an impure sample of the same compound. Although the use of patterns of mixtures is somewhat limited because of their complexity, such patterns are of value for procedural purposes. DISCUSSION
Voltage recordings are a useful supplement to laboratories that analyze a variety of materials. They, in conjunction with the spectrograms, are direct evidence of the responses of sample materials to analytical conditions and are indicators for the improvement of these conditions. The recordings show not only consumption time but also arc stability and irregularities due t o sample ejection, incomplete consumption, etc., which are not readily discernible with spectrograms alone, Voltage recordings in conjunction with moving plate studies are particularly useful for the interpretation of events that are taking place in the arc and are somewhat similar to a motion picture of
the arc. With experience a preliminary identification of a material can be made prior to the development of the spectrogram. Since recordings are dependent on the analytical conditions and the properties of the analyzed material and not on the method of recording, it is possible to use these patterns as a reference standard between laboratories. For example, in publications of d.c.-arc procedures a pattern would contribute to the comprehension and duplication in other laboratories. Voltage fluctuation recordings are a source of data for the understanding of the mechanism of the arc under analytical conditions. While information on the physics of the arc is available in the literature-e.g., (2)-much does not apply to the spectroscopist confronted with a large number of analyses. This investigation is an application of known technology in another field for the solution of problems in analytical spectroscopy.
ACKNOWLEDGMENT
The author expresses his appreciation to B. F. Frowner, F. M. Plock, and J. J. Finnegan for their helpful assistance throughout the course of this study. LITERATURE CITED
(1) Ahrens, L. H., Taylor, S. R., “Spectrochemical Analysis,” p. 186, AddisonWesley, Reading, Mass., 1961. (2) Loeb, L. B., “Fundamental Processes
of Electrical Discharges in Gases,” Wiley,.New York, 1939. (3) Mellichamp, J. W., unpublished data, November 1964. (4) Mellichamp, J. W., Buder, R. K., Appl. Speclros. 17, 57 (1963). ( 5 ) Oertel, A. C., “Spectrochemical Analysis of Mineral Powders,” p. 63, Div. of Soils, C.S.I.R.O., Adelaide, Australia, 1961. (6) Semenova, 0. P., Compt. Rend. Acad. Sca. URSS 51. 683 (1946). ( 7 ) Vallee, B. L., Thiers, ’R. E., J . Opt. SOC.Am. 46,83 (1956).
RECEIVEDfor review April 21, 1965. Accepted June 23, 1965.
Calculation of Concentration Corresponding to the Point of Intersection of High and Low Concentration Segments of Analytical Curves in Atomic Emission Flame Spectrometry JAMES WINEFORDNER, THOMAS VICKERS,l and LLOYD REMINGTON2 Department o f Chemistry, University o f Florida, Gainesville, Fla.
b Analytical curves in atomic emission flame spectrometry plotted on logarithm coordinates are generally characterized by two distinct regions. In such cases, the slope of the linear portion of the high concentration segment is about one half of the slope of the low concentration segment. By means of simple theory, the concentration corresponding to the point of intersection between the extrapolations of the linear segments of the high and low concentration portions of an analytical curve can be calculated. The case in which a multiplet is not resolved by the experimental system is also considered. Experimental data is in good agreement with calculated results for several spectral lines of several elements in several flame types.
A
CURVES in atomic emission flame spectrometry are generally characterized by two distinct regions (1, 2, 7 ) . The slope of the analytical curve plotted on logarithmic coordinates in the high concentration region is, in many rases, approximately NALYTICAL
1216
ANALYTICAL CHEMISTRY
one-half of the slope for the low concentration region, as one would predict from astrophysical growth curves (8). Deviation from this ratio (1, 2, 7) may occur a t very low sample concentrations because ionization may then vary significantly with concentration, and a t very high sample concentration because compound formation may vary significantly with concentration and because of instrumental reasons such as saturation of the photodetector. For analytical purposes, working in the concentration region of maximum slope of analytical curves is obviously advantageous. Two points on analytical curves in atomic emission flame spectrometry are therefore quite important when characterizing spectral lines of atoms for analytical purposes. These two points are the limiting detectable concentration and the concentration corresponding to the point of intersection between the extrapolations of the linear segments of the low and high concentration portions of an analytical curve. The limiting detectable concentration can be calculated according to the
method of Winefordner and Vickers (12). The concentration corresponding to the point of intersection between the extrapolations of the linear segments of the high and low concentration portions of an analytical curve can be simply calculated by the equations given in the following section. THEORY
The flame source will be assumed to be in thermal and chemical equilibrium (6). This assumption is approximately valid for the central region of the outer cone of most analytical flames. The integrated intensity, 11, of a single, isolated spectral line for an optically thin medium-i.e., for a dilute atomic vapor of the emitting species-in units of watts cm.+ ster.-’, is given (12) by the well known equation Present address, U. S. Army Missile Command, Directorate of Research and Development, Physical Sciences Laboratory, Redstone Arsenal, Ala. Present address, Asheville-Biltmore College, Asheville, N. C.
I 1
=
10-7 NLh v , A t 4n
su
-exp(-Eu/kT)
B(T)
(1)
where h is Planck's constant in erg. sec., is the frequency of maximum intensity of the spectral line in set.-', A t is the transition probability in set.-', N is the concentration of atoms in the flame gases in atoms per cc., L is the average diameter or thickness in cm. of the flame region being focused on the monochromator entrance slit, gu is the statistical weight of the upper state involved in the transition, B(T) is the partition function over all states, E , is energy of the upper state, u , involved in the transition, k is the Boltzmann constant, and T is the temperature in ' K. of the hot flame gases (11). For a resonance line, the energy of the lower state, El, is 0 and hu, = E,. The integrated intensity, I2 of a single isolated spectral line for an optically thick medium-Le., for a concentrated atomic vapor of the emitting species-in units of watts cm.-2 ster.-', is given (3-5) by the well known square root of A' equation, namely I 2
there will be a different value of A;, for each line of the multiplet which is due to the different values for gu. Because the concentration of atoms of a given species per cc. of flame gases has little significance to most chemists, it is convenient to calculate the solution concentration, Cd, in moles liter-' introduced into the specified flame, which produces the atomic concentration, N , . Winefordner and Vickers (12) give the following equation which allows conversion from atomic concentration, N to solution concentration, C,
c = 3.3 x
10-22
crystals into atoms and for atomic losses due to ionization and compound formation with flame gas products and varies with sample type and concentration. Of course, a t the point of intersection, C, N , and 0 are replaced by C,, N a , and Pi, respectively. The sample solution concentration, C,, which corresponds to the intersection point of the analytical curve is therefore given by
c, = 2.0 x
10-O
x
x
where n T and nZQ8are the number of moles of combustion products at temperatures T and 298' K., respectively, Q is the flow rate of unburnt gases in cmS3sec.-l introduced a t room temperature and one atmosphere pressure, @ is the sample solution flow rate into the flame (aspiration rate) in ~ m min.-l, . ~ B is the sample introduction efficiency (IO) and p is the factor (9) which accounts for incomplete dissociation of salt
The value of C,, calculated using Equation 6, should agree quite well with the experimentally measured value for any element if the value of p does not vary significantly with concentration in the concentration region near the intersection point. The evaluation of most of the parameters in Equation 6 is not difficult and has been briefly described in the article by Rinefordner and Vickers ( 12 ) . The evaluation of the parameter 0 (9) is considerably more difficult because it requires a detailed knowledge of the
=
Table
I.
Calculated and Measured Values of
Ci
C, (calcd. using Eqn. 6 )
where c is the speed of' light in cm. sec.-l, bDis the Doppler half-intensity width of the spectral line in sec.-l, and a is the classical damping constant (8), which is a parameter, with no units, that indicates the relative contribution to the broadening of a spectral line by the damping factors. I t is defined by
where Au, is the collisional (3, 8) halfintensity width in set.-' and AV.Vis the natural half-intensity width in sec.-l There is, of course, a small intermediate region ( 1 , S, 8) in which the integrated intensity expression does not correspond to either Equation 1 or 2. However, the point of intersection, which results by extrapolation of the linear segments of the low and high concentration portions (asymptotes) (3, 4)of the analytical curve, can be calculated by equating Il to I 2 and letting N = N , , the atomic concentration (atoms cm.-9 a t the point of intersection. Therefore
aAvDB(T)
60 _ _ - A tLho2gtt
(4)
I n the case of a spectral line multiplet,
Element-Line ( A ) Flame type" C, (measured) Ref. Na 5890b C2H2/air 3.6 x 1 0 - 4 ~ 3 x 10-4~ (4) Na 5890b,g Hz/OZ 2.3x 1 0 - 3 ~ 2 x 10-3~ (9) 1 x 10-3~ (9) Na 589Obt~ c2a*/o2 2.9 x 1 0 - 3 ~ Na 3302.3c CzHZ/ajr 1 . 5 x 10-2M K 76Gd CzHdair 1.2 x 1 0 - 3 ~ 1 ,o X ' i o - 3 ~ K 40446 C2Hz/air 9.7 x 1 0 - 3 ~ (4) Cu 3274j CzHZ/air 7.7 x 1 0 - 4 ~ 4 x 1 0 - 4 ~ (4) a Flame conditions for C2H2/air flame: 7560 cc. air/min. and 702 cc. CZHt/min.; @ = 0.20 cc./min. (chamber type atomizer-burner); Q = 137 cc./sec.; nT/n298 = 1.1; T = 2480" K. ( 4 ) ; E = 1.0; L = 2.2 cm. Flame conditions for C*H2/02 flame: 4500 cc. Oa/min. and 1800 cc. CZHJmin.; @ = 1.7 cc./min. (total consumption atomizer-burner); Q = 126 cc./sec., nT/n298 = 1.2; T = 2850" K. ( 1 1 ) ; E = 0.5: L = 1.0 em. Flame conditions for H2/02 flame: 2500 cc. Op/min. and 5000 cc. HZ/min.; + = 2.0 cc./niin. (total consumption atomizer-burner); Q = 125 cc./sec.; nT/n298 = 1.2; T = 2700" K. ( 1 1 ) ; E = 0.4; L = 0.5 cm. ?r'a 5890 Ah: g,AT = 1.8 X IO8 sec.-l; B ( T ) = 2 ; a = 0.86 [This is an assumption for C2H2/air,C2H2/02 and H z / O ~flames based on measurements by Hinnov and Kohn ( 4 ) ]; pi is taken as 0.5, 0.04, and 0.10 for NaCl solution introduced into CzHZ/air, C*H2/02, and H2/02 flames, respectively, (pi values estimated from data in Tickers' thesis (9); A V D = 3.9 X l o 9 set.-' Na 3302.3 Ah: g,At = 0.65 X lo8 see.-'; a = 2.3 [from Hinnov and Kohn ( . $ ) I ; B ( T ) = 2 ; p is taken as 0.5 for NaCl introduced into C2H2/airflame: AVO = 7 X l o 9 sec. -l K 7665 Ah: guAt = 1.6 X lo8 see.-'; B ( T ) = 2; a = 2.7 [from Hinnov and Kohn ( 4 ) j ; 8' is taken as 0.21 for KCl introduced into CzHz/air flame; A V O = 2.2 X l o 9see.-' e K 4044 Ah: & A T = 0.95 X lo8 sec.-l; B ( T ) = 2; A = 2.2 [from Hinnov and Kohn ( d ) ] ; p same as in d; A V O = 4.2 X logsee.-' f Cu 3274 Ah: g u A t = 1.9 X lo8 see.-'; B ( T ) = 2 ; a = 0.46 [from Hinnov and Kohn ( 4 ) ]; pL is taken as 0.41 for CuC12 introduced into C2H2/02flame: A V D = 4.1 x lo9 sec.-I 0 Experimental measurements of Na in the C P H ~ / O and ~ the H2/02 flame were taken using Beckman DU spectrometer and so these data are corrected for doublet measurement using Equation 7. All other measurements were taken on a spectrometer of better dispersion by Hinnov and Kohn ( 4 ) . All spectral data comes from references listed in the article by Winefordner and Vickers (12). The value of 0 for NaCl int'roduced into a CzHS/air flame was assumed to be 1.0 by Hinnov and Kohn ( 4 ) . Calculations by Vickers (9) have shown p to be closer to 0.5 and so p was taken as 0.5. All other B's (for KCl and CuC12) were taken from Hinnov and Kohn ( 4 ) but were corrected for the new value of p for NaC1--i.e., Hinnov and Kohn ( 4 ) used NaCl as a reference compound to evaluate an instrumental factor and then measure all other p's with respect to NaC1.
If!
VOL. 37, NO. 10, SEPTEMBER 1965
1217
equilibrium constants for the ionization and compound formation processes as a function of flame temperature and composition. If p and the other parameters in Equation 6 can be evaluated, then C, can be calculated. Perhaps of more significance than the absolute calculation of C, is the use of Equation 6 to predict the influence of variation of parameters on the value of C,. For example, since AVDvaries ( I S ) with h 0 - l , C, varies linearly with and so elements with resonance lines in the ultraviolet region will have higher values of C, than elements with resonance lines in the visible region if all other parameters in Equation 6 are similar. Thicker flames (greater L ) show greater self-absorption than thinner flames, and so C, shifts to lower values as L increases. For a given flame and line, the value of C, occurs a t lower values as the product @ E increases. For a given flame type, flame composition, and solution flow rate, C, shifts to lower values as the product SUAt increases. USE
OF EQUATIONS AND DISCUSSION
Values of C, calculated using Equation 6 and measured experimentally are given in Table I for several lines of Na, K, and C, under several different flame conditions. Most of the data listed in Table I are for spectral lines and flame conditions studied by Hinnov and Kohn (4). Most experimentalists do not list sufficient information in scientific papers on flame emission spectrometry to allow calculation of values of C,. However the data in Table I indicate that the theory is valid and that good values for C, should result if reliable values of parameters in Equation 6 are available. The small discrepancies in the calculated and measured values in Table I are most likely a result of the inaccuracies in the values of p, and E used in the calculations and a result of ionization causing the slope of the low concentration segment to differ from unity. The difference between measured and calculated values can be understood by considering the methods used in obtaining the two values. A plot of the logarithm of the photodetector signal us. the logarithm of the atomic concentration produced by the sample for a given flame composition and temperature always gives a curve with two straight line regions, one with a slope of 1.0 and the other with a slope of 0.5. This may be seen by recalling that the signal is proportional to the intensity, I I or Iz,and hence porportional to N or for the two limiting cases. Extrapolating from the two straight line regions yields a value for N , equivalent to that calculated from Equation 4. Calculated values of C, are obtained
a,
1218
ANALYTICAL CHEMISTRY
by substituting N , , as given by Equation 4, into Equation 5. A value of p appropriate to the flame conditions and the concentration region of the point of intersection must be used in Equation 5 . The measured values of C, are obtained from experimental analytical curves. An experimental analytical curve consists of a plot of the logarithm of the photodetector signal us. the logarithm of the sample concentration for a given flame composition and temperature and for a given element and spectral line. The low concentration portion of this curve will be influenced by ionization ( 2 , 7 ) which will cause the slope of the linear portion of the low concentration segment to be greater than 1.0. This results in a shift in the measured values of C, to lower concentrations than the values of C, calculated using Equation 6. The high concentration portion of the curve will be influenced by incomplete dissociation of the salt introduced into the flame gases and by compound formation of the atom in question with flame gas products. This will cause the slope to be less than 0.5. This effect generally causes the measured values of C, to be larger than the calculated values ( 7 ) . Instrumental effects such as saturation of the photodetector can also influence the shape of the analytical curve. An exact value of C, could be calculated if an entire curve of the logarithm of the signal us. the logarithm of N were calculated and each log N value on this curve were converted to log C, where C is the sample concentration in moles per liter. Calculated values of C could be obtained from calculated values of N by use of Equation 5. More accurate calculated values of C, could then be obtained from this calculated analytical curve by extrapolation of the linear portions of the high and low concentration regions. Appropriate values of p would be needed for each N value converted to a C value in calculating the analytical curve. The improvement obtained in calculating C, values by the above method hardly justifies the additional work, because the calculated values of C,, as obtained from Equation 6, are good approximations for most atoms in flame emission spectrometry, and the uncertainty in the values of p would still lead to deviations. I n most instances onIy an approximate idea is needed of the range of maximum slope of an analytical curve in atomic emission flame spectrometry, and hence only an approximate value of C, is needed if the range of maximum slope is taken as the concentration region between the limit of detectability (la)and the point of intersection. If the experimental system has a monochromator which is unable to re-
solve a doublet-e.g., the S a 5890-6 A. doublet when measured using the Beckman DU monochromator, then the point of intersection can be anywhere between the values of N, calculated for each line-Le.,
1 ” 7
KjNij
(7)
Kjj=l j=1
where K~ and K Z are the slit functions for the two lines (9, I $ ) , namely,
where K , is the slit function factor for line j , h is the wavelength setting of the monochromator, h,, is the wavelength of the line center of line j , and s is the spectral bandwidth (12) of the monochromator in units consistent with the A’s. The expression on the right of Equation 7 is a general equation for a multiplet and the summations are over all spectral components emerging from the exit slit of the monochromator. The terms ATtl, AT,*$ and YtJ are the values of N, for lines 1, 2, and j , respectively, and are calculated using Equation 4. By combining Equations 4, 7, and 8 with 5 , C, can be calculated for the case of measuring a multiplet rather than a single, isolated, sharp spectral line. LITERATURE CITED
(1) Alkemade, C. T. J., Ph.D. thesis,
University of Utrecht, Setherlands, 1954.
(2) Herrmann, R., Alkemade, C. T. J., “Flammenphotometrie,” 2nd ed., Springer Terlag, Berlin, 1960, “Ckmical Analysis by Flame Photometry, P. T. Gilbert, transl., Wiley, New York, 1963. (3) Hinnov. E.. J . Oat. SOC.Am. 47. 151 4 1 947 ). ( 4 ) Hinnov, E., Kohn, H., Zbid., p. 156. ( 5 ) James, C. G., Sugden, T. M., AViature 171,428 (1953). (6) Narvrodineanu, R., Boiteux, H.,
“L’Analyse spectrale quantitative par la flamme,” Masson et Cie., Paris, 1954. ( 7 ) Poluektov, N. S., “Techniques in Flame Photometric Analysis,” Consultants Bureau, N. y., 1961. (8) ‘C‘nsold, A., “Physik der Sternatmosphere,” Springer Terlag, Berlin, lQi5 -1--.
( 9 ) Tickers, T. J., Ph.D. thesis, University of Florida, Gainesville, Fla., 1964. (10) Winefordner, J. D., Mansfield, C. T., Trickers, T. J., ANAL. CHEM.35, 1607 (1963). (11) Zbz’d., p. 1611. (12) Winefordner, J. D., Vickers, T. J., ANAL.CHEM.36, 1939 (1964). (13) Zbid., p. 1947.
RECEIVEDfor review May 25, 1965. Accepted June 21, 1965. Research supported by a NASA Institutional Grant NASA-NSG-542-Project 20 and by a National Science Foundation Grant NSFP15944.
