Anal. Chem. 1986, 58,3103-3108 (6) Murtha, D. P.; Walton, R. A. Inorg. Chem. 1973, 12, 368. (7) Birchall, T.; Connor, J. A,; Hillier, I. H. J . Chem. SOC.,Dalton Trans. 1975, 2393. ( 8 ) Chatt, J.; Elson, C. M.; Hooper, N. E.; Leigh, G. J. J . Chem. Soc., Dalton Trans. 1975, 2393. (9) Chatt, J.; Eison, C. M.; Leigh, G. J.; Connor, J. A. J . Chem. SOC., Dalton Trans. 1976, 1351. (IO) Umapathy, P.; Badrinarayanan, S.:Sinha, A. P. 8. J . Electron Spectrosc. Reiat. Phenom. 1983, 28, 261. (11) Demanet, C.M. South Afr. J . Chem. 1982. 35, 45. (12) Lin'Ko. I . V.; Zaitzev. 8. E.: Molodkin, A. K.: Ivanova, T. M.; Lin'Ko, R. V. Zb. Neorg. Khim. 1983, 28, 1520. (13) Folkesson. B.; Sundberg, P.: Johansson, L.; Larsson, R. J . Electron Spectrosc. Reiat. Phenom. 1983, 32, 245. (14) Gerasimov, V. N.; Kryuchkov, S. V.; Kuzina, A. F.; Kulakov, V. M.; Pirozhkov, S. V.; Spitsyn, V. I. Doki. Akad. Nauk. SSSR, Engi. Transi. 1982, 266, 148. (15) Gerasimov, V. N.; Zelenkov, G. A.; Kuiakov, V. M.; Pcheiin, V. A,; Sokolovskaya, M. V.; Soldatov, A. A,; Chistyakov, L. V. Zh. Eksp. Teor. Fir. 1984, 86, 1169. (16) Fiser, M.; Brabec, V.; Dragoun, 0.: Kovalik, A,; Frana, J.; Rysavy, M. I n t . J . Appl. Radiat. b o t . 1985, 36, 219.
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(17) Deutsch, E.; Nicollni, M.; Wagner, H. N., Jr. Technetium in Chemistry and Nuclear Medicne; Cortina International: Verona, Italy (Distributed by Raven Press, New York), 1983. (18) Jackels, S.B.; Rose, N. J. Inorg. Chem. 1973, 12, 1232. (19) Bradbury, M. The Concept of a Blood-Brain Barrier; Wiley: New York, 1979. (20) Lister-James, J. In Radionuclide Imaging of the Brain; Hoiman, B. L., Ed.: Churchill-Llvingstone: New York, 1985; p 75. (21) Clark, D. T.; Adams, D. B.; Briggs, D. J . Chem. SOC. D 1971, 12, 602. (22) Fryer, C. W.; Smith, J. A. S.J . Chem. SOC.A 1970, 1030. (23) Bandoli, G.; Mazzi, U.; Roncari, E.; Deutsch, E. Coord. Chem. Rev. 1962, 4 4 , 191. (24) Handbook of Photoelectron Spectroscopy;Perkin-Elmer: Eden Prairie, MN, 1979. (25) Bremser. W.; Linneman, F. Chem. Ztg. 1972, 96,36.
RECEIVED for review May 2,1986. Accepted August 6, 1986. The support of the Natural Sciences and Engineering Research Council of Canada to M.T. is gratefully acknowledged.
Theoretical Basis for Line Number to Line Intensity Logarithmic Relationship Alexander Scheeline School of Chemical Sciences, University of Illinois, 1209 West California Avenue, 79 R A L Box 48, Urbana, Illinois 61801
A linear relationship between the logarlthm of the number of lines having a given spectral Inlenslty and the logarithm of the relative lntenslty of those llnes wlth respect to the weakest observable llnes In the spectrum Is crltlcally evaluated. Use of exact quantum mechanical formulas tor electrlc dlpole transltlons In hydrogen allows slmulatlon of spectral behavlor that can be generallzed to elements whose spectra can be described In the Russell-Saunders limit. The linear relationship Is shown to be of narrower appllcablllty than orlglnally concelved. Some apparent anomalles In llterature data are explalned. Results are dlscussed In terms of Interferences expected from line overlaps In emlsslon spectrochemical analysis.
In a recent article ( I ) , experimental evidence for a general relationship between the number of observable lines in an emission spectrum and the relative intensities of those lines was discussed. An empirical relationship proposed by Learner (2) was critically evaluated, based on the spectrum of neutral arsenic obtained under conditions similar to those used by Learner in generating his hypothesis (3). The relationship employed was loglo Nk = logl, (No)- km (1) where N k is the number of lines with emission intensity in octave k , N o is the number of lines emitting a t the limit of detection (signal approximately 3 times the observation system limiting noise), k is the octave number (recall an octave is a factor of 2 in emission intensity), and m is the slope of the supposedly linear relationship between octave number and number of lines. Learner found that m was very close to 0.1505, which is log,, 21/2,for several elements excited in hollow cathode lamps. Analysis of arsenic data ( I , 3) also revealed that, for data collected on the McMath solar telescope in-
terferometer, the sameslope line could be fit to observed data. What remained unclear was whether the slope of 0.1505 was a true physical constant, an artifact of measurement, or a coincidental value that applied only to the species observed. In the absence of instrumentation having sufficiently well characterized spectral response to independently generate intensity data, a theoretical approach to the problem was pursued. The only neutral element for which spectral properties can be accurately calculated in closed form (ignoring relativistic corrections) is hydrogen. The appropriate formulas can be found in general works on atomic spectra ( 4 ) ,specific references on quantum mechanics (5), and the journal literature (6). Consideration was restricted to dipole-allowed transitions. Oscillator strengths for hydrogen have been tabulated for all absorption transitions between n (principal quantum number) levels up to n = 50 (6),and tabulations for restricted sets of transitions including levels up to n = 500 are available (7). There is thus a sufficient data base to allow simulation of the intensity distribution in the hydrogen spectrum. Comparison of the theoretical distribution to that predicted by Learner allows for critical appraisal of the validity of eq 1. Clearly, the hydrogen spectrum differs from that of all other elements in that there are no electron-electron interactions. However, judicious use of various theorems concerning transition probabilities allows extrapolation to more complicated atoms. There appears to be some parallel between the current discussion and the statistical theory of spectra (8). However, such theory has been directed mainly a t the distribution of energy levels rather than the intensity of transitions between those levels. Indeed, other than some general sum rules for oscillator strengths, the entire issue of distribution of transition moments among various levels appears to be largely empirically based. In the following sections, the necessary formulas for the intensity distribution in the hydrogen spectrum are presented
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without derivation. The distributions resulting from the application of these formulas are presented. Interpretation of these distributions, in terms of their implication for interferences in emission spectrochemical analysis, is then given.
THEORY In the absence of perturbing electric or magnetic fields, it is difficult to see structure in the thermally excited hydrogen atomic emission spectrum other than that attributable to the n quantum number. In the first approach to be used in analyzing the line intensities, all structure other than that caused by transitions from one n quantum state to another n state is ignored. Later, a second approach will be given in which the antithetical approximation is made: that all ( n ,I , j ) quantum states can be individually resolved. While the latter case is only approachable experimentally for low values of n using Doppler-free spectroscopy, it allows for linkage of the current work to more complex atoms describable by the Russell-Saunders coupling scheme. Level-averaged oscillator strengths f(n’,n ) ,where n’is the principal quantum number of the lower state and n is the principal quantum number of the upper state, were taken from Goldwire’s tables (6). Einstein spontaneous emission coefficient A ( n , n ? are computable from the oscillator strengths via eq 2 , also taken from Goldwire. where L‘ is the frequency
Table I. Least-Squares Slopes of Plots in Figures 1-5” figure
slope
k range
1A 1B
0.088 f 0.003 0.158 f 0.006 0.121 f 0.011 -0.133 f 0.005 0.109 f 0.005 0.168 f 0.007 -0.112 f 0.005 0.076 f 0.002 0.074 f 0.002 0.118 f 0.002 0.094 f 0.002 0.120 f 0.004 0.159 f 0.002 0.100 f 0.0035 -0.149 f 0.009 0.1504 f 0.003 -0.145 f 0.006 0.1187 f 0.005 -0.143 f 0.006 0.2004 f 0.005 -0.145 f 0.006 0.115 f 0.008 -0.145 f 0.006 0.1875 f 0.004 -0.147 f 0.006
7-16 1-11 15-22 0-13 4-22 18-28 0-17 4-32 4-32 4-22b 4-28 4-23’ 4-1 1 19-41 0-12 17-32 0-12 19-37 0-13 17-28 0-12 19-38 0-12 17-30 0-12
1c 2A 2B 3A 3B 3c 4A 5A 5B
5c 5D 5E
5F
” Sign convention is consistent with ea 1. ’Omitting n = 1 and 2. of the transition in Hz, p is the reduced mass of the hydrogenic system being considered, and the remaining symbols are the common representations for electron charge and the speed of light. The ratio (n’*/n2)represents the ratio of the degeneracies of the upper and lower n states. Given the Einstein coefficient, emission intensity is readily computable both in terms of photons s-’ cm-’
I , = Nu A ( n , n3 1 / ( 4 ~ )
(3)
and in terms of W cm-?
I , = hcN, A ( n , n’) 1/47~X
(4)
where h is Planck’s constant, h is the wavelength of the transition, 1 is the optical path length viewed through the source, and Nu is the population of the upper state of the transition. For convenience, local thermal equilibrium (LTE) is assumed to determine the populations of the various states, so that a simple Boltzmann distribution can be employed. The issue of deviations from LTE, while important in real emission sources, is not addressed here. Equations 3 and 4 are general for any transition (not just for n to n’transitions), given the A coefficient for that transition. To calculate the oscillator strength for transitions in atoms described by Russell-Saunders coupling of spin and orbital angular momentum, A coefficients for specific ( n , 1, j ) to (12’. I’. j ? transitions are necessary. The procedure for obtaining these can be found in Sobelman ( 4 ) . As only emission is being studied, an emission oscillator strength is computed as follows:
If(n, I , j ; n’, I’, j ’ ) l = (n’-’
-
n-2)1,,,(2j’+
1) (Racah)’R2/3 (5)
Here primed symbols refer to the lower state,R is the radial dipole transition matrix element normalized to the Bohr radius, l, is the larger of ( I , 17, and (Racah)refers to the Racah 6 j symbol for the transition. The radial dipole transition matrix element depends only on n and 1 quantum numbers, whereas the 6; symbol depends only on 1 and j , not n. Formulas for the 6 j symbols can be found in Sobelman, and formulas for the radial dipole transition matrix elements are given in Goldwire, -4dditional information that may assist
in interpreting Goldwire’s formulas can be found, for example, in general mathematical tables such as Gradshteyn and Ryzhik (9). All calculations were performed assuming an infinite nuclear mass, as finite mass effects shift all transition probabilities in a proportional manner. The Turbopascal programs written on the basis of the cited formulas are available from the author. For those situations where only n quantum numbers were employed, 1225 transitions were employed in generating results. This is the total number of n n’ transitions available if the maximum for n and n’ is 50. For those situations in which all n, I , j, n’, l‘, and j’quantum numbers were used independently, the combined constraints on (n,1, j ) combinations for any level and for transition selection rules meant that 1397 transitions through n = 12 were used. In the cases were n = 11 and n = 13 were the highest n’s employed, 1055 and 1806 transitions, respectively, were accounted for.
-
RESULTS AND DISCUSSION Where uncertainties are shown, ranges are f l standard deviation. Slopes of the various plots are listed in Table I for easy comparison. Plots related to n quantum numbers only are in Figures lA, l B , 2A, 3, and 4; plots based on n, 1, and j quantum number variations are in Figures l C , 2B, and 5 . As can be seen from the equations in the Theory section, spectral intensities are based on level populations, level degeneracies, state couplings (via the radial dipole transition matrix elements), and the gap between energy levels. Furthermore, the difference between monitoring intensities via photon counting and via radiant flux (power) measurement can introduce an additional energy level difference dependence. I t is thus instructive to observe the distribution of spectral intensity development as the various contributing factors are convoluted. Figure 1 shows n dependent oscillator strengths. In inset A, the absorption oscillator strengths for n’+ n, n E 11,501 appears. There is only a short linear region, and there appears to be an absence of low-strength transitions compared to that expected from extrapolating the linear region. As the square points indicate, the missing weak transitions are due to omission of transitions to the high n levels in the Lyman (n’ = 1) and Balmer (n’ = 2) series. Omitting levels n = 1 and 2
ANALYTICAL CHEMISTRY, VOL. 58,NO. 14,DECEMBER 1986
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A
\
0 5,;
I
1
'1
%r\ h
,
20
IO Binad Number
-
0
,
12
IO Binod Number
-0
20
IO
30
Binad Number
I IO
20
Figure 2. Einstein A (spontaneous emission) coefficients: (A) n resolved. Symbols are the same as in Figure 1. (6) j resolved. All levels up to n = 12 are included.
Binad Number
Figure 1. log frequency of occurrence vs. log bin-sorted value plots for oscillator strengths: (A) n-resolved absorption oscillator strength, n E [ 1, 501;(6) n-resolved emission oscillator strength, n E [ l , 501; (C) /-resolved emission oscillator strength, n E [ 1, 121;(triangles) including all n E [l, 501;(circles) all transitions except those connecting with n E [48,501; (squares) all transitions except those connecting with n E [ 1, 21. Where no circle is shown, data overlap with items denoted with triangles.
removes more weak lines than omitting levels n = 48,49, and 50. Removing either set of levels from consideration has little effect on the shape of the log (line number)/(oscillator strength) plot. The slope of the linear region, 0.088 f 0.003, is significantly less than Learner's 0.1505. In inset B, emission oscillator strengths for the same transitions are shown. These vary only by a degeneracy factor n2/n12)compared to inset A. The change in plot shape is readily evident. The range of oscillator strengths has decreased from 221in inset A to only 212 in inset B. The profound importance of level degeneracy is thus illustrated. The slope here is close to that recorded by Learner, even though spectral distribution, level population, and observation parameters are not yet convoluted into the intensity distribution functions. Related plots that are independent of level degeneracy can be found in Cowan (10). Next, the distribution of spontaneous emission coefficients (Einstein A coefficients) is shown in Figure 2A. The slope of 0.109 f 0.005 applies to the case where all levels n = 1-50 are considered. Omission of n = 1 and 2 slightly increases the apparent slope. Twenty-seven binads or 8 orders of magnitude encompass the range of spontaneous emission coefficients. Apparently for Rydberg series, the relationship in eq 1 is at least a reasonable approximation to the distribution of decay constants of excited levels. Formulas in Sobelman ( 4 ) indicate that within a given series (either upper or lower n quantum number fixed), the Einstein coefficient should fall off approximately aa n4.2, or the slope of plots based on eq 1 should be 0.060. A slope nearly twice this large and corresponding approximately to n-ll3 dependence appears
A
25
50
75
Binad'Number
:u 20
IO
30
40
Binad Number
1
10
1
2b
30
Binad Number
Figure 3. n-Resolved intensity distributions (W cm-2) as a function of temperature. Symbols are the same as in Figure 1: (A) T = 5000 K, (B) T = 20000 K, (C)T = 40000 K.
when summing over all series as was done here. Work is in progress to demonstrate this limiting behavior based on approximate formulas for transition probabilities (11).
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h
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Predicted spectral distributions for n-resolved emission intensities: (A) intensity in terms of photon counts cm-* s-l and (B) intensity in terms of w s-'. Figure 4.
Table 11. Slopes Jf Plots Analogous to Those in Figure 3, s-' but with Intensities Measured in photons temp. K
slope
k range
5 000 20 000 40 000
0.076 f 0.002 0.125 f 0.004 0.151 f 0.006
3-32 5-24 8-22
The level population dependence of emission measured in terms of watts per square centimeters is evident from the plots in Figure 3. At 2000 K, the Lyman and Balmer series are a t least 225or over 7 orders of magnitude more intense than higher level series. Within the higher level series, the log (line number)/(intensity range) slope is only half the value stated by Learner. As the temperature is increased, higher levels become more populated and the various series coalesce into a single distribution which follows the form of eq 1, but with a slope that is substantially less than Learne. 's observation. That higher temperature results in more nearly predicted behavior leads one to extrapolate behavior to infinite temperature. The result appears in Figure 4. Inset B shows the intensity distribution predicted for infinite temperature with detection in terms of watts per square centimeter. No slope was calculated, as visual inspection shows no linear region to the plot. Inset A is the same set of conditions, except that intensity is shown in units of photons s-l cm-2. Not only is behavior nearly linear but the slope is approximately 0.16, close to (though significantly larger a t the 3a level than) Learner's value. Reexamination of the data in Figure 3 in terms of photon counting rather than power intensity measurements showed the results in Table 11. At low temperature, there was no significant difference in slope between the two intensity scales. However, a t 40000 K, the photon basis for intensity measurement gave a slope statistically indistinguishable from Learner's result. This is an important result. Under the conditions that Learner (and later Howard and Andrew) worked, the range of photon energies was small (on the order
of a factor of 21, so differences between the two detection approaches should be small. In the case of hydrogen, the spectral lines considered range from the vacuum ultraviolet ( n = 50 to n = 1 has X = 912.1 A) to the ultra-high-frequency radio range ( n = 50 to n = 49 has X = 5.5 mm). Photon statistics vary drastically over such a range. It appears that Learner's result can only be valid for photon counting detection for nearly infinite temperature sources. In the li lit that the lines being observed are over a narrow energy rar.,se, power detection may be feasible. Requiring infinite temperature sources is not a particularly difficult restriction; if recombination is the dominant source of excited atoms, very high excitation temperatures can appear. This is consistent with the conditions of neutral atom excitation in hollow cathode discharges (12) and electrodeless discharge lamps (EDLs), the sources used in generating the spectra previously tested against the Learner hypothesis. Atoms more complex than hydrogen will obey the relationships in eq 3 and 4, provided that the appropriate quantum numbers replace n and n'. Conservation rules giving the relative intensity of multiplet components of Russell-Saunders coupled levels show that, aside from slight shifts in level populations due to energy level shifts, the relative intensity of multiplet components is independent of the extent of the shifts. Thus, by accounting individually for 1 and j quantum numbers, the statistics of a hydrogenic Russell-Saunders atomic spectrum can be computed in a manner analogous to that already discussed for the 1-j degenerate hydrogen system. Again, details can be found in Sobelman ( 4 ) ,and a detailed derivation is available from the author. In real atoms, high n states tend to be hydrogen-like, whereas lower states are strongly split. Thus, the following presentation probably overstates the effects of LS coupling. Emission oscillator strength distributions are shown in Figure 1C. Notice the radical difference in shape between plots B and C. Evidently, many weak transitions sum together to produce the fewer, stronger transitions obtained when only n quantum numbers are considered. The long upslope region at low oscillator strengths has no parallel in Learner's work. Similarly, the Einstein A coefficients, plotted in Figure 2B, are distributed quite differently than in Figure 2A, where only n was considered. The downslope of 0.168 f 0.007 is close to Learner's value. However, more transitions are accounted for in the upslope region than in the downslope region. However, eq 1 was hypothesized without any knowledge of an upslope region. Figure 5 summarizes the intensity distributions for the Russell-Saunders coupled hydrogen atom, with the left column showing distributions as a function of emitted power and the right column showing distributions as a function of emitted photons per second. The differences are more subtle than were those between, for example, parts A and B of Figure 4. Both photon counting and emitted power plots have nearly identical shapes. The plots of arsenic emission data previously repoi ted ( I ) bear some resemblance to right-hand column plots, provided only data for k > 13 or 14 are considered. Regardless of temperature, the downslope for the left column (intensity as a function of power emitted) is 10.115. There is similar temperature ambiguity in the right column, with downslopes ranging from 0.15 to 0.20. Inset F indicates the changes that occur when the highest n level is deleted from consideration (round dots) or an extra n level is added (dashed curve). The shape of the curve is preserved; only its position along the ordinate shifts. This self-similarity suggests that the limitation to n = 12 reveals most of the significant features of the log (frequency-of-occurrence)/ (intensity range) plots. I t supports the idea that the distribution of the relative intensity of spectral lines is independent of temperature, in
ANALYTICAL CHEMISTRY, VOL. 58, NO. 14, DECEMBER 1986
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Binad Number
Binad Number
I C
PI
0'5 OO
I
IO
20
30
1
IO 20 Binad Number
40
Binod Number
I. 30
\
01-
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Binad Number
-1
IO 20 Binad Number
x)
Figure 5. Predicted intensity behavior, j resolved: (A, C, and E) power basis (W cm-'), (B,D, and F) photon basis (photons cm-' s-I); temperatures (A and B) 2000 K, (C and D) 10 000 K, (E and F) infinite temperature. In inset F, circles show behavior if model is restricted to n 5 11; dashed line includes all n 5 13.
distinct contrast to the data in Figure 3. However, when Russell-Saunders coupling occurs, the shape of the plots is radically different than Learner's hypothesis suggested it would be. Because the degree of coupling is a function of the details of atomic structure, there is no theoretical support for eq 1as a universal explanation for the distribution of intensities in atomic spectra. What remains unclear is (1) why Learner obtained the data he did for iron, (2) why the arsenic spectrum collected on the same instrument could be fit to the same relationship, and (3) whether an analysis of hydrogen, which is somewhat artificially stretched to model more complex systems, is in fact applicable to transition-metal species. It is for such species that one would expect Learner's relationship to hold generally, since eq 1was first proposed after analyzing a spectrum in which iron was the analyte. The plots shown in Cowan (10) suggest that there are only minor changes in the distribution of oscillator strengths from one transition metal to another.
CONCLUSION Original interest in eq 1was due to the implication that the number of interferences between two spectra could be computed simply by knowing the concentration ratio of the elements involved. If eq 1 described all atomic spectra, the
ultimate dynamic range for emission spectrochemical analysis of mixtures using thermal excitation sources would also be computable. What has been shown here is that eq 1 does not describe line spectra of aU the elements. However, the patterns of numbers of lines as a function of line intensity do suggest two interesting results: (1)in some instances (systems with regular Rydberg series, if one can extrapolate the hydrogen data based on n quantum numbers only) eq 1 describes the distribution of spectral intensities. If photon counting detection is used and there is an infinite excitation temperature, Learner's theoretical slope of 0.1505 is a good approximation to the intensity distribution. (2) In other instances (systems described well by Russell-Saunders coupling) the number of weak lines is actually less than predicted by eq 1, meaning weak-line interferences will be less of a problem in such systems than in pure Rydberg systems describable by eq 1. This is a more optimistic result than the Learner hypothesis, as it implies that, once some fixed number of interferences are detected, additional dynamic range will not reveal still more line interferences. The lowering of ionization potential in plasmas, which destroys high n levels, could serve to further reduce the number of emitted lines. The conventional wisdom that suppression of background continuum will perpetually improve detection limits would thus be supported. Learner
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(13)has suggested that, in fields sufficient to cause ionization potential lowering, selection rules may also be relaxed so that lines forbidden in isolated atoms may become weak lines, and a multitude of weakly dowed transitions would appear. More complex calculations than presented here would be necessary to access this suggestion. Thus, the application of eq 1 to very dense plasmas requires additional consideration. In the previous paper (I), it was suggested that slopes of plots that were less than 0.15 were due to poor photographic intensity calibration. The current work indicates that such shallow slopes may in some instances occur. Now that it is clear that eq 1 is not a universal descriptor of the intensity distribution of spectral lines, there is a need for reexamination of the conditions under which the arsenic and iron experimental data, which appeared to support the hypothesis, were collected. Careful intensity calibration of the instrumentation and attention to the effects of data reduction algorithms will be required.
ACKNOWLEDGMENT Discussions with Sanford Asher led to the approach employed. Registry No.
HP,1333-74-0.
LITERATURE CITED (1) Scheeline, A. Anal. Chem. 1986, 5 8 , 802-807. (2) Learner, R. C. M. J . Phys. 6 1982, 15, L89LL895. (3) Howard, L. E.; Andrew, K . L. J . Opt. SOC. A m . 6 1985, 2 . 1032-1077. (4) Sobelman. I . I. Atomic Spectra and Radiative Transitions, Springer Series in Chemical Physics V. 1; Springer-Verlag: Berlin, Heidelberg, and New York, 1979. (5) Bethe, H. A.; Salpeter. E. E. Ouantum Mechanics of One- and TwoElectron Atoms ; Springer-Verlag: Berlin, 1957. (6) Goidwire. H. C.,Jr. Astrophys. J . Suppl. Ser. N o . 152 1968. 17, 445-457. Menzel. D. H. Astrophys. J . Suppl. Ser. 161 1969, 18, 221-246. Porter. C. E. Statistical Theories of Spectra : Fluctuations ; Academic Press: New York and London, 1965. Gradshteyn, I . S.; Ryzhik, I . M. Table of Integrals, Series, and Products; Academic Press: New York, 1980. Cowan, Robert D. The Theory of Atomic Structure and Spectra ; University of California Press: Berkeley, CA, 1981; pp 625-631. Stolarsky. K.; Scheeline. A,, work in progress. Farnsworth, P. B.; Walters, J. P. Spectrochim. Acta, Part B 1962, 376. 773-788. Learner, R. C. M. personal communication.
RECEIVEDfor review May 30,1986. Accepted August 21,1986. Financial support of the National Science Foundation (Grant CHE-81-21809) and the Office of Basic Energy Sciences, United States Department of Energy (Grant DE FG02-84ER13218), is gratefully acknowledged.
Production and Initial Characterization of an Imploding Thin-Film Plasma Source for Atomic Spectrometry Kevin P. Carney and Joel M. Goldberg* Department of Chemistry, University of Vermont, Burlington, Vermont 05405
An Imploding thin-film plasma source for the direct atomic spectrochemkal analysis of solid samples is described. The plasma Is produced by an axially directed capacltlve electrical discharge through a conductive silver thin film that has been chemicaHy deposited on the lnterlor wall of a polycarbonate tube. Discharge Instrumentation and methods for thln-fllm depositlon are descrlbed in detail. The plasma Implodes symmetrically at a constant velocity and then fllls the dlscharge tube. Solid powder microsamples of pure vanadium and V205 are sampled by the plasma from the dlscharge tube wal. Peak power dissipation in plasmas generated by moderate energy (200-1600 J) dkcharges Is In the megawatt range with corresponding peak power densities In the megawatt per cubic centimeter range. Initial emission spectroscopic measurements are presented.
The use of pulsed discharges as atomic spectrochemical sources has been widely reported (1-3) due to their ability to deliver large amounts of energy to a small sample area in a very short period of time. The more popular pulsed discharge sources (e.g., spark and laser plasmas) are best noted for their ability to directly sample solid materials. More recently, exploding conductor plasma sources have demonstrated the capability of directly analyzing solid samples for trace metallic elemental constituents with surprisingly few matrix effects. All of these pulsed discharge sources possess very attractive features as direct solid sampling devices due to their extremely high power density capabilities. Their usefulness for the direct 0003-2700/86/0358-3 108$01.50/0
atomic spectrochemical analysis of solid materials, however, has been limited by their relatively poor excitation characteristics. While reexcitation of the atomic vapor produced by these discharges is possible, it is complicated by the rapid expansion of the resultant sample atomic vapor. Thus, direct in situ reexcitation is limited by the short residence time of analyte species in the postdischarge environment. As such, reexcitation schemes using spark and laser atom cells have typically involved transport of the sampled analyte vapor to a conventional high-frequency excitation source (e.g., an ICP or microwave-induced plasma) (4-6). The relatively long sample transit times (seconds) characteristic of these schemes, however, can result in significant condensation and/or dilution of the sampled atomic vapor before it reaches the excitation source, severely degrading its analytical characteristics. In this report, we describe initial studies of a new type of pulsed discharge source for atomic spectrochemical analysis: the imploding plasma. By producing a transient plasma through implosion, we hope to generate a spatially confined atom cell capable of very high power densities as well as long analyte atomic vapor residence times. Development of a suitable device for the production of imploding plasmas for atomic spectroscopy must rely upon the wealth of available reports of electromagnetic compression devices in the plasma physics literature. Theoretical discussions of magnetically self-pinched plasmas can be found in the literature as early as 1934 (7); however, reports of experimental investigations of imploding plasmas are not found in the open literature until the late 1950s (8). The 0 1986 American Chemical Society
