CONCLUSIONS
To take advantage of the limited amount of solution converted into a fog composed of small droplets by this ultrasonic transducer and t o increase stability, a burner design is required that utilizes low gas flow rates. The multihole longpath type burner seems to be the most stable configuration for atomic absorption methods and provides increased sensitivity and a low rate of sample consumption. The departure from the absorption law, pathlength relationship with increasing burner length is attributed t o the size of the ultrasonic generator-transducer and suggests that with a sufficiently powerful nebulization system, the 10-cm burner could perform a t the same efficiency as the 0.7-cm burner. Stability is improved at low flow rates by averaging short-time variations in nebulization rate. While this study used absorption of radiation as a
measurement of the increased atomic vapor concentration, other flame techniques such as emission or fluorescence should benefit as well. In addition, the very rapid conversion of solution t o atomic vapor indicates that for atomic fluorescence methods, the optimized ultrasonic nebulization burner system should decrease noise resulting from light scattering and increase atomic vapor production in low temperature flames. For ultimate sensitivity, a multipass optical system could be employed. Not t o be overlooked is the cost saving because of-the decreased rate of consumption of both fuel and oxidizer gases when compared t o conventional burners. RECEIVED for review May 26, 1971. Accepted August 11, 1971. Work partially supported by National Science Foundation Research Grants GP 9206 and GP 18910.
Measurement of Flame Temperatures by a Two-Line Atomic Absorption Method R. F. Browner and J. D. Winefordner’ Department of Chemistry, Unioersity of Florida, Gainesoille, Fla. 32601 Temperatures of analytical flames are determined quickly and reliably with systematic and random errors of about 1% by measuring the ratio of a-values (a is the fraction of radiation absorbed by the analyte atoms) for atoms with spectral lines having different lower energy states and similar wavelengths, e.g., the In 410.18 nm and 451.13 nm lines. The experimental system consists of a quartz iodine continuum source and an atomic absorption flame spectrometer. The measured temperatures are slightly dependent upon the concentration of the analyte, the monochromator slit width, and the flame path length, and so optimum experimental conditions are given for temperature measurements. The measured flame temperatures for two Ar/02/H2 premixed shielded flames, one air/CzH2 premixed unshielded flame agreed to within about 20 O K or better with reversal temperature measurements for the same flame. The measured flame temperature for a N20/C2H2flame agreed with the two-line temperature to within 35 O K . The two thallium lines at 377.57 and 535.05 nm should be more useful for hotter flames, and the two gallium lines 403.30 and 417.20 nm should be more useful for cooler flames. THE NEED TO MEASURE flame temperatures probably occurs in spectrometric analysis more often than it is accomplished. Undoubtedly, one reason for this is the somewhat daunting techniques which are presently available. The two major spectrometric methods, line reversal and the iron two-line emission method, are time consuming and tedious t o use if errors are t o be avoided (1-4). Furthermore, they both requre standards of spectral radiance to be available, although this may be avoided with the two-line emission method if the
Author to whom reprint requests should be sent. A. G. Gaydon and H. G. Wolfhard, “Flames, Their Structure, Radiation and Temperature,” Chapman & Hall, London, 1960. (2) R. H. Tourin, ‘‘Spectroscopic Gas Temperature Measurement,” Elsevier Publishing Co., Amsterdam, 1966. (3) W. Snelleman, Ph.D. Thesis, University of Utrecht, 1965. (4) G. F. Kirkbright, M. Sargent, and S . Vetter, Specrrochim. A r m ,
(1)
25B, 465 (1970).
approximation is made that the detector response is constant over a wavelength range of about 10 nm. Thermocouples lend themselves conveniently to the measurement of temperature profiles in flames, but empirical correction factors must be employed to allow for radiation losses, and in any case they can only be used for low temperature flames ( I , 5). Spectrometric techniques are also preferred because the process of measurement does not itself influence the flame temperature. The proposed method is a straightforward atomic absorption technique using a simple uncalibrated continuum light source, such as a quartz iodine lamp. It is applicable directly, with n o modification required, to any atomic absorption spectrometer with a monochromator having a spectral bandpass of about 0.04 nm. THEORY
Basic Equations. The relative absorption, cy, of the radiation from a continuum light source by atoms in the light path is described in the limiting case of low optical density by (6):
where e and m are, respectively, the charge and mass of the electron, c is the velocity of light, I is the absorption pathlength, Xo is the peak wavelength of absorption, n is the concentration of atoms a t the lower energy level involved in the transition, f’ is the absorption oscillator strength, do is the radiant flux of the continuum source transmitted through the flame gases when blank is being introduced into the flame, is the radiant flux of the continuum source absorbed by the analyte atoms when introduced into the flame, and s is ( 5 ) R. Smith, C. M. Stafford, and J. D. Winefordner, ANAL. CHEM., 41,947 (1969). (6) P. J. Th. Zeegers, R. Smith, and J. D. Winefordner, ibid., 40 (1 3), 26A (1968).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
247
the spectral bandwidth of the monochromator. Equation 1 holds only if s 2 4AXa, where AXa is the total half-width of the absoption line; for atoms, in flames, a monochromator having s about 0.02 nm or greater must be used. F o r high optical densities, Equation 1 becomes : ff=-[
1
1 2.rre2lXO2nfaAX~ li2 m e 2 6 2
s
Table I. Physical Constants for Gay In, and TI Wavelength, Spectral term value, cm-1 Element nm fl Lower Upper Ga 403.29 0.258 0 24,789 417.20 826 24,789 0.405 0.288 0 24,373 In 410.18 451.13 0.628 2,213 24,373 TI 377.57 0.250 0 26,478 535.05 0,540 7,793 26,478 a gfvalues from Penkin and Shabanova (14).
(2)
where AXD is the Doppler half-width of the line, and a is the damping constant; this is further defined by :
Equations 2 and 5 . The temperature, T, is now given a t low optical densities by :
where AXL is the Lorentz (collisional) half-width, and AXN is the natural half-width of the atomic absorption line. At normal flame temperatures, AXN is negligible compared to the Lorentz half-width (7, S), and so Equation 2 reduces to: ff
=
-[
1
1 2ae2lhO2nfAXL S me2
T = kln
m
(6)
EI - Eo
where c y 0 and cy1 refer to the relative absorption signals a t the lines of wavelength XO and XI, whose lower states have energies EO and El and whose Lorentz half-widths are AXL~and A h , . To ensure that the values of u may be measured under conditions approaching a n optimum signal level, the energy separation of 0 and 1 must not be too great-Le., q l eV for flame temperatures below 4000 OK. Also, the absorption oscillator strengths must be comparable. If the measurements are made at low optical densities, it is necessary t o know only the relative f-values of the transitions in order t o obtain a value for the absolute excitational temperature of the flame-i.e., all other parameters in Equation l are precisely and accurately known. At high optical densities, however, the ratio of Lorentz half-widths is also required. If a n atomic line source were used instead of a continuum, the exact profiles for both the source emission line and the atomic absorption line would also have to be known for either the low or high optical density case. Information concerning line shapes is generally not available and so the continuum source is preferred. The measured temperature of the flame will be an absolute value (although it may differ from the translational, rotational, vibrational, or ionization temperature) in spite of the use of relative CY
(7) E. Hinnov and H. Kohn, J . Opt. SOC.Amer., 41, 156 (1957). (8) M. L. Parsons, W. J. McCarthy, and J. D. Winefordner, Appl. Spectros., 20, 233 (1966). (9) C. Th. J. Alkemade, App/. Opt., 7, 1261 (1968).
Indium
- En
and a t high optical densities by :
(4)
where EOand El are the energy levels of the states 0 and 1 and go and gl their statistical weights, k is the Boltzmann constant, and T is the absolute temperature. Atoms with degenerate ground states have one or more electronic levels close to the ground state and, within a periodic group, the energy separation of these levels increases with increasing atomic number. For a particular atom with such a split ground state, it is possible t o accurately relate the relative absorption at the resonance line and at a nonground state line to the relative populations of these levels by combining
Gallium
El
gofo
Equations 2 and 4 do not hold at very high optical densities (i.e., CY 7 0.3), because parts of the absorption line wings extend beyond the spectral bandwidth of the monochromator (9). Influence of Temperature on CY.When a n atom is in a state of thermal equilibrium with its surroundings, the relative populations no and nl of two electronic levels 0 and 1 are related by:
4x18-
[(G)(?>"(:>I
Tho Iliurn
s X lo3 0
E8
Figure 1. Partial energy level diagram for gallium, indium, and thallium showing the first terms of the sharp series
2x103
h
P
e
w
Ix
d' 0 .
248
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
~
~ ~
.-t I t
5 e
e
\
I
4m1
01 0
’
I
2
I
‘
4
1
’
8
’
’
0
’
lo
P
I Y~ absolute temperature Figure 2. Variation of ( Y ~ / C with for gallium, indium, and thallium
values, because only atoms of a single element are considered and factors which influence the spatial distribution of the atomization of that element will not alter the measured ratio ao/al--i.e., this ratio will depend only upon the flame ternperature as long as excitational equilibrium is approximately upheld. The populations of atomic energy levels in excess of 1 eV above the ground state are known to achieve a non-equilibrium distribution in the secondary reaction zones of some low temperature flames, particularly in fuel-rich hydrogenlair flames, due to participation of the atoms in three body collisions with flame gas radicals (10-12). This can lead to erroneous line reversal (12) or iron two-line emission temperatures. However, in the proposed method, the energy level of the nonresonance line considered is within 0.3 eV of the ground state, so there will be less likelihood of excitational disequilibrium. Of those elements with suitable energy levels and J values (e.g., Al, G a , In, T1, Fe, Co, Ni, Sn, Ir, Rh, Os, V, and Y ) , and which are also appreciably atomized in most flames (12, I.?), the series G a , In, and T1 seemed most suitable; the relative f values for the two lines of the sharp (n2P1i2,3/2rn2Sli2) series for G a , In, and T1 have been determined by Penkin and Shabanova (14) with a n error of less than 3x. The use of these f values appears to introduce no detectable systematic error into the temperature values, when compared with the reproducibility of the absorption measurements themselves. The lines of the first term of the sharp series of G a (403.30 and 417.20 nm), In (410.18 and 451.13 nm), and T1 (377.57 and 535.05 nm) all lie close to the emission/ transmission maximum of a typical continuum (blackbody temperature -3200 OK) grating monochromator-S5 re(10) J. L. J. Rosenfeld and T. M. Sugden, Combust. Flame, 8, 44 (1964). (11) D.R . Jenkins, Proc. Royal Soc., A313, 551 (1969). (12) L. deGalan and G . F. Samaey, Spectrochim. Acta, 25B, 245 ( 1970). (13) L. deGalan and J. D. Winefordner, J. Quant. Specfrosc. Radiat. Transfer, 7, 251 (1967). (14) N. P. Penkin and L. N. Shabanova, Opt. Spectros., 14, 5 (1963).
Figure 3. Growth curves for indium in Ar/02/H2 flame (Reversal T = 2098 OK) (a) 410.18 nm. (6) 451.13 nm. Flame shielded Meker burner with 20-mm path length. Mean measurement height = 10 mm above burner head sponse photomultiplier combination, and so a maximal signalto-noise is obtained. Partial energy level diagrams for G a , In, and T1 are shown in Figure 1, and the wavelengths, gf values, and energy levels of the lines used are given in Table 1. The ratio cyo/alfor each line pair is a n exponential function of temperature (Equations 6 and 7), whose position on a plot of T vs. cyo/cyl (Figure 2) depends on the constants in these equations. Greatest sensitivity requires arjd (cyr/al)to be small and therefore widely-different a values to be measured. However, this will lead to poor precision in the ratio cy~/a~. Practically, ao/almay be measured with good precision over the approximate range 1.1 2 cyo/cyl 2 5 . This restricts the working ranges of temperature for the elements to G a , 650-2200 OK; In, 1220-3500 OK; and T1, 36507750 OK. Clearly for normal flames, In will be the most useful element, but G a may be useful for “cool” flames and T1 for plasma jets. Temperature Measurements Utilizing Low Optical Density Region of Curve of Growth. Without knowledge of the Lorentz half-widths, the low optical density region of the curve of growth must be used for temperature measurements, and this limits both a0 and cy1 to 2 0 . 0 3 in many cases. At such low values of a , the error in the temperature measurement is about is% (-120 OK) for low temperature flames and *lOz (-240” K) for higher temperature flames (e.g. NzO/CzH2); these errors are not acceptable for many purposes. Temperature Measurements Utilizing High Optical Density Region of Curve of Growth. In order to determine temperatures by the measurement of cy at high optical densities, it is necessary to know the ratio AAL,/Ah0. To find whether any general relationship could be established which related the ratio of Lorentz half-widths to atomic parameters, this ratio was measured experimentally for the In lines 410.18 and 451.13 nm. The method of Hoffman and Kohn (15) (15) F. H. Hoffman and H. Kohn, J. Opr. Soc. Amer., 51, 512 (1961).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
-~
~
-
249
L 10
I
I
# , , , # , I
K?
I
I
,,,,,I
I
lo*
108
6
I
I I
,,I
I
I
I I l l l l
I
1
I
I
I l l
Indium concentration @g/ml)
Figure 4. Growth curves for indium in Ar/02/H2 flame (Reversal T = 2250 OK) ( a ) 410.18 nm.
(b) 451.13 nm.
Flame shielded Meker burner with 20-mm path length. Mean measurement height = 10 mm above burner head
was used, as modified for atomic absorption meaurements by McGee and Winefordner (16). In this, a curve of growth (log CY us. log solution concentration) is plotted for each line. The intersection point of the low (slope = 1) and high (slope = 1/2) density asymptotes of each curve allows the evaluation of the individual Lorentz half-widths. However, here, only the ratio of Lorentz half-widths is required; this is given by: = (Y‘~/cY’o
AXLI/AXLo
(8)
where the primed values of CY refer to the intersection points of the low and high density asymptotes. Four flames were examined : two low temperature Ar/02/H2 flames, an airiCzH2 flame, and a N20/C2H2flame. The temperature range (2098-2950 OK) and variety of collisionally broadening species present in the gases were selected to cover a wide variety of possible flame types. The experimental curves of growth are shown in Figures 3-6. Table I1 contains the for each flame, together with the ratio ratio Ah~4al,l/AX~,10 cvl/cr0 at one arbitrarily selected indium concentration from the high optical density asymptote and one from the low. Within the limits of experimental accuracy, C Y ~ / C Y O and Q’I/CY/O are seen to be identical. However, it should be noted that this may be uniquely the case for the stated lines of Ini.e., the plots of cy 6s. concentration for two lines of another element may have a considerably different form in the intersection region and the intersection points for both lines should not occur at the same concentration. Because of the above identity, it is now possible to substitute ~ ~ / C Y Ofor AXLJ A X L ~in the high optical density expression (Equation 7), and the expression becomes identical with Equation 6 for low optical densities. Substitution of the constants for indium into Equation 6 gives: T =
3146 In [2.637(aO/ai)]
(9)
(16) W. W. McGee and J. D. Winefordner, J . Qnnrzt. Spectrosc. Radiat. Transfer, 7, 261 (1967). 250
( i ) Unshielded slot burner with 50-mm path length (Reversal T =
2480°K). (ii) Flame shielded Meker burner with 20-mm path length (Reversal T = 2430 OK). ( a ) 410.18 nm. (b) 451.13 nm. Mean measurement height 4.5 mm above burner head
Table 11. Experimental Values of Lorentz Half-Width Ratios from Growth Curves ffliff0
Temperature, A X L ~ ~ , . ~ / A X LLow ~~~,~ High Flame “K ( = ff’l/(Y/o)a o.D.~ o.D.~ Ar/OP/H1 2098 (R) 0.56 0.56 0.58 2250 (R) 0.69 0.71 0.66 Air/C2H2 2430 (R) 0.76 0.78 0.73 2470 (R) 0.78 0.77 0.74 NzO/CPH~ 2995 (Fe) 0.90 0.85 0.91 Values of A X L ~ ~ ~ . ~ / Afrom X L ~ the ~ ~ . ~growth curves and of al/aomeasured at low optical densities (O.D.) have an error of approximately 10%. The error in the ratio of al/cu~ at high optical densities (O.D.) is about 1 %. R = Reversal temperature. Fe = Iron two-line temperature. 0
which holds for all CY’S below about 0.3 (at higher optical densities, a is no longer exactly described by Equaton 4,and so Equation 9 cannot be applied). Therefore, CY may now be measured at high optical densities without the need to evaluate AXL,/AXt, in each instance. EXPERIMENTAL ARRANGEMENT AND PROCEDURE FOR TEMPERATLJRE MEASUREMENTS Fundamental Setup. The specific components of the experimental system used for the temperature measurements are given in Table 111. A conventional single-beam atomic absorption arrangement, with synchronous detection, was used for all measurements. The continuum source was a 150-W quartz iodine lamp coupled uia a 24-V, 10-A transformer to a stabilized power supply. This was preferred t o the more common xenon arc as it produced more than adequate spectral radiance at the wavelengths of interest and had a lower noise level (0.1 % rms noise for the quartz iodine lamp compared with 0.2% for a 150-W xenon arc-a 0.1-sec time constant was used
ANALYTiCAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
~~
~~
-
Iron two-llnr T 2995.K
I-
t
I
IO IO2
103
, 1 1 1 1 1
104
Indium concentration (ug/ml)
Figure 6 . Growth curves for indium in N20/C2H2flame (Fe two-line T = 2995 OK) Unshielded circular capillary burner, 10-mm diameter. (i) Spectral bandwidth = 0.02 nm. (ii) Spectral bandwidth = 0.04 nm. Mean measurement height = 4.5 mm above burner head. Temperatures indicated on different portions of growth curves were derived from ( Y ~ / C Yat ~ that particular solution concentration with both sources). Its small size also makes it convenient for the lamp compartment of most commercial atomic absorption spectrometers. Stock solutions of indium were prepared from the metal which was dissolved in concentrated HC1 and diluted with 0.1M HC1. In order to examine a wide variety of burner configurations as well as flame types, two of the flames (Ar/02/H2and air/C2H2)were maintained on a flame-shielded burner of the Meker type (17) with a 20 x 20 mm central test zone. The air/C2H2 flame was also burned on a 50-mm slot burner and the N20/C2H2flame on a circular capillary burner (18). The temperatures of the Ar/02/H2 and air/C2H2flames were measured, for comparison purposes, by the sodium D-line reversal method. A tungsten ribbon filament lamp calibrated against an NBS reference standard, was the standard of spectral radiance employed, and the correction for transmission loss through the focusing lens was determined experimentally. All the usual precautions t o ensure small systematic errors were taken ( I ) . It was not possible to operate the lamp at sufficiently high currents to measure reversal temperatures for the N ~ O / C Z Hflame, ~ and so the iron two-line emission method was used, with the iron lines at 372.26 and 374.95 nm as recommended by Kirkbright, Sargent, and Vetter (4). In all temperature measurements, whether by two-line absorption, line reversal, or two-line emission methods, the measurement zone through the flame was identical, and had a conical cross section approximately 2 X 0.01 mm at the flame center, subtending a solid angle there of about 0.01 steradians. Influence of Monochromator Slit Width. The measured temperature is independent of slit width, provided the spectral (17) P. J. Th. Zeegers and C. Th. J. Alkemade, Combust. F h w , 5, 247 (1965). (18) K. M. Aldous, R. F. Browner, R. M. Dagnall, andT. S . West, ANAL.CHEM. 42, 939 (1970).
Table 111. Specific Components of Experimental System 1. Spectral continuum Quartz iodine lamp, 150-W (General Electric Co., Model FCS), powered by a regulated ac supply and a 24-V, 10-A transformer (Sola Electric Co., Chicago, Ill.) 2. Optics Single pass, light beam chopped mechanically at 666 Hz (PAR, Princeton, N.J.; Model 125). All lenses of UV grade quartz 3. Monochromator 0.5 meter Ebert (Jarrel-Ash Co., Waltham, Mass.; Model 82-000). Grating blazed at 350.0 nm 4. Photomultiplier E.M.I. Model 6256B (Varian/EMI, Plainview, N.Y.), run at -1200 V by regulated high-voltage power supply (Fluke Mfg. Co., Seattle, Wash.; Model 418A) 5. Amplifier-readout Low-noise pre-amplifier (PAR; Model CR-4) set at Hi-2 SE with 30 Hz low frequency cut-off and 30 kHz high frequency cut-off. Lock-in amplifier (PAR; Model JB4) set for 666 Hz. Potentiometric recorder (E. H. Sargent and Co., Chicago, Ill. Model SR)
bandwidth is constant between measurements, as shown in Figure 6 for the N20/C2H9flame. A wider spectral bandwidth simply displaces the curves of growth to lower values a~ constant. The region with of a,while the ratio a ~ / remains slope = 1/2 is also increased at the expense of that with slope = 1. The erroneous temperature values which result at relative absorptions y 0 . 3 should be noted. A spectral bandwidth of 0.04 nm was found to be ideal, as this allowed accurate setting of the peak absorption wavelength while still maintaining good sensitivity. Influence of Absorption Path Length. An increase in path length displaces the analytical curves horizontally to lower concentrations. The ratio aliaois still constant, but a lower solution concentration is needed to produce a values which can be reliably measured. Because the absorption signal is always set to an optimum by the correct choice of solution concentration, increasing the path length actually degrades the signal-to-noise ratio slightly by causing greater nonspecific flame absorption noise. Experimental Procedure. After the absorption wavelength is set while spraying a concentrated solution, a solution is selected which gives an close to 0.2 at 410.18 nm and with this same solution the cy1 at 451.13 nm is measured. The usual sequence of spraying water/sample/water is followed. Wavelength drift should be checked periodically, especially when the flame is close to the monochromator, although in this work, it was found to be negligible. Scale expansion of about 2.5 X should be used to improve precision. The use of a narrower slit (spectral bandwidth of less than 0.04 nm) together with a scan of the absorption line is not to be recommended because a short time constant is necessary (
