7078
J. Phys. Chem. 1996, 100, 7078-7084
Production of the NaHg Molecule by Reactive Three-Body Collisions following Energy-Transferring Processes of Laser-Excited Na(3 2P) Atoms D. Gruber,* U. Domiaty, K. Iskra, S. Dinev, and L. Windholz Institut fu¨ r Experimentalphysik, Technische UniVersita¨ t Graz, Petersgasse 16, A-8010 Graz, Austria ReceiVed: October 27, 1995; In Final Form: February 2, 1996X
We report on the production of the NaHg molecule Via resonant excitation of the sodium D-lines following energy-pooling collisions of laser-excited Na(3 2P) atoms. In addition to the chemiluminescence on the red NaHg(II1/2-X1/2) band system, we observed emission on the blue-band system. Production mechanisms as well as the dependence on particle density and excitation laser intensity are discussed, and the rate coefficients are determined.
I. Introduction The most common way of producing intermetallic molecules consisting of one atom of group Ia and one of group IIb is the photochemical reaction of a laser-excited alkali-metal dimer Ia2 with a ground-state IIb atom, according to
Ia* 2 + IIb f IaIIb* + Ia
(1)
Employing these kinds of reactions, several IaIIb intermetallic molecules have been investigated. An overview of this topic is given by Milosˇevic´.1 However, in previously published works on the NaCd molecule,2,3 we showed that in addition to reaction,1 a photochemical reaction involving the electronically excited Cd atom according to
Ia2 + IIb* f IaIIb* + Ia
(2)
leads to the production of the electronically excited NaCd molecule as well. Moreover, we found that the most effective production channel is represented by a reactive three-body collision
Ia + IIb* + M f IaIIb* + M (3) involving the metastable Cd atom. Applying this scheme to the system NaHg, it was not possible to force production of NaHg by excitation of the Hg atom to its 6 3P1 state. The reason for this might be the rather high energy of the Hg(6 3P1) state, 39 412 cm-1, which nearly equals the Na atomic dissociation energy of 41 450 cm-1. Therefore, production of molecular and atomic ions of sodium and population of high-lying Hg states by energy-pooling collisions seem to be favored against production of NaHg molecules.4 On the other hand, resonant excitation on the second resonance lines of sodium at 330.2 and 330.3 nm resulted in strong nonlinear effects that masked any features of molecule production by collisions.5 In this paper, we present a completely new way of producing diatomic intermetallic molecules by energy-pooling collisions of two laser-excited atoms with a subsequent reactive threebody collision. Following this mechanism, we observed welldeveloped and, in many cases, isolated NaHg red and blue bands, corresponding to the II1/2-X1/2, III1/2-X1/2, IV1/2-X1/2, and II3/2-X1/2 electronic transitions, respectively. As a result of a theoretical analysis, we derived the rate coefficients and cross sections of relevant production channels. X
Abstract published in AdVance ACS Abstracts, April 1, 1996.
0022-3654/96/20100-7078$12.00/0
Figure 1. Schematic representation of the reactive three-body collisions (A and B), following energy-pooling collisions (C and D) of laserexcited Na atoms.
Figure 2. Experimental setup: LC, Nd:YAG laser controller; JM, Joule meter; F, filter; M, mirror; L, lens; PD, fast photodiode; HP, heat pipe oven; Mo, monochromator; PMT, photomultiplier tube; Osc, digital two-channel storage oscilloscope; DA, image-intensified diode array; OMA, optical multichannel analyzing system controller; PC, laboratory computer.
Figure 1 presents the scheme of the investigated processes. The potential energy curves of NaHg are those presented by Windholz et al.6 and Gruber et al.7 Numerical data of excitedstate potential curves are provided by Gleichmann and Hess,8 whereas a discussion of these ab initio potential energy curves is given by Windholz et al.6 We excited Na atoms on the Dlines to saturate the transition Na(3 2S1/2-3 2P3/2) and to prepare © 1996 American Chemical Society
Production of the NaHg Molecule
J. Phys. Chem., Vol. 100, No. 17, 1996 7079
reactants in the intermediate Na(3 2P3/2) state. The excited sodium atoms experience reactive three-body collisions that result in the production of NaHg(II1/2) molecules, according to
Na(3 2P) + Hg(6 1S0) + M f NaHg(II1/2) + M
(4)
where M represents any third collision partner needed to conserve energy and momentum. Schlejen et al.9 previously reported the observation of NaHg red bands upon excitation of one of the D-lines. In addition to reaction 4, the excited Na(3 2P3/2) atoms participate in energy-transferring collisions according to k1
Na(3 2P3/2) + Na(3 2P3/2) 98 Na(5 2S) + Na(3 2S1/2) (5) k2
Na(3 2P3/2) + Na(3 2P3/2) 98 Na(4 2D) + Na(3 2S1/2)
(6)
Rate coefficients for these kinds of reactions are given by, e.g., Allegrini et al.,10 Geltman,11 and Nijland et al.12 Subsequent reactive three-body collisions k3
Na(5 2S) + Hg(6 1S0) + M 98 NaHg(III1/2,IV1/2,II3/2) + M (7) k4
Na(4 2D) + Hg(6 1S0) + M 98 NaHg(III1/2,IV1/2,II3/2) + M (8) finally lead to the production of NaHg molecules in the highly excited III1/2, II3/2, and IV1/2 states and to subsequent emission to the repulsive as well as the bound part of the electronic X1/2 ground state. Actually, NaHg molecules are produced in a higher electronic state than stated in eqs 7 and 8. But since the energy range above 25 000 cm-1 is congested with electronic states showing many avoided crossings and degeneracies of rovibrational levels, which make relaxations happen on a picosecond scale, we regard the electronically excited states III1/2, IV1/2, and II3/2, experimentally observed, as immediately populated by the reactive three-body collisions. The rate coefficients k3 and k4 were determined by employing a kinetic model based on rate equations to describe the population distribution of the atomic and molecular states involved. II. Experiment The experimental setup used throughout these experiments is similar to those reported in previously published papers.13 As a reaction vessel, we used a stainless steel crossed heat pipe oven with an inner diameter of 25 mm terminated by four quartz windows. Argon was used as the buffer gas. A Baratron vacuum gauge was used to determine the buffer gas pressure; the temperature was controlled by a thermocouple device and a current-stabilized power supply. The central heated zone was about 5 cm in each direction from the crossing point of the heat pipe tubes. A stainless steel mesh was used as a wick to bring back condensed alkali metal and Na-Hg amalgam into the central zone, such that a permanent cycle of evaporation and condensation could be maintained. However, it was not possible to prevent loss of Na and Hg completely, since the melting point of the Na-Hg amalgam is much higher than the melting points of the isolated elements. In order to ensure stable experimental conditions, we therefore had to recharge the heat pipe oven after only a few hours of operation. The second harmonic output of a Q-switched Nd:YAG laser (Spectra Physics, Quanta Ray GCR 170) was used to pump a homemade dye laser consisting of an oscillator with a 20-mm dye cuvette and a holographic grating (2400 grooves/mm) in
Figure 3. Overview spectrum covering the spectral range 350-830 nm for a temperature of 700 K and a buffer gas pressure of 30 kPa, using 150 grooves/mm grating. The region in the vicinity of the Na D-lines is dropped in this spectrum since the detection system always was saturated by the strong laser-induced fluorescence. Caused by different exposure times of the diode array applied in the blue and red region, respectively, the intensities are not to scale.
near-grazing incidence configuration, followed by a 20-mm amplifier cell. The output energy at 589 nm was about 20 mJ maximum with an estimated bandwidth of 3 cm-1. In order to enlarge the reaction volume in the central zone of the heat pipe, we omitted focusing the laser. Furthermore, we chose to detect the fluorescence perpendicular to the incident laser beam, since in this way we also can exclude nonlinear parametric and induced emission that was always observed throughout previous experiments with resonant one- and twophoton excitation of the Na atom.5,14 Fluorescence light was focused by a quartz lens onto the end of an optical fiber. Spectral resolution was obtained by means of a 50-cm scanning monochromator (Acton; Mo) equipped with three holographic gratings (150, 600, and 1200 grooves/mm) mounted on a computer-controlled turntable and with appropriate optical filters to block the second-order lines of the monochromator. Fluorescence spectra were detected by an optical multichannel analyzing system (OMA), consisting of an image-intensified 1024 diode array (DA) which was triggered by the TTL signal of the Nd:YAG laser controller (LC). Total exposure time was varied as required. The monochromator was also equipped with a mirror that enabled either selection of the diode array to serve as a multichannel detection device or, by rotation through 90°, imaging of the light passing through the monochromator onto an exit slit. Time behavior of fluorescence was detected by a fast potomultiplier tube (Hamamatsu R-955) with a rise time of 2.2 ns as well as by a photodiodide with an effective rise time of 1 ns (PMT) mounted on the exit slit and connected to a 600-MHz LeCroy digital storage oscilloscope (Osc) that was triggered externally by a fast photodiodide (PD). Raw data were stored in a laboratory computer (PC), connected by a DMA board to the OMA and by a GPIB interface to the storage oscilloscope. The wavelength scale of the monochromatorOMA system was standardized against a Hg lamp. III. Results and Discussions A. Fluorescence Spectra. Figure 3 shows an overview fluorescence spectrum of a Na/Hg vapor mixture, excited resonantly on the Na(3 2S1/2-3 2P3/2) transition. The wavelengths of observed fluorescence and respective atomic and molecular assignments are summarized in Table 1. In the spectral region in the vicinity of the Na resonance lines, our detection system would always be saturated by the strong laserinduced fluorescence; thus, we spared this region in Figure 3.
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TABLE 1: Wavelengths (λ) of the Experimentally Observed Spectral Features along with an Assignment of Atomic and Molecular Transitionsa λ, nm
assignment
comment
498.3 498.8 514.9 515.3 568.3 568.8 589.0 589.6 615.4 616.1 818.3 819.5
Atomic Transitions Na(5 2D5/2-3 2P3/2) Na(5 2D3/2-3 2P1/2) Na(6 2S1/2-3 2P1/2) Na(6 2S1/2-3 2P3/2) Na(4 2D3/2-3 2P1/2) Na(4 2D5/2-3 2P3/2) Na(3 2P3/2-3 2S1/2) Na(3 2P1/2-3 2S1/2) Na(5 2S1/2-3 2P1/2) Na(5 2S1/2-3 2P3/2) Na(3 2D3/2-3 2P1/2) Na(3 2D5/2-3 2P3/2)
430-480 553 (peak) 630-690 700-800
Molecular Transitions NaHg(III1/2,IV1/2,II3/2-X1/2) Na2(c 3Πg-x 3Σu+) NaHg(II1/2-X1/2) Na2(A 1Σu+-X 1Σg+)
w w w w sa sa
w
a
Weak (w) and self-absorbed (sa) fluorescences are marked as a comment.
TABLE 2: Delay Times (τdelay) with Respect to the Laser Pulse and Decay Times (τ1 and τ2) according to Single- and Double-Exponential Fits, Respectively, of Fluorescence Observed λ, nm
transition
τ1, ns
668.0 658.0 652.0 602.6 568.8 552.3 498.0 469.8 465.3 462.1 452.6 447.4 443.6
NaHg(II1/2-X1/2) NaHg(II1/2-X1/2) NaHg(II1/2-X1/2) Na(3 2P-3 2S), wing Na(4 2D-3 2P) Na2(c 3Πg-x 3Σu+) Na(5 2D-3 2P) NaHg(III1/2-X1/2) NaHg(III1/2-X1/2) NaHg(III1/2-X1/2) NaHg(II3/2-X1/2) NaHg(II3/2-X1/2) NaHg(II3/2-X1/2)
48.7 50.0 50.9 56.0 7.3 31.1 40.7a 54.6 55.8 57.2 57.8 58.7 55.8
a
τ2, ns
280.0 31.0 157.8
τdelay, ns 29.5 29.0 25.0 20.0 25.0 25.0 31.0 44.0 40.0 43.0 44.0 45.0 42.5
Double-exponential fit; τ1 ) 39.7 ns, τ2 ) 2200 ns.
Besides the chemiluminescence of NaHg, we observed strong emission on both the Na(5 2S-3 2P) and the Na(4 2D-3 2P) atomic lines of Na, which are originating in the energy-pooling collisions (5) and (6). We also observed weak emission on the Na(5 2D-3 2P) and Na(6 2S-3 2P) atomic lines at 498.5 and 515.0 nm, respectively. We ascribe this fluorescence to energypooling collisions similar to eqs 5 and 6 but resulting in a population of the 5 2D and 6 2S states. For energy-pooling collisions, the range of energy excess compared to twice the energy of the intermediate state, which in our case ist the 3 2P state, lies within 3kT, corresponding to 490 cm-1 for temperatures applied in our experiments. Since the energy excess of the 5 2D state is about 3100 cm-1 and of the 6 2S state it is 2440 cm-1, an effective population of these states by EP collision of two Na(3 2P) atoms is rather unlikely, so the fluorescence originating in these electronically excited states is very weak. We also observed some spectral features due to the Na2 dimer. In the red wing of the Na(4 2D-3 2P) line, a shoulder peaking at 553 nm can clearly be seen (Figure 3) that is identified as the Na2(c 3Πg-x 3Σu+) free-free emission.15 The origin of this band lies in the collision of a Na(3 2S) atom with a laser-excited Na(3 2P) atom in which the upper electronic potential is populated by the conversion of translational energy of the colliding atoms to internal energy of the quasimolecule, resulting in radiative decay. Besides this diffuse band, we only observed
Figure 4. Fluorescence spectrum of a Na/Hg vapor mixture at T ) 700 K and pAr ) 30 kPa following resonant excitation of the Na(3 2P3/2) state. NaHg features are marked according to spectral positions used for measurements of the time behavior.
weak emission on the Na2(A 1Σu+-X 1Σg+) band, whose upper state is populated by laser radiation. Chemiluminescence of NaHg was observed on the II1/2-X1/2 band system and as a completely new result on the blue bands as well. Figure 4 presents detailed fluorescence spectra of the wavelength regions 639-710 (a) and 420-490 nm (b), using the 1200 grooves/mm grating at the same experimental conditions as in Figure 3. The Si assignments in Figure 4a are given in accordance with Schlejen et al.9 Oscillations S1, S2, S3, and S4 are identified to originate in the transitions NaHg(II1/2-X1/2), of which oscillation S1 is of pure bound-free (bf) and S3 of pure bound-bound (bb) character, whereas oscillations S2 and S4 represent convolutions of both bound-free and bound-bound emissions.7 Since the NaHg red bands in these experiments are congested with fluorescence on the Na D-line wing, we decline to analyze these bands. The NaHg blue bands recorded in our experiments appeared well developed and showed bound-free features as well as a large variety of bound-bound features. The bf emission is identified to originate from the III1/2-X1/2, IV1/2-X1/2, and II3/2X1/2 electronic transitions, whose spectral regions are shown in Figure 4. A detailed analysis of the NaHg blue bands is in progress and will be published. The T1-T6 assignments in Figure 4b indicate spectral positions for which measurements of the time behavior were taken (see below). B. Dependence of Fluorescence Intensity on Particle Density. The dependence of the intensity of the fluorescence
Production of the NaHg Molecule
J. Phys. Chem., Vol. 100, No. 17, 1996 7081
Figure 5. Dependence of fluorescence intensity of the Na(4 2D-3 2P) line at 568.8 nm (down triangles) and of the NaHg(III1/2-X1/2) emission at 460.8 nm (circles) on Na particle density. The slopes are calculated from a linear fit of the experimental points.
lines on particle density was monitored by variation of heat pipe temperature. Since changing the temperature in the heat pipe oven might cause turbulences in the flow of the metal vapors, the system was allowed to stabilize again for 1 h. We consider the particle density inside the fluorescence zone as being connected to the temperature T simply by
pi(T) (9) kT where pi(T) is the partial pressure of the considered species, k is the Boltzmann constant, and ni is the particle density. For sodium located in the center of the heat pipe oven, we assume T to be the temperature measured by the thermocouple. Therefore, pi(T) can be taken from vapor pressure tables16 corresponding to the number densities of atomic Na from 1.8 × 1014 to 7.9 × 1015 cm-3 for the temperature range 570-700 K. The total pressure ptot can be seen as the sum of the partial pressures, according to ni )
ptot(T) ) ∑pi(T)
(10)
i
and is in a heat pipe mode equivalent to the buffer gas pressure monitored directly by the vacuum gauge. Thus, the partial pressure of mercury is the difference of the total pressure and the partial pressure of sodium. The partial pressure for Hg is therefore influenced only marginally by pNa and thus assumed to be constant (=30 kPa), corresponding to nHg = 2.5 × 1018 cm-3. Figure 5 depicts the variations of the intensities of the atomic fluorescence line Na(4 2D-3 2P) at 568.8 nm (down triangles) and of the NaHg(III1/2-X1/2) emission at 469.8 nm (circles) on sodium particle density. The slopes shown in Figure 5 are determined from a linear fit of the experimental values and revealing an I1.8 law for the atomic and an I1.7 law for the molecular emission. Taking into consideration the absorption of the exciting laser pulse with increasing particle density, the agreement between experimental results and the theoretically predicted I2 law for energy-pooling collisions is sufficiently good. C. Time Behavior of Fluorescence. In order to verify the reaction processes given by eqs 5-7 and 16, we recorded the time behavior of the atomic as well as of the molecular fluorescence lines employing the photomultiplier tube and the photodiode mentioned previously. Figure 6 shows the time profiles of the Na D1-line wing at 602.6 nm, of the Na(4 2D3 2P) line at 568.8 nm, and of the NaHg(III1/2-X1/2) emission at 469.8 nm. The parameters describing the time behavior of fluorescence are summarized in Table 2, where the decay times τi are given according to the best fit, either single exponential
Figure 6. Time behavior of the Na(3 2P-3 2S) line wing at 602.6 nm (a), of the Na(4 2D-3 2P) line at 568.8 nm (b), and an example of the NaHg emission bands at 469.8 nm (c), where the intensity to be seen before 0 ns is due to the detection system and has no physical relevance. The dashed curve in a represents a double-exponential fit of the experimental values, used to estimate the initial population distribution in the Na(3 2P3/2) state prepared by the laser pulse, whereas the dashed curves in b and c represent the time behavior obtained by applying the kinetic model of eqs 11-14.
or double exponential, along with the delay times τdelay with respect to the exciting laser pulse. It can be seen that the delay of the Na D-line is lowest for all transitions observed and that the decay time is fitted best by a double-exponential decay profile, resulting in decay times τ1 ) 56 ns and τ2 ) 280 ns, both being much higher than the natural lifetime τ ) 15.87 ns of the isolated atom.17 We ascribe this particular behavior of the resonance line to radiation-trapping effects occuring in the dense vapor mixture investigated in our experiments. The effect of radiation trapping has been investigated both theoretically18,19 and numerically.20,21 Since the kinetics of the vapor mixture investigated in our experiments is complicated and so is the geometry of the vapors inside the heat pipe oven, we decline from a theoretical description of this effect in our experiment. Moreover, we confine ourselves to a description of imprisoned lifetimes of the Na D-lines through an analysis of experimental determined decay times (see below). Furthermore, the delay times observed can be divided into two groups. The first one is characterized by a delay time of some 30 ns, including fluorescence due to the NaHg(II1/2-X1/2) and Na2(c 3Πg-x 3Σu+)
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Gruber et al.
electronic transitions as well as fluorescence originating in EP collisions of laser-excited Na(3 2P) atoms, i.e., Na(4 2D-3 2P) and Na(5 2D-3 2P). The second group shows delay times of some 45 ns and covers chemiluminescence of NaHg(III1/2,II3/2X1/2). Caused by the low intensity and the low S/N ratio in the case of the Na(5 2D-3 2P) line at 498.0 nm, in Table 2 we present the results of a single-exponential fit, whereas the results of the less reliable double-exponential fit are stated only in a footnote. We developed a kinetic model employing an open set of firstorder differential equations to describe the temporal evolution of the populations of the atomic and molecular states involved, considering a Hg atom in any arbitrary electronic state to serve as a third collision partner since the particle density of Hg is much higher than that of sodium:
(
)
dn1(t) 1 1 - k1n12(t) - k2n12(t) ) -n1(t) + dt τ1 τ2
(11)
dn2(t) ) k1n12(t) - n2(t)(A5S4P + A5S3P) - k3n2(t)nHg2 (12) dt dn3(t) ) k2n12(t) - n3(t)(A4D3P + A4D4P) - k4n3(t)nHg2 (13) dt dn4(t) (14) ) k3n2(t)nHg2 + k4n3(t)nHg2 - ANaHgn4(t) dt where n1(t), n2(t), n3(t), and n4(t) are the number densities of the Na(3 2P), Na(5 2S), Na(4 2D), and NaHg(III1/2,IV1/2,II3/2) states, respectively; τ1 and τ2 are the experimental decay times of the Na(3 2P) state accounting for radiation-trapping effects; k1 and k2 are the rate coefficients for the EP collisions according to eqs 5 and 6; Ai are the Einstein coefficients for spontaneous emission; nNa and nHg are the number densities of the sodium and mercury atoms, respectively; and k3 and k4 are the rate coefficients for the production of NaHg via the Na(5 2S) and Na(4 2D) states, respectively, according to eqs 7 and 8. The rate coefficients k1 ) (1.9 ( 0.6) × 10-10 cm3 s-1 and k2 ) (3.0 ( 0.9) × 10-10 cm3 s-1 for the EP collisions (5) and (6) are taken from Allegrini et al.10 The overall particle densities of Na and Hg are taken according to the considerations outlined in the previous subsection. The exciting laser pulse has a time duration of about 6 ns, and in the model, it is taken to be infinitely short. Further, we assume that the power of the laser is high enough to saturate the transition Na(3 2S-3 2P) and thus to prepare the upper electronic state with half the population of the Na ground state. Therefore, the initial conditions for eqs 11-14 are given by n1(0) )
nNa n2(0) ) n3(0) ) n4(0) ) 0 2
(15)
In order to avoid a complicated treatment of radiation-trapping effects on the Na D-lines, we took the experimentally determined decay times, neglecting the time delay presented in Table 2, to describe the time evolution of the population of the Na(3 2P) states within the solid angle experimentally observed. In the first step of computation, we solved the set of differential equations numerically by estimating the collision rate of the reactive three-body collisions according to
kT ZNa(3P)HgHg ) 54x3π d4τn1nHgnHg (16) m with d and m being the mean atomic diameters and masses for Na and Hg.22 The lifetime τ of the activated complex, namely, the time the laser-excited Na(3 2P) atom is within sufficiently
TABLE 3: Experimental Decay Time of the Na(3 2P) State along with a Comparison of Experimental and Simulated Decay Times of the Na(4 2D) and NaHg(III1/2) States experiment λ, nm
τ1, ns
transition
τ 2, ns
τdelay, ns
model τ1, ns
τ2, ns
τdelay, ns
602.6 Na(3 2P-3 2S), wing 56.0 280.0 20.0 568.8 Na(4 2D-3 2P) 7.3 31.0 25.0 7.8 35.6 25.0 469.8 NaHg(III1/2-X1/2) 52.3 44.0 48.7 42.5
TABLE 4: Rate Coefficients (k3 and k4) for the Reactive Three-Body Collisions (7) and (8), respectivelya reaction
rate const, 1030 cm6 s-1
Na(5 2S) + Hg(6 1S) + Hg(6 1S) f NaHg** + Hg(6 1S) Na(4 2D) + Hg(6 1S) + Hg(6 1S) f NaHg** + Hg(6 1S)
k3 ) 4.22 k4 ) 4.18
a The error of the rate constants we found by variation of k3 and k4 in the simulation procedure to be 20%.
close internuclear distance to the Hg atom so that the collision with a third partner may stabilize the molecule, is estimated from a comparison of the potentials of Hess23 with those of Persico,24 calculated for NaCd. Since we found sufficient agreement in the qualitative course between both of them, we took the highly excited nonadiabatic potential curves of NaCd to estimate the width as well as the depth of the highly excited NaHg states that are not available from the calculations of Gleichmann and Hess. Then we determined the mean kinetic energy by a numeric integration employing several excited electronic states dissociating into Na(5s) as well as Na(4p). Finally, via the mean kinetic energy E ) 1/2µV2 of the collision partners in a shallow bound excited state, we found the lifetime τ of the activated Na-Hg complex to be some 10 ps. Finally, the three-body reaction cross section σtbc is obtained by employing the relation
ZNa(3P)HgHg ) n1nHgnHg introduced by Smith,25,26 where
µ)
kT σ (15π8 )x2πµ
x
tbc
mNamHgmHg mNa + mHg + mHg
(17)
(18)
The reaction rate is computed by applying the relation
ktbc ) σtbcVjrel
(19)
with Vjrel being the mean interatomic velocity [Vjrel ) (8kT/πµ)1/2]. The Einstein coefficients of spontaneous emission for the sodium transitions, A5S4P, A5S3P, A4D3P, and A4D4P, are taken from Wiese et al.,17 whereas the Einstein coefficient for the NaHg transitions, ANaHg, is taken from Musso et al.27 Since the behavior of all time profiles of the NaHg blue bands is the same (see Table 2) and, for simplicity of the model, the NaHg III1/2, IV1/2, and II3/2 electronically excited states are treated collectively, we took the integrated intensity of the NaHg blue chemiluminescence as being a normalizing factor for the experimental time profiles. The results of this first modeling step showed good agreement with the experimental results so that we could be sure that the estimated reaction rate constant lies within the right order of magnitude. In the second step of calculation, we iteratively varied the values of the respective reaction rates k3 and k4 to obtain the best agreement between the experimental and modeled time profiles. Figure 6 compares the experimental time decays with the results obtained by applying the kinetic model. It can be seen clearly that not only the decay times and the time delays are reproduced with high accuracy but also the relative intensities. Table 3 presents a comparison of the experimental and
Production of the NaHg Molecule
J. Phys. Chem., Vol. 100, No. 17, 1996 7083
Figure 7. Representation of the fractions contributing to production of the electronically excited NaHg molecule via the Na(5 2S) state (A) and the Na(4 2D) state (B).
theoretical parameters describing the time behavior of the considered transitions. Table 4 states the obtained reaction coefficients k3 and k4 of the reactive three-body collisions (7) and (8). Curves A and B in Figure 7 show the different fractions of reactions 7 and 8, respectively, contributing to the formation of the NaHg blue emission bands. D. Dependence of Fluorescence on Laser Intensity. The dependence of the fluorescence intensities on laser intensity was determined by attenuation of the maximum laser intensity using neutral density filters. Figure 8a shows the dependency of the NaHg emission on laser intensity (squares). In the following, the symbols indexed by 0 stand for a normalizing value of the considered quantity that is chosen accordingly to an experimentally well-defined starting value of the measurement. The slope was determined from a linear fit of the experimental values and found to be kexp ) 0.95 ( 0.07. The evolution of the fluorescence intensity of the Na(4 2D-3 2P) line at 568.8 nm (down triangles) shows a slope of kexp ) 1.13 ( 0.09 (Figure 8b). The results are in contradiction with theory, which predicts a slope k ) 2 for transitions originating in EP collisions of two laser-excited atoms, neglecting any saturation effects caused by the laser intensity applied. Since in our experiments we applied high laser intensities, saturation effects cannot be neglected when investigating the dependence of fluorescence intensity on laser intensity. Figure 9 shows the dependence of the fluorescence in the Na D-line wing at 602.6 nm on laser intensity, clearly exhibiting saturation for higher laser intensities (down triangles). A theoretical description of the fluorescence intensity of the Na D-lines vs the laser intensity IL is complicated since the fluorescence intensity for an inhomogeneously broadened line (subscript i) varies as
IL/IS (1 + IL/IS)1/2
) Ii(IL)
(20)
whereas for a homogeneously broadened line (subscript h), it varies as
IL/IS ) Ih(IL) 1 + IL/IS
(21)
where IS is the saturation parameter.28 Considering the results reported by Allegrini et al.,10 we fitted the experimental results
Figure 8. Dependence of atomic and molecular fluorescence intensity on exciting laser intensity. Solid lines represent the best linear fit of the experimental points.
to a linear combination of eqs 20 and 21 according to
I3P-3S ) e-aILIi(IL) + (1 - e-aIL)Ih(IL)
(22)
with a representing an adjustable parameter. The result of the fit is shown in Figure 9 (dashed curve). A linear fit of experimental results in a double-logarithmic plot reveals a ∝I1/2 law. We again used the model represented by eqs 11-14 to reproduce the dependence of fluorescence intensity on laser intensity. In order to account for the saturation effects outlined previously, we took the experimental values shown in Figure 9 as normalizing factors to describe the saturated initial population of the Na(3 2P) state, prepared by the exciting laser pulse, according to
n1(0) )
()
nNa Ifl 2 IL
(23)
The discrete values in Figure 10 show the numerical results for the Na(4 2D-3 2P) line (circles) and for the NaHg blue bands (down triangles), on the basis of the rate coefficients stated in Table 4. The slopes (dashed curves) are determined by a linear fit of the numerical values and compared to the experimental ones (solid curves). IV. Conclusions We investigated a new mechanism in producing NaHg in the electronically excited III1/2, IV1/2, and II3/2 states by a reactive three-body collision of highly excited Na atoms with groundstate Hg atoms. The reactions investigated in our experiments represent a unique reaction cycle where reactants, namely, Na(5 2S) and Na(4 2D) atoms, are produced by energy-transferring
7084 J. Phys. Chem., Vol. 100, No. 17, 1996
Gruber et al. A kinetic model was developed to describe the time behavior of Na atomic lines as well as of NaHg molecular emission which resulted in the first determination of the rate coefficients of the three-body collisions under consideration. The model and the obtained rate coefficients proved their reliability by reproduction of the dependence of fluorescence intensities on laser intensity with excellent agreement between experiment and theory. Acknowledgment. We thank Prof. H. Ja¨ger for permanent scientific support and X. Li for fruitful discussions and critically reading the manuscript. We also thank Prof. M. Allegrini, who always helped us in the field of energy pooling. S.D. thanks the members of the institute for warm hospitality and an exciting scientific atmosphere and for financial support from the National Science Foundation, Bulgaria. This work was financially supported by the Fonds zur Fo¨rderung der Wissenschaftlichen Forschung, Project P-9929-PHY, by the Jubila¨umsfonds der O ¨ sterreichischen Nationalbank, Project 4873, and by the European Scientific Foundation in the framework of the REHE programs (relativistic effects in heavy-element chemistry and physics). References and Notes
Figure 9. Dependence of the fluorescence on the Na D1-line wing on laser intensity, showing saturation for higher applied laser intensities (a). A double-logarithmic plot reveals the Na D-line to obey a ∝I0.5 law (b).
Figure 10. Comparison of slopes determined by the experiment (solid lines) and by application of the numeric model (dashed lines and points) accounting for saturation effects on the basis of the results represented in Figure 9. The slopes are determined from a linear fit of the numerically calculated points.
collisions of initially populated Na(3 2P) atoms. The dependence of the observed fluorescence intensities on Na particle density is found to be in good agreement with theory.
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