Reaction dynamics of Al+O2→AlO+O studied by the crossed-beam laser-induced fluorescence technique

Article abstract of DOI:10.1063/1.1591177

A study was performed on the reaction dynamics of Al+O ₂→AlO+O. The crossed-beam technique at five collision energies from 6.9 to 25.3 kJ/mol was used for the purpose. The laser-induced fluorescence technique was used for the detection of product AlO. The determination of the rotational-vibrational distributions was also discussed.

Full text of DOI:10.1063/1.1591177

Reaction dynamics of Al + O 2 → AlO + O studied by the crossed-beam laser-induced
fluorescence technique
Kenji Honma
Citation: The Journal of Chemical Physics 119, 3641 (2003); doi: 10.1063/1.1591177
View online: http://dx.doi.org/10.1063/1.1591177
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 7
15 AUGUST 2003
Reaction dynamics of Al¿O2\AlO¿O studied by the crossed-beam
laser-induced fluorescence technique
Kenji Honma
Department of Material Science, Himeji Institute of Technology, 3-2-1 Kohto, Kamigori, Hyogo,
Japan 678-1297
͑Received 4 April 2003; accepted 22 May 2003͒
Dynamics of the reaction, AlϩO2→AlOϩO, was studied by using the crossed-beam technique at
five collision energies from 6.9 to 25.3 kJ/mol. The Al atomic beam was generated by laser
vaporization and crossed with the O2 beam at a right angle. The product AlO was detected by
laser-induced fluorescence of the AlO(B 2⌺ϩ –X 2⌺ϩ) transition and the rotational-vibrational
distributions were determined. The observed rotational and vibrational distributions displayed
greater populations in lower vibrational and rotational levels than expected statistically. Rotational
distributions were also determined for two spin–orbit states of Al, Al(2P1/2) and Al(2P3/2), at two
collision energies. At a collision energy of 12.2 kJ/mol, the higher energy spin–orbit excited state,
Al(2P3/2), showed lower reactivity, i.e., about one-third of the ground spin–orbit state, Al(2P1/2).
However, the rotational distributions for the two states were almost identical. Both the reactivity and
rotational distributions for Al(2P1/2) and Al(2P3/2) became similar at a higher collision energy, 18.5
kJ/mol. These results suggest that the reaction of Al with O2 proceeds via an intermediate complex.
Both spin–orbit states lead to the complex, lose memory of the initial electronic state, and provide
identical rotational distributions. © 2003 American Institute of Physics.
͓DOI: 10.1063/1.1591177͔
͑
͒ϩO X 3⌺Ϫ͒
2
g
2
I. INTRODUCTION
Al P
͑
1/2,3/2
3
→AlO X 2⌺ϩ͒ϩO P ͒
͑
͑
One characteristic of metal atom reactions originates
from the presence of low-lying electronically excited states.
Typical examples are provided by the gas-phase transition
metal atoms which usually have several low-lying electroni-
cally excited states. Once the transition metal atoms interact
with reactant molecules, the potential energy surfaces
evolved from these states couple with one another. There-
fore, information about the interaction among these surfaces
is essential for understanding the reaction dynamics of the
reactions of the transition metal atoms. Since the coupling
between electronic states can be easily mediated by the col-
lisions with nonreactive atoms or molecules, experimental
information derived from multiple collision conditions such
as in flow experiments provides only qualitative knowledge
about the dynamics of the metal atom reactions.
We have studied the reactions of the first row transition
metal atoms with simple molecules, and various important
information has been accumulated.1–5 However, this infor-
mation is more or less qualitative with respect to the inter-
action potential surfaces and dynamics on them because of
the limitation of the experimental technique we used, i.e., the
multiple collisions with buffer gas species. One experimental
approach to obtain detailed information about the interaction
potentials is the crossed-beam technique, which has been ap-
plied for reactions of transition metal atoms.6–8 In order to
extend our previous kinetic studies, a new crossed-beam ap-
paratus has been constructed to study the reaction dynamics
of gas-phase transition metal atoms, and we selected the fol-
lowing reaction as the first system to be studied by this ap-
paratus,
J
⌬rH00ϭϪ14.96 kJ/mol9.
͑1͒
The oxidation reactions of aluminum atoms are of con-
siderable interest in studies of combustion, since aluminum
compounds are frequently used as an ingredient in propellant
formulations.10 However, the interest in combustion is not
centered on reaction ͑1͒ but the oxidation to form much more
stable products, AlO2 and Al2O3 . The exothermic reaction
͑1͒, which is the only possible pathway under single collision
conditions, has a large rate constant at room temperature, and
a negative temperature dependence of the rate constant has
been reported.11 The dynamics of this reaction has also been
studied
from
experimental12–17
and
theoretical
viewpoints.18–20 However, only little information has been
available for the potential energy surface of this reaction un-
til the recent multiconfigurational study carried out by Pak
and Gordon.21
Naulin and Costes have studied this reaction by using a
crossed beam technique combined with the laser-induced
fluorescence detection of product AlO.17 A variable angle
crossed beam apparatus enabled them to determine the reac-
tion cross section as a function of collision energy between
6–255 meV ͑corresponding to the range from 0.6 to 24.6
kJ/mol͒. As expected from the negative temperature depen-
dence of the rate constant, the reaction cross section has been
observed to decrease monotonically with increasing collision
energy. One interesting issue is the reactivity of the excited
spin–orbit state, Al(2P3/2), which lies 112.04 cmϪ1 above
0021-9606/2003/119(7)/3641/9/$20.00
3641
© 2003 American Institute of Physics
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3642
J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Kenji Honma
TABLE I. Summary of the properties of the Al beam.
N͓Al(2P1/2)͔/N͓Al(2P3/2)͔
Ecoll /kJ/mol
Carrier gas
/m/s
v
͗ ͘
Kr
Ar
N2
Ne
610
870
55/45
50/50
90/10
50/50
75/25
55/45
70/30
6.9
9.7
1045
1045
1400
1400
1700
12.2
12.2
18.5
18.5
25.3
25%N2 /He
30%Ne/He
10%N2 /He
4% Mg͒ which was rotated and translated by a stepping mo-
tor. Typical laser intensity was 0.8 mJ/pulse and a 500 mm
focal length lens was used. Vaporized Al atoms were cooled
and issued as an atomic beam by the carrier gas flow ex-
panded from a pulsed valve ͑Jordan PSV, 1.0 mm diam͒. The
oxygen molecular beam was generated from another pulsed
valve ͑General Valve 9-series, 0.5 mm diam͒. Pure oxygen
was used for all measurements. Both beams were collimated
by skimmers ͑Beam Dynamics, 2 mm diam͒ and crossed
each other at a right angle in the reaction chamber. The metal
atomic beam source, the O2 beam source, and the reaction
chamber were pumped by 6 in., 10 in., and 6 in. diffusion
pumps ͑Edwards, Difstak͒, respectively. When both beams
were operated, typical background pressures of the source
chambers and reaction chamber were 1ϫ10Ϫ5 and 4
ϫ10Ϫ6 Torr, respectively.
The Al beam and the reaction product AlO were detected
by the laser-induced fluorescence technique. For detection of
Al, Al(2S–2P1/2,3/2) transitions, 394.513 and 396.265 nm,
were excited by frequency doubled output of a titanium–
sapphire laser ͑Continuum TS-60͒ pumped by a YAG laser
͑Continuum NY-82͒. Total fluorescence was collected by a
lens system and detected by a photomultiplier tube
͑HAMAMATSU R928͒. For the AlO detection, the
AlO(B 2⌺ϩ –X 2⌺ϩ) transition was used for the LIF. The
FIG. 1. Schematic diagram of the crossed-beam apparatus.
the ground spin–orbit state, Al(2P1/2).22 Spin–orbit selective
reactivity was first reported by Chen et al.16 They used a
fluorescence-imaging technique in a crossed-beam experi-
ment and observed that only ground state, Al(2P1/2), reacts
with O2 . This selectivity was explained by an electrostatic
interaction model. Naulin and Costes determined relative
cross sections of two spin–orbit components at various col-
lision energies. They used two carrier gases, N2 and Ne, for
the Al beam. The populations of the two spin–orbit states of
Al are drastically different in these carrier gases while they
provide identical Al mean velocity, i.e., the same collision
energy. The relative cross sections determined under two
conditions were converted to those for two spin–orbit states.
The results showed that the spin–orbit excited state,
Al(2P3/2), reacted with O2 but was less reactive than the
ground state, Al(2P1/2), at low collision energies. The rela-
tive cross section of Al(2P3/2) increased with collision en-
ergy. These results were consistent with the theoretical study
based on the adiabatic capture centrifugal sudden approxima-
tion ͑ACCSA͒ method on the long-range interaction poten-
tial made of the quadrupole–quadrupole and dispersion
interactions.19
⌬ ϭ1 sequence of this transition was excited by a dye laser
v
͑Lambda Physik, SCANmate using LC4700 as a dye͒
pumped by a XeCl excimer laser ͑Lambda Physik, COMPex
100͒. A short wavelength cutoff filter ͑HOYA Y-48͒ was used
to eliminate intense signal from scattered laser photons. After
the filter, the fluorescence was detected by the photomulti-
plier tube. The output of the photomultiplier tube was ampli-
fied by a preamplifier ͑Ortec VT120B͒ and fed into a gated
integrator ͑SRS SR-250͒. The excitation laser intensity was
measured by a fast photodiode and its signal was also aver-
aged by another gated integrator. The averaged signals of the
fluorescence and laser intensity were stored in a computer for
further analysis.
In the present study, we wish to present recent experi-
mental results obtained from our new crossed-beam appara-
tus. Laser-induced fluorescence is applied to detect the prod-
uct AlO. Rotational and vibrational distributions of product
AlO are determined at five collision energies between 6.9
and 25.3 kJ/mol. The product rotational and vibrational dis-
tributions are also determined for two spin–orbit states,
Al(2P1/2) and Al(2P3/2). The latter information is expected
to be sensitive to the interaction potential and reaction
mechanism for each spin–orbit state. Based on these distri-
butions and energy partitioning, the mechanism of reaction
͑1͒ is discussed.
Some properties of the Al beam were determined by us-
ing the LIF detection of atomic transitions. Relative popula-
tions of the two spin–orbit states were determined by the
intensities of the LIF signals for the Al(2S–2P1/2,3/2) transi-
tions. The velocity distribution of the Al beam was deter-
mined by the LIF intensity as a function of the time between
the vaporization laser pulse and the detection laser pulse. The
relative populations of Al(2P1/2,3/2) and mean velocities of
Al are summarized in Table I. The velocity of the O2 beam
was determined by a fast ionization gauge ͑Beam Dynamics,
II. EXPERIMENT
A. Apparatus
The experiment was carried out by using a crossed-beam
apparatus shown in Fig. 1. The apparatus consists of three
parts which are differentially pumped. Al atoms were gener-
ated by laser vaporization. The second harmonic or fourth
harmonic of a YAG laser ͑Spectra Physics GCR-150-10͒ was
focused onto an Al rod ͑99.999% purity Al or Al alloy with
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J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Reaction dynamics of AlϩO2→AlOϩO
3643
FIG. 2. Laser-induced fluorescence
spectrum of AlO formed by the reac-
tion, AlϩO2→AlOϩO. The spectrum
was measured at the collision energy
of 12.2 kJ/mol.
states of AlO23 and also shown in this figure. The spectrum is
similar to those observed by Naulin and Costes at similar
collision energies.14,17
FIG-1͒. The peak velocity of O2 was 760 m/s and the width
was about 7%. Collision energies calculated from velocities
of both beams are also summarized in Table I.
The transition line intensities were converted to the ro-
tational distributions. Because the B–X transition of AlO has
a large absorption coefficient, the effect of saturation of the
absorption must be taken into account. Figure 3 shows the
LIF intensities of AlO as a function of the laser intensity
measured by the photodiode. Measurements were carried out
at the R-head ͓around R(14)] and P(32) line of the 1–0
band. Both intensities showed nonlinear dependence and it is
clear that the absorption of AlO was partially saturated at the
laser intensity used ͑indicated by the arrow in Fig. 3͒. The
effects of the saturation for the population determined by the
LIF measurement have been described by Altkon and Zare
by using the directional Eistein coefficients.24 There might be
some polarization of the rotational angular momentum of the
reaction product, AlO, with respect to a space-fixed frame
under the crossed-beam conditions. However, since no infor-
mation about the polarization is available, we assumed that
the rotational angular momentum of AlO is isotropically dis-
tributed in the space-fixed frame. Under this condition, the
B. AlO in the primary beam
The laser vaporization Al beam source was found to gen-
erate a small amount of AlO. Although several kinds of Al
rods, different purities of Al and alloys with Mg, were tried,
no significant difference was observed. Two wavelengths of
the vaporization laser, 266 and 532 nm, also showed no dif-
ference. An in-line gas purifier ͑Puron 6P-05-N2-N2͒ re-
duced the AlO signal, however its effect was not enough to
eliminate AlO completely. Therefore, we had to eliminate the
contribution of AlO in the Al beam by a subtraction method.
That is, the O2 beam was operated with 5 Hz, while the Al
beam containing a small amount of AlO was operated with
10 Hz. The 5 Hz signal synchronized with the O2 beam and
that synchronized without O2 were averaged independently
by two gated integrators and accumulated by a computer.
The difference of two spectra was obtained by simple sub-
traction. Because AlO in the Al beam is populated in low
rotational levels of the vibrational ground state, the subtrac-
tion was essential to determine the distribution of these lev-
els.
III. RESULTS
A. LIF spectra of AlO„B 2⌺¿ –X 2⌺¿…
and rotational-vibrational distribution
A typical LIF spectrum of AlO is shown in Fig. 2. This
spectrum was obtained by the subtraction method described
in the previous section. The collision energy for this spec-
trum was 12.2 kJ/mol and vibrational levels of AlO up to
v
ϭ2 are energetically accessible. Assignment of each line
was given by spectroscopic constants available for B and X
FIG. 3. The intensities of LIF measured as a function of laser intensity.
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3644
J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Kenji Honma
relationship between the rotational state population and the
LIF intensity can be derived from the rate equation approach
based on a two-level model, which is described in the Ap-
pendix. As described in the Appendix, the population of the
J th rotational state, N , divided by its degeneracy, 2J
ϩ1, is related to the LIF intensity, ILIF , of the P or R branch
Љ
Љ
J
Љ
by the following equations:
NJ
ILIF
Љ
For the P-branch:
For the R-branch:
ϰ
ϰ
;
n
2J ϩ1
Љ
J ␳
Љ
NJ
ILIF
Љ
.
n
2J ϩ1
Љ
J ϩ1͒␳
Љ
͑
Here, ␳ is the density of radiation, and ILIF has the nth power
dependence on ␳, i.e., nϭ1 corresponds to linear depen-
dence and nϭ0 corresponds to the full saturation condition.
These equations indicate that the saturation of absorption
affects only the dependence of ILIF /J or ILIF /(J ϩ1) on
Љ
Љ
the radiation density, ␳. Because the variation of the laser
intensity is small over the LIF spectrum in the present study,
NJ /(2J ϩ1) is proportional to I /J ͑for the P-branch͒
Љ
Љ
LIF
Љ
or ILIF /(J ϩ1) ͑for the R-branch͒, no matter how the ab-
Љ
sorption is saturated.
At each collision energy, several spectra were measured
and averaged rotational distributions are summarized in Fig.
4. Except for the lowest collision energy, 6.9 kJ/mol, the
vibrational level of ϭ2 is energetically possible. ( ϭ3 is
v
v
also possible for the highest collision energy.͒ However, just
the rotational distributions of ϭ0 and 1 are shown in this
v
FIG. 4. Rotational state distributions of AlO ( ϭ0 and 1͒ formed by the
v
reaction, AlϩO2→AlOϩO. Collision energies were 6.9 kJ/mol ͓͑a͒ and
͑b͔͒, 9.7 kJ/mol ͓͑c͒ and ͑d͔͒, 12.2 kJ/mol ͓͑e͒ and ͑f͔͒, 18.5 kJ/mol ͓͑g͒ and
͑h͔͒, and 25.3 kJ/mol ͓͑i͒ and ͑j͔͒.
figure, because not enough transitions were observed for the
rotational state distribution of ϭ2. Also shown in this fig-
v
ure are rotational distributions expected from statistical en-
ergy partitioning which were estimated by N0( ,J)ϰ(2J
v
ϩ1)(EavϪEvϪEr)1/2, where Eav , Ev , and Er are total
available energy of reaction, vibrational energy of AlO, and
its rotational energy, respectively. Rotational distributions
determined at several collision energies summarized in this
figure are quite similar each other. At all collision energies,
the populations were observed until the highest energetically
possible rotational levels. The observed rotational distribu-
tions have a little more population in low rotational levels
and relatively less population in high rotational levels than
N0( ,J) in both vibrational states, ϭ0 and 1.
tions of vibrational states as adjustable parameters. In this
analysis, the rotational distributions of all vibrational states
were assumed to be characterized by a single surprisal pa-
rameter, ␪, and the distribution was given by P( ,J)ϰ(2J
v
ϩ1)(EavϪEvϪEr)1/2 exp(Ϫ␪Er). The Franck–Condon fac-
tors were taken from the calculation by Michels.25
One example of the simulated spectrum is shown in Fig.
5. This observed spectrum was measured for Al with 30% Ne
in He of the carrier gas, i.e., 18.5 kJ/mol of collision energy.
The best fit surprisal parameter was ␪ϭ1.3, slightly non-
v
v
In Figs. 3͑e͒, 3͑f͒, 3͑g͒, and 3͑h͒, the rotational distribu-
tions determined for two different Al conditions are shown.
Under these conditions, the relative populations of two spin–
orbit states of Al are different, while the collision energies
are identical. It is clear that no remarkable difference of ro-
tational distribution is seen between the two Al beam condi-
tions.
In the analysis applied to obtain the rotational distribu-
tion, each rotational line was identified and its intensity was
converted to the population. However, several rotational
lines, especially the transitions originating from low rota-
tional states, were so congested that their intensities could
not be obtained directly from the peak height. In order to
determine the vibrational distribution, the observed spectra
were simulated by using the surprisal parameter and popula-
statistical, and relative populations of ϭ0, 1, and 2 levels
were 1.00, 0.27, and 0.06, respectively. Again several spectra
were analyzed and vibrational populations were averaged.
v
B. Energy partitioning
Rotational and vibrational energy partitions are summa-
rized in Table II and Fig. 6. Averaged rotational and vibra-
tional energies based on the statistical energy partitioning are
also shown in this table and figure. The observed rotational
energies were around 30% of the available energies at low
collision energies, and decreased to about 20% at the highest
collision energy. These results were common for ϭ0 and 1
v
vibrational states. On the other hand, those expected from the
statistical energy partitioning were 40% at all collision ener-
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J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Reaction dynamics of AlϩO2→AlOϩO
3645
FIG. 5. Observed and simulated spec-
tra of AlO. The measurement was car-
ried out at 18.5 kJ/mol of collision en-
ergy and the spectrum was simulated
for the available energy of 2800 cmϪ1
.
gies. As expected from the rotational state distribution, the
energy partitioning into rotation of AlO is lower than statis-
tical.
energy. At all collision energies, the vibrational energy par-
titioning observed was slightly smaller than statistical.
The observed vibrational energies were around 10% of
the total available energy and showed no strong dependence
on the collision energy. The statistical energy partitioning
predicts that slightly greater energy goes into the vibrational
motion of AlO and the branching increases with the collision
C. Rotational state distribution for each spin–orbit
state
As we described in the Introduction, an understanding of
the reactivity of the two spin–orbit states of Al, Al(2P1/2
)
TABLE II. Summary of energy partition.
30%Ne/
He
25%N2 /
He
10%N2 /
He
Carrier gas
Kr
Ar
Ne
N2
6.9
21.9
9.7
24.7
12.2
27.2
12.2
27.2
18.5
33.5
18.5
33.5
25.3
40.3
Ecoll ͑kJ/mol)
Eavail ͑kJ/mol)
N
1/2 :N3/2
55:45
50:50
50:50
90:10
73:27
54:46
70:30
E
Obs. 617Ϯ29
͑33.7%͒
681Ϯ68
͑33.0%͒
828
677Ϯ50
͑29.8%͒
911
668Ϯ41
͑29.4%͒
911
711Ϯ30
͑25.4%͒
1120
734Ϯ32
͑26.2%͒
1120
783Ϯ23
͑23.3%͒
1352
͗
͘
vϭ0
rot
cmϪ1
PDa
735
͑40.1%͒
ϭ1 Obs. 264Ϯ14
͑30.5%͒
͑40.1%͒
346Ϯ62
͑31.5%͒
441
͑39.6%͒
40Ϯ2
͑27.3%͒
58
͑39.6%͒
0.33Ϯ
0.05
͑40.1%͒
396Ϯ26
͑30.4%͒
521
͑39.9%͒
115Ϯ9
͑32.5%͒
142
͑40.2%͒
0.26Ϯ
0.04
0.44
0.017Ϯ
0.008
͑40.1%͒
404Ϯ17
͑31.0%͒
521
͑39.9%͒
113Ϯ13
͑32.0%͒
142
͑40.2%͒
0.25Ϯ
0.04
0.44
0.019Ϯ
0.001
͑40.0%͒
556Ϯ29
͑30.3%͒
735
͑40.0%͒
285Ϯ9
͑32.3%͒
353
͑40.0%͒
0.35Ϯ
0.05
0.54
0.072Ϯ
0.004
͑40.0%͒
545Ϯ57
͑29.7%͒
735
͑40.0%͒
284Ϯ13
͑32.2%͒
353
͑40.0%͒
0.29Ϯ
0.04
0.54
0.051Ϯ
0.012
͑40.2%͒
543Ϯ45
͑22.6%͒
964
͑40.1%͒
421Ϯ11
͑29.0%͒
581
͑40.1%͒
0.35Ϯ
0.05
0.61
0.072Ϯ
0.004
v
v
PDa
ϭ2 Obs.
PDa
347
͑40.1%͒
¯
¯
N
vib /N0
Obs.
PDb
0.21Ϯ
0.05
0.33
¯
ϭ1
v
v
0.39
0.012Ϯ
0.008
ϭ2 Obs.
PDb
Obs.
¯
0.019
0.063
0.063
0.18
0.18
0.29
E
167Ϯ34
͑9.1%͒
238
247Ϯ23
͑12.0%͒
294
228Ϯ35
͑10.0%͒
362
225Ϯ26
͑9.9%͒
362
264Ϯ50
͑9.4%͒
502
267Ϯ50
͑9.5%͒
502
336Ϯ16
͑10.0%͒
670
͗
͘
vib
cmϪ1
PDa
͑13.0%͒
͑14.3%͒
͑16.0%͒
͑16.0%͒
͑17.9%͒
͑17.9%͒
͑19.9%͒
aAverage energy appears as the product rotation or vibration calculated by statistical energy partitioning.
bStatistical vibrational population.
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3646
J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Kenji Honma
vide both states. The relative populations of the two states
can be determined by the LIF of Al, and then one can convert
the cross sections determined by using two different carrier
gases, one containing N2 and the other without N2 , to those
for two spin–orbit states.
We have applied this technique to determine the rota-
tional state distributions for two spin–orbit states. The popu-
lations of each rotational state determined using two different
Al beam conditions, N(J,A) and N(J,B), can be given in
terms of the populations of two spin–orbit states at these
beam conditions, P1/2(A), P3/2(A), P1/2(B), and P3/2(B),
and the rotational populations generated from two spin–orbit
states, N1/2(J) and N3/2(J), by the following equation:
P1/2 A͒P A͒
͑
͑
3/2
N J,A͒
N J,B͒
͑
N1/2 J͒
͑
N3/2 J͒
͑
͑
ϭ
.
͑2͒
ͩ
ͪ
ͩ
ͪ
ͩ
ͪ
P1/2 B͒P B͒
͑
͑
3/2
Therefore, the rotational populations determined experimen-
tally can be converted to those for the spin–orbit states by
Ϫ1
P1/2 A͒P A͒
͑
͑
N1/2 J͒
N J,A͒
͑
N J,B͒
͑
͑
3/2
ϭ
.
͑3͒
ͩ
ͪ
ͩ
ͪ
ͩ
ͪ
N3/2 J͒
͑
P1/2 B͒P B͒
͑
͑
3/2
Measurements were carried out at two collision energies,
12.2 and 18.5 kJ/mol. Two carrier gases were used at each
collision energy. As already shown in Table I, pure Ne and
pure N2 provided identical mean velocity of Al with different
FIG. 6. Summary of energy partitioning into rotation (fr) and vibration (fv)
of AlO.
populations of the spin–orbit states, i.e., Al(2P1/2)/Al(2P3/2
)
is 50/50 in Ne or 90/10 in N2 . Ne and N2 were diluted by He
to increase the mean velocity. These mixtures again provided
two substantially different populations of the two states, i.e.,
Al(2P1/2)/Al(2P3/2) is 55/45 in Ne/He or 75/25 in N2 /He.
Because the populations of spin–orbit states were slightly
different from day to day, they were measured prior to and
after the LIF spectrum measurements of the reaction product
AlO. Several measurements were averaged and results are
summarized in Fig. 7. Also shown in these figures are the
ratios of N3/2(J)/N1/2(J) as a function of rotational energy.
and Al(2P3/2), is needed to clarify the mechanism of reaction
͑1͒. Experimentally, Naulin and Costes have opened the way
to determine the cross sections for specific spin–orbit
states.17 The laser vaporization generates both spin–orbit
states, however the carrier gas containing N2 effectively
quenches the excited Al(2P3/2) state. Therefore, the Al beam
of N2 containing carrier gas is expected to provide mostly
the ground state Al(2P1/2). Since rare gases are not efficient
to quench the excited state, the Al beams of rare gases pro-
FIG. 7. Rotational state distributions
of AlO formed by the reaction,
Al(2P1/2,3/2)ϩO2→AlOϩO. Collision
energies were 12.2 kJ/mol ͓͑a͔͒ and
18.5 kJ/mol ͓͑c͒ and ͑e͔͒. Also shown
are ratios of rotational populations
formed from the two spin–orbit com-
ponents, N1/2 /N3/2
.
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J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Reaction dynamics of AlϩO2→AlOϩO
3647
At the collision energy of 12.2 kJ/mol, the rotational
populations of AlO from the higher energy Al(2P3/2) are
systematically lower than those from the ground state,
Al(2P1/2). However, there is no significant difference be-
sured the contribution of the inelastic collisions with NO
which is unreactive with Al. Only a little change was ob-
served in the LIF spectrum of AlO when the NO beam was
crossed with the AlO containing Al beam. Since this change
was negligible compared with the original AlO signal, we
concluded that the inelastic collisions have negligible effect.
tween the rotational distributions for Al(2P1/2
)
and
Al(2P3/2). The similarity of the distributions is also clear in
Fig. 6͑b͒. The ratios seem to remain almost constant in spite
of large fluctuations. The averaged ratio was 0.33Ϯ0.11,
which is consistent with the ratio of reaction cross sections
for two spin–orbit states determined by Naulin and Costes at
the same collision energy.17 At higher collision energy, 18.5
kJ/mol, the rotational distributions were also quite similar
each other ͓Figs. 6͑c͒ and 6͑e͔͒. The averaged ratios of
2
2
B. Rotational distribution for Al„ P1Õ2… and Al„ P3Õ2
…
and the reaction mechanism
The rotational distributions discussed above were those
for the reaction products from the mixed reactants, Al(2P1/2
)
and Al(2P3/2). The interaction potentials for these two states
have been suggested to be different,19 and the product state
distribution for each state is expected to provide more de-
tailed information about the reaction mechanism. The results
are summarized in the following:
N3/2(J)/N1/2(J) are 0.96Ϯ0.60 and 0.98Ϯ0.73 for ϭ0 and
v
1 vibrational levels, respectively. The increase of these ratios
with the collision energy is also consistent with the results
obtained by Naulin and Costes.
͑1͒ The rotational distributions are quite similar to each
other for Al(2P1/2) and Al(2P3/2) at two different colli-
sion energies, 12.2 kJ/mol and 18.4 kJ/mol;
͑2͒ The relative reactivity of the two components depends
on the collision energy. At lower collision energy, 12.2
kJ/mol, Al(2P1/2) is about three times more reactive than
Al(2P3/2), while their reactivities are comparable at a
collision energy of 18.5 kJ/mol.
IV. DISCUSSION
A. Energy partitioning
The rotational and vibrational state distributions for re-
action ͑1͒ were first determined by Dagdigian et al.13 The
LIF method was applied in a beam-gas arrangement and the
internal state distributions were compared with those calcu-
lated from phase space theory. They concluded that the par-
titioning of energy was not completely statistical at a mean
collision energy of 12.6 kJ/mol. Pasternack and Dagdigian
also studied the same reaction by using a velocity-selected
beam condition and observed a significant deviation from
statistical energy partitioning in product rotation at three col-
lision energies from 4.2 to 35.1 kJ/mol.12 The surprisal pa-
The second result is consistent with the observation by Nau-
lin and Costes.17 They determined the relative cross sections
for two components by measuring band heads of the AlO
transition. They observed that Al(2P1/2) is more reactive
than Al(2P3/2) at low collision energies while their cross
sections become comparable each other at high collision en-
ergies. Our result again confirms that the excited spin–orbit
state does react with O2 but is less reactive at low collision
energy. More importantly we observed that the rotational dis-
tributions for the two spin–orbit states are very similar at
low and high collision energies. That is, at low collision
energy, the difference between the two spin–orbit states ap-
pears only in their reactivity, and the rotational distribution
does not depend on the initial spin–orbit state.
rameters they determined for ϭ0 and 1 levels were nega-
v
tive, which indicated that the experimental rotational
distribution populates lower rotational levels than expected
statistically. In their crossed-beam study, Costes et al. ob-
served completely statistical energy partitioning at low colli-
sion energies, 8.0 and 18.3 kJ/mol, and a slight deviation
from the statistical prediction at higher collision energies,
28.0 and 47.3 kJ/mol.
The energy partition determined in the present study
shows that both rotational and vibrational energies of AlO
are a little lower than those expected from statistical energy
partitioning. This result agrees with the observation by Pas-
ternack and Dagdigian. The rotational energy partitioning de-
termined here was around 30%, which is the same as their
value. Although the rotational energy partitioning determined
by Costes et al. was slightly higher at low collision energies,
35% and 33%, the difference seems to be minor. At higher
collision energies, the present results are consistent with
those of Costes et al., i.e., the energy partitioning deviates
from the statistical expectation. One possible explanation for
the minor discrepancy between our results and those of
Costes et al. might be inelastic collisions of AlO in the Al
beam in our experiment. The rotationally inelastic collisions
of AlO in the Al beam may contaminate the population of
low rotational states. Because O2 is reactive with Al to form
AlO, it is difficult to estimate the effect of the rotational
inelastic collision with O2 directly. Instead of O2 , we mea-
The different reactivity of the two spin–orbit states has
been explained by the long-range interaction potential con-
sisting of the quadrupole–quadrupole and the dispersion
interactions.18,19 In the case of Al(2P1/2), the reaction is con-
trolled by dispersion forces, which are attractive and lead to
barrierless reaction at any collision energy. On the other
hand, the reaction of Al(2P3/2) is dominated by the electro-
static quadrupole–quadrupole interaction at very low colli-
sion energy while it is controlled by dispersion forces at
higher energy. For the quadrupole–quadrupole interaction,
the potential depends on the orientation of the approach of Al
to O2 , i.e., collinear approach leads to an entirely repulsive
interaction for Al(2P3/2) and this repulsive interaction is re-
duced by changing the orientation from collinear to bent. The
lower reactivity of Al(2P3/2) is ascribed to this steric factor
in the interaction potential. Based on this model, it could be
expected that the difference of the entrance channel between
two spin–orbit states lead the difference in the product rota-
tional state distribution. However, the results we observed
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3648
J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Kenji Honma
show no substantial difference between the rotational distri-
butions for Al(2P1/2) and Al(2P3/2). One reasonable expla-
nation is the occurrence of an intermediate complex in the
course of reaction ͑1͒. This intermediate complex might be
formed for Al(2P1/2) for any orientation of approach while
only a limited range of orientations can lead to the interme-
diate for Al(2P3/2). Although the limited range orientations
of reactive encounters for Al(2P3/2) leads to lower reactivity,
the system loses memory of the formation of the intermedi-
ate complex, and provides the same rotational distribution
for both spin–orbit states of Al.
According to the long-range interaction model, the dis-
persion interaction becomes dominant for both Al(2P1/2) and
Al(2P3/2) at high collision energy.18,19 The attractive interac-
tion for both states leads to the intermediate complex and the
reaction again loses memory of the initial state in the com-
plex. Therefore, it is reasonable that both the rotational dis-
tribution and reactivity become similar for the two spin–
orbit states at high collision energy.
and Dr. Christian Naulin at the Universite de Bordeaux, and
also thanks Dr. Yo Fujimura at Kyoto University for his help-
ful suggestion in the analysis of the LIF spectra.
APPENDIX: THE LIF INTENSITY FOR PARTIALLY
SATURATED ABSORPTION
In the two-level model consisting of lower level 1 and
upper level 2, the rate equation for the population of the level
2, N2 , is given by the equation,
dN2
ϭB ␳N Ϫ B ␳ϩA ͒N ,
͑A1͒
͑
12
1
21
21
2
dt
where N1 , N2 , ␳, B12 , B21 , and A21 are the populations of
levels 1 and 2, the density of radiation, the integrated Ein-
stein coefficients for absorption, stimulated emission, and
spontaneous emission, respectively. In the transition from the
level of rotational quantum number, Ji to Jj , Bij is expressed
¨
by the Honl–London factor, Sij , as
kSij
kSij
gi
The formation of the intermediate complex is consistent
with the potential energy surface calculated recently by Pak
and Gordon.21 According to their calculation, two doublet
Bijϭ
ϭ
.
͑A2͒
2Jiϩ1
Here, gi is the degeneracy of the Ji level and k
ϭ2␲2R2/3⑀0h2 ͑R is the vibrational and electronic part of
the transition moment, h is the Planck constant, ⑀0 is the
permittivity of vacuum͒.26 Then the rate Eq. ͑A1͒ is given by
2
2
potential surfaces, A1 and A2 , have global minima at a
cyclic AlO2 structure while no reaction path leading from
AlϩO2 directly to AlOϩO is located. From the viewpoint of
energy randomization, formation of the intermediate com-
plex may not be consistent with the energy partitioning we
observed. If the energy randomizes completely within the
complex, the energy partitioning is expected to be statistical.
Our results showed a little deviation from statistical energy
partitioning, and it might suggest the existence of an exit
channel interaction between departing products or short life-
times of the complex.
dN2 kSij
kSji
gj
ϭ
␳N Ϫ
␳ϩA21 N .
͑A3͒
ͩ
ͪ
1
2
dt
gi
By using the relation of SijϭSji , and neglecting the contri-
bution of spontaneous emission which is small compared to
the stimulated emission under the saturation condition, the
rate equation can be integrated for the rectangular pulse du-
ration, ⌬t. The result under the condition of N2(tϭ0)ϭ0 is
the following:
V. SUMMARY
g2
g1ϩg2
N2ϭN
1Ϫexp Ϫ
S ␳k⌬t
.
͑A4͒
ͫ
ͩ
ͪ
ͬ
12
The reaction of Al with O2 was studied by using a
crossed-beam technique at five collision energies. The rota-
tional and vibrational distributions of the product AlO were
determined from the LIF spectra of the AlO(B 2⌺ϩ –X 2⌺ϩ)
transition. The energy partitioning into the rotation and vi-
bration of AlO was observed to be a little lower than that
expected from the statistical model. The rotational state dis-
tributions of AlO were determined for the first time for two
spin–orbit components of Al, Al(2P1/2) and Al(2P3/2). The
relative reactivity of these components was different at low
collision energy, however their product rotational distribu-
tions were observed to be almost identical. Their reactivities
and rotational distributions became similar at higher collision
energy. These results suggest that the reaction proceeds via
an intermediate complex in which the initial condition such
as an orientation of approach is lost and the available energy
randomizes almost completely.
g1ϩg2
g1g2
Here, NϭN1ϩN2 is the population of the molecule initially
prepared in the lower level. The LIF intensity is proportional
to the population of the upper level, N2 , then given by
g2
g1ϩg2
I
LIFϭcN
1Ϫexp Ϫ
S ␳k⌬t
12
,
͑A5͒
ͫ
ͩ
ͪ
ͬ
g1ϩg2
g1g2
where c is the propotionality constant determined by experi-
mental conditions. In the two extreme cases, the absorption
is fully saturated or depends linearly on the radiation density,
and the equation is reduced to the following equations, re-
spectively:
g2
I
I
LIFϭcN
,
͑A6͒
͑A7͒
g1ϩg2
NS12␳k⌬t
LIFϭc
.
g1
ACKNOWLEDGMENTS
In the intermediate case, the dependence of the LIF
intensity may be approximated as ␳n, where n changes
from 0 to 1. This corresponds to the replacement of the
This research was supported by Grants ͑Contract Nos.
12440168 and 14340186͒ from the Ministry of Education,
Science, Sports, and Culture. The author also acknowledges
helpful discussions and comments from Dr. Michel Costes
factor
1 Ϫ exp Ϫ (g ϩ g )S ␳k⌬t/g g
by
(g
͕
1
͓
͔
͕
͖
1
2
12
1
2
ϩg2)S12␳k⌬t/g1g2 n, then ILIF is given by
͖
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J. Chem. Phys., Vol. 119, No. 7, 15 August 2003
Reaction dynamics of AlϩO2→AlOϩO
3649
2 K. Honma, M. Nakamura, D. E. Clemmer, and I. Koyano, J. Phys. Chem.
98, 13286 ͑1994͒.
n
g2
g1ϩg2
I
LIFϭcN
ϭc
S ␳k⌬t
12
ͩ
ͪ
g1ϩg2 g1g2
3 K. Senba, R. Matsui, and K. Honma, J. Phys. Chem. 99, 13992 ͑1995͒.
4 R. Matsui, K. Senba, and K. Honma, J. Phys. Chem. A 101, 179 ͑1997͒.
5 C. L. Haynes and K. Honma, J. Chem. Soc., Faraday Trans. 94, 1171
͑1998͒.
1Ϫn
N
g1g2
S ␳k⌬t͒n.
͑A8͒
͑
ͩ
ͪ
12
g1 g1ϩg2
6 P. A. Willis, H. U. Stauffer, R. Z. Hinrichs, and H. F. Davis, J. Chem.
Phys. 108, 2665 ͑1998͒; Rev. Sci. Instrum. 70, 2606 ͑1999͒.
7 P. Luc and R. Vetter, J. Chem. Phys. 115, 11106 ͑2001͒.
8 R. Vetter, C. Naulin, and M. Costes, Phys. Chem. Chem. Phys. 2, 643
͑2000͒; C. Naulin, I. M. Hedgecock, and M. Costes, Chem. Phys. Lett.
266, 335 ͑1997͒.
For the B 2⌺–X 2⌺ transition of AlO, S12 for P and
R-branches are approximated by J and J ϩ1, respectively.
Then Eqs. ͑A6͒–͑A8͒ are given for the P-branch in the fol-
Љ
Љ
lowing:
9 Derived from D00(O–O)ϭ5.114 eV ͓K. P. Huber and G. Herzberg, Mo-
N
g1g2
N
2J ϩ1͒ 2J Ϫ1͒
J N
͑
͑
Љ
Љ
Љ
I
LIFϭc
ϭc
Ϸc
,
lecular Spectra and Molecular Structure, Constants of Diatomic Mol-
g1 g1ϩg2
g1
4J
g1
Љ
ecules ͑van Nostrand, New York, 1979͔͒ and D00(Al–O)ϭ5.27 eV ͓C.
͑A9͒
Naulin and M. Costes, Chem. Phys. Lett. 310, 231 ͑1999͔͒.
10 P. Politzer, P. Lane, and M. E. Grice, J. Phys. Chem. A 105, 7473 ͑2001͒.
11 S. D. Le Picard, A. Canosa, D. Travers, D. Chastaing, B. R. Rowe, and T.
Stoecklin, J. Phys. Chem. A 101, 9988 ͑1997͒; N. L. Garland and H. H.
Nelson, Chem. Phys. Lett. 191, 269 ͑1992͒.
J N
Љ
I
I
LIFϭc
LIFϭc
Ϸc
␳k⌬t,
͑A10͒
g1
1Ϫn
12 L. Pasternack and P. J. Dagdigian, J. Chem. Phys. 67, 3854 ͑1977͒.
13 P. J. Dagdigian, H. W. Cruse, and R. N. Zare, J. Chem. Phys. 62, 1824
͑1975͒.
N
2J ϩ1͒ 2J Ϫ1͒
͑
͑
Љ
Љ
n
J ␳k⌬t͒
͑
Љ
ͩ
ͪ
g1
4J
Љ
14 M. Costes, C. Naulin, G. Dorthe, C. Vaucamps, and G. Nouchi, Faraday
Discuss. Chem. Soc. 84, 74 ͑1987͒.
N
J N
Љ
1Ϫn
J ͒
Љ
J ␳k⌬t͒nϭc
␳k⌬t͒n.
͑
͑A11͒
͑
͑
Љ
g1
g1
15 C. Naulin and M. Costes, J. Phys. Chem. 98, 5593 ͑1994͒.
16 K.-M. Chen, C.-H. Sung, J.-L. Chang, T.-H. Chung, and K.-H. Lee, Chem.
Phys. Lett. 240, 17 ͑1995͒.
Since the electronic and vibrational transition moment and
the pulse width of the laser are constant, the LIF intensity for
the P-branch is given by Eq. ͑A12͒,
17 C. Naulin and M. Costes, Chem. Phys. Lett. 310, 231 ͑1999͒.
18 D. Reignier, T. Stoecklin, S. D. Le Picard, A. Canosa, and B. R. Rowe, J.
Chem. Soc., Faraday Trans. 94, 1681 ͑1998͒.
J N
Љ
19 T. Stoecklin, Faraday Discuss. 110, 231 ͑1998͒.
I
LIFϭC0
␳n,
͑A12͒
20 P. Marchall, P. B. O’Connor, W.-T. Chan, P. V. Kristof, and J. D. Goddard,
in Gas-Phase Metal Reactions, edited by A. Fontijn ͑North–Holland, Am-
sterdam, 1992͒, Chap. 8, p. 147.
g1
where C0ϭc(k⌬t)n. A similar derivation is applied for the
LIF transition of the R-branch and the LIF intensity is given
by Eq. ͑A13͒,
21 M. V. Pak and M. S. Gordon, J. Chem. Phys. 118, 4471 ͑2003͒.
22 C. E. Moore, Atomic Energy Levels, NSRDS-NBS 35 ͑U.S. GPO, Wash-
ington, D.C., 1971͒, Vol. 1.
J ϩ1͒N
Љ
23 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure,
Constants of Diatomic Molecules ͑van Nostrand, New York, 1979͒.
24 R. Altkorn and R. N. Zare, Annu. Rev. Phys. Chem. 35, 265 ͑1984͒.
25 H. H. Michels, J. Chem. Phys. 56, 665 ͑1972͒.
͑
I
LIFϭC0
␳n.
͑A13͒
g1
26 See, for example, P. F. Bernath, Spectra of Atoms and Molecules ͑Oxford
University Press, Oxford, 1995͒.
1 D. E. Clemmer, K. Honma, and I. Koyano, J. Phys. Chem. 97, 11480
͑1993͒.
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