X2
Fig. 1. Experimental verification of the Lorentz equation.
X 4 2.0 -; I
8
12 I
16
20 1
'1, ,
-
for Ill 1,/x
-
for In Ix/X2
\ \ , \
-0.2 I 20
I 40
I 60
I 80
100
120
I 140
'. .
160
X2
Fig. 2. Experimental verification of the Gauss equation.
180
I 2M)
-
Application of line width measurements in spectrographic analysis
In
$
545
-;{yx2+ln(l+BX2)}
=
(3)
0 In
which is the same as the limited solution of the Maxwellian distribution of intensity [3]. The experimental investigation represented in Fig. 3 showed that Eqn (3) needs some modifications to fit closely the instrumental line profile in the regions of high intensities. Thus we propose an equation of the type; ln 4 = -f{ux+ln(i+j.k’)) 0 RI The experimental verifications (Fig. 3) showed that Eqn (4) is satisfactory for most practical purposes, even for small x values. The statistically calculated values of both the correlation coefficient and the slope of the line are - 0.9996 and - 0.508 respectively. 3. 3.1.
EXPERIMENTAL
Analytical applications
Spectrographic investigations were carried out to determine rare earth elements in rare earth oxides. The specific example discussed physical and chemical properties spectrum of rare earths consists largest dispersion of the prism
here is the determination of lanthanum. The great similarity of both of rare earths has induced us to use cerium as internal standard. As the of many lines, care was taken to select lines that lie in the region of the spectrograph used.
2.0
1.5
,* 5
1.c
I
0.:
‘\
‘.
04
I
I
0.5
1.0
I
1.5
I
I
1
1
I
2.0
2.5
3.0
3.5
4.0
Maxwcllmn
Fig. 3. Experimental
verification
thlcknesS
of an assumed Maxwellian
intensity distribution.
\
546
A. M. KABIEL PI al.
In order to extend both the lower and the higher limits of the analysis range so as to cover the wide range of concentrations often occurring in the samples, it was necessary to use the most sensitive spectral lines of the analyte. The homologous line pair La III 237.942 nm and Ce III 237.237 nm proved to be satisfactory. 3.2. Preparation and excitation of the sample In preparing the actual samples for analysis [12], the proper values of the standards as well as the analysis samples free from Ce [13, 141, 0.5 mgml-’ of Ce,O, taken as internal standard and 25 mg ml- ’ of NaCl used as buffer were mixed well and adjusted in a measuring flask. One ml of the composite solution was evaporated on two hat-topped, 10 mm dia. spectrographically pure graphite electrodes, to which a drop of an adhesive resin has been previously applied. The two electrodes were excited in a 15 kV spark at 6 pF and 0.5 mH. An image was focussed at the collimator lens of a medium quartz prism spectrograph with an aperture ratio l/30 at 257.3 nm. After a pre-exposure of 5 s, an exposure of 90 s was used so that the sample was burnt to completion. For width measurements, a recording microphotometer of the type M+ - 4 was used. The spectra were recorded on 13 x 18 cm photographic plates and the widths were measured from the photographic record by aid of a magnifier. 3.3. Results Using the experimentally determined minimum slit width [6], the profile of I_a 111-237.942 nm was recorded. The determined values of both y and /I are 0.162 and 0.030 respectively. An analytical curve was prepared from measurements of spectrograms of standard samples ranging from 0.01 mg ml-’ to 10 mg ml- ’ of La,O,. The standards contained in addition Y,O, [123 which was added in such a quantity that the sum of La,O, and Y,O, was 10 mg ml- ‘. The analytical curve is shown in Fig. 4, where (yx + In (1 +/Ix’)) is plotted vs the logarithm of concentration of the analyte. The value of x is the La-line width measured at the maximum opacity of the Ce line. The width measurements on repeated exposures of the same sample at about 107, La,O, concentration showed a precision of about 10 7; relative standard deviation.
2.5-
I 10
1.0
Cone of La2O3tm percent)
Fig. 4. Analytical
[12] [13] [I41
A. M. SHOAEB, F.
evaluation
curve for La,O,
in rare earth oxides.
I. NASR and Y. S. YOUSSEF, Delco J. Sci. (accepted for pubhcation (1980)). B. S. HOPKINS, C. N. MCCARTY, L. R. SCRIBNERand M. ZAWRENZ, Ind. Eng. Chem. Anal. Ed. IO, 184 (1938). V. A. CHERNIKHOVand T. A. USPENSKAYA,Zauod. Lab. 9, 276 (1940).
Application
ol’ lint width mcasurcmcntb
in spectrographic
analysis
547
4. CONCLUSION It is not surprising that neither the Lorentzian nor the Gaussian form is exact for the whole range of experimental values of the line widths since both forms are expected to be valid only when the radiation is purely coherent. This is naturally not the case because the radiation is a mixture ofcoherent and incoherent radiation. The modified Maxwellian distribution form is, therefore, expected to be valid for most practical purposes even when the line is subjected to self-reversal or self-absorption. The only comment which should be added here is that, care must be taken when the two opacity maxima are approached. In this case the deviation is due to failure in accurately measuring the width.
4.p~ 54-547. 1983.
Application of line width measurements in spectrographic analysis A. M. KABIEL, A. M. SHOAEB, M. M. MOSSAAD, and M. K. NASRA Medical Research Institute and Faculty of Sciences, Alexandria University, Alexandria, Egypt (Receioed 14 April 1982) Abstract-Investigations Based on theoretical assumptions and experimental results were carried out for usmg the line width as a concentration index in spectrographic analysis of complex materials.
1. INTR~DUCH~N IT IS well known that the spectrum lines have an observable width that results from a combination of both physical and instrumental factors [l-3]. Several investigators [4,5] have developed spectrographic methods based on so-called “effective line widths”. KABIELer al. [6] have recently pointed out that the line width factor is precisely proportional to the apparent intensity. Although their proposal is the best one to represent and fit the instrumental profile, yet the determination of the line width factor is too lengthy and becomes tedius when applied in practical spectrographic analysis of complex material. The aim of this article is to discuss some aspects about the line width and report its application to attain in a simple way precise spectrographic results. 2. PRELIMINARYINVESTIGATIONS The line profile of the emission line was considered to be Lorentzian [2,3,7-91. Taking into consideration the assumption given in [6], the Lorentz equation can have the form: 1,
cm
1
1 +/?x2
where I,,, is the apparent maximum intensity, I, the apparent intensity at a profile width x and /.I a constant to be determined. Others [2,3, lo] found that it is convenient and probably reasonable to assume that the profile of the emission line is Gaussian. We can bring the Gauss equation in the form: I, = I, exp ( - yx’)
(2)
where y is a constant. Using the experimentally determined minimum slit width [6], verification of the above two equations are shown in Figs. 1 and 2, where it was found that Eqn (1) is only valid for small x values while Eqn (2) is only valid for large x values. Since both Lorentzian and Gaussian forms are statistically independent, the combined treatment of both leads to the form: [l] P. COHEUR,J. Opt. Sot. Am. 36,498 (1946). [Z] H. E. WHITE,Introduction to Atomic Specrra. McGraw-Hill, New York (1963). [3] I. I. SOBEL'MAN, An Introduction to the Theory of the Atomic Spectra, Academy of Sciences of the U.S.S.R (1972). [4] W. GERLACH and W. ROLLWAGEN, Met. Wirfschaff 16. 1083 (1937). [S] E. J. EASTMOND and B. E. WILLIAMS, J. Opt. Sot. Am. 38, 800 (1948). [6] A. M. KABIEL,A. M. SHOAEB.F. I. NASRand Y. M. ALI, Specrrochim.Ada 36B, 129 (1981). [7] G. V. MARR,Plasma Spectroscopy. Elsevier, Amsterdam (1968). [S] H. G. KUHN, Atomic Spectra, Longman. London (1971). [9] C. S. WILLIAMS and A. BECKLUND, Oprics. Wiley-Interscience, New York (1972). [lo] S. BRODERSEN, J. Opt. Sot. Am. 44, 22 (1954). [l I] IUPAC, Spectrochim. Acta 33B, 228 (1978).
A. M.
544
KABIEL ef al.
1 zo.14 lm
1.0 -
$= slope of straight
portion
p zo.030
I 50
0.0'
I 100
I 150
I 200
X2
Fig. 1. Experimental verification of the Lorentz equation.
X 4 2.0 -; I
8
12 I
16
20 1
'1, ,
-
for Ill 1,/x
-
for In Ix/X2
\ \ , \
-0.2 I 20
I 40
I 60
I 80
100
120
I 140
'. .
160
X2
Fig. 2. Experimental verification of the Gauss equation.
180
I 2M)
-
Application of line width measurements in spectrographic analysis
In
$
545
-;{yx2+ln(l+BX2)}
=
(3)
0 In
which is the same as the limited solution of the Maxwellian distribution of intensity [3]. The experimental investigation represented in Fig. 3 showed that Eqn (3) needs some modifications to fit closely the instrumental line profile in the regions of high intensities. Thus we propose an equation of the type; ln 4 = -f{ux+ln(i+j.k’)) 0 RI The experimental verifications (Fig. 3) showed that Eqn (4) is satisfactory for most practical purposes, even for small x values. The statistically calculated values of both the correlation coefficient and the slope of the line are - 0.9996 and - 0.508 respectively. 3. 3.1.
EXPERIMENTAL
Analytical applications
Spectrographic investigations were carried out to determine rare earth elements in rare earth oxides. The specific example discussed physical and chemical properties spectrum of rare earths consists largest dispersion of the prism
here is the determination of lanthanum. The great similarity of both of rare earths has induced us to use cerium as internal standard. As the of many lines, care was taken to select lines that lie in the region of the spectrograph used.
2.0
1.5
,* 5
1.c
I
0.:
‘\
‘.
04
I
I
0.5
1.0
I
1.5
I
I
1
1
I
2.0
2.5
3.0
3.5
4.0
Maxwcllmn
Fig. 3. Experimental
verification
thlcknesS
of an assumed Maxwellian
intensity distribution.
\
546
A. M. KABIEL PI al.
In order to extend both the lower and the higher limits of the analysis range so as to cover the wide range of concentrations often occurring in the samples, it was necessary to use the most sensitive spectral lines of the analyte. The homologous line pair La III 237.942 nm and Ce III 237.237 nm proved to be satisfactory. 3.2. Preparation and excitation of the sample In preparing the actual samples for analysis [12], the proper values of the standards as well as the analysis samples free from Ce [13, 141, 0.5 mgml-’ of Ce,O, taken as internal standard and 25 mg ml- ’ of NaCl used as buffer were mixed well and adjusted in a measuring flask. One ml of the composite solution was evaporated on two hat-topped, 10 mm dia. spectrographically pure graphite electrodes, to which a drop of an adhesive resin has been previously applied. The two electrodes were excited in a 15 kV spark at 6 pF and 0.5 mH. An image was focussed at the collimator lens of a medium quartz prism spectrograph with an aperture ratio l/30 at 257.3 nm. After a pre-exposure of 5 s, an exposure of 90 s was used so that the sample was burnt to completion. For width measurements, a recording microphotometer of the type M+ - 4 was used. The spectra were recorded on 13 x 18 cm photographic plates and the widths were measured from the photographic record by aid of a magnifier. 3.3. Results Using the experimentally determined minimum slit width [6], the profile of I_a 111-237.942 nm was recorded. The determined values of both y and /I are 0.162 and 0.030 respectively. An analytical curve was prepared from measurements of spectrograms of standard samples ranging from 0.01 mg ml-’ to 10 mg ml- ’ of La,O,. The standards contained in addition Y,O, [123 which was added in such a quantity that the sum of La,O, and Y,O, was 10 mg ml- ‘. The analytical curve is shown in Fig. 4, where (yx + In (1 +/Ix’)) is plotted vs the logarithm of concentration of the analyte. The value of x is the La-line width measured at the maximum opacity of the Ce line. The width measurements on repeated exposures of the same sample at about 107, La,O, concentration showed a precision of about 10 7; relative standard deviation.
2.5-
I 10
1.0
Cone of La2O3tm percent)
Fig. 4. Analytical
[12] [13] [I41
A. M. SHOAEB, F.
evaluation
curve for La,O,
in rare earth oxides.
I. NASR and Y. S. YOUSSEF, Delco J. Sci. (accepted for pubhcation (1980)). B. S. HOPKINS, C. N. MCCARTY, L. R. SCRIBNERand M. ZAWRENZ, Ind. Eng. Chem. Anal. Ed. IO, 184 (1938). V. A. CHERNIKHOVand T. A. USPENSKAYA,Zauod. Lab. 9, 276 (1940).
Application
ol’ lint width mcasurcmcntb
in spectrographic
analysis
547
4. CONCLUSION It is not surprising that neither the Lorentzian nor the Gaussian form is exact for the whole range of experimental values of the line widths since both forms are expected to be valid only when the radiation is purely coherent. This is naturally not the case because the radiation is a mixture ofcoherent and incoherent radiation. The modified Maxwellian distribution form is, therefore, expected to be valid for most practical purposes even when the line is subjected to self-reversal or self-absorption. The only comment which should be added here is that, care must be taken when the two opacity maxima are approached. In this case the deviation is due to failure in accurately measuring the width.