48 1
Anal. Chem. 1983, 55, 481-488 N3+
+ 02
-+
Nz
+ N + 02'
-+
N2
+ 0 + NO'
Generally, even in highly purified nitrogen gas, 10-100 ppb of oxygen exists. Oxygen also exists in NO standard gas. Actually, in the l/lo diluted NO standard gas (50 ppb of NO concentration) which was used in this experiment, 12% 02' relative intensity (IoJIT, where IO, is O2 ion intensity) was observed. Since O2 relative ion intensity for sample gas B1 is only about 0.2%, it is concluded that most of the oxygen in the diluted gas is from the NO standard gas. For determination of the influence of O2 concentration on NO+, the intensity was observed relation between NO' intensity and 02+ by measuring mass spectra for the standard oxygen gas (a nitrogen gas including 5.2 ppm of 0,)mixed with the sample gas B1 a t various flow ratios. The relation between NO+ intensity and 02+intensity is expressed as the following experimental formula: INo/ZT =
(1.1 x IO-')(I~,/IT)
+ (1.5 x
(4)
With this relation and 02+relative intensities from the same spectra where eq 3 was obtained, eq 3 is compensated. The result is expressed a8 the following experimental formula:
+
INo/ZT = (1.05 x 10-4)CN0 (1.2 x
(5)
This is the calibration curve which does not depend on oxygen concentration. With this curve, NO concentrations in sample gases B1 and B2 are estimated to be 12 f 5 ppb and 5 f 2 ppb, respectively, by means of the same calculation method used for COz quantitative analysis. In addition, the detection limit of NO is estimated to be 60 pptr from eq 5 and Figure 9. 3. N 2 0 . For the N 2 0 calibration curve, N 2 0 standard gas and nitrogen gas including 100 ppm of Kr were mixed with sample gas B1. The relation between NzO+intensity and NzO concentration is expressed as the following experimental formula: 1
~
+
=~4 30 C ~ ~ o74
(6)
where 1 ~ is~ N02 0 ion intensity A) and C N z 0 is N20 concentration (parts ber billion). Since most N20+is produced through a simple charge transfer reaction from N4+, N20+ intensity is proportional to NzO concentration. In eq 6, INzO is the N20+ion current, not the relative ion intensity. The reason is that ion transmission is poor in the high mass range and Kr," intensity (Krz+being the major component in the
spectra) is not measured appropriately. Consequently, relative ion intensities that are more adequate for obtaining the calibration curve were not obtained. The N 2 0 concentration in sample gas B1 is estimated to be 1.7 f 1.0 ppb by eq 6. 4. 02. The calibration curve of O2 for sample gas B1 is expressed as the following experimental formula:
Ioz/IT = (1.9 x ~ O - ~ ) C + ~(2.5 , x
(7)
where Coz is the O2 concentration (parts per billion). Since oxygen has a lower ionization potential than H20,oxygen ion intensity is not influenced by the coexisting water. Since impurities having ionization potentials lower than O2 are in very low concentrations, the influence from those impurities on oxygen ion intensity can be neglected. Actually, the slope of the curve in eq 7 matches that of other highly purified nitrogen gases. Therefore, the calibration curve expressed by eq 7 can be used universally. With eq 7, the O2concentration in B1 is estimated to be 13 f 2 ppb. In addition, the O2 concentration in B2 is estimated to be 50 f 10 ppb. The detection limit of O2 is estimated to be 10 pptr on the basis of eq 7 and Figure 9. Registry No. N2, 7727-37-9;C02, 124-38-9;NO, 10102-43-9; NZO, 10024-97-2;02, 7782-44-7; C3H8, 74-98-6;H20, 7732-18-5; NH,, 7664-41-7.
LITERATURE CITED (1) Kreuzer, L. B.; Patel, C. K. N. Science 1971, 173,45. (2) Kreuzer, L. B.; Kenyon, N. D.; Patel, C. K. N. Science 1972, 177,347. (3) Hinkley, E. D.; Ku, R. T.; Kelly, P. L. "Laser Monitoring of the Atmosphere"; Springer-Verlag; Berlln, Heidelberg, New York, 1976; Topics In Applied Physics Vol. 14, Chapter 6. (4) Kaldor, A.; Olson, W. B.; Makl, A. G. Science 1972, 176, 508. (5) Siegel, M. W.; Fite, W. L. J . Phys. Chem. 1976, 80, 2871. (6) Kambara, H.; Kanomata, I. Anal. Chem. 1977, 49, 270. (7) Kambara, H.; Ogawa, Y.; Mitsui, Y.; Kanomata, I.Anal. Cbem. 1980, 52, 1500. (8) Horning, E. C.; Hornlng, M. G.;Carroll, D. I.; Dzidic, I.; Stillwell, R. N. Anal. Chem. 1973, 45, 936. (9) Hornlng, E. C.; Carroll, D. I.; Dzidic, I.; Haegele, K. D.; Lin, S. N.; Oertli, C. U.; Stillwell, R. N. Clin. Chem. (Winston-Salem, N.C.) 1977, 23, 13. (IO) Reld, N. M.; French, J. B.; Buckley, J. A,; Lane, D. A,; Lovett, A. M. Sciex Inc. Application Note No. 677-P 1977. (11) Karnbara, H.; Mitsui, Y.; Kanornata, I.Anal. Chem. 1979, 51, 1447. (12) Good, A.; Durden, D. A.; Kebarle, P. J . Chem. Phys. 1970, 52,212. (13) Price, P. C.; Swofford, H. S., Jr.; Buttrili, S. E., Jr. Anal. Chem. 1977, 51, 1447. (14) Wlncel, H. I n t . J . Mass Spectrom. Ion Phys. 1972, 9 ,267.
RECEIVED for review February 17, 1982. Resubmitted April 30, 1982. Accepted November 4, 1982.
Calculation of Ion Yields in Atomic Multiphoton Ionization Spectroscqpy Charles M. Miller and Nicholas S. Nogar" Groups INC-7 and CHM-.Z, Los Alamos National Laboratory, Los Alamos. New Mexico 87545
A rate equations formalism is used to calculate ion yields for laser-Induced multiphoton Ionization. Ion yield Is examlned for both continuous wave (CW) and pulsed excltation under a varlety of analytically realistic conditions, in whlch both optical and atomlc parameters are varied. These calculations show that for the model system, CW excitation may equal or surpass pulsed excitation for the production of ions.
The use of resonance-enhanced multiphoton ionization
(MPI) for the detection of ultratrace quantities is a much publicized and well-studied process (1-7). The advantages and disadvantages, in terms of both sensitivity and selectivity, for single atom detection via MPI have been discussed previously. Necessary conditions for the successful detection of single atoms are now well-known (4-7). For the case of simple two-photon ionization through a resonant intermediate state, these conditions can be stated as follows; d 2 ) F > k(P) (la) and
0003-2700/83/0355-04S1$01.50/00 1983 Amerlcan Chemical Society
482
ANALYTICAL CHEMISTRY, VOL. 55, NO. 3, MARCH 1983
where u(2) is the effective cross section for ionization from the excited state, F and f are, respectively, the photon flux and fluence, k(p) is the rate of irreversible loss from the excited state, and g(0) and g(1) are, respectively, the degeneracies of the ground and excited states. However, most analytical applications of MPI will not require the detection of single atoms (8-10). Instead, the requirement is for efficient, and in some cases highly selective, detection of atoms. Inasmuch as there exists a trade-off between volume probed and duty cycle on one hand, and probability of ionization of the other, the optimum disposition of experimental (particularly laser) parameters is not straightforward. In this paper we examine the efficiency of MPI as a function of atomic and experimental parameters via numerical simulation. “Efficiency” in this context will denote the total number of ions produced in a given volume integrated over the time duration of the experiment. The phenomenology of continuous wave (CW) laser MPI will be discussed in detail. In addition, we wish to consider whether CW ionization offers a viable, or even more attractive, alternative to pulsed MPI, and under what conditions each may be most applicable. We choose both the physical system and the mathematical model to be as simple as possible, in order to make the results physically intuitive. Experimental parameters within the range of good modern equipment and “reasonable” physical parameters are examined in order to simulate typical laboratory analyses as closely as possible. The remainder of this paper is divided into four parts. In the section immediately following, we discuss the physical system to be considered, along with its mathematical representation and the method of solution for ion yields. We next report results for several specific examples of typical laser and atomic properties, using both pulsed and CW excitation. The third section contains a general discussion of the multiphoton ionization process derived from the modeled cases. Lastly, we compare pulsed and CW ionization with respect to applicability to analytical situations.
THEORY The Physical System. The model system chosen for these calculations is the simple two-level atom shown in Figure 1, with symbols defined in Table I. For simplicity, we have assumed the ground and excited states to be of equal degeneracy. For the moment we also neglect hyperfine and isotope splittings, though these will be discussed in a later section. The irreversible loss of atoms from the intermediate level 11) corresponding to the rate k(p) may be due to chemical or physical losses, including reaction, quenching to states other than IO), diffusion, and nonresonant fluorescence. We assume that these processes remove the atoms of interest for the duration of the experiment. For concreteness, the resonant transition in the model atom is assumed to be 3.0 eV (420 nm) and the ionization potential to be 5.5 eV. We assume that when this system is exposed to a radiation field or fields, the level populations can be treated via population rate equations (PRE). The PRE provide a physically intuitive picture of the MPI process, are an excellent approximation for our simulated conditions (11),and are easier to apply than the optical Bloch equations (11-13). Rate equations for the system depicted in Figure 1 can be written dn(0) - - - [k(-l) + k(O)]n(l) - k(l)n(O) (2a) dt
(2b)
with the symbols defined in Table I. In general, since k ( l ) , k(-l), and h(2) are proportional to the laser intensity I(x,y,z,t), the ionization efficiency will depend on both the spatial and = J’, Stntemporal profile of the laser field, with n(c)(total) ( c ) ( % , ~ , ~dv , $ )dt. The complicated nature of this expression generally requires numerical integration (14-16). However, for the special case of temporally and spatially invariant Fadiation fields, the PRE may be solved explicitly (17) to give
with
P+Q
X(2) = 2
P-Q
X(3) = 2
(3b)
and
P = k(1)
+ k(-1) + k(2) + k(0) + k(p)
Q = (P2- 4k(l)[k(2) + k ( ~ ) ] ) ’ / ~
(3c)
With the exception of the irreversible loss term, this solution is equivalent to that for reversible first order reactions followed by irreversible first order product formation (18). Experimental Parameters. For simplicity, we assume that the atomization source produces a spatially uniform distribution of atoms and that this distribution persists for a period of time much longer than T. For concreteness, we assume that the ions produced can be efficiently collected over a cube with 0.5 cm sides centered at the laser focus. We will consider two spatial distributions for the laser field: a Gaussian distribution in which
and a “flat” pulse for which
I(0) I = - for x 2 + y 2 r(cI2
(4b)
where r(c) = ~ ( z ) / 2 ~This / ~ choice . of r(c) ensures that the central intensity, I(O),of the flat pulse matches that of the Gaussian pulse. In either case, we assume that the wave front propagates as a Gaussian, that is (19)
where z is the distance from the focus of the beam. We have examined a number of possible temporal pulse shapes for the laser, including square, (several) triangular, and Poisson. Atomic and laser parameters used in these calculations are shown in Table 11. Calculations. Given that the laser intensity is specified everywhere within the ion collection region, the various laser-induced rates [k(l),h(-l), k ( 2 ) ] may be calculated at every point (x, y , z ) . Thus the P R E may be written, also as a function of coordinates, reflecting temporal and spatial variation of the laser pulse and movement of atoms through the
ANALYTICAL CHEMISTRY, VOL. 55,NO. 3, MARCH 1983
483
Table 11. Nominal Atomic and Laser Parameters
IC>
~ ( 1= )u(-1) = io-'* cm2 ~ ~ ( ~ =(v1I ,)* ( - l ) = 0.05 cm-' ~ ( 2 =) lo-'' cm2 k ( 0 ) = 0 s-' k ( p ) = 0 s-' g(0) =&?(I) =1 uaVe = 5.2 x IO4 cm s-l Pulsed Laser h ( 0 - 1 ) = 420 nm
Atom
t
d
k121
k0j 4 >
CW Laser
Figure 1. A simplified level diagram for the model atomic system. The solid horizontal lines represent discrete atomic states and the dotted line represents the ionization limit of the atom. Transitions are shown with arrows. For further explanation and definition of symbols, see the text and Table I .
Table I. Definition of Symbols ground and excited states, and IO), I n , IC) continuum probability of occupying a particular n(O),n ( l ) , n(c) level rates o f absorption, stimulated k ( l),k ( - l ) , k ( 2) emission, and ionization, defined by k ( i ) = ~ ' u ( i ) ( v ) l ( i ) (dv, v ) where ~ ( iis)the cross section for the process and I ( i ) is the photon intensity rate of spontaneous emission from k(O) 11)to '0)
k(P) v112
T
V w(0) w(z)
z(c) Uave
rate of irreversible loss from 11) optical frequency half width time period of exposure to the photon flux volume over which ions are collected tieam radius ( l i e 7 intensity) at focus beam radius at distance z from focus confocal distance, z(c) = ~ w ( O ) ~ / h average atomic velocity -
beam. As might be inferred, the magnitude of the problem can quickly grow enormous. In the present system, several simplifications have been made to reduce the size of the problem to a manageable level. For pulsed laser excitation, variation in laser intensity caused by motion of the atoms is neglected, an approximation easily justified by considering that the puke duration of 10 ns allows little motion. We treat the CW case as pseudopulsed, using only the "flat" laser profile (eq 4b) and defining the effective irradiation time as the average thermal transit time for the atom across a beam of diameter 2r(c). Admittedly, this only approximates the true (distribution of transit times and irradiation histories, as it neglects atoms traveling obliquely through the beam and those traversing a chord. However, computational difficulty is significantly reduced through the elimination of time-varying irradiation intensity during transit. With these provisions, it is thus possible to integrate the PRE a t any point. For time varying pulses, this is done by using a modification (20) of Gillespie's method (21-23) for solving coupled kinetic equations. For time invariant (square) pulses and CW irradiation, the time integration can be carried
h(1--c) = 420 nm v 1 , 2 = 0.25 cm-' T=10ns E = 1 0 mJ per pulse repetition rate = 10 Hz h(O-1) = 420 nm h( 1-c) = 420 or 488 nm = 0.25 cm-' power = 200 mW (420 nm) or 5 W (488 nm)
out analytically to yield eq 3a for any point in the integration volume. Numerical integration over the ionization volume is still required in order to determine the total ion yield. To do this we utilize a Monte Carlo technique (24) which relies upon random choices of points (2, y, z ) within the integration volume. At each point, n(c) is evaluated, with the appropriate intensity and rates for that location. After rn points, the total ion yield is calculated
where x-, y, and z, are the dimensions of the integration volume. The number of trials, rn, is chosen such that r ~ ( c ) ( ~ ~ ) converges to a final value with reasonable statistics. The units of n ( ~ ) ( , ~thus ) calculated have the dimensions of cm3, representing an equivalent volume over which 100% ionization occurs. This may be converted into ions per second for the pulsed case by simply multiplying by the laser repetition rate (the number of exposures) and the atom density in the ionization region. In the CW case the same concept applies, where the repetition rate is replaced by the inverse of the transit time of atoms across the probe volume a t the average thermal velocity. For the data presented here, the density term is neglected as a scaling factor for both cases, leaving the dimensions of our calculated results as cm3 s-l.
RESULTS Pulsed Laser. Initial calculations were carried out to simulate pulsed laser ionization. Results in Figure 2 show ion yield as a function of focal spot size for a number of laser pulse energies, for both Gaussian and spatially invariant beams. We have assumed in this set of calculations that no irreversible losses occur. The curve shape for the spatially invariant case essentially mirrors the beam volume contained within the ionization integration region. This reflects the fact that the ionization is at or near saturation over the entire beam volume for all pulse energies shown in this figure and further indicates the ease with which the MPI process can be saturated under favorable conditions. The divergence of the yield curves at extreme defocusing suggests that at the lower intensities implied by defocusing, the ionization process is no longer being saturated. If the time history of the level populations is followed as a function of time, as can be done in these calculations, one finds the ground- and excited-state populations equilibrate on a very short time scale, t 2 X tegration volume in a nearly parallel fashion. Thus, the beam volume goes through a minimum in proceeding from a tight to a loose focus. Since pulsed excitation saturates, or nearly saturates, the ionization yield for the spot sizes discussed so far, the ion yield will follow a similar trend: moderate overall ionization efficiency at tight focus, low efficiency at moderate focus, and a linear increase a t mild focus. The latter will continue until the beam gets so large, and hence the intensity so low, that the ionization is no longer saturated within the beam volume. For the atomic parameters we have considered, this will occur at a spot size of approximately 0.5 cm for 10-mJ pulses. In the case of CW excitation, the curve shapes are entirely different, due largely to the fact that the ionization is not near saturation anywhere within the beam volume. A variety of competing effects dictate the shapes of these curves. At any point along the laser axis, as the beam diameter increases, the photon intensity decreases, while the transit time and the number of atoms exposed increases. For a nonsaturated process, this yields a net decrease in the total number of ions produced. As can be seen from Figure 6, the average beam diameter goes through a minimum in proceeding from small to larger focal spot sizes, and thus the ion yield displays an intermediate maximum. This is observed in Figure 4. Laser Power (Pulse Energy). The dependence of the ionization efficiency on pulse energy can be rationalized easily in terms of the rate equation formalism, which views the resonance-enhanced two photon ionization process as a fast equilibrium followed by irreversable removal (via ionization). In the absence of an irreversible loss term, k(p), the criteria for saturation of the ionization process is just (4-7) 1 - exp[-a(2)fl
> 0.95
or a(2)f
>3
(7b)
If we assume, as in the above calculations, that u = lo-” cm2, then f > 3 X lo1’ cm-2 for saturation. Over the region of focal
spot sizes for which all pulse energies saturate the ionization, the ionization efficiency curves will be superimposable. As w gets larger, however, low energy laser pulses will cease to effect saturation. For spatially invariant pulse energies of 0.1 mJ, and X = 420 nm, this corresponds to a laser spot size w =2 X cm. As can be seen from Figure 2, this is just the region of focal spot size where the various pulse energy curves begin to diverge. This is a manifestation of the fact that the low energy pulses are no longer saturating the ionization, while the high energy pulses will continue to do so for much larger spot sizes. The divergence seen at very small focal spot sizes is due to a similar phenomenon occurring near the edges of
the integration region for these strongly diverging beams. Similar, though less distinctive behavior is seen for the Gaussian pulses, at approximately the same spot size. In addition, the Gaussian curves are somewhat displaced from one another over the entire range of w due to nonsaturation in the wings of the intensity profile. The curves of Figure 4, representing CW excitation, show a nonlinear dependence on the dye laser (420 nm) power, as noted previously. This is due to the fact that neither the bound-bound transition nor the bound-free transition are saturated. Thus, as the 420-nm power is increased, both the rate at which level 11)is populated and the fraction of excited species ionized increase, leading to the nonlinear behavior. At sufficiently high powers, the bound-bound transition will saturate on a time scale short compared to ionization, and the overall ionization efficiency will appear linear with respect to laser power for the single wavelength case. We note in passing that placing the ionization region inside the cavity of the dye laser may saturate the (0) to 11) transition and should increase the ionization efficiency greatly, as the intracavity circulating power is typically 1G-100 times the output power of a CW dye laser. Addition of a second laser at 488 nm does in fact lead to a linear increase in ionization with laser power, since the 488-nm photons do not effect the resonant transition. The only effect, then, of the addition of photons at 488 nm is to increase the yield of the ionization step. Atomic Properties: Cross Sections and Irreversible Loss. In the absence of irreversible loss, variation of the cross section for pulsed laser excitation will have no effect on the ionization efficiency, as long as the criterion (r(2)f > 3 is met. This is demonstrated by the similarity of the solid curves in Figure 3a for most of the range of w . Again, for very small and very large w , the curves diverge because of the areas of low intensity. When irreversible loss is introduced, the ionization efficiency depends on the rate of ionization (photon flux) rather than just on the total probability of ionization (photon fluence). Assuming that the resonant transition is saturated, the fraction of atoms ionized will just be h(2)/[k(2) k(p)]. Thus, irreversible loss will not have a substantial effect on the ionization efficiency until h(p) O.lh(2). A brief calculation shows that for pulse energies of 5 mJ, and using the cross sections of Table 11, one expects that a h(p) of lo9 s-l should begin to effect the ionization efficiency at w 3 X cm, in agreement with Figure 3a. Qualitatively similar behavior is reflected in the curves for Gaussian pulsed beams (Figure 3b). Again, the effects of changing atomic parameters are more pronounced and are manifest for smaller changes due to the areas of low intensity in the Gaussian pulses. In the case of CW ionization, the qualitative effect of h(p) is essentially independent of power: in all cases, the yield curves as a function of k(p) begin to drop off sharply at h(p) lo7 s-l. The similarity of these curves suggests that it is not the rate of ionization with which k(p) is competing but rather another loss mechanism. The yield in this case is in fact fluence limited, with the fluence restricted by the passage of the atom through the beam. Only when h(p) reduces the effective exposure time of 11) to the ionizing field, by reducing the 11) lifetime below the transit time, will an increase in k(p) be manifest as a decrease in the ion yield. For a beam waist of low3cm and an atomic velocity of lo4 cm/s, the transit time is s. The irreversible loss term is thus expected to reduce the ion yield for values of h(p) > lo7 s?, in agreement with the results of Figure 5 . Pulsed vs. CW Ionization. While studies of CW MPI have not been numerous, the process has been demonstrated for both atoms (25) and small molecules (26). The question
+
-
-
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 3, MARCH 1983
remains whether CW lblPI may be useful for chemical analysis, and under what conditions. We consider first "bulb" type applications, where "bulb" IS used here to denote non-highvacuum conditions. Under these circumstances, where one may wish to detect atoms of a particular type in an inert atmosphere, pulsed MPI is almost certainly the choice. We have shown that collisions of reasonable frequency and cross section have almost no effect on the pulsed MPI process, whereas they may severely degrade the performance of CW MPI. In addition, under bulb conditions, parallel plate detection of ions is used most frequently (27,28), so that ions can be collected over a large volume. Thus the laser spot size can be large, and pulsed lasers can be used to maximum effect. Lastly, it is most often under bulb conditions that temporal resolution is important (29), and pulsed excitation clearly excels in this respect. The situation is lesg straightforward when MPI is carried out under high vacuurnl conditions, as one may wish to do for mass spectral analysis (8, 10, 30). In making a comparison between pulsed and CVV MPI under high vacuum conditions, we restrict ourselves to magnetic or quadrupole instruments that can monitor selected masses continuously. Again, if pulsed analysis, such as with a time of flight mass spectrometer (30), is used, pulsed MPI is obviously the technique of choice. We also consider only constant, spatially uniform atom sources, as described earlier, and neglect a number of very clever methods for pulsed ionization (9, 30). Under these constraints, a number of interesting comparisons can be made. First, since the collection efficiency and resolution of magnetic instruments are inversely related t o the volume over which ionization occurs, CW MPI has obvious advantages for ion production. The ionization efficiency of CW MPI peaks cm, while much larger spot at rather tight focus, w v 2 X sizes are required to efficiently generate ions via pulsed MPI. In the use of pulsed lasers, then, some sacrifice must be made in either ion production or ion collection efficiency. We note in passing that MPI in general may yield unusually good m,ms spectral resolution since the product ions are highly monoenergetic, in contrast to other methods of ion generation (31). Secondly, considerations of ion detection also suggest the use of CW excitation. Pulse counting, with its potential advantages in sensitivity and dynamic range, is well suited to detecting small continuous ion currents. Pulsed MPI is difficult to use with pulse counting electronics because of problems associated with ion bunching and pulse pair resolution. On the other hand, spectral coverage is certainly greater with pulsed lasers than with CW lasers. While recent strides have been made in generating CW tunable ultraviolet (32-34), coverage is still spotty outside the spectral region 400-800 nm. This may limit the number of systems that can be analyzed via simple (single color) resonance MPI schemes. Whnle multicolor excitation schemes can be used to ionize most elements, even given the spectral limitations noted above, the increase in complexity attendant with multiple lasers renders such processes problematic for analytical applications. Lastly, we have so far considered only the case of a single Doppler broadened resonance absorption feature and have not considered the effects of population depletion. In a real system, of course, one must be concerned with isotopic and hyperfine splitting, particularly if the ions produced are to be used for isotope ratio measurements (8). One must also be concerned with the problem of optical hole burning in the Doppler profile of any given absorption feature. In general, these problems are less severe for pulsed lasers, since the frequency width of pulsed sources is typically as large as 1-3 cm-l, without well-formed longitudinal modes. This breadth,
e
487
coupled with power broadening of the resonant transition ( I ) , allows pulsed lasers to address all hyperfine, isotopic, and Doppler components in a routine fashion. CW lasers, on the other hand, will typically oscillate on only a few (1-5) very narrow (-MHz) longitudinal modes at any time. In order to correctly measure isotope ratios, one of two tactics must be followed. In one case the laser output may be artificially frequency broadened, as by frequency modulation (35,36). In this case, the laser can address all spectral components, albeit at a loss in ionization efficiency resulting from the decrease in intensity a t any given frequency. Alternately, a laser running single mode may be alternately tuned from a hyperfine component of one isotope to that of another and account taken of the relative strengths of the various hyperfine transitions (37). This results in a slight decrease in effective duty cycle but should not degrade practical performance significantly since the mass spectrometer must also be tuned from one mass to another. Similar considerations apply to the problem of optical hole burning, though this is apt to be a factor only at very high laser intensities.
CONCLUSIONS We have examined the use of resonance-enhanced multiphoton ionization for detecting atoms for analysis purposes. Dependence of the MPI signal on a variety of experimental parameters has been examined for both CW and pulsed sources. For the model system, CW excitation may equal or surpass pulsed excitation for the production of ions in some circumstances. In order to judge the applicability of CW MPI in real systems, however, one must consider other factors. In general, the choice between CW and pulsed ionization must be made on a case by case basis. Further experimental investigations into CW MPI are clearly needed for comparison with the results presented here. LITERATURE CITED (1) Letokhov, V. S. I n "Chemical and Biochemical Applications of Lasers"; Academic Press: New York, 1980; pp 1-38. (2) Bekov, G. I.; Vidaiova-Angelova, A. B.; Letokhov, V. S.;Mishin, V. I . "Proceedings of FICOLS", Springer: Heidelberg, 1979: pp 283-294. (3) Alkemade, C. Th. J . Appl. Spectrosc. 1981, 35, 1-14. (4) Hurst, G. S.;Payne, M. G.; Kramer. S. D.; Young, J. P. Rev. Mod. Phys. 1979, 51,767-819. (5) Hurst, G. S.;Payne, M. G.; Kramer, S. D.; Chen, C. H. Pbys. Today 1980, 33, 24-29. (6) Young, J. P.; Hurst, G. S.;Kramer, S. D.; Payne, M. G. Anal. Cbem. 1979, 51, 1050A-1060A. (7) Hurst, G. S. Anal. Chem. 1981, 53, 1448A-1456A. (8) Miller, C. M.; Nogar. N. S.; Gancarz, A. J.; Shields, W. R. Anal. Cbem. 1982, 54,2377-2378. (9) Mayo, S.;Lucatorto, T. B.; Luther, G. G. Anal. Cbem. 1982, 54, 553-556. (10) Donahue, D. L.; Young, J. P.; Smith, D. H. I n t . J . Mass Spectrom. Ion Pbys. 1982, 43,293-307. (11) Ackerhalt, J. R.; Shore, B. W. Pbys. Rev. A , 1977, 16, 277-282. (12) Agostini, P.; George, A. T.; Wheatley. S. E.; Lambropolous, P.; Levenson, M. D. J . Phys. B 1978, 1 1 , 7733-1747. (13) Swain, S. J . Pbys. B 1980, 13,2375-2396. (14) Cervenan, M. R.; Isenor, N. R. Opt.Commun. 1975, 14, 175-178. (15) Francisco, J. S.;Steinfeld, J. I.; Gilbert, R. G. Cbem. Pbys. Left. 1981, 82, 311-314. (16) Kolodner, P.; Kwok, H. S.; Black, J. G.; Yablonovltch, E. Opf. Left. 1979, 4 , 38-39. (17) Zakheim, D. S.;Johnson, P. M. Cbem. Pbys. 7880, 4 6 , 263-272. (18) Frost, A. A.; Pearson, R. G. "Kinetics and Mechanisms"; Wiley: New York, 1987. (19) Harris, J. M.; Dovichi, N. J. Anal. Cbem. 1980, 52,895A-700A. (20) Barker, J. R. J . Cbem. Pbys. 1980, 72, 3686-3694. (21) Gillespie, D. T. J . Pbys. Cbem. 1977, 81,2340-2361. (22) Gillespie, D. T. J . Stat. Pbys. 1977, 76. 311-318. (23) Gillespie, D. T. J . Cbem. Pbys. 1981, 7 4 , 5295-5299. (24) Hammersley, J. M.; Handscomb, D. C. "Monte Carlo Methods"; Chapman and Hall: London, 1979. (25) Brinkmann. U.; Hartig, W.; Woste, H. Appl. Pbys. 1974, 5 , 109-115. (26) Leutwyler. S . ; Herrmann. A.: Woste. L.: Schumacher, H. Cbem. Pbvs, 1980,.48, 253-267. (27) Whitaker, T. J.; Bushaw, B. A. Cbem. Pbys. Left. 1981, 79,506-508. (28) Hurst, G. S.;Nayfeh, M H.; Young, J. P. Pbys Rev. A 1977, 15, 2283-2292. (29) Kramer, S. D.: Bemis, C. E.: Youna. J. P.: Hurst. G. S. Oot. Lett. 1978, 3 , 16-18. (30) Beekman. D. J. W.; Callcott, T. A.; Kramer, S D.; Arakawa, E. T.; Hurst, G. S. Int. J . Mass Specfrosc. Ion Pbys. 1980, 89-97.
Anal. Chem. 1903, 5 5 , 488-492 Bahr, U.; Schulten, H. R. "Topics in Current Chemistry"; Sprlnger: New York, 1981; Vol. 95. Coulllaud, B.; Bloomfield, L. A,; Lawler, J. E.; Siegel, A,; Hansch, T. W. Opt. COmm~fl.1980, 35, 359-362. Coulllaud, B.; Dabkiewicz, Ph.; Bloomfieid, L. A,; Hansch, T. W. Opt. Lett. 1982, 7 , 265-267. Webster, C. R.; Woste, L.; Zare, R. N. Opt. Commufl. 1980, 35, 435-440. Bjorkland, G. C. Opt. Left. 1980, 5 , 15-17. Gallagher, T. F. Kachru, R.; Gounand, F.; Bjorklend, G. C.; Lenth, W.
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RECEIVEDfor review September 10,1982. Accepted November 9, 1982. Support of the Department of Energy, under the auspices of Los Alamos National Laboratory, is gratefully acknowledged.
Sectored Wheel Wavelength Modulation for Flame Atomic Fluorescence Spectrometry John 1. McCaffrey and R. G. Mlchel" Department of Chemistry, University of Connecticut, Storrs, Connectlcut 06268
Further studles of the sectored wheel (rotating quartz mechanical chopper) are descrlbed. The sectored wheel allows for hlgh-frequency, squarswave-form, wavelength modulatlon for background correction of contlnuum source exclted flame atomlc fluorescence spectrometry (AFC) and provides efficient square-wave wavelength moduiaflon over the large wavelength intervals necessary for AFC. Results of studles to determine the magnltude of transmisslon losses, reflection losses, and defocusing at large moduiatlon intervals (1.0 nm or more) are described. Efflcient square-wave modulatlon at 160 Hz has been demonstrated, and the system has potentlal for higher modulation frequencies. The sectored wheel Is potentlally useful for both atomlc emlssion and atomic absorption spectrometrles as well as for AFC.
The sectored wheel has been described previously ( I ) and proposed as an alternative to oscillating refractor plate wavelength modulation for atomic spectrometry. The most significant advantage of the sectored wheel is its ability to provide square-wave-form wavelength modulation at high modulation frequencies. Square wave forms have been shown both theoretically (2) and experimentally (3, 4 ) to lead to improved signal-to-noise ratios (SNRs) in atomic spectrometry. A second advantage of the sectored wheel is its ability to modulate over larger wavelength intervals than the oscillating refractor plate while still maintaining the square wave form at all modulation frequencies. This advantage is particularly significant for background correction of continuum source excited atomic fluorescence spectrometry (AFC) where short focal length monochromators with wide slit widths are used to maximize the collection of fluorescence from the atom cell. Such instrumentation necessitates large modulation intervals in order to measure the spectral background a t each side of the analyte atomic fluorescence wavelength of interest. For atomic emission and atomic absorption, where required modulation intervals are usually much smaller, the advantages of the sectored wheel are primarily in the square modulation wave form and higher modulation frequencies. The use of the sectored wheel has already been demonstrated for atomic emission with an echelle monochromator (5), and Harnly (4) has suggested that the construction of a sectored wheel with more than four sectors will allow extension of the linear dynamic range of calibration curves of continuum source excited atomic absorption spectrometry (AAC). Such extension has
already been shown to be possible when using oscillating refractor plates (6). High-frequency modulation allows discrimination against low-frequency flicker noise inherent in the instrument. The effect of modulation frequency on the rise and fall times of the square wave form was studied together with some preliminary studies of the relationship between SNR and modulation frequency. Placing the sectored wheel in the monochromator defocuses the image a t the exit slit and leads to light losses at the wheel by reflection and absorption at the quartz sectors. In addition, these losses differ for the different thicknesses of the sectors. This causes some incidental source intensity modulation. These effects were studied to determine their effect on the SNR and accuracy of AFC measurements. Such effects are usually regarded as insignificant when oscillating refractor plates are used, because of the use of small modulation intervals. Here, large intervals were being used thus necessitating detailed study.
EXPERIMENTAL SECTION The components used in the instrument system were similar to those used in an instrument described previously (1, 7). The performances of the two instruments were identical in all respects. The sectored wheel, an improved version of that described previously (I), was constructed from four quadrants of optical quartz plate, arranged as in ref 1. The two diametrically opposite quadrants were each 'I8 in. thick, the third and fourth quadrants were '/I6 in. and 3/16 in. thick, respectively. They were held in place with a circular metal collar grooved to hold each piece securely. A chain drive was used t o connect the sectored wheel to a dc motor (TRW Globe, Dayton, OH, Model 403A117-3). A set of photographs of the whole assembly is shown in Figure 1. The assembly was placed just after the middle slit of the double monochromator that was used (Jobin Yvon DHZOA; linear dispersion, 2 nm/mm). The position of the wheel was arranged such that the image of the middle slit passed through the bottom half of the wheel and was aligned along the vertical diameter. In order to provide a frequency reference signal, a small two-blade mechanical chopper, mounted directly on the motor shaft, chopped the beam from a miniature infrared light-emitting diode. A phototransistor directly across from the light emitting diode was used to detect the chopped IR radiation and provide the reference signal for the photon counter. A handle was used to pivot the whole sectored wheel assembly. Mechanical stops limited the travel of the assembly to 60". The housing was marked with the angle of incidence from 0 to 60' at 0.5" intervals. The arrangement of the sectors of the wheel (1) provided primarily for 2F detection although pseudo-1F detection ( I ) was
0003-2700/83/0355-0488$01.50/0 0 1983 American Chemical Society
