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Anal. Chern. 1980, 52, 2192-2195
Among the commonly occurring elements expected to interfere with this method would be copper, since it would also deposit a t the potential employed. Copper(I1) a t a concentration 10 times that of arsenic was found to reduce the arsenic peak height by about half. For development of method for the analysis of samples such as foods by the described cathodic stripping procedure, several factors had to be considered. These included the digestion of samples, reduction of arsenic(V) to arsenic(III), and the elimination of interferences. Digestion in a closed system ensured that no arsenic would be lost through volatilization, and heating with magnesium nitrate ensured the destruction of all traces of organic matter. Reduction with sodium bromide in the presence of hydrazine sulfate was effective and did not introduce interfering ions into the solution. Interference due to copper and other cations was easily eliminated by removing them from solution by extraction with dithizone in carbon tetrachloride (8). The National Bureau of Standards Reference Material 1571 Orchard Leaves, certified to contain 14 f 2 Kg/g arsenic, was analyzed by the described procedure and yielded 13.2 bg/g arsenic (average of five determinations) with a standard deviation of 1.1 pg/g.
ACKNOWLEDGMENT The author wishes to thank Mildred M. Cody, of FDA, New York, and of the Department of Home Economics and Nutrition of New York University, New York, and Thomas Medwick, Professor of Pharmaceutical Chemistry, Rutgers University, New Brunswick, NJ, for their invaluable assistance in the preparation of this paper.
LITERATURE CITED (1) Arnold, J. P.; Johnson, R . N. Taknta. 1989, 76, 1191-1207. (2) Myers, D. J.; Osteryoung, J. Anal. Chem. 1973, 45, 267-271. (3) Foisberg, Y.; O'Laughlin, J. W.; Megargle, R. E.; Korlyohann, S. R. Anal. Chem. 1975, 47, 1586-1591. (4) Davis, P.H.; Dulude, G. R.; eiffin, R. M.; Matson, W. R.; Zink, E. W. Anal. Chem. 1978, 50, 137-143. (5) Cox, J. A.; Chang, K., Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, IL, 1975. (6) "Official Methods of Analysis of the Association of Official Analytical Chemists", 12th ed.;George Banta Co. Inc.: Menasha. WI, 1976: paragraph 25.106. (7) Christian. G. D.; Knoblock, E. C.; Purdy, W. C. Anal. Chem. W63, 35, 1128- 1 132. (8) Lossen, G. L. Chemist-Analyst 1977, 67, 4.
RECEIVED for review April 2,1980. Accepted August 18,1980.
Absorbance Determination by Time Interval Measurements J. Michael Ramsey" and William B. Whitten Analytical Chemistry Division, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37830
Absorbance measurements are accomplished by placlng the sample Inside the cavity of a laser which is impulsively pumped. I f the laser contains an appropriate gain medium, there will exist a measurable time delay between pumplng and the onset of lasing. It Is shown that this time delay Is related to the optical losses In the laser cavlty. Increased time delays due to an intracavity sample can therefore, be related to the absorbance of the sample. The result of this process is that absorbance Is determined by measuring a differential time rather than optlcal power. Absorbances as small as are measured wlth an instrument utilizing this new approach. I n the small absorbance reglme, the dlfferentlal delay time Is linearly related to the absorbance.
Optical absorbance measurements are among the oldest and most utilized techniques employed by the analyst. In recent years, absorbance measurements have become more sophisticated, so that, in many cases, detection limits are reduced significantly. These new measurement techniques are primarily laser based such as laser photoacoustic, laser-induced thermal gradient, and laser intracavity absorption measurements. All of these methods are capable of measuring ab(1-3). We present in this paper sorbances of less than a new approach to the measurement of small optical absorbance ( N ~ O - , ) . This novel method is also based upon the use of lasers and is compatible with all types of samples: gases, liquids, or solids. An important feature of this approach is that it accomplishes the absorbance determination by measuring a time difference rather than optical power. Such a transformation is attractive because of the ease in which accurate and precise time differences can be determined. In 0003-2700/80/0352-2192$0 1.OO/O
addition, convenience is derived from the fact that under certain conditions (e.g., low absorbance) this time difference is linearly related to the absorbance. The new measurement scheme utilizes laser gain materials which exhibit a relatively slow rise of optical gain after the injection of pump energy. As a result of the slowly rising gain, there is a significant time delay between the initiation of pumping and the onset of lasing. This delay corresponds to the time required for the optical gain to increase beyond the optical losses of the laser cavity. From the dependence of delay time on cavity losses, it follows that one can determine the absorption (an optical loss) caused by materials located in the laser cavity by measuring the resulting time delay. The difference in delay time with and without the intracavity sample is indicative of the absorption of that sample a t the laser wavelength. In the following sections, the measurement scheme is explained in greater detail and the expected response theoretically modeled. The experimental approach we utilize to measure the delayed lasing phenomena is described, and data are presented which demonstrate the capabilities of such an instrument.
THEORY The gain media utilized in these experiments generally can be treated as four-level systems. An appropriate four-level energy diagram is shown in Figure 1. We will assume that the gain medium is instantaneously pumped (energy injected) so as to populate level 3. The population density of level 3 at this instant is defined as N3 These excited states now relax to populate the upper laser level, energy level 2. T h e rate of this relaxation is k,,, a characteristic of the active medium. The nature of the upper laser level is that of a metastable state (i.e., the population loss from level 2 is negligible over the time 0 1980 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
2e I
2103
0-SWITCHED Nd-YAGtSHG
ik32
v
LASER
A
n
DISC
I u
-
SAMPLE
r - 5
START
I"O
0
Flgure 1. Energy diagram for a four-level laser gain medium.
period being discussed). Thus, the population of level 2, N2, increases with time in a simple manner ( 4 ) as described by eq 1. The lower laser level, energy level 1, is sufficiently energetic to avoid being thermally populated and klo is large compared to k 3 2 which allows a rapid depletion of any population a t energy level 1. Therefore, when the population of level 2 grows, a population inversion exists between states 1 and 2. This invenion is responsible for providing the necessary optical gain for laser action. When the population of level 2 reaches the threshold population density, the laser will begin to operate and emit laser radiation. The time delay between the pump pulse and the onset of lasing is determined by the initial population of level 3, N 3 ,the decay rate constant, k32, and the laser threshold population density. The first of these parameters is linearly related to the pump energy, the second is a constant characteristic of the laser gain medium, and the latter is a constant determined by the gain medium and laser cavity design. Assuming constant pump energy, the delay time between the pump pulse and the laser pulse is a constant for a given laser system. This delay time is related primarily to the threshold population density of the laser with the above assumptions. An expression for the delay time, tTo,can be derived from eq 1 assuming some necessary threshold population density, NT, viz.
Flgure 2. Schematic diagram of the experimental apparatus.
sample has a path length b, absorptivity a , and concentration c. The new expression for NT is then NT = NT' (2(ln [10])abc A) (4)
+
The factor of 2 above accounts for the fact that two passes are made through the sample during one round trip in the laser cavity. Equation 4 indicates that the additional absorptive losses have just added to the conventional laser cavity losses. The delay time when the intracavity absorber is in place, t T , is given by substituting eq 4 into eq 2, viz.
1 tT=--1n k32
[
NT = NTOA
( 3)
where h is a coefficient related to the optical losses encountered per round trip in the laser cavity, Le., the transmittance of the laser mirrors and all other losses distributed throughout the cavity (5). The quantity NTois the threshold population density which would be required if the loss coefficient were equal to 1. Thus, larger cavity losses imply a larger threshold population density. Ideally, A should be as small as possible. One can now introduce additional loss into the laser cavity such as through optical absorption. When a substance which absorbs at the laser wavelength is placed in the cavity, the losses are increased and hence the threshold population density has been increased. This increase results in a larger time delay between the pump and the laser pulses as indicated by eq 2. The absorbance of the material placed in the cavity is related to the increased time delay. It is assumed that the
N T ' ( ~In
[lo] abc + A) N3
]
(5)
The value of tTo given in eq 2 represents the blank signal for the absorption experiment and t T given in eq 5 represents the sample signal. The difference between these two delay times, A t , is the value of interest and is given in eq 6. All factors
in eq 6 are constants for a given laser system except for those describing the intracavity absorber. Therefore, any At is related to a specific absorbance, abc. Furthermore, if the second term of both the numerator and the denominator in eq 6 is much less than one, then the following first-order approximation is valid. ~ N T 'In [10]UbC
at The threshold population density is determined by the physics of the gain medium and the optical losses associated with the laser cavity. In fact, the threshold population density is that required to produce a gain which is equal to the losses. The threshold population density can be written as
1-
E
k32N3
(7)
In this "low loss-high pump energy" regime one has the additional advantage of a linear relationship between differential delay time and absorbance or concentration. Equation 6 indicates that it is preferable to employ an active medium with a low NToand a laser cavity with low loss so that the linear region of operation is obtained with smaller pump energies. The smaller pump energy in turn increases the sensitivity of the measurement. The temporal resolution required by the experiment is determined primarily by the decay rate constant, 1232. Therefore, this rate constant is an additional parameter of importance when selecting the active medium to be used.
EXPERIMENTAL SECTION The laser gain medium used in these initial experiments was Nd-YAG. The experimental setup employed is shown in Figure 2. A frequency-doubledQ-switched Nd-YAG laser (Chromatix Model CMX-1000) was used to optically pump the second NdYAG oscillator. The pump laser emits 532-nm pulses af 50-11s duration at a repetition of 80 Hz with a per pulse energy of 1mJ. The optical pulses were directed by two high reflecting dielectric coated mirrors to a 25-cm fused silica lens. The 532-nm radiation was focused by the lens at the first face of the Nd-YAG rod. The
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
rod had flat-flat ends and was enclosed in a nearly hemispherical (L= 27.5 cm) optical cavity. The cavity mirrors were dielectric coated for maximum reflectivity at 1064 nm, the fundamental Nd-YAG laser wavelength. These mirrors were mostly transmitting at 532 nm. A cuvette with a 2-mm path length was also placed within the laser cavity. The infrared laser radiation was detected with a high-speed avalanche photodiode (Texas Instruments No. TIED-56). A colored glass filter (Corning CS2-58) and variable neutral density filter were used at the laser output to block the green pump radiation and to control the irradiance of the infrared radiation arriving at the photodiode. For time synchronization purposes, a second photodiode (Hewlett-Packard No. 5082-4205)was used to measure the pump radiation which leaked through the second folding mirror. The optically pumped laser was aligned by minimizing the time delay between the pumping pulse and laser emission. This minimum time delay also corresponds to maximum energy per pulse. The angular orientation of the intracavity cuvette was also adjusted during the alignment procedure. The optimum position of the cuvette was near normal to the optical axis. During this procedure the cuvette was filled with the sample blank, in this case deionized HzO. The time delay was conveniently observed with an oscilloscope during the alignment procedure. The oscilloscope can also be used to measure time delays associated with the sample absorbances. Pulse-to-pulse energy fluctuations in the pump laser resulted in fluctuations of the delay time, and thus, we chose to record the delay time observed over many laser pulses using the instrumentation shown in Figure 2. The photodiode outputs were attached to two separate discriminators. The discriminated pump pulse signal was used to start a time-to-amplitude converter (TAC) while the infrared laser pulse stops the TAC. Time delay data were compiled over many pump pulses by connecting a pulse height analyzer (PHA) to the output of the TAC. Solutions of CuS04.5Hz0(Reagent Grade) in deionized H,O were used as the absorbing sample for the purpose of demonstrating the concept. A stock solution was made with a concentration of 41.8 mmol L-'. Various dilutions of the stock solution were used in the absorbance measurements. The signal from the photodiode monitoring the pump pulse was approximately 150 mV peak amplitude. The discriminator for this signal was operated in the constant fraction mode with a discrimination level of approximately 50 mV. The output from the photodiode observing the infrared laser radiation was always adjusted to a peak amplitude of 300 mV with the variable neutral density filter. The discriminator for this signal was operated in the leading edge triggered mode with the discrimination level at 50 mV. The TAC and PHA were adjusted such that each channel corresponded to approximately 1.5 ns. Data were collected on the PHA for each sample and blank until the peak channel had accumulated approximately lo3counts. The delay time given by the peak channel was then recorded.
RESULTS AND DISCUSSION An absorbance spectrum of the stock solution, relative to deionized H20, was measured on a Cary-14 spectrometer from 900 to 1160 nm. This portion of the spectrum is featureless with the absorbance slowly decreasing as the wavelength increases. The absorbance at 1064 nm was determined to be 0.255 for a 1-cm path length, thus, corresponding to an absorbance of 0.051 for the stock solution in the intracavity cell ( b = 2 mm). The lasing time delay measured for the blank solution was 140 ns. The stock solution gives a time delay of 220 ns while the most dilute solution, one-tenth the stock concentration implying an absorbance of 0.0051, results in a delay time of 149 ns. A plot of the differential delay times vs. absorption for the sample and blank solutions is shown in Figure 3. The theoretically expected response (eq 6) is plotted, along with the experimental data, as the solid line. We have previously determined ( 4 ) the rate constant, k32,to have a value of 1.6 x lo6 s-' and the other parameters of eq 6 were determined from the blank delay time and by fitting to the stock solution response.
I
i
i
/'
/
p''
l i _ _ L - - - L S 00
0 132
C
04
0 OE
A 6 S046 A N C E
Figure 3. Differential delay time vs. absorbance for a series of CuSO, solutions. The triangles represent the experimental data and the solid curve is the theoretical response predicted by eq 6.
Figure 3 indicates that theory and experiment are well matched. The response curve is mostly linear under these experimental conditions, but close inspection reveals the upward curvature expected as the linear approximation becomes invalid. All but one of the experimental points fall on the theoretical curve when error bars are included. The experimental error (the time delay distribution width at 95% amplitude) ranged from *0.6% of the absolute delay time for the blank to *1.5% for the stock solution. The delay time jitter is the result of pulse-to-pulse energy fluctuations in the pump laser. These fluctuations become increasingly significant as the pumped laser approaches threshold, hence the increased experimental error at large absorbances. The time delay jitter limits the minimum detectable absorbance, Le., a t a given pump energy the ability to resolve two delay time values. Under the conditions of these experiments an absorbance of approximately 0.001 was the minimum detectable. Ideally, the upper limit would be that absorbance which increased the cavity losses above the available gain. This ideal limit is not attainable in the multiple pulse experiment, again because of the very large jitter in the pump energy. Near threshold, a number of pump pulses contain insufficient energy to overcome threshold, and thus a skewed time delay distribution results. Assuming no jitter and extrapolating the theoretical curve displayed in Figure 3 to an infinite delay time yields an upper limit of 0.425 A. The theory given above is not valid at infinite delay time because of the finite upper laser level lifetime. Nonetheless, use of the lifetime for Nd-YAG as the delay time (230 ps) yields the same result to three significant figures, indicating the steepness of the response curve at these large delay times. Certainly a number of advantages can be accrued by employing a pump laser with greater pulse-to-pulse energy stability. Since there is a practical limit to such stability, a better approach to improving the time-delay jitter would be to saturate the active medium transitions a t the pump wavelength. The saturation condition would make N3 independent of the pump energy. A third alternative for reduction of the time-delay jitter is the accurate monitoring of the pump pulse energy with appropriate normalization for each pulse. Equations 6 and 7 also indicate that increased dynamic range would be available with increased pump energy u p t o the saturation limit. The latter statement assumes that the temporal resolution of the pump pulse is less than the min-
Anal. Chem. 1980, 52, 2195-2201
imum delay time. Obviously, the dynamic range of this measurement system can be extended by using various cell path lengths. Solvents other than HzO should be used with greater path lengths because of its rather "large" absorbance a t 1064 nm. The absorbance of H 2 0 with a 1-cm path length a t this wavelength is -0.043 (6, 7). Heavy water, DzO, is a good alternative having an absorbance 12 times smaller at this wavelength. The lower limit of detection with the present experimental apparatus is limited by the pump pulse energy fluctuations and the inherent optical losses of the laser cavity. We feel that both of these limitations can be improved by a t least 1 order of magnitude, lowering the detectable absorbance to 10-j or less. T h e inherent pulsed nature of these experiments also permits time-resolved absorption measurement, Le., rapid absorbance determinations. In the present work, the maximum duration of a single pulse experiment is approximately 200 ns. With the experimental apparatus used, it would be necessary to accurately determine the pump pulse energy in order to perform single pulse absorbance measurements. Unlike laser-induced thermal gradient experiments these measurements do not depend on the thermooptical properties of the solvent provided a single shot or low repetition rate experiment is performed. The instant that lasing commences at the 1064-nm wavelength, the absorption experiment is over.
2195
Prior to lasing, extremely low optical powers are impingent on the sample minimizing the formation of a thermal lens. Thus, these absorption experiments have the same requirements of the samples as conventional absorption spectrometry. Nonscattering samples of any kind, gas, liquid, or solid, can be measured easily. The current apparatus is limited by the fact that the sample must absorb at the delayed laser wavelength. This limitation is only temporary as other laser gain media can be utilized providing alternative wavelengths, and the possibility of a tunable system cannot be precluded.
LITERATURE CITED (1) Tam, A. C.; Patel, C. K. N. Appl. Opt. 1979, 78,3348. (2) Harris, J. M.; Dovichi, N. J. Anal. Chem. 1980, 52, 695A. (3) Harris, S. J. J. Chem. Phys. 1979, 77, 4001. (4) Ramsey, J. M.; Whitten, W. B., unpublished work, April 1980. (5) Yariv, A. "Quantum Electronics", 2nd ed.;Wiley: New York, 1975; Chapter 9. (6) Tyler, J. E. In "Handbook of Optics"; Driscal, W. G., Ed.; McGraw-Hill: New York, 1978; Chapter 15. (7) Koechner, W. "Solid-State Laser Engineering"; Springer-Verlag: New York, 1976; Chapter 7.
RECEIVED for review July 11,1980. Accepted August 25,1980. Research sponsored by the Office of Basic Energy Sciences, U.S. Department of Energy under Contract W-7405-eng-26 with the Union Carbide Corp. J.M.R. wishes to acknowledge the support of the Eugene P. Wigner Fellowship Program.
Proton-Induced X-ray Emission Analysis of Deep-sea Ferromanganese Nodules Stephen J. Kirchner,
H. Oona,
Steven J. Perron, and Quintus Fernando*
Department of Chemistry, University of Arizona, Tucson, Arizona 8572 1
John Jong-Hae Lee and Harry Zeitlin Department of Chemistry, University of Ha waii, Honolulu, Hawaii 96822
Seven samples of deep-sea ferromanganese nodules from the Pacific and Atlantic Oceans were analyzed by protoninduced X-ray emission (PIXE). The concentrations of Na, Mg, AI, Si, K, Ca, Ti, V, Mn, Fe, Co, Nil Cu, Zn, As, Rb, Sr, Mo, Ba, TI, and Pb in the nodules were determined, and the accuracy of the determinations was verified independently by flame atomic absorption and emission techniques. Thin sample targets on Nuclepore filter disks backed with Kapton were used with I-MeV protons for the low-energy region (0-8 keV) and 2-MeV protons and a 0.004-in. AI filter for the high-energy region (5-35 keV) of the X-ray spectrum. X-ray yield data were obtained for elements from Na to U ( 1 1 < 2 < 92), wlth standards of 99.999 YO purity and the thin target technique. Five different NBS standard reference materials (orchard leaves, pine needles, bovine ilver, coal, and coal fly ash) were analyzed by this method to determine the precision and accuracy that could be achieved under the operating conditions of the PIXE system.
The particle-induced X-ray emission technique (PIXE) has been firmly established as a rapid and sensitive method for 0003-2700/80/0352-2195$01 .OO/O
trace analysis (1-4). For multielemental analysis, 1-2-MeV protons are an optimum choice for X-ray excitation, because of the relatively high ionization cross sections for a given proton energy. The sensitivity of the method depends on a number of factors, the most important of which me the energy of the incident proton beam, the nature of the sample target, and the background bremsstrahlung, which determines the lower limit of detection of an element. A major component of the bremsstrahlung originates from the secondary electrons produced in the sample target. If a thin target is used, the composition and thickness of the backing material affect the background bremsstrahlung. An ideal backing, therefore, for a thin target is an inert high-purity hydrocarbon film that has a high mechanical strength and high thermal and electrical conductivities. A decrease in the energy of the proton beam will result in a reduction of the background bremsstrahlung, but this apparent improvement in the signal-to-noise ratio is offset by a decrease in the production of characteristic X-rays. It is evident from all these considerations that the energy of the incident proton beam must be optimized for a given sample type and thickness and target backing. For the kind of samples that we have analyzed in this work we have employed 1-and 2-MeV proton beams with thin sample targets mounted on thick Kapton (Dupont) backings. The charac$2 1980 American Chemical Society
