J. Phys. Chem. 1987, 91, 2086-2090
2086
+
+
striking (Figure 5). For the Mg(’S) C12, Mg(3P) N20,and Ca(’S) F2 (proceeding through the doubly ionic surface) reactions, this is a consequence of the early decoupling of RM-xfrom the reaction coordinate; the vibrational population reflects the range of impact parameters that lead to reaction. In the other systems (Ca + C12, F2 (proceeding on the singly ionic surface), this reflects the fact that the same Coulomb interaction is acting in the entrance channel and in the M X molecule along the RM-x coordinate.
+
2
1
I
3
re(%)
I
4
Figure 5. Plot of the turning point of the highest populated MX vibrational level against the crossing radius (r,) of the covalent and ionic surfaces (circles) for the M + XY reactions of Table IV. The squares correspond to the Ca + F2reaction; the filled square corresponds to the chemiluminescent CaF(BZZ+)state, where r, = rc+is calculated for the excited C a - m i- FT surface; the open square corresponds to the u = 0 peak of the bimodal vibrational population distribution found in CaF ground state, for which r, = r:+ (see text).
ionic) may be interacting in the electron jump region; this possibility can be roughly examined by considering the first and second electron jump distances: for Mg the estimated crossing distances are 2.7 and 2.3 A for the covalent-singly ionic and singly-doubly ionic crossings, respectively (Table IV); these distances are so close that separate consideration of the first and second electron jumps is meaningless; the vibrational distributions arising from the two paths are expected to be indistinguishable, and it is not surprising that the distribution found for MgCl in this work is not bimodal. For the Ca + C12 system which is intermediate between Mg C12 and Ca + F2, no bimodal distribution was reported.23 Empirical Correlation between r, and the Highest Populated Vibrational Level. In Table IV are given the highest vibrational level populated in the reaction, together with r,, the turning point of this vibrational level, calculated using a Morse potential. r, may be compared to rc+ (Mg C12, N 2 0 , Ca C12, F2 (B state and v == 40 peak of the X state vibrational population distribution)), or r:+ (Ca F2, v = 0 peak of the X state vibrational population distribution). The correlation between r, and r, is
+
+
+
+
V. Summary and Conclusion The formation of the MgCl(X2Z+) ground state from the Mg(’S) + C12 reaction was probed by L I F detection of MgCl. The results allow for a reliable estimation of the fraction of the available energy going into MgCl internal energy. In marked contpast to the similar Ca + C12, F2reactions, the MgCl vibrational excitation is quite low (14% of the exothermicity of the reaction), whereas the rotational excitation is as high as 36% of the exothermicity. This great difference in the dynamical behavior of the Mg + Clz system with respect to the similar Ca + CI,, F2 systems may be rationalized in the framework of the harpooning mechanism. The reaction dynamics is closely related to the electron jump internuclear distance. In the Mg + C12system, this distance is of the order of magnitude of the MgCl equilibrium bond length, and the system gGG3irectly in the exit valley as C12dissociates; in this process, the MgCl bond is little affected. The relatively high population of high J levels of MgCl is due to the fact that short impact parameter collisions most probably do not lead to reaction because of potential energy barriers in the entrance valley, for all approaches. Details of the similar Ca C12, F2 reactions are also discussed in light of the harpooning mechanism. An empirical relation between the electron jump distance and the turning point of the highest popul&ed Vibrational level is indicated.
+
Acknowledgment. R. F. Barrow is acknowledged for having made available the rotational analysis of the MgC1(A211-X2Z+) (0-0)and (0-1) bands. J. McCombie is acknowledged for the calculation of the MgCl(A211-X2Z+) spectra. The authors are greatly indebted to M. Bonneau for his work-on the experimental setup. The assistance of J. LeEvre for the figures is acknowledged. This work was supported by the GRECO “Dynamique des rgactions moleculaires” of the CNRS. The authors thank the referee for his valuable comments. R e S t V NO. Mg, 7439-95-4; CI,, 7782-50-5; MgCI, 14989-29-8.
Energy Transfer and Pooling between Mg(3P) and Bi Atoms M. A. Chowdhury and D. J. Benard* Rockwell International Science Center, Thousand Oaks, California 91 360 (- x e i v e d : November 3, 1986)
A pulsed dye laser was used to excite Mg(’P) metastables in the presence of Bi atoms. The resulting Mg and Bi emissions were analyzed and found to be consistent with a resonant ladder-climbing mechanism in Bi pumped by Mg(3P). The data suggest that, with sufficient Mg(3P) concentration, inversion of the 472.2-nm transition in Bi may occur.
Introduction For about a decade energy-pooling reactions of metastable Mg(3P) atoms have received attention in the literature.1-4 The
possibility of utilizing these reactions for producing higher excited states O f Mg and other species is attractive from the viewpoint Of developing new short wavelength lasers, particularly Since Mg(3P) has been generated in chemical reaction^.^-^ Recent
(1) Taieb, G.; Broida, H. P. J . Chem. Phys. 1976, 65, 2914. (2) Breckenridge, W. H.; Nikolai, W. L.; Stewart, J. J . Chem. Phys. 1981, 74, 2073. (3) Pritt, A. T., Jr.; Patel, D.; Benard, D. J. Chem. Phys. Lezt. 1984, 105, 661.
0022-3654/87/2091-2086$01.50/0
(4) Husain, D.; Roberts, G. J. Chem. SOC.,Faraday Tram. 2 1986, 82,
21. ( 5 ) Benard, D. J.; Slafer, W. D.; Lee, P. H. Chem. Phys. Lett. 1976, 43,
69.
0 1987 American Chemical Society
Energy Transfer between Mg(3P) and Bi Atoms
I
SIGNAL AVERAGER
H
TRANSIENT DIGITIZER PREAMPLIFIER
4
BOXCAR INTEGRATOR
The Journal of Physical Chemistry, Vol. 91, No. 8, I987
2087
I 48.000
POWER He
LzEJ
P
c VACbUM
QYH-1 -I
LASER
EXCIMER LASER
Figure 1. Schematic of the experimental apparatus.
studies, however, have shown that even though energy pooling of Mg('P) occurs rapidly, yields of the more highly excited states of Mg are too low to create significant population i n v e r ~ i o n . ~ , ~ Therefore, attention has been focused instead on energy transfer from Mg(3P) to other suitable emitting species. Pritt et a1.7 have investigated energy transfer from Mg(3P) to Ca atoms and found that energy transfer and subsequent pooling reactions produced highly excited Ca atoms. The rate of energy transfer from Mg(3P) to the Ca atoms, however, required high pressures of the buffer gas to achieve gas kinetic values. Therefore, the Mg/Ca system was judged to be unsuitable for development as a chemical laser that could operate at low pressure. More recent work by Chang and D j e d has investigated energy transfer from Mg(3P) to Sm cm3 s-I have atoms and energy transfer rates greater than been demonstrated. In this paper we report the results of a similar investigation of energy transfer from Ms(~P)to Bi atoms. Analysis of our data, consisting of spectrally and temporally resolved emission intensities from the various excited states of Mg and Bi, also demonstrates rapid energy transfer and pooling, as well as the possibility of lasing on the 472.2-nm transition of the Bi atom.
Experimental Section A schematic diagram of the experimental apparatus is shown in Figure 1. A mixture of Mg and Bi vapors is supported in a cross-shaped heat pipe similar in design to one used by Malins and Benard.9v'o The temperature and total pressure of the heat pipe were monitored by a thermocouple gauge and a combination of bourdon tube and Validyne inductance pressure transducers. The heat pipe was operated in the range of 900 to 950 OC with a charge of one part Mg and two parts Bi by weight and with 50 to 500 Torr of ultrahigh-purity He buffer gas. The composition of the metals was chosen so that compound formation did not occur at the operating temperature of the heat pipe." Therefore, both metals were present in the vapor phase above the liquid alloy. The metals, Puratronic Grade 1 Mg chips and 99.99% pure Bi powder, obtained from Johnson Mathey and Alfa Chemicals, respectively, were used without further purification as was the buffer gas which was obtained from Matheson. The ground-state Mg atoms (in the vapor phase) were optically pumped to the metastable 3P state by the 10-mJ output of a 457.1-nm excimer driven dye laser with a 2 4 s pulse, 0.1-8, line width, and 2-mm beam diameter at the center of the heat pipe. The resulting fluorescence was collected at right angles to the laser beam and was focused by a lens onto the entrance slit of a 0.3-m Michels, H.H.; Meinzer, R. A. Chem. Phys. Lett. 1983, 98, 6. Pritt, A. T.; Patel, D.; Benard, D. J. J . Phys. Chem. 1986, 90, 72. Chang, R. S.F.; Djeu, N., private communication. Vidal, C. R.; Cooper, J. J. Appf. Phys. 1969, 40, 3370. (10) Malins, R. J.; Benard, D. J. Chem. Phys. Lett. 1980, 74, 321. (11) Schmorak, J. Handbook of Binary Metallic Systems; U S . Department of Commerce: Springfield, VA, 1967; Vol. 11. (6) (7) (8) (9)
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4 S 3 / 2 (11
Figure 2. Energy level diagram for Mg and Bi atoms. The metastable states have been indicated by an asterisk.
grating monochromator. A 1P28 photomultiplier tube (PMT) was used as a detector at the exit slit. The resulting anode currents were fed to a wide-bandwidth preamplifier which drove either a boxcar integrator (PAR Model CW-1) or a transient digitizer (Biomation Model 8100). Synchronizing pulses for triggering the signal processors were obtained directly from the excimer laser. The output of the transient digitizer was stored in a signal averager (Nicolet 12/70) and summed over repetitive shots of the dye laser. The resolution of the detection system was 10 ns. The boxcar integrator was initially employed with a chart recorder to generate emission spectra while scanning the monochromator. The monochromator was then set to each line in the emission spectrum and time profiles were gathered via the signal averager. The relative concentrations in the different excited states were then inferred from the ratios of the peak intensities of the correponding emission lines, the known A coefficient^,'^^'^ the relative wavelength dependence of the monochromator and the detector, and factors which accounted for the change in sensitivity due to variations of the slit width and PMT voltage. The instrument response was measured with a Hg lamp for which the relative intensities of the various lines are known.I4 The concentration of the ground-state Bi atoms in the heat pipe was also monitored by measurements of absorbance at 306.7 nm by using a Bi hollow cathode lamp manufactured by Westinghouse. For the absorbance measurements, the output of the P M T was directed to an electrometer (Keithley Model 610) instead of the preamplifier as shown in Figure 1. The absorption diagnostic was calibrated by developing a curve of growth from knowledge of the Bi vapor pressure15and measurements of absorbance in a heat pipe that contained only Bi metal and He buffer gas. Since the absorbance of the Bi radiation was too large to measure at the operating temperature of our experiment, the Bi concentration was inferred from an extrapolation of the measured Bi concen(12) Weast, R. C. Handbook of Chemistry and Physics; CRC Press: Boca Raton FL, 1985. (13) Furcinitti, P. S.; Wright, J. J.; Balling, L. C. Phys. Reo. 1975, AJ2, 1 1 - 7
I ILJ.
(14) Childs, C. B. Appl. Opt. 1962, 1, 711. (15) Hultgren, R.; Orr, R. C.; Kelley, K. K. Selected Values of Thermodynamic Properties of Metals and Alloys; University of California: Lawrence Berkeley Laboratory, 1970; Vol 1.
Chowdhury and Benard
2088 The Journal of Physical Chemistry, Vol. 91, No. 8, 1987 TABLE I: Yields and Time Profiles of Excited Mg States state
energy, cm-’
wavelength, nm
Mg(6d1D2) Mg(5d1D2) Mg(4d3D2) Mg(5s’SJ Mg(3d3Dd Mi3(4s3S1) Mg(3p’Pi)
58 023 56 308 54 192 51 872 47 957 41 197 35051 21 870
435.0 470.2 309.5 333.6 383.5 517.8 285.2 457.1
Mg(3p”PJ)
decay rate,
yield/ Mg(”P),
105 s-1 4.4 5.1 22 8.7 4.2 7.3 25 14
0.62 1.9 0.03 0.09 3.3 2.8
0.003 105
time of peak, ns 100 210 200 260 230 380 100 0
TABLE I 1 Yields and Time Profiles of Excited Bi States
cm-I
transition
wavelength, nm
yield/Bi (total), 10”
decay rate,
state
energy,
10s s-’
time of peak, ns
Bi( 13)
49461
Bi( 12)
Bi(l0)
48 490 45916
Bi(9)
44 865
Bi(7)
43 913
Bi(5)
32 588
13-6 13-4 12-3 10-4 1042 9-3 9-2 7-3 7-2 5-2 5 4 1
613.8 359.6 302.5 412.1 289.8 339.7 298.6 351.1 307.7 412.2 306.7
1290 390 65 52 31 320 45 320 184 1580 17
8.4 6.0 6.2 6.3 3.0 4.6 4.4 4.2 4.7 8.5 5.0
130 170 190 160 200 170 180 120 170 140 240
tration vs. temperature, in a heat pipe containing both Mg and Bi. As might be expected, since Mg-Bi compunds form at lower temperature,” the measured Bi concentration in the presence of Mg was typically much smaller than the vapor pressure of pure Bi.I5 Results Optical pumping of Mg(3P) in the presence of Bi produced both visible and UV emission. By segregating the M g and Bi in the heat pipe it was possible to obtain more intense emissions at lower temperatures; however, the operation of the heat pipe was unstable o : , and there was considerable; molecular emission. When the metals, were mixed and the heat pipe operated at higher temperatures, stability was achieved and the molecular emissions disappeared. Under these conditions, the fluorescence spectrum consisted of atomic lines that originated from several excited states of Mg and Bi with up to 50 000-cm-I excitation. Figure 2 is an energy level diagram which shows some of the key transitions that were observed. The time profile of each emission line typically rose to its peak intensity in less than 1 p s and decayed in less than 10 PS.
Absolute concentrations were obtained from the relative emission data by referencing the detector to a known concentration of Mg(3P) in a heat pipe containing only Mg and He. Figure 3 shows the initial yield of Mg(3P), as measured by extrapolating the 457.1-nm emission back to t = 0, vs. the energy of the dye laser pulse. In the saturation regime (36 mJ) the initial Mg(3P) yield can be equated to 90% of the Mg vapor p r e s s ~ r e since ’ ~ the J = 0, 1, and 2 states of the 3P manifold equilibrate during the laser pulse. This result was previously demonstrated by the absence of an observable dependence on the buffer gas p r e ~ s u r e . ~ Also, within the saturation region, the yield of Mg(3P) was observed to track the M g vapor pressure curvelS as the temperature of the heat pipe was varied. The initial yield of Mg(’P) was substantially diminished by the addition of Bi to the heat pipe which is attributed to a corresponding reduction of Mg vapor pressure. The yields and time profiles of the excited Mg states, however, were not significantly affected by the presence of Bi, provided the temperature was adjusted to yield the same initial concentration of Mg(3P). This result is not surprising since the Bi concentration was typically 30 times smaller than the initial concentration of Mg(3P) atoms. Attempts were made to visually observe the Mg(’S-’P) emission at 1190 nm by using an IR viewer and a long-pass filter. Although the Mg(3S-*3P) emission was easily observed through the viewer, no IR emission was observed through the viewer and
0.4,
t
1-
o.eC
o
10 LASER ENERGY Imll
Figure 3. Saturation of Mg(3P) produced by dye laser pumping. ”- I
501
I
h
I
I
,’-
I=
I
i
BUFFER GAS PRESSURE ltorrl
Figure 4. Pressure dependence of various Mg and Bi emission intensities.
long-pass filter. Observations of a high-temperature filament lamp through the viewer and appropriate interference filters demonstrated comparable sensitivity to near-infrared and visible radiation. Therefore, the excited Mg(IS) state a t 43 503 cm-I was not significantly populated. Tables I and I1 report the peak concentration or yield of each excited state that was observed along with the time of peak intensity and the corresponding exponential decay rate. For convenience of discussion, the electronic states of Bi have been designated in this paper by the numbers 1 through 13 starting with the ground state and increasing in energy, as shown in Figure 2. The yields were calculated by ignoring radiation trapping; thus, the entries in Tables I and I1 should be considered as lower limits. As will be shown later, radiation trapping is significant in this system. The data reported in Tables
Energy Transfer between Mg(3P) and Bi Atoms I and 11, collected at 950 OC with 85 Torr of He buffer gas, were typically reproducible to within f10% of the reported value. Under these conditions, the initial Mg(3P) and Bi concentrations ~, The Mg decay were 2.0 X 10l6and 6.5 X 1014~ m - respectively. rates were observed to vary significantly with temperature but were relatively insensitive to the pressure of the buffer gas. The peak emission intensities, due to all the observed transitions in Mg and Bi, were also measured as a function of buffer gas pressure. Typical examples of the variation of peak intensities with pressure are shown in Figure 4. In general, the intensity of the Mg emissions increased with pressure while the intensity of the Bi emissions declined.
Discussion Table I shows that the yields of all the observed excited states of the Mg atoms are very small (typically < 0.003% of [Mg(3P)]). Husain and Roberts4 also have measured the production of Mg(’P) and Mg(4s3S) under similar experimental conditions and our yield results agree with theirs. Our decay rates, however, are much faster which we attribute to impurities generated by the heat pipe, since the effect does not seem to involve the buffer gas. Husain and Roberts, as well as Breckenridge et a1.,* have assigned the production of Mg(IP) to energy pooling between two Mg(’P) atoms and the production of Mg(4s3S) to reactions of Mg(3P) atoms with excited Mg2 molecules. The observed rate of decay of the Mg(’P) state, approximately twice that of Mg(3P), is consistent with this theory as is the observed pressure dependence of the 517.8-nm Mg(4s3S-’P) emission, since the buffer gas is involved in the formation of the excited Mg2 dimers. The proposed mechanism, however, fails to account for the population of the states of Mg above 44 000 cm-I. Emission from Mg(3D) atoms at 383.5 nm was observed by Lebedev et a1.16 following two-photon resonant ionization of ground-state Mg atoms through the ‘P state. In our experiments, three-photon absorption is capable of reaching the ionization continuum via resonant and near-resonant processes. However, the time profiles of the emissions at Mg concentrations similar to our experiment were much faster than we observed. Therefore, it appears unlikely that three-photon ionization is responsible for the production of the higher Mg states observed in our experiments. The most plausible explanation is energy pooling between Mg(’P) and either Mg(4s3S) or Mg(’P). These reactions are possible because the high density of Mg(3P) allows energy-pooling collisions to occur on a time scale that is comparable to the 1-ps radiation trapped lifetimes of Mg(lP) and Mg(4s3S). The peak yields of the excited Bi atoms (relative to total Bi) are typically much larger than the yields of the excited Mg atoms (relative to the 3P state). Of the Bi states that were observed in emission, the 5 and 13 states are the most heavily populated. One possible mechanism for production of Bi( 13) is energy transfer from the nearly resonant 3d3D2and higher states of Mg above 48 000-cm-’ excitation. The yields of these highly excited states of Mg are so low, however, that this mechanism seems improbable. Indeed, accounting for the observed rate of spontaneous emission from the Bi( 13) state requires a concentration of secondary Mg states approaching that of Mg(3P) itself, given a gas kinetic rate of energy transfer of cm3 s-l. The concentrations of the Mg(3d3D2)and higher states, reported in Table I, however, are likely to be underestimated due to radiation trapping, since the corresponding transitions terminate in the heavily populated 3P state. The magnitude of the radiation trapping effect can be evaluated from Holstein’s model” using the equation
-
where u is the cross section at line center, N is the concentration of the terminal state, and r is the radius of the radiating cylinder. Taking r = 0.1 cm and N = 2 X lOI6/cm3, calculating u from the known radiative ratel2 of the 385.3-nm transition. and as(16) Lebedev, V. V.; Provorov, A. s.; Troshin, B. I.; Chernenko, A. A,; Chebotaeve, V. P. Sou. Tech. Phys. Letr. (Engl. Transl.) 1980, 6, 5 8 5 . (17) Holstein, T. Phys. Rev. 1947, 72, 1212.
The Journal of Physical Chemistry, Vol. 91, No. 8, 1987 2089 suming Doppler line width yields a corrected Mg(3d3D2) concentration that is less than 3% of the initial Mg(3P). The similarly corrected yields of the other Mg states above 48 000 cm-’are even smaller. Therefore, the yields of Mg(3d3D2)and higher states are still too small to account for the production of Bi(13) by direct energy transfer to ground-state Bi atoms. The concentrations of the Bi metastable states’* that were not observed in emission can also be estimated by an analysis of radiation trapping on transitions which terminate in these energy levels. Table I1 shows significant variation between transitions out of a common upper state in the observed values of the yield, as well as the time of peak emission and the decay rates. These differences occur because the effects of radiation trapping vary with the concentrations of the terminal energy levels. If, for example, it is assumed that there is no radiation trapping on the 613.8-nm (13 6) transition and that radiation trapping on the 359.6-nm (13 4) transition accounts for the different apparent concentrations of the Bi(13) state, then a lower limit on the concentration of the Bi(4) state can be inferred from eq 1. Using the data in Table I1 and calculating as above yielded a Bi(4) concentration of greater than 4.6 X lOI3/cm3 (approximately 7% of total Bi). Depending on the choice of initial state used in the analysis, lower limits for the Bi(2) state of 0.8 X lOI3, 5.2 X lo’’, and 28 X lOI3/cm3 were also obtained from the data in Table 11. The results for the Bi(2) state are scattered in part due to the propagation of errors in the data, due to variations in the time of peak yield from line to line, and due to nonzero concentrations in the other energy levels involved in the calculation. The value of 5.2 X lOI3/cm3 (8% of total Bi) inferred from the 9 3 and 9 2 intensities is probably the least subject to error since the measured effect of the radiation trapping by Bi(2) is strongest for this pair of transitions which also have very similar time profiles. The radiation trapping effect on the 7 2 transition is small because of a relatively low cross section,I2 while the trapping of the 10 2 transition is less evident relative to the 10 4 transition due to significant concentration in the Bi(4) state. While these results cannot be taken as highly accurate, they do show significant population of the Bi(2) and Bi(4) states within 100-200 ns of the initial appearance of Mg(3P). Of course, the transitions which terminate on the Bi(1) ground state are also strongly radiation trapped as can be seen, in Table 11, by com2) and paring the Bi(5) yields measured on the 472.2- ( 5 1) transitions. The Bi(1) concentrations cannot 306.7-nm ( 5 be inferred from these data, however, since the Bi(1) atoms are not spatially confined to the pump beam. On the other hand, the 2 and discrepancy between the observed time profiles of the 5 5 1 emissions suggests that a considerable fraction of the Bi atoms have been removed from the ground state due to pumping by Mg(’P). Assuming that resonant transfers occur rapidly, we anticipate the following sequence of events once Mg(’P) appears in the presence of Bi atoms. Initially, ground-state Bi( 1) atoms are pumped to the metastable Bi(4) state. Upon subsequent interactions with Mg(3P) the Bi(4) atoms are pumped to the Bi(7) state which decays radiatively by allowed transition (307.7 nm) to the Bi(2) state, which is also metastable. The Bi(2) state upon collision with Mg(3P) is then pumped to the Bi(5) and Bi(6) states. The Bi(6) state is metastable but is assumed to be coupled to the nearby Bi(5) state through collisions with the buffer gas. The Bi(5) state then decays by radiating to the 1 and 2 states. Because of the large population in the Bi( 1) and Bi(2) states, these decays are slowed significantly by radiation trapping. Consequently, the pumping by Mg(3P) maintains a significant population in the Bi(5) and Bi(6) energy levels. Energy pooling collisions between Mg(3P) and Bi(5) or Bi(6) are then capable of producing the Bi(13) state. Above 43 9 13 cm-I, the Bi states are dense and of varied symmetry. Moreover, collisional relaxation between these states is likely to be rapid. Consequently, it is difficult to explain in detail why the Bi( 13) state is populated in preference to other nearby states that are also energetically accessible.
--
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-
-
-
-
-
-
-
(18) Garstang, R. H. J . Res. Natl. Bur. Stand., See. A 1964, 68, 61.
2090
The Journal of Physical Chemistry, Vol. 91, No. 8,1987
The ladder-climbing model described above explains the heavy population of the Bi(2), Bi(4), Bi(5), and Bi(13) states and is consistent with the observed rates of photon emission if the transfer rates are gas kinetic. A lower limit on the rate of pumping of the Bi(5) and Bi(6) states to the Bi( 13) state can be inferred by setting the concentration of Bi(5) and Bi(6) to the total Bi concentration and requiring the rate of pumping of the Bi(13) state to match the observed rate of Bi(13) photon emission. Following cm3 this procedure yields a minimum transfer rate of 1.3 X s-I. By similar argument, one can estimate a minimum Bi(5) and Bi(6) concentration of 8.9 X l O I 3 cm-3 (13% of total Bi) by assuming that the transfer rate is less than lo4 cm3s-I. *Thisresult is about one order of magnitude larger than is given in Table 11 from the intensity of the 5 2 transition, consistent with radiation trapping due to the previously estimated concentration of Bi(2). Applying similar arguments to the other pumping reactions also suggests gas kinetic transfer rates and significant concentrations of the other metastable states as well. Two aspects of the Bi emission data are difficult to explain, namely, the negative pressure dependence shown in Figure 4, and the decay rates which are slower than the decay of the Mg(3P) state. The negative pressure dependence implies quenching of some of the Bi intermediates by collisions with the buffer gas or associated impurities. Impurity quenching was evident for the excited states of Mg; however, these effects were correllated with temperature rather than pressure. Consequently, the effect of buffer gas pressure on the Bi excited states must be due to collisions with He. The known ratesI9 of Bi(2) and Bi(3) quenching by He (typically cm3 s-I) are much too small to be effective on the microsecond time scale of this experiment. Collisions with the buffer gas could have a significant impact on the higher metastable states of Bi if their quenching cross sections are larger. The complexity of the pumping mechanism, however, makes it impossible to extract these rates from the present data with any degree of certainty. In any case, the observed pressure dependence of the Bi emissions is in contrast to the pressure dependence3 of energy transfer from Mg(3P) to Ca. Therefore, operation of the Mg(’P)-Bi system as a low pressure transfer laser may be feasible, other factors permitting. The slower decay rates of the Bi emissions seem to track the decay of the Mg states above 40 000 cm-I, with the exception of the Mg(4d3D2)state at 54 192 cm-I. This result tends to suggest that the pumping of the Bi ladder is perhaps related to the production of the 4s3S and higher states of Mg. Direct transfer from these states seems to be ruled out because of their low yield, as previously noted. On the other hand, the excited Mg, precursor to the Mg(4s3S) state could be significant with respect to the Bi emissions; however, in this case one
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(19) Trainor, D. W. J . Chem. Phys. 1977, 67, 1206.
Chowdhury and Benard would expect similar pressure dependences for both the Mg and Bi emissions, contrary to our observations. Further research will be required to resolve this seeming contradiction in the data. The potential of this transfer system to operate as a laser appears to be greatest on transitions out of the Bi(5) and Bi( 13) states to lower energy levels. Self-terminating laser action has been reported on the 5 2 transition at 472.2 nm in fast risetime Bi discharges.20 The Bi( 13) state could in principle lase to a number of lower states if they were depopulated; however, approximately 85% of the free radiative decay of Bi( 13) is into the 2 and 3 states.’, Under the conditions of the present experiment, the Bi(2) concentrations are probably larger than the Bi(5) and Bi( 13) concentrations since the Mg(3P) concentration is marginal to sustain inversion of the 5 2 transition on a steady basis. Maintenance of inversion requires the product of the transfer rate constant and the Mg(3P) concentration to be significantly larger than the lo7 s-l free radiative decay rate of the Bi(5 2) laser transition.12 With a gas kinetic transfer rate of cm3 s-l, a Mg(3P) concentration approaching 10’’ cm-3 is needed, approximately 5 times larger than is achieved in the present experiment. Since the Bi(5) state is intermediate to the production of the Bi(13) state and since the Bi( 13) state decays an order of magnitude more rapidly than Bi(5), it follows that the [Ms(~P)]threshold for inversion of the 5 2 transition is probably smaller than for the 13 2 and 13 3 transitions. Consequently, the Mg(3P)-Bi transfer system is most easily operated as a laser at 472.2 nm. 2) transition by transfer from Mg(’P) Inversion of the Bi(5 will also require a minimum percentage of the Mg atoms to be in the 3Pstate. As in the oxygen-iodine laser,21v22 an equilibrium will set up between the nearly resonant Mg(3P,1S) and Bi(2,S) states when the Mg(3P) concentration is large enough to dominate the radiative decay of the Bi(5 2) transition. Since the transfer reaction from Mg(3P) to Bi(5) is approximately 700-cm-’ exothermic, the equilibrium constant favors population of the Bi(5) state, so that, at a temperature of 1000 “C, inversion can be obtained with only 45% of the Mg atoms in the 3Pstate. Because dye laser pumping can achieve 90% yields of Mg(3P), it follows that lasing may be achieved upon operating the heat pipe at higher temperature to produce greater initial Mg(3P) concentrations.
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Acknowledgment. This work was sponsored by the Innovative Science and Technology Office of the Strategic Defense Initiative Organization under subcontract 9-X25.X145 1-8 administered by the Los Alamos National Laboratory. (20) Markova, S.V.; Petrash, G. G.;Cherezov, V. M. Sou. J . Quantum Electron. (Engl. Transl.) 1979, 9, 707. (21) Derwent, R. G.; Thrush, B. A. Faraday Discuss. Chem. Soc. 1972, 53, 162. (22) McDermott, W. M.; Pchelkin, N. R., Bernard, D. J.; Bousek, R. R. Appl. Phys. Lett. 1978, 32, 469.
