Instrumentation
T. C. O'Haver Department of Chemistry University of Maryland College Park, Md. 20742
Derivative and Wavelength Modulation Spectrometry The requirements of a satisfactory analytical method are many, but certainly selectivity must be counted among the most important. Often the measurement techniques that are the most sensitive lack the inherent selectivity to allow straightforward application to the kind of highly complex materials for which the analytical chemist is more and more often called upon to develop analytical methods. Prior separation procedures involving extraction, chromatography, etc., are often useful, and indeed essential, in such cases. But there are applications in which, for reasons of speed and simplicity, a more direct approach will be desirable. Thus, there has always been interest in techniques that can improve the selectivity of the measurement methods themselves. Among the most conceptually simple of these methods are derivative and wavelength modulation spectrometry. In derivative spectroscopy the first or higher derivative of spectral intensity or of absorbance with respect to wavelength is recorded vs. wavelength to enhance the detectability of minor spectral features such as weak shoulders. In wavelength modulation spectroscopy the wavelength to which the monochromator (or filter, laser, or interferometer) is tuned is repetitively and rapidly scanned back and forth over a small spectral interval called the modulation interval, AX. In the photodetector signal this results in a ripple or alternating current (ac) component that can be isolated and measured electronically. These two concepts are closely related in that wavelength modulation is a commonly used method for obtaining derivative spectra. If the wavelength modulation interval is small compared to the width of a spectral band, then the ac component of the photosignal at the modulation frequency will be closely propor0003-2700/78/0351 -091 A$01.00/0 © 1978 American Chemical Society
tional to the first derivative (i.e., slope) of the spectral band with respect to wavelength. However, derivative spectra may be obtained in other ways not involving wavelength modulation. Moreover, there are other applications of wavelength modulation that do not involve recording deriva-
tive spectra. The principle of operation of all these techniques is essentially the same; it is based on measurement of the change in intensity or absorbance with wavelength. We will presently see that this can be a most useful approach in several areas of analytical spectrometry.
Normal Spectra
Analyte Band Alone
With Interfering Band
First Derivatives
Analyte Band Alone
With Interfering Band
Figure 1 . First derivative for quantitative measurement of intensity of a small band obscured by a broader overlapping band
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Figure 2. Fluorescence emission spectrum of an optical brightener absorbed onto a piece of cotton fabric laundered in a mod ern commercial laundry product (A) Normal spectrum, (B) first derivative, (C) second derivative
Derivative Spectroscopy
Why would one want to take the de rivative of a spectrum? Essentially, in the derivative spectra the ability to detect and to measure minor spectral features is considerably enhanced. This enhancement of characteristic spectral detail can distinguish very similar spectra and follow subtle changes in a spectrum. Moreover, it can be of use in quantitative analysis when it is desired to measure the con centration of an analyte whose peak is obscured by a larger overlapping peak due to something else in the sam ple. Let us arbitrarily consider the case in which the interfering peak has a height and width twice that of the analyte peak, as shown in Figure 1. Let us normalize the height of the an alyte band alone (upper left) to 1.0. We might try to neglect the interfer ing peak altogether and simply mea sure the total intensity (or absorbance) at the analyte maximum. The yield of a reading of 1.9 units in this example is clearly an unsatisfactory approximation. Or we could try the tangential baseline technique to com pensate for the presence of the inter fering band. Actually in this particular case we cannot even draw a unique tangent, but if we make a reasonable guess, our reading of 0.4 units is far too low. Now referring to the deriva tive spectra in the bottom half of Fig ure 1, we can take as the measure of the analyte intensity the vertical dis tance between the adjacent maximum and minimum of the first derivative. In the presence of the interfering band, this measure is reduced by only
12%, a much smaller effect than for the nonderivative measures. More im portant, the effect of changes in the intensity of the interfering band is correspondingly reduced. As might be expected, the advantage of the deriva tive measurement depends strongly on the relative width of the two bands. If the interfering band is at least a fac tor of two broader than the analyte band, it will usually be advantageous to base the measurement on the deriv ative spectra. The above comments are based only on a consideration of the systematic errors; we must, of course, also consid er the effect of random errors. Usual ly, the process of differentiation de grades signal-to-noise ratio (SNR); thus, random measurement errors may be aggravated in the derivative mode. The extent of SNR degradation depends upon a host of experimental variables, but a factor of two for every successive order of differentiation is commonly observed in practice. Fig ure 2 shows a typical case. This is the fluorescence emission spectrum of an optical brightener in a commercial laundry product. Each of the spectra is a superposition of five separate re corded scans. The SNR degradation, particularly in the second derivative, is obvious. In general, one would not expect derivative techniques to be helpful if poor SNR is already appar ent in the undifferentiated spectrum. To make sure that a spectral feature seen in a derivative spectrum is real and not simply a random noise event, it is always a good idea to record the derivative several times as in Figure 2.
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Experimental Techniques
A variety of different experimental techniques have been used to obtain derivative spectra. If the spectrum has been recorded digitally or is otherwise available in computer-readable form, then the differentiation can be done numerically, for example, by means of the techniques popularized by Savitsky and Golay (1). Alternatively, the derivative spectra may be recorded di rectly in real time, either by wave length modulation or by obtaining the time derivative of the spectrum scanned at a constant rate. In the lat ter case, a quite simple electronic dif ferentiator can be used; many suitable circuits have been published (2). This approach is based on the idea that if the wavelength scan rate, dX/dt, is constant, then the derivative of inten sity / with respect to wavelength, dll dX, is proportional to the derivative of intensity with respect to time, dll dt, which is measured by means of the electronic differentiator: dl = dl/dt d\ dX/dt The wavelength modulation tech nique for obtaining derivative spectra is illustrated in Figure 3. If the wave length of measurement is modulated, in this case sinusoidally, with a modu lation interval, Δλ (small compared to the width of the spectral band), then the amplitude of the resulting intensi ty modulation will be proportional to the slope of the spectrum within the modulation interval and thus to the first derivative of the spectrum in that region. One normally employs some
sort of frequency and phase selective ac amplification system, such as a lock-in amplifier, to measure the in tensity modulation. To measure the first derivatives, this system will be tuned to the frequency of wavelength modulation. It is perhaps not quite so intuitively clear that one can also ob tain the second derivative by tuning the detection system to the second harmonic, i.e., twice the frequency of modulation. Also, the waveform of ap plied wavelength modulation need not be sinusoidal; square wave modulation is also commonly used, particularly in absorption spectrophotometry (3). Among the experimental techniques used to produce wavelength modula tion are: • Vibration or oscillation of the slits, mirror, grating, or prism of the monochromator • Insertion of an oscillating or ro tating refractor plate in the light beam inside the monochromator • Oscillation (tilting) of an interfer ence filter • Oscillation of a Fabry-Perot in terferometer • Use of a rotating half-sector or vi brating mirror to time-share light of two different wavelengths provided by two gratings or two exit (or entrance) slits • Modulation of the electron beam scan pattern in a vidicon or image-dis sector photomultiplier spectrometer. Several authors have compared the relative advantages of these different approaches to obtaining derivative spectra (4-6). In general, it is safe to say that electronic differentiation of fers simplicity and low cost, but suf fers from the inability to obtain deriv atives at fixed wavelengths and is sus ceptible to signal-to-noise degradation caused by purely temporal changes in spectral intensity not accompanied by genuine changes in wavelength depen dence. Wavelength modulation gener ally provides superior signal-to-noise ratio in absorption spectrometry or in any spectral measurement in which a time-dependent background signal is likely to be encountered, e.g., in flame, furnace, or plasma emission spectrom etry. Several commercial spectrometers capable of recording derivative spectra are now available. Some models of the newer UV-visible absorption spectro photometers have a switch-selectable derivative range; these are mostly based on electronic differentiation with operational amplifier circuits. An outboard electronic derivative attach ment is also available. Dual-wave length spectrophotometers, such as those made by Perkin-Elmer and the American Instrument Co., can obtain first derivative spectra by wavelength modulation. A wavelength modulation absorption spectrometer designed to
measure only second derivative spec tra is made by Lear Siegler, Inc. This instrument has heated long-pass cells for gas analysis as well as a conven tional cuvette holder for solution work. Derivative Applications
Derivative spectrometry has been profitably applied to quantitative analysis situations in which the pres ence of a broad, unstructured back ground spectrum overlaps the bands of interest. Examples include the mea surement of aqueous solutions of er bium salts in the presence of an excess of cerium (3), the analysis of highly scattering samples and turbid solu tions (3), and the measurement of bili rubin in the presence of albumin (7). Derivative techniques have also been applied to the analysis of multicomponent mixtures. Hawthorne and Thorngate (8) describe a commercial wavelength modulation second deriva tive absorption spectrophotometer that has potential for determining the vapor-phase concentrations of volatile polynuclear aromatic hydrocarbons (PNA's), as a means of analyzing PNA's in a solvent extract from par ticulates collected on filters, and as a monitor for aqueous pollution. Absorption spectrophotometry of molecules in the gas phase is another application area in which derivative techniques have proved useful (4, 9). Hager (4) has reviewed this subject. With long path length, multiple reflec-
tion gas cells, 1-200 ppb concentra tions of nitric oxide, nitrogen dioxide, sulfur dioxide, ozone, ammonia, ben zene, toluene, xylene, styrene, formal dehyde, and benzaldehyde can be de tected. The absorption (and reflectance) spectra of many solids exhibit subtle spectral features that contain infor mation about the electronic structure of the material. The structure-enhanc ing capabilities of derivative spec trometry have been found helpful in studying the optical properties of such materials (10). In addition to its applications to ab sorption spectrometry, derivative techniques are being used in fluores cence spectrometry as well. Applica tions have included the quantitative analysis of overlapping spectra (2), de tection of impurities in PNA fractions separated by liquid chromatography (11), and enhancement of fine struc ture of low-temperature fluorescence spectra of petroleum oils (12). In fluo rescence, derivative spectra of good quality can be obtained with a simple electronic time differentiator circuit. (In contrast, derivative absorption spectra are often obtained by the more elaborate wavelength modulation technique to reduce the effect of fluc tuations in the 100% Τ baseline.) Wavelength Modulation Spectroscopy
In addition to obtaining derivative spectra, wavelength modulation tech-
Sinusoidal Modulation of Wavelength Ira by wavelength modulation Figure 3. Generation of derivative spectra
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niques are used in some measure ments in which recordings of the de rivative of the spectrum are not actu ally obtained. In atomic spectroscopy in the vapor phase, wavelength modulation can measure the intensity of a weak line superimposed on an intense and un stable spectral background due to the atomization device or the sample ma trix. The resulting measurement prob lem is depicted schematically in Fig ure 4. The spectrum of the back ground is often broad and unstruc tured, as shown in 4A. The compara tively narrow atomic lines are super imposed on this background (4B-D). The wavelength is modulated sinusoidally as indicated over the interval Δλ centered on the desired line. The background by itself will generate a "ripple" (alternative current compo nent) in the photocurrent at the same frequency as that of the applied wave length modulation (usually 50-1000 Hz). If a spectral line is present in the modulation interval, a second har monic component, at twice the ap plied modulation frequency, will also be generated. This is clearly seen in Figure 4D; but even in Figure 4B, where the line is very weak, a small second harmonic is present, as evi denced by the deviation of the photo-
Figure 4. Wavelength modulation to measure amplitude of a weak spectral line superimposed on an intense back ground
signal from a pure sine wave. Only a pure sine wave, with no second har monic component, is produced by a background which is linear over the interval Δλ. This will not be strictly true for real backgrounds, but in most cases the modulation interval is so small (as little as 0.01 nm) that this is a very good approximation. The next step is to separate the sec ond harmonic component from the possibly much larger first harmonic component; this is easily done with a commercially available lock-in ampli fier tuned to the second harmonic fre quency. The essential point here is that if the background fluctuates or drifts in intensity, the amplitude of the second harmonic component will remain unchanged or nearly un changed. This technique has been applied to the measurement of atomic emission in flames (13), graphite furnace atom izers (14), and plasmas (15); of atomic absorption in flames (16) and in graphite furnace atomizers (17); and of atomic fluorescence in flames (18). The benefits obtained are the in creases in the accuracy and precision of analysis due to the reduced influ ence of background spectral interfer ence. A good example of these benefits can be seen in the application to graphite furnace atomic absorption spectrometry. This technique is among the most sensitive in common use today, but when applied to the measurement of very low concentra tion of certain elements in very com plex samples, serious errors can result from the interfering light absorption and scattering of the sample matrix. Consider, for example, the measure ment of chromium in human urine, an important measurement in chromium metabolism and nutrition studies. The normal levels are very low, typically less than 1 ng/mL. Moreover, urine contains a large amount of dissolved sodium chloride, the concentration of which is roughly 107 times that of the chromium concentration. The molecu lar absorption and scattering signal due to the very large excess of sodium chloride can be quite large compared to the atomic absorption signal of the chromium. Most commercial atomic absorption spectrometers can be equipped with a background corrector attachment which is intended to cor rect for spectral background interfer ence continuously as each sample is measured. A discussion of the opera tion of these devices is beyond the scope of this paper, but for various reasons they do not work well in cer tain extreme cases, for example, in the case of chromium in urine. In such cases, wavelength modulation can pro vide superior results. A recently de scribed new type of atomic absorption instrument, called the CEWM Sys-
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Figure 5. Determination of chromium in human urine by graphite furnace atomic absorption spectrometry Tracings show atomic absorbance as a function of time. Top tracing obtained on a commercial atomic absorption spectrometer with a conven tional background corrector attachment. Results of measurement of four aliquots of sample are shown; atomic absorption peaks are narrow dou ble peaks. Bottom tracing shows two measure ments of same urine sample by means of a proto type continuum source atomic absorption spec trometer that utilizes wavelength modulation
tern, is based on wavelength modula tion (19). This instrument uses a con tinuum primary source, as opposed to the narrow line sources in convention al atomic absorption instruments, and has a specially designed monochromator with much higher resolution than is usual. The wavelength of this mono· chromator is modulated at approxi mately 100 Hz over a 0.01-nm spectral interval centered on the desired atom ic line. The second harmonic of the photosignal is measured. The ability of this system to correct for large amounts of background is shown in Figure 5, which shows absorbance vs. time tracings of the graphite furnace atomic absorption measurement of chromium in human urine containing approximately 0.2 μg/mL chromium (20). The upper tracing was obtained on a modern commercial background corrected instrument. Four atomizations are shown. The double peaks and drifting baseline make quantita tion difficult and uncertain. The wavelength-modulated CEWM system gives the results shown in the bottom tracing (two atomizations shown). The lower baseline drift is a result of the superior background correction capa bilities of wavelength modulation. Another application in which wave length modulation is particularly valu able is in gas chromatography with an
element-selective microwave plasma emission detector. Here again the transient nature of the signal makes conventional background correction methods impractical. However, with wavelength modulation, excellent background correction was achieved, and in one study it was possible to de tect as little as 15 pg of dimethyl selenide and 6 pg of tetramethyl lead (21). In addition to its capabilities of compensating for broad-banded back ground spectral interference, wave length modulation has the unique ability to correct for direct spectral line overlaps as well (22). Such over laps occur occasionally in the analysis of alloys and other materials contain ing large concentrations of transition metals whose spectra are very com plex. For example, the determination of traces of zinc in high-purity copper metal cannot be done directly by atomic absorption because copper has a weak absorption line only 0.003 nm away from the zinc 213-nm line, which is the only useful zinc absorption line. Since the true widths of the lines are about the same as the separation be tween them, increased spectrometer resolution alone cannot eliminate the interference. With conventional in strumentation a prior separation (e.g., by electrolysis) is necessary. Wave length modulation, which can be used to correct for this interference, allows a direct analysis without separation. The concept is illustrated in Figure 6. Let us say that peak Β represents the analyte absorption, and peak A repre sents the interfering absorption. The modulation conditions (width and po sition of the modulation interval) are carefully adjusted so that the analyte peak generates a predominantly first harmonic signal, whereas the interfer ing peak generates a purely second harmonic signal with no first harmon ic component. Selective detection of the first harmonic component would result in a signal due only to the ana lyte peak. (Alternatively, the modula tion conditions could be adjusted so that the analyte would generate a pre dominantly second harmonic signal, whereas the interfering peak generates a signal with no second harmonic com ponent.) The required modulation conditions can be determined a priori if the shape and exact wavelength sep aration of the two lines are known, or the conditions can be found empirical ly by zeroing the instrument response to a sample of pure interfering materi al (if available). As before, the dynam ic nature of the correction assures that fluctuations and drift in the intensity of the interfering band will be reject ed. This approach has been used to measure the zinc contamination in NBS Benchmark Copper without prior separation (23).
The concept just described can also be applied in a particularly useful way to another area of spectroscopy where overlapping bands are a common oc currence: fluorescence spectrometry. In some favorable cases the excitation peaks of two fluorescent compounds in a mixture may be well enough sepa rated in wavelength that it is possible to adjust the excitation monochromator to selectively excite one compound and not the other; this is referred to as selective excitation. Thus, the emis sion spectrum of the selected com pound could be recorded without in terference from the other compound, even if its emission spectrum coincides with that of the selected compound. In practice, however, this ideal situation is seldom approached; much more commonly the excitation spectra of two compounds overlap too much to allow the simple selective excitation idea to be used effectively. In this case, too, wavelength modulation pro vides a possible solution. Referring back to Figure 6, suppose that the two peaks A and Β represent the excita tion spectra of the two compounds. The proper choice of modulation con ditions will modulate the fluorescence emission of the two compounds at dif ferent frequencies. This applies to all wavelengths of emission; therefore, it is possible to record the completely re solved emission spectrum of either compound by tuning the lock-in am plifier to the appropriate frequency and scanning the emission monochro-
mator. Because of the rather large widths of the fluorescence bands of most compounds, rather large values of Δλ are used, typically 30-60 nm. The optimum modulation conditions are usually established empirically, ei ther to null out the spectrum of one component (especially useful for bina ry mixtures) or to selectively enhance the spectrum of one component (24). An example of the application of this technique to a two-component mixture of chrysene and anthracene in cyclohexane is shown in Figure 7. Both of these polycyclic hydrocarbons are fluorescent, but the emission and excitation spectra overlap extensively. Figure 7A shows, for reference, the fluorescence emission spectrum of so lution of chrysene alone, excited at its excitation maximum. Figure 7B shows the emission spectrum of a mixture of chrysene and a severalfold concentra tion excess of anthracene. Here an at tempt has been made to extract the spectrum of chrysene from the mix ture by exciting the mixture at the ex citation wavelength which yields the greatest chrysene-to-anthracene in tensity ratio. This turns out to be clos er to an excitation minimum of an thracene than to an excitation maxi mum of chrysene, which accounts for the reduction in the intensity ob served. Clearly, the resulting spectrum is a poor match to that of pure chry sene; the residual anthracene emission has changed the peak height ratios and has added new peaks and shoul-
Figure β. Wavelength modulation to compensate for mutual spectral interference of two overlapping spectral lines or bands ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 · 99 A
Literature Cited
Figure 7. Excitation wavelength modulation to allow measurement of fluorescence emission spectrum of one component in a mixture of two fluorescent compounds whose excitation and emission spectra are extensively overlapped (A) Emission spectrum of pure chrysene solution excited at its excitation maximum; (B) emission spec trum of a mixture of chrysene in the presence of an excess of anthracene excited near an excitation minimum of anthracene; (C) emission spectrum of same mixture obtained by excitation wavelength modulation with conditions adjusted to strip out spectrum of anthracene
ders. Figure 7C shows the emission spectrum of the same mixture record ed with excitation wavelength modu lation. T h e conditions are chosen to null out the anthracene emission. (The instrumental sensitivity has been increased to normalize the height of this spectrum to t h a t of pure chrysene for easier comparison.) T h e recovery of the chrysene spectrum is nearly perfect. Note, however, the slight de crease in signal-to-noise ratio, an un avoidable consequence of the modula tion process. This technique has been applied to the analysis of two- and three-compo nent mixtures of polycyclic aromatic hydrocarbons. It is especially useful for isomers t h a t are difficult to sepa rate chromatographically and there fore might be expected to occur to gether in fractions collected from chromatographic separations of com plex samples. Fox and Staley (25) have used the technique to detect and identify small amounts of benz[a]anthracene coeluting with chrysene in a reverse-phase liquid chromatographic separation of extracts of atmospheric particulate matter. T h e wavelength modulation tech nique just described does not have the power or the generality of the tech niques t h a t are based on computer manipulation of the whole excitation emission matrix (26). On the other hand, wavelength modulation does not require a computer, produces results in real time, and would seem to be more suitable for routine analytical
applications in well-characterized samples, e.g., in quality control or in clinical chemistry. T h e excitation wavelength modula tion technique described above also finds use in Raman spectroscopy. Funfschilling and Williams (27) de scribe a wavelength-modulated CW dye laser to allow the observation of weak Raman lines buried in the back ground fluorescence of impurities in the sample. Conclusions Interest in derivative and wave length modulation techniques has been increasing in recent years as evi denced by the fact t h a t the number of literature references to these tech niques has tripled every decade for the last three decades. If we consider their conceptual simplicity and relative ease of implementation, there is every rea son to believe t h a t these techniques will be even more widely applied in the future.
Thomas C. O'Haver is professor of chemistry at the University of Mary land, College Park. His main research interests are in the areas of analytical spectroscopy and instrumentation, with particular emphasis on atomic spectroscopy, luminescence methods, modulation techniques, and the ap plication of microprocessors in chemi cal instrumentation.
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(1) A. Savitsky and M. Golay, Anal. Chem., 36, 1628 (1964). (2) G. L. Green and T. C. O'Haver, ibid., 46,2191(1974). (3) T. J. Porro, ibid., 44,93A (1972). (4) R. N. Hager, Jr., ibid., 45,1131A (1973). (5) T. C. O'Haver, "Wavelength Modula tion Spectroscopy," in "Contemporary Topics in Analytical and Clinical Chem istry," D. Hercules, Ed., Vol. 2, Chap. 1, Plenum Press, New York, N.Y., 1978. (6) T. C. O'Haver, "Modulation and Deriv ative Techniques in Luminescence Spec trometry: Approaches to Increased Ana lytical Selectivity," in "Modern Fluores cence Spectroscopy," E. L. Wehry, Ed., Vol. 1, Plenum Press, New York, N.Y., 1976. (7) T. E. Cook, R. E. Santini, and H. L. Pardue, Anal. Chem., 49,871 (1977). (8) A. R. Hawthorne and J. H. Thorngate, Appl. Opt.. 17, 724 (1978). (9) J. W. Strojek, D. Yates, and T. Kuwana, Anal. Chem., 47,1051 (1975). (10) M. Cardona, "Modulation Spectrosco py," Academic Press, New York, N.Y., 1969. (11) M. A. Fox and S. W. Staley, Anal. Chem., 48,992(1976). (12) D. A. Kolb and Κ. Κ. Shearin, "Fin gerprinting Petroleum Oils with Low Temperature Derivative Fluorometry," Paper 300, 28th Pittsburgh Conference, Cleveland, Ohio, Mar. 3, 1977. (13) W. Snelleman, T. Rains, K. Yee, H. Cook, and O. Menis, Anal. Chem., 42, 394 (1970). (14) M. S. Epstein, T. C. Rains, and T. C. O'Haver, Appl. Spectrosc, 30, 324 (1976). (15) R. K. Skogerboe, P. J. Lamothe, G. J. Bastiaans, S. J. Freeland, and G. N. Coleman, ibid., ρ 495. (16) W. Snelleman, Spectrochim. Acta, 23B, 403 (1968). (17) J. M. Harnly and T. C. O'Haver, Anal. Chem., 49,2187(1977). (18) E. Lipari and F. W. Plankey, ibid., 50, 386(1978). (19) Α. Τ Zander, T. C. O'Haver, and P. N. Keliher, ibid., 48,1166 (1976). (20) Unpublished work in our laboratory. (21) D. Reamer, T. C. O'Haver, and W. Zoller, "Determination of Alkyl Lead and Selenium Compounds in the Atmo sphere Using a GC/MPD with Wave length Modulation," 8th Materials Re search Symp., NBS, Gaithersburg, Md., Sept. 23,1976. (22) G. L. Collier and F. Singleton, J. Appl. Chem., 6,495 (1956). (23) Α. Τ Zander, T. C. O'Haver, and P. N. Keliher, Anal. Chem., 49, 838 (1977). (24) T. C. O'Haver and W. M. Parks, ibid., 46, 1886 (1974). (25) M. A. Fox and S. W. Staley, ibid., 48, 992(1976). (26) I. M. Warner, E. R. Davidson, and G. D. Christian, ibid., 49, 2155 (1977). (27) J. Funfschilling and D. F. Williams, Appl. Spectrosc, 30,443 (1976).
