Relationship between Resonance Line Profile and Absorbance in

Atomic Line Profiles in Hollow Cathode Lamps and a Glow Discharge Atomizer ... Atomic line profiles—their measurement and importance in analytical a...
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( 3 ) Gunstone, F. D., Russell, W. C., Ibid., 3782. ( 4 ) Hopkins, C. Y Bernstein, H. J., Can. J . Chem. 37,”775 (1959). (5) Jacobs, T. L., “Organic Reactions,” Vol. 5 , p. 48, Wiley, Xew York, 1949. ( 6 ) Johnson, L. F., Shoolev, J. N., ANAL. CHEY.34, 1136 (1962). (7) Kass, J. P., Burr, G. O., J . Am. Chem. SOC.61, 1062 (1939). (8) Lindlar, H., Acta 35, 446 (1952). ( 9 ) Meyer, L. H., Saika, A,, Gutowsky,

H. S., J . Am. Chem. SOC. 75, 4567 (1953). ( 1 0 ) Nukada, K., Yamamota, o., S u z M T., Takeuchi, RI., Ohnishi, RI., A x . ~ L . CHEM.35, 1892 (1963). ( 1 1 ) Purcell, J. M., Connelly, J . A., Ibid., 37, 1181 (1965). ( 1 2 ) Purcell, J. AT., Susi, H., A p p l . Spectr. 19, 105 (1965). ( 1 3 ) Roberts, J. D.1 “An Introduction to the Analysis of Spin-Spin Splitting in

Nuclear Magnetic Resonance Spectra,” p. 57, W. A. Benjamin Inc., New York,

1961. (14) Tiers, G.

V. D., “Characteristic

Suclear Magnetic Resonance Shielding Values for Hydrogen in Organic Structures,” Part I : Tables of 7-Values for a Variety of Organic Compounds, RIinnesota Mining and Manufacturing Co., St. Paul, hlinn., 1958. RECEIVED for review September 28, 1965. Accepted February 2, 1966. First hliddle Atlantic Regional Xeeting, ACS, Philadelphia, Pa., February 3-4, 1966. Mention of commercial products does not constitute an endorsement by the United States Department of Agriculture over others of a similar nature not mentioned.

Relationship Between Resonance Line Profile and Absorbance in Atomic Absorption Spectrometry KAZUO YASUDA Application Laboratory, Naka Works, Hatachi Ltd., Katsuta-shi, Ibaraki-ken, Japan The relationship between the profile

CAMWE LAMPc

of the resonance emission line of the calcium hollow cathode lamp and the absorbance of calcium atomic vapor in the flame, and the relationship between the profile of the resonance absorption line of calcium in the flame and its absorbance were studied theoretically. It was found that the decrease in the absorbance of calcium in the flame caused by the increase in the discharge current of the lamp is due to the self-absorption of the resonance emission line from the lamp, and that the increase in the Doppler breadth of the resonance emission line has a slight effect on the absorption intensity. The center of the resonance absorption line of the flame shifts to longer wavelength, and the resonance absorption line is not symmetrical. Consequently, the difference in the relationship between the absorbance of the flame and the discharge current in various flames is presumably due to the shift and asymmetry of the absorption line.

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N ATOMIC ABSORPTION SPECTROMETRY, the profiles of the resonance

emission line and the resonance absorption line have an influence on the absorbance of atomic vapor in the flame (7). I n order to increase the absorbance (1, 4, the atomic vapor temperature, gas pressure, and the degree of selfabsorption, all of which determine the breadth of the resonance emission line from a hollow cathode lamp as a light source, must be low values. I n developing the initial theory of atomic absorption spectrometry, Walsh (9) assumed that the breadth of the resonance emission line from a hollow cathode lamp is extremely narrow, that 592

ANALYTICAL CHEMISTRY

Figure 1. Schematic diagram of pressure-scanning Fa bry-Perot interferometer

the central wavelength of the resonance emission line from the lamp corresponds to the central wavelength of the resonance absorption line, and that the breadth of this absorption line is determined by the Doppler effect. Shimazu and Hashimoto (8)measured sodium line profiles, and showed that the breadth of the resonance emission line from the sodium discharge lamp is of the same order as the resonance absorption line breadth of sodium in the airacetylene flame, and that a n increase in the self-absorbance of the resonance emission line caused a decrease in the absorbance of the flame. Winefordner (10) made clear theoretically that the absorbance is independent of the absorption line breadth as long as the breadth of the resonance emission line from the lamp is much smaller than the breadth of the resonance absorption line. The relatively high density of gases in flames at atmospheric pressure results in a resonance absorption line with extensive collisional broadening. The relationship between the discharge current of the calcium hollow cathode lamp and the absorbance of calcium in a flame is different according to the kind of flame-Le., oxyhydrogen, oxypro-

pane, or oxyacetylene. This may be due to the fact that there is a shift in the absorption line ( 3 ) . R e studied the following two subjects: (1) the determination of the profile of the resonance emission line from the calcium hollow cathode lamp, and the relationship between the increase in the Doppler breadth or the degree of self absorption of the resonance emission line and the absorbance of calcium in the flame; and (2) the determination of the resonance absorption line profile of calcium in the flame, and the difference in the absorbance of calcium in various flames. EXPERIMENTAL

Measurement of t h e Profile of the Resonance Emission Line from t h e Calcium Hollow Cathode Lamp. T h e breadth of t h e resonance emission line from the lamp is related to t h e temperature of calcium atomic vapor. T h e temperature of atomic vapor in t h e discharge is higher than t h e cathode temperature. By t h e use of t h e pressure scanning Fabry-Perot interferometer, shown in Figure 1, the profile of the resonance emission line at various discharge currents was observed. The emission lines from the lamp (the hollow cathode was made of calcium aluminum alloy) mere dispersed by the monochromator, and the bright lines 4228.9, 4227.5, and 4226.8 A. of aluminum neighboring the calcium resonance line a t 4226.7 A. were excluded. Only one resonance emission line was introduced into the interferometer. After the etalon chamber was evacuated, air was introduced gradually into the chamber by opening stopcock 1 (see Figure 1). The interference fringe at the center grew with the increase of air pressure in the chamber. The intensity at the center of the fringe was determined with the photomultiplier tube.

ca HOLLOW CATHOOE LAMP I

IITTER

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\MONOCHROMATORI Figure 2.

NEW LIGHT SOURCE

HOLLOW CATHODE LAMP 2

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FCTOR

Measurement of absorbance of the lamp

Measurement of Self-Absorption of t h e Resonance Emission Line from t h e Calcium Hollow Cathode Lamp. I n order to obtain the atomic vapor temperature of calcium in the lamp, it is necessary to measure the amount of self-absorption of the resonance emission line. Therefore, we measured the atomic density of the ground state in the lamp by the experimental method shown in Figure 2. The light of the resonance emission line from lamp 1 was passed through the cathode of lamp 2. The atomic density of the ground state could then be measured by observing the degree of absorption of the light from lamp 1. Lamp 2 was used as the light source in all observations except this one. Measurement of Self-Absorption of t h e Resonance Emission Line from t h e Calcium Hollow Cathode Lamp and Absorbance of Calcium in t h e Flame. By keeping the discharge current of t h e lamp a t 60 ma., the light of the resonance emission line from the lamp was passed through flame 1, as shown in Figure 3. T h e reversal of the resonance emission line was caused by the calcium atomic vapor in flame 1. By spraying calcium solutions of various concentrations into flame 1, the degree of reversal of the emission line was changed. This reversed line (analogous to a self-absorbed emission line) was taken as a new light source; this light was passed through flame 2. The decrease in the absorbance of flame 2 due to an increase in the absorbance of flame 1 (analogous to the increased self-absorption of the resonance emission line from the new light source) was measured. In order to reduce the calcium emission intensity of flame 1, the air-propane flame was used.

Figure 3. Measurement of absorbance of the flame by the resonance emission lines having self-absorption

Measurement of the Wavelength Shift of t h e Calcium Resonance Absorption Line in t h e Flame. The wavelength shift between the center of t h e resonance emission line from the hollow cathode lamp and the center of the resonance absorption line of calcium in the flame was measured with the Fabry-Perot interferometer. The apparatus shown in Figure 1 was modified by placing the flame between the lamp and the monochromator. The profile of the resonance emission line passing through the flame was observed by the same method mentioned above. Measurement of t h e Resonance Emission Line Profile of Calcium in t h e Flame. Because the emission intensity of calcium in the flame was unstable and weak, the profile of this emission line could not be measured b y the photoelectric method shown in Figure 1. Therefore, the pin hole and the detector of this apparatus were removed and the pressure scanning system was not used. A photograph of the concentric interference fringe forming with the etalon was taken, and the

line profile was measured with a densitometer. The burning condition of a flame differs with the shape of burner and the kind of fuel gas; therefore the gas density, the kind of radical, and the temperature are dependent upon these conditions. Consequently, it is considered that the collisional and Stark broadening effects are dependent upon the shape of burner. In order to achieve constant burning conditions, the burner shown in Figure 4 was developed. The profile of the resonance emission line of calcium in the oxyhydrogen, in the oxyacetylene, and in the oxypropane flames was observed by keeping the oxygen flow rate a t a fixed value when using this burner. Because the emission intensity of calcium in the air-acetylene flame was very weak, the profile could not be observed. RESULTS

Profile of t h e Resonance Emission Line from t h e Calcium Hollow Cathode Lamp. The measured profiles of the resonance emission lines are RED

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FUEL

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Figure 4.

Figure 5.

Profile of resonance emission line from the lamp Measured half breath

0.027 A. at 4 0 ma. 0 . 0 3 1 A. at 60 ma. 0 . 0 3 6 A. at 8 0 ma. 0 . 0 4 1 A. at 90 ma.

Schematic diagram of burner

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Figure 6. Relationship between discharge current and absorbance of the lamp

shown in Figure 5, where t h e values of discharge current of t h e lamp were 40, 60, 80, and 90 ma. T h e emission intensity was recorded on t h e vertical axis. Wavelength is used on t h e horizontal axis because wavelength is approximately proportional to wavenumber on t h e small wavelength range of the resonance line width. Amount of Self-Absorption of the Resonance Emission Line from the Calcium Hollow Cathode Lamp. Since the breadth of t h e resonance emission lines from lamps 1 and 2 is of the same order of magnitude, the atomic ground state concentration in lamp 2 will not be proportional to the absorbance when t h e absorbance becomes greater. Therefore, t h e absorbance of lamp 2 was measured at various currents through lamp 1, and was calculated graphically at zero current value through lamp l. The calculated value is approximately proportional to the atomic ground state concentration and, therefore, this value is designated the true absorbance of

0.100 r

lamp 2. Next, at the various currents through lamp 2, the true absorbances were observed. The results are shown in Figure 6, where the true absorbance was placed on the vertical axis and the discharge current values on the horizontal axis. Amount of Self-Absorption of the Resonance Emission Line from the Calcium Hollow Cathode Lamp and Absorbance Calcium in the Flame. The decrease in the absorbance of flame 2 due to the increase in the absorbance of flame 1 (analogous to increased selfabsorption of the resonance emission line from the hollow cathode lamp) is shown in Figure 7 . The absorbance of flame 1 was placed on the horizontal axis and the absorbance of flame 2 on the vertical axis. Profile of the Resonance Absorption Line of Calcium in t h e Flame. The profile of t h e resonance emission line from the hollow cathode lamp being transmitted through the oxyhydrogen flame is shown in Figure 8. The results obtained in the oxyacetylene and the oxypropane flames were almost the same. Further, the profile of the resonance emission line was observed in the case of calcium dissolved in an organic solvent (EtOH-H20) and sprayed into the oxyhydrogen flame. The results were also almost the same as those obtained with the above oxyacetylene and oxypropane flames. I n order to obtain the wavelength shift of the resonance absorption line center, the wavelength of the reversed line center was measured (see Figure 8). The wavelength shift with respect to the center of the resonance emission line from the lamp a t various absorbances of the flame was plotted in Figure

0

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ABSORBANCE OF F L A M E I ( loglfl)

Figure 7. Relationship between selfabsorption factor of the resonance emission line and absorbance of the flame

9. The wavelength shift of the absorption line center was obtained by the following graphical calculation. Since the wavelength of the reversed line center in Figure 8 is related to the line profiles and the line centers of the resonance emission line from the lamp and of the resonance absorption line of calcium in the flame, the reversed line center does not always appear a t the absorption line center. Therefore, the wavelength shift of the reversed line center corresponding to various absorbances of the flame was plotted on Figure 9. The wavelength shift having a constant value as a function of the decrease in the intensity of the transmitted light is not dependent upon the profiles of the emission line and the absorption line. Here IO indicates the light intensity of the resonance emission line from the lamp when it is not absorbed by the flame, and I is the inten-

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0 p.p.m.

20 p.p.rn.

0 50 p.p.rn.

100 p.p.rn.

Figure 8. Profile of resonance emission line of the lamp after absorption by the oxyhydrogen flame

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Figure 9. Wavelength shift of calcium resonance absorption line of the flames

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kinds of flame, the relationship between t h e increase in the discharge current of t h e hollow cathode lamp and the decrease in absorbance of atoms in t h e flame is dependent upon t h e kinds of flame. Figure 11 shows the changes in absorbance of the oxyhydrogen, the oxyacetylene, and the oxypropane flames due t o t h e increase in the discharge current of the lamp, and the change in absorbance when calcium dissolved in the organic solvent (EtOHH20) is sprayed into the oxyhydrogen flame. DISCUSSION

WAVELENGTH

Figure

10.

(A. )

Profile of the calcium res-

Onance emissionlinesfrom the lam,, the flames 1. 2,

3.

and

Calcium resonance emission line from lamp at discharge current of 90 ma. Calcium resonance emission (absorption) line in oxyhydrogen flame; sample concn. 40 p.p.m. in aqueous solution Calcium resonance emission (absorption) line in oxypropane flame; sample concn. 40 p.p.m. in aqueous solution

sity of the emission line after absorption by the flame. The profile of the resonance emission line of calcium in the flame can be considered to be the same as that Of the absorption line* The profiles Of the resonance emission lines from the oxyhlrdrogen and the oxypropane flames are sho'vn in Figure lo. The emission intensity (absorption coefficient) was placed On the axis and wavelength on the horizontal axis. Absorbance Of in the Various If the profile Of the resonance absorption line Of in the flame is dependent upon the

tering or vaporization is considered to be very low. Therefore, it is considered that the resonance breadth is narrow. Furthermore, it is conceivable that the Stark breadth is also narrow since the discharge voltage of the lamp is below 400 volts (5) and the electric field is constant in the hollow cathode. In view of the above facts, it was assumed that the breadth of the resonance emission line from the lamp as the light source was determined by Doppler broadening. From the measured results shown in Figures 5 and 6, the profile of this resonance emission line was calculated as follows. Since the profile of the resonance emission line is the same as that of the absorption line, the emission intensity a t any wavelength is proportional to the absorption coefficient a t the wavelength. The absorption coefficient k , of a resonance line is generally given by Equation 1 ( 5 ) .

Profile of t h e Resonance Emission Line from t h e Calcium Hollow Cathode Lamp. The resonance emission line from the lamp is due to a spontaneous rather than a n induced transition. Collisional, resonance, and Stark broadening for the ground state of a n atom differ from these broadening effects for the excited state. Therefore, the e-uzdy profile of the resonance emission line is kv = lie (1) a 2 (a - y)Z not the same as the profile of the resonance absorption line. However, in all AVS the preceding discussion, it has been a =-d 1 n 2 AVD assumed that the intensity Of the resonance emission line a t any wave2 ( V - YO) length within the resonance line width a=dln2 (2) is proportional to the absorption coefAVD ficient. 26 The factors determining the breadth y =l/L2 AVD of the resonance emission line from the lamp are the natural, ~ i j ~ col~ l ~ ~ , lisional, resonance, and Stark broadA' ' f enings, and self-absorption. Of them, the natural breadth is of the order of 10-3 to 10-4 .1.;this is very narrow where A v . ~and A v are ~ the natural and when compared with the other breadths. the Doppler breadths. Since the resSince the pressure of argon gas in the onance absorption line of calcium a t lamp is less than 5 mm. of Hg, i t is 4227 -4.is a singlet-singlet transition, conceivable that the collisional breadth 0.04 was used for the value of a ( 5 ) . is narrow as compared with the Doppler A value of Y represents the frequency of breadth from the experimental results of radiation, Y O represents the frequency of Zemansky ( 5 ) . The temperature of radiation a t the maximum absorption the hollow cathode is les's than 800' coefficient, 6 is a variable distance from K.; furthermore, the calcium atomic the point ( V - y o ) > AT the number of vapor pressure due t o cathode sputatoms that can absorb the resonance + o i

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SELF- ABSORPTION FACTOR 0 00% ( 0 ma

209 h ( 4 0 m o )

59 6 % ( S o m a )

OXYHYDROGEN

XYHYOROGEN SCLVENT;E tOH-HtO)

100

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-2 0

C U R R E N T (ma)

Figure 1 1. Relationship between discharge current and absorbance of the flames

0

+20 W

Figure 12. absorption

Profile of resonance line having self-

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emission line, and f is the oscillator strength, The absorption line profile (analogous to the emission line profile) plotted against w is shown in Figure 12. I n the hollow cathode lamp, since there exist calcium atoms in the ground state, the resonance emission line is self-absorbed. The profile of this line was calculated in the following way. The central wavelength of the resonance emission line is coincident with the center of the resonance absorption line, The light intensity of the resonance emission line at a value of w is expressed in Equation 1. The absorption coefficient of the atom is also obtained from Equation 1. The light intensity passed through the atomic vapor a t each value of w was calculated by Beer's law. These results are shown in Figure 12. The light intensity a t each value of w was integrated, and the ratio of the integral light intensity of a selfabsorbed line to the integral intensity of a line having no self-absorption was calculated. This ratio is designated the self-absorption factor of the resonance emission line. The profiles of the resonance emission line having percentage self-absorption factors of 20.9, 43.3, 59.6, and 67.2% are shown in this figure. The resonance line emitted from the lamp is the sum of the emissions from various regions inside the hollow cathode, Therefore the resonance line emitted from the part in the hollow cathode placed most closely to the w k l o w has no self-absorption, and the resonance line emitted from the opposite side has great self-absorption. Therefore, the resonance emission line emitted from the lamp has the average value of these two self-absorptionfactors, T o obtain this value, we assumed the following. First, although the sputtered atomic vapor stays slightly outside of the hollow cathode (6), there exist no atomic vapor in the outside of the cathode, and the atomic density is constant within the cathode. Second, the amount of self-absorption of the resonance emission line is not the absorption a t the central wavelength of the emission line, but the average of the absorption a t each wavelength within the resonance line width. However, the self-absorption factor is approximately equal to the absorption a t the central wavelength-Le., approximately the same as the true absorption mentioned above. On the basis of these assumptions, we derived Equation 3 from Lambert's law. The numerator indicates the intensity of the emission line having self-absorption, the denominator indicates the intensity of the line having no self-absorption. By introducing the measured value in Figure 6 into Equation 3, the average self-absorption factor of the resonance emission line was calculated. It was 596

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50

IO0

DISCHARGE C U R R E N T (ma.)

Figure 13. Relationship between discharge current and atomic vapor temperature of the lamp 7, 2.

Atomic vapor temp. Hollow cathode temp.

found that there is a self-absorption factor of 20.9% a t 40 ma., 43.3% a t 60 ma., 59.6y0 at 80 ma., and 67.2a/, a t 90 ma. ff=

where is the average self-absorption factor

x is the distance between one point in the hollow cathode and the other end 1 is the length of the hollow cathode is the absorption coefficient at the central wavelength of the resonance emission line from the lamp I,, is the intensity of the resonance emission line having no self-absorption Since the measured breadth of the resonance emisssion line from the hollow cathode lamp (Figure 5) is related to the dispersion of the apparatus, its breadth is greater than the true one. Therefore, the true breadth can not be obtained directly from the results shown in Figure 5. T o obtain the true breadth a t a given discharge current, the following calculations were made. First, the frequency of radiation between the maximum values of the self-reversed line has generally no relation with the dispersion of the apparatus. The resonance emission line having a per cent self-absorption factor of 67.2% in Figure 12 is analogous to the resonance emission line a t 90 ma. in Figure 5. By measuring ~ ] ~ the the frequency [2(v - v ~ )between maximum values of the self-reversed emission line a t 90 ma. and by obtaining the value of w between the

maximum values of that resonance emission line in Figure 12, the Doppler breadth was calculated by introducing these values into Equation 2. Second, from Figure 12, the half breadth of the resonance emission line having a percent self-absorption factor of 67.2% was obtained by the value of W . Substituting this value and the Doppler breadth a t 90 ma. obtained by the above section into Equation 2, the half breadth [2 ( Y - v O ) , ] h was calculated. From Figure 5 , the half breadth [2 ( Y YO)^]^ of the self-reversed emission line a t 90 ma. was measured. The latter value was taken as equal to the half breadth [2 ( Y - V O ) ~ ] ~ . The ratio between the two values was taken as the correction coefficient for the dispersion of the apparatus. The measured breadths of all the resonance emission lines were corrected by this coefficient. Third, it is impossible to measure the Doppler breadth of the un-self absorbed resonance line. Therefore, the Doppler breadth of this line was calculated as follows. Substituting the (measured) absorbance a t a given discharge current from Figure 6 int'o Equation 3, the selfabsorption factor was calculated. From the profile of the resonance emission line having this self-absorption factor plotted in Figure 12, the ratio between the half breadths of the resonance emission lines having no self-absorption and self-absorption was calculated. This ratio was taken as the correction coefficient relating to the self-absorption a t a particular discharge current. By multiplying the measured half breadth of the resonance emission line by these two coefficients, the true half breadth was obtained. Substituting the true half breadth into Equation 4, the calcium atomic vapor temperature ( T ) was calculated. These results are shown in Figure 13. This calculated temperature has error limits of +5% to -2O$ZO.

where

R is the gas constant izf is the atomic weight v0 is the central frequency of the reso-

nance line

T is the absolute temperature (" K.) of atomic vapor c is the velocity of light For comparison, the cathode temperature of the hollow cathode lamp was measured by fixing a thermocouple to the cathode; the temperaturecurrent curve is shown in Figure 13. Iron was used for the cathode. Since the voltage-current characteristics of this lamp were almost the same as those of the calcium hollow cathode lamp, there should not be a wide difference between

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Figure 14. Profiles of the calcium resonance line from the lamp and the flame Proflle of resonance emission line having no selfabsorption I . Temp. 1500'K. 2. Temp. 1 8 0 0 ' K. 3. Temp. 2000' K. 4. Temp. 2500' K. Profile of resonance emission line having selfabsorption 5 . Temp. 1 5 0 0 ' K., self-abs. 20.9% 6 . Temp. 1 8 0 0 ' K., self-abs. 43.3% 7 . Temp. 2000" K., self-abs. 59.670 8 . Temp. 2500' K., self-abs. 67.2% Proflie of resonance absorption line 9. Temp. 2500' K., symmetry IO. Temp. 3 3 0 0 ' K., symmetry I I . Temp. 2500' K., asymmetry 72. Temp. 3 3 0 0 ' K., asymmetry

the cathode temperatures of the iron and the calcium lamps. From these results, the profile of the resonance emission line having no selfabsorption was calculated by Equation 1. These profiles a t 1500, 1800, 2000, and 2500 O K. (40, 60, 80, and 90 ma.) are shown in Figure 14. Because the Doppler breadth could be obtained by the above method, the value w corresponding to wavelength was calculated by Equation 2. The same method as in the calculation of the line profile having no self-absorption was applied to the resonance line having self-absorption in Figure 12, and the profiles were calculated. The profiles a t 40, 60, 80, and 90 ma. are shown in Figure 14. Simplest Profile of the Resonance Absorption Line of Calcium in t h e Flame. Since t h e flame has a high gas pressure and temperature, t h e profile of the resonance absorption line is not determined by the Doppler broadening effect alone, as the line undergoes collisional broadening also. An empirical relationship between the collisional breadth AVCand the Doppler breadth AVO ( 5 ) is shown in Equation 5.

On the assumption that the ground state atom in the flame has the same temperature as the flame gas, and that the flame temperature remains in the

Table 1. Model of the Atomic Absorption Resonance emission line from lamp Wavelength shift Factors Resonance absorption between tm-o determining line of calcium in flame line centers Curved line the profile Factors determining the profile (A.1 in figure 15 Doppler, no Doppler, collisional, symmetry, 0 la self-absorptemp. 2500" K. tion Doppler, no Doppler, collisional, symmetry, 0 lb self-absorptemp. 3300" K. tion Doppler, selfDoppler, collisional, symmetry, 0 2a absorption temp. 2500" K. Doppler, selfDoppler, collisional, symmetry, 0 2b absorption temp. 3300" K. Doppler, selfDopple, collisional, symmetry, 0.006 3a absorption absorption temp. 2500" K. Doppler, selfDoppler, collisional, symmetry, 0.006 3b absorption temp. 3300" K. Doppler, selfDoppler, collisional, asymmetry, 0 4a absorption temp. 2500' K. Doppler selfDoppler, collisional, asymmetry, 0 4b absorption temp. 3300" K. Doppler, selfDoppler, collisional, asymmetry, 0.006 5a absorption temp. 2500' K. Doppler, selfDoppler, collisional, asymmetry, 0.006 5b absorption temp. 3300" K. Result in experiment of Figure 3 6 Rleasured result 7 range of 2500 to 3300' K. because of the measurement of the flame temperature being unsuitable with the Fabry Perot interferometer (2), the profile of the resonance absorption line having Doppler and collisional broadenings was calculated by substituting the value (0.5) of Equation 5 for the a of Equation 1. The calculation of this profile was made on the assumption that there is no wavelength shift in the resonance absorption line due to the collisional effect and that the line is symmetrical. The profile is shown in Figure 14, where the absorption coefficient is placed on the vertical axis and the wavelength on the horizontal axis. This wavelength was obtained as follows. The value of the flame temperature was introduced into Equation 4, and the Doppler breadth was calculated. By introducing this breadth into Equation 2, the wavelength corresponding to the value of w was obtained. D6ppler Breadth of t h e Resonance Emission Line from t h e Calcium Hollow Cathode Lamp and t h e Absorbance of Calcium in t h e Flame. T h e decrease in t h e absorbance of calcium in t h e flame d u e t o t h e increase in the Doppler breadth of the resonance emission line was studied, with the following assumptions. The resonance emission line from the lamp has no self-absorption and has a profile which isdetermined by Doppler broadening alone (see Figure 14). The resonance absorption line of calcium in the flame has the profile in Figure 14, and is symmetrical. The central wavelengths of the emission line and the absorption line are coincident. Under the above assumptions, h-hen the res-

onance emission line from the lamp was absorbed by calcium atomic vapor in the flame, the sum of light intensity of the resonance emission line a t each wavelength within the resonance line width was calculated. The above resonance absorption model is shown in Table I, and the results in Figure 15. From the results obtained (curved lines l a and b), it has been found that there is no substantial decrease in the absorbance of calcium in the flame, even if the Doppler breadth of the resonance emission line from the lamp-Le., the discharge current of the lamp-has been increased. Self-Absorption of the Resonance Emission Line from t h e Calcium Hollow Cathode Lamp and t h e Absorbance of Calcium in t h e Flame. When t h e resonance emission line from the lamp having Doppler broadening and self-absorption as shown in Figure 14 was absorbed by calcium atomic vapor, whose line profile was

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Figure 15. Relationship between one of the resonance line profiles and a b sorbance of the flames VOL. 38, NO. 4, APRIL 1 9 6 6

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shown in Figure 14, the relationship between the profile of the resonance emision line-Le., the discharge current of the lamp-and the absorbance of calcium in the flame was obtained by the same calculation method au in the above sections. The above resonance absorption model is shown in Table I, and the results are given in Figure 15. I t was recognized that the measured result (curved line 7) corresponds better to the results (2a, b) obtained by this section than to those ( l a , 6) obtained by the above section. The reason for this is as followvs. As a result of increase in the self-absorption of the resonance emission line, the line is reversed, and the maximum intensities of the line are shifted to shorter and longer wavelengths from the center; consequently much of the resonance absorption has taken place a t points on the absorption line of relatively low absorption coefficient. .Is a result, the absoibance of calcium in the flame has decreased depending upon the increase in the -elfabsoiption of the reqonance emission line. For compari~on 1%ith the experimental result, the result in Figure 7 was plotted in Figure 15 in the following way. First, from the sum of the selfabsorption factor of lamp 2 a t 60 ma. and the absorbance of flame 1, the absorbance of the new light source was calculated. The discharge current corresponding to this absorbance was obtained from Figure 6. Second, to facilitate the comparison of the absorbance in Figure 15, a value 1.7 times the absorbance of flame 2 in Figure 7 was taken. Though the Doppler breadth of the new light source is constant, it was ascertained that this experimental result (curved line 6) is approximately coincident with the measured result. To be exact, the following fact has been found. When the atomic density of the ground state in the lamp increases with the increase in the discharge current, the self-absorption factor of the resonance emission line increases. The increase in self-absorption constitutes the chief cause of the decrease in the absorbance of the flame. When the resonance emission line passes through the flame, this line is selfabsorbed. Since the absorbance of the flame differs depending upon the selfabsorption factor of the resonance emission line, it is to be consideied that the absorbance is not accurately proportional to the atomic density. Profile of t h e Resonance Absorption Line of Calcium in the Flame. The temperature and the density of gas are so high in the flame that the Doppler and the collisional broadening effects are great. Consequently the breadth of the resonance absorption line of calcium in the flame is larger than that of the resonance emission line from the hollow 598

ANALYTICAL CHEMISTRY

cathode lamp. Furthermore, it is conceivable that the center of the resonance absorption line is shifted to shorter or longer wavelength compared to the center of the resonance emission line from the lamp due to the collisional effect and others, and that the resonance absorption line profile becomes asymmetrical (6). .Is shown in Figures 8 and 9, the center of the resonance absorption line is shifted to longer wavelength (0.0010.005 -4.)compared with the center of the resonance emission line from the lamp, and this shift is dependent on the kind of flame. -4lthough no definite wavelength shift was obtained, the shift in the oxyhydrogen flame was smaller than that in the oxyacetylene and the osypropane flames. As shown in Figure 10, the center of the resonance emission line of calcium in the flame shifted to longer wavelength (0.004 0.01 -1.). can be seen from Figure 5 , the reuonance emission line from the lamp is shifted to longer wavelength compared with the resonance absorption line of the atoms in the lamp; this explains the asymmetry of the selfreversed resonance emission line a t 90 ma. Then, i t is conceivable that the shift of the resonance absorption line of calcium in the flame is not greater than that of the resonance emission line of the flame in Figure 10. The asymmetrical profile of the resonance absorption line was calculated as follows. The ratios ~ A v , / ( A v , A v ~ ) and 2 A v L (Av, A Y ~ )were calculated from Figure 10, where A v , is the half breadth of the absorption line in the shorter wavelength region from the line center, and h r i is the half breadth in the longer wavelength region. By multiplying the horizontal intensity (wavelength) in the shorter wavelength region from the center of the resonance absorption line in Figure 14 by the ratio 24v,/(hv, A v J , and multiplying the horizontal intensity in the longer wavelength region by the ratio 2 A v l (Ava A v J , the asymmetrical absorption line profile can be calculated. This profile could not be obtained theoretically; therefore, no definite results were obtained. This profile is shown in Figure 14. Collisional Shifts of t h e Resonance Absorption Line and t h e Absorbance of Calcium in t h e Flame. Since calcium in t h e flame is influenced b y the collisional effect and other factors, the central wavelength of t h e resonance absorption line is dependent upon the kind of flame. Hence, i t is conceivable that the absorbance of calcium in the flame is dependent upon the kind of flame. I n the case of the oxyhydrogen flame in Figure 11, there is a slight decrease in the absorbance as the discharge current increases. In the case of the oxyacetylene and the

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oxypropane flames, however, there occurs a big decrease. Spraying the organic solvent (EtOH-H20) into the oxyhydrogen flames, there is a big decrease in the absorbance. T o study the results mentioned above, the following model was assumed, and the decrease in the absorbance of the flame against the increase in the discharge current of the lamp was calculated graphically. The resonance emission line from the lamp has a profile having Doppler broadening and self-absorption in Figure 14. The resonance absorption line of calcium in the flame has the symmetrical profile having Doppler and collisional broadenings in Figure 14. The shift between the center of the resonance absorption line in the flame and the center of the reuonance emission line from the lamp is 0.006 -l. as the experimental mean value. The relationship betxeen the profile of the resonance emission lineLe., the discharge current of the lampand the absorbance of calcium in the flame was obtained by the same calculation method mentioned above. The above resonance absorption model is shown in Table I, and the results are shown (3a, b) in Figure 15. The following was found: first, there is a considerable difference between the curved line qhowing the relationship between the discharge current and the absorbance in the 2500" E(. flame, and the curved line in the 3300" K. flame. Second, the curved lines (3u, b) are similar to the measured curved line. However, the decrease in the absorbance with an increase in the discharge current is not so great as the measured result. Asymmetry of the Resonance Absorption Line Profile and t h e Absorbance of Calcium in the Flame. I n order to study the measured result, the relationship between the discharge current and the absorbance was calculated graphically using the following assumptions. The resonance emission line from the lamp has a profile having Doppler broadening and self-absorption as in Figure 14. The resonance absorption line of calcium in the flame has the asymmetrical profile shown in Figure 14. The shift between the two centers is 0 or 0.006 A. The light intensity of the resonance emission line passed through calcium atomic vapor having this asymmetrical profile in the flame was calculated by the same method mentioned above. This resonance absorption model is shown in Table I , and the results are shown (4a, b, and 5u, b) in Figure 15. These calculated results are very similar to the measured result. Unless the absorption line has an asymmetrical profile such as the profile of the resonance emission line of calcium in the flame, and shifted to longer wavelength, the measured results cannot be explained satisfactorily.

Difference of the Absorbance of Calcium in the Various Flames.

Resonance absorption has been caused a t shorter and longer wavelengths rather t h a n a t the central wavelength of t h e resonance emission line from t h e lamp 1% he? t h e self-absorption of the emission line was increased, or t h e line was reversed. Therefore, the absorbance indicated approximately the mean value of the absorbances or the absorption coefficient k , on the sides of the resonance absorption line. Consequently, the difference between the curved lines in Figure 11 is mainly due to the asymmetry, the shift and the broadening of the resonance absorption line of calcium in the flame. I n Figure 11, the second derivative of this cuived line in the oxyhydrogen flame is negative, but the others are poqitive. This fact is considered to mean the following. Since the shift of the absorption line in the Oxyhydrogen flame is smaller than that in other flamey, the center of the resonance emision line from the lamp is in the

wavelength region in which the second derivative of the absorption line profile is negative. Accordingly, the second derivative of the curved line in the oxyhydrogen flame has a negative value, but the curved line in the other flames have a positive value so that the absorption line is shifted considerably. Since calcium is affected by a carbon radical which has an energy level close to one in calcium, it can be understood why the shifts in the oxyacetylene, oxypropane flames, and oxyhydrogen flame into which the organic solvent (EtOH-H20) was sprayed, become larger than the shift in the oxyhydrogen flame in which water was sprayed. ACKNOWLEDGMENT

The author expresses his gratitude to ll.Shimazu of Hitachi Central Research Laboratory, K. Xakamura of Hitach Perkin-Elmer, W. E. L. Grossman of Iowa State TJniversity and I. Alakino and H. Okagaki of Hitachi S a k a Works for their helpful suggestions in conducting a series of the present experi-

ments and also to S. llatsudaira, K. Kurita, and K. Cchino for their kind assistance in the experimental work. LITERATURE CITED

( 1 ) David, D. J., Analyst 85, 779 (1960). ( 2 ) Gaydon, A. G., Wolfhard, H. G., “Flames,” p. 243, Chapman and Hall, Ltd., New York, London, 1953. ( 3 ) L’vov, B. V.,. Spectrochim. Acta 17, . 761 (1961). (41 Menzies. A. C.. ANAL.CHEM.32. 898 (1960). ‘ ( 5 ) Mitchell, A. C. G., Zemansky, AI. ’

W., “Resonance Radiation and Excited Atoms,” pp. 169, 31.2, 101, 99, 173, 174, 175, Cambridge University Press, London, 1934. (6) Robinson, J. W.,ANAL. CHEM.33,

1067 (1961). ( 7 ) Russel, B. J . , Shelton, J., Walsh, A., Spectrochim. Acta 8, 317 (1957). (8) Shimazu, M., Hashimoto, A., Science of Light (Tokyo) 1 1 , 131 (1962). ( 9 ) Walsh, A., Spectrochim. Acta 7, 108 (1955). (10) Winefordner, J. D., A p p l . Spectry. 17, 109 (1963).

RECEIVEDfor review June 12, 1964. Resubmitted September 10, 1965. Accepted December 23, 1965.

Effect of Pulse Amplitude Shifts on Electron Probe I ntensity Ratios D. R. BEAMAN’ Paul D. Merica Research Laboratory, The International Nickel Co., Inc., Sferling Foresf, Suffern, N. Y. Serious errors in electron probe microanalysis can arise as a result of the dependence of the pulse amplitude output of a proportional detector upon the incident x-ray intensity at relatively low counting rates. Such errors can b e avoided when utilizing pulse height selection techniques b y controlling either the pulse height selector position or the location of the intensity distribution. Pulse height discrimination eliminates these errors at the expense of sensitivity. In this experiment pulse amplitude shifts and the associated errors are determined using magnesium, silicon, chromium, and a dilute iron-silicon alloy. Large errors are encountered, but it is shown that they can b e eliminated and it is concluded that it is possible to simultaneously obtain accurate intensity ratio measurements and high peak/background ratios.

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dependence of the pulse amplitude output from a proportional detector upon the x-ray intensity at relatively low counting rates has been HE

well established. Birks ( 2 ) first mentioned this behavior and more recently a thorough investigation of the phenomenon has been completed by Bender and Rapperport ( I ) , who have noted that this behavior can lead to errors in electron probe microanalysis when pulse height selection is utilized. Because the limit of detection decreases with increasing peak/background ratio, in analyzing low concentrations i t is necessary to measure the intensity ratio using pulse height selection in which pulses from a narrow amplitude range are counted as a result of adjusting the base line and channel width of a single-channel pulse height analyzer. The pulse amplitude dependence on intensity complicates the use of pulse height selection since the base line and channel adjustments selected to accept the intensity from a pure standard will not be correct for an alloy. I n the present investigation the existence and magnitude of the pulse amplitude shift is established for a flow and sealed proportional detector. The errors caused by the amplitude

shifts are measured over a range of intensity ratios from 0.008 to 0.500. Techniques of correcting for the amplitude shifts are described and the accuracy of such procedures is then determined. The purpose is to illustrate that it is possible to obtain accurate intensity ratios concurrent with high peak/background ratios when using pulse height selection techniques regardless of changes in counting rate, anode potential or x-radiation wavelength. EXPERIMENTAL

A xenon-filled sealed proportional detector and a flow proportional detector (argon 10% methane at 30 cc./minute) were used in conjunction with a standard electronic counting circuit. All measurements were made on a Cameca electron probe microanalyzer operated a t 21.6 kv. I n the measurement of pulse amplitude shifts, pulse amplitude positions

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Present address, The Dow Chemical Co., Metallurgical Laboratory, Midland, Mich. VOL. 38, NO. 4, APRIL 1966

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