Determination of nitrogen atoms heterogeneous recombination probabilities γN
by the use of TALIF atomic concentration profiles at surfaces vicinity
B. Rouffet3, F. Gaboriau1,2 and J.P. Sarrette1,2
1
Université de Toulouse; UPS, INPT; LAPLACE (Laboratoire Plasma et Conversion d'Energie);
118 route de Narbonne, F-31062 Toulouse cedex 9, France.
2
CNRS; LAPLACE; F-31062 Toulouse, France
3
Laboratoire d’Electronique des Gaz et des Plasmas, Université de Pau et des Pays de l’Adour, 64000 Pau, France
Abstract: Atomic nitrogen recombination probabilities (γN) are presented for different materials. They were obtained in late afterglow conditions through comparison between local
measurements of the nitrogen atom density with the TALIF technique and atomic concentration profiles calculations obtained with a 3D-CFD code at the vicinity of the substrates. For
each of the studied materials, an inverse pressure dependence was found.
Keywords: Atomic recombination probabilities, nitrogen, afterglow, TALIF.
1. Presentation
In flowing afterglow treatment reactors operating at reduced pressure (1 – 30 torr), the spatial distribution of the
atomic species is governed by the heterogeneous recombination processes (on reactor walls and on substrates),
characterized by the recombination probability γ.
The surface recombination processes were extensively
studied in the past but the methods used were either based
on non-local N-atom concentration measurements (afterglow spectroscopy, mass spectrometry) [1-3] or based on
indirect data such as the wall temperature increase due to
the heat deposited by the exothermic wall recombination
[4-5]. This can explain the large discrepancies in the γ
values published in the literature and the lack of knowing
of the γ variations with the operating parameters (pressure, gas temperature, wall temperature), even for the
most commonly used materials.
This paper presents a method for obtaining the atomic
nitrogen recombination probabilities (γN) on different
materials in late afterglow conditions. It is based on the
comparison between direct local measurements of the
nitrogen atoms density using the TALIF (Two-photon
Absorption Laser Induced Fluorescence) technique and
calculations of atomic density profiles at the vicinity of
the substrates submitted to the afterglow flow. (Fig. 1)
The presented method is close to the one proposed by
Adams and Miller for a parallel plate rf discharge reactor.
[6]
2. Experimental setup (Fig. 1)
2.1. Flowing afterglow
A cylindrical Pyrex reactor (φ = 160 mm, h = 300 mm)
is filled with pure nitrogen at controlled mass flow rates
in the range (0.1-3.0 Nl/min). The vacuum in the chamber
is obtained through a primary pump (Edwards two stage
rotary vane pump 30 m3 h-1) and the pressure is regulated
by a valve allowing to modify the diameter of the pumping orifice.
The discharge is created with a microwave surfatron
generator working at a frequency of 2450 MHz for an
injected power adjustable between 50 and 300 W.
The length L of the discharge tube (quartz, φι = 5 mm)
can also be modulated between 20 and 60 cm in order to
reach different afterglow conditions [7]. All the results
presented in the present paper were obtained with L = 35
cm and for pressures higher than 5 torr, providing full late
afterglow conditions.
The connection between the discharge tube and the reactor is realized through an injector (quartz, φι = 19 mm, l
= 92 mm) ensuring a correct mixing between the afterglow flow and the Ar/2%NO injection during NO titration
[8].
The top of the reactor is a removable window which
allows the installation of plates (10 cm x 10 cm, t = 5
mm) of different materials on four Pyrex supports.
P
M
Narrow band filter
and lenses
Fluorescence
signal
746 nm
Pressure
gauge
Ar - 2% NO
inlet for titration
Mass flow
controller
Laser
windows
L
Plate of the
studied material
Laser
axis
Micro-wave
generator
(surfatron)
2.45 GHz
To
primary
pump
N2 inlet
Computerized
detection
system
Optical fibre
Fig. 1 : Schematic diagram of the flowing afterglow and of
the fluorescence detection systems used for TALIF measurements.
In the direction perpendicular to the laser beam, the size
of the excitation volume is about the size of the beam (≅ 1
mm). As the radial and axial evolutions of the fluorescence signal are similar (Fig.3), one can infer that the
axial extension of the excitation volume is also about 1
mm. This spatial resolution is sufficient enough to obtain
a precise mapping of the atomic concentrations, even near
the walls, where density profiles are more pronounced.
0,009
Along the laser
beam axis
Perpendicularly to
the laser beam axis
0,008
Fluorescence signal (au)
2.2. TALIF
Laser-induced fluorescence is based on the forced transition from a low state of energy E1 of a given species
(atom or molecule) to a radiative higher energy state E2
with a laser tuned to the wavelength equal to the difference in energy between the two states (∆Eexc = E2 - E1 = h
νlaser). The fluorescence signal is emitted during the radiative desexcitation of the E2 state to a third state of lowest
energy E3 (∆Efluo = E2 - E3 = hνfluo).
The duration of the laser pulse (8 ns) being much shorter
than the lifetime of the excited state E2, the mechanisms
of population and depopulation of this state can be temporally separated, allowing the determination of the concentrations of the excited state E2 and of the initial state E1,
often identified with the ground state of the chemical species.
The intensity of the fluorescence signal, directly proportional to the density of the ground state, is usually observed in an optical axis different from the incident laser
beam.
0,007
0,006
0,005
0,004
0,003
0,002
0,001
0,000
-6
N(3p) 4S3/2
96750.81 cm-1
N(3s) 4P5/2,3/2,1/2
206.65 nm
97945.97 cm-1
742-747 nm
826.3 nm
Kr(5s ’) [1/2]1
204.13 nm
204.13 nm
N(2p3) 4S3/2
0 cm-1
-2
0
2
4
6
Fig. 3 : Axial and radial evolutions of the fluorescence signal.
85847.50 cm-1
83364.62 cm-1
83317.83 cm-1
83284.07 cm-1
206.65 nm
-4
Shift from the focal point (cm)
Kr(5p’) [3/2]2
Kr(4p6) 1S0
0 cm-1
Fig. 2 : Energy levels of the two-photon excitation and fluorescence mechanisms of atomic nitrogen and krypton.
Unlike classical spectroscopic methods, only providing
information on the population of the radiative states, LIF
methods give access to ground states densities. They also
have the advantage of high temporal and spatial resolutions, the laser energy being deposited in a defined volume more or less controllable.
However, when the excitation threshold (energy of the
first radiative state) is large (greater than 6 eV), which is
the case for most of the light atoms (H, N, O), the excitation wavelength of the laser requires the use of VUV
photons (λ<200 nm), more complex to use (absorbed by
the air they require to be transported in a nitrogen atmosphere). It is then preferable to use the TALIF technique,
associated with a 2-photon excitation scheme (Fig. 2),
whose wavelengths are greater than 200 nm [9].
In the laser system used in this work, the second harmonic of a Nd-YAG laser (532 nm) was used to pump a
dye laser (619 nm). This output frequency was tripled by
two non-linear crystals (BBO and KDP) to obtain the excitation wavelength at 206.65 nm. The laser beam (of
pulse energy about 50 µJ) was then focused into the afterglow reactor, equipped with 8 Brewster angle windows at
different heights to allow the passage of the laser beam
without reflection. The fluorescence signal is collected
perpendicularly to the laser beam, passed through a narrow band filter (to avoid interferences with the natural
radiation of the afterglow) and focused by two lenses on
the entrance slit of a HAMAMATSU (R 928) PMT, before amplification and averaging (Fig. 1).
By introducing krypton (without flow) into the afterglow reactor at a controlled pressure PKr and a temperature T, it is possible to deduce the absolute concentration
of the nitrogen atoms from the fluorescence ratio of the
two species [10] :
2
Kr
 I 826
P
 . N .3 nm . Kr ,
(1)
 I 745 nm k B T
where I is the intensity of the fluorescence signal, ν is the
laser excitation frequency, E is the deposited laser energy,
σ is the two-photon absorption cross section, a23 is the
optical branching ratio and K is the detection sensitivity.
This expression can be used provided no change is
made in the acquisition system between calibration and
measure and under the condition that the two-photon excitation schemes of the two species are similar (Fig. 2).
For nitrogen and krypton, coefficients a23 and σ were
taken from Niemi [10].
( 2)
ν E
K Kr .3 nm a Kr
23 σ Kr
.
. N N
[ N] = 826
.
N
N
( 2) 
K 745 nm a 23 σ N  ν Kr E Kr
3. Model
For typical operating conditions (P > 5 torr, T = 300 K,
QN2 = 500-1000 sccm), the Knudsen number of the afterglow flow is much less than unity and the Reynolds number is about 250. Continuity equations can then be used to
simulate the behaviour of the nitrogen flow. Steady state
laminar transport equations (for momentum, heat and
mass fractions) closed by the ideal gas law were solved in
the actual 3D geometry taking into account the eventual
presence of the sample plates, using the Fluent software,
as exposed in detail in a previously published paper [5].
At the reactor entrance, the boundary condition for the
concentration of the nitrogen atoms was given by NO
titration [8].
In such conditions, the conservation equation of the nitrogen atoms can be written as :
r
r
∇.(ρ u m N − D N / N ρ ∇ m N ) = SN .
(2)
r
-3
Here, ρ and u are the gas density (in kg m ) and the
gas velocity (in m s-1), mN and D N / N are respectively the
2
ment with values obtained by different authors in similar
late afterglow conditions [3,12-13].
1,0
2
4. Results
To validate the model, concentration profiles were first
performed in the empty afterglow reactor (without plates).
(Table 1 and Fig. 4)
0,8
[N]z / [N]centre
mass fraction (adimensional) and the diffusion coefficient
(in m2 s-1) of the N atoms in molecular nitrogen while SN
is the source term (in kg m-3 s-1) for the atomic species
due to chemical reactions.
In full late post discharge conditions, SN is reduced to
the atomic nitrogen losses due to the recombination
mechanisms :
- in the gas phase, following the reaction :
N(4S) + N(4S) + N2 → N2(B,v=11) + N2
(i)
with the rate Kvol = 3.0 108 exp(500/T) m6 kmole-2 s-1 [11]
- at the walls, assuming a first order reaction :
N(4S) + wall → ½ N2 + wall.
(ii)
The corresponding rate coefficient (in s-1) was obtained
using the expression :
(3)
Ksurf = γ vth / 2r,
where γ is the N-atom recombination probability on the
wall and vth is the gas thermal velocity. In the results presented below, the γ-value was used as a parameter in the
model, allowing to fit the calculated N-atom density spatial profiles to the measured ones.
R
calc
ci
15
6.9
20
6.2
25
5.7
30
5.3
10.0 14.4 16.3 17.6 17.9 17.8
0.52 0.48 0.42 0.35 0.32 0.30
Profile calculated with γN/Pyrex = 10
Profile calculated with γN/Pyrex = 10
-7
-6
-5
Profile calculated with γN/Pyrex = 2 10
0,4
-4
0,0
0,00
0,05
0,10
0,15
0,20
0,25
0,30
z (m)
Fig. 4 : Comparison between the TALIF measurements of the
[N]-atom density and the calculated profiles normalised along
the reactor axis for different γN/Pyrex values (QN2 = 500 sccm, pN2
= 30 torr, PMW = 100 W). The C point is located at the intersection between the afterglow axis and the reactor axis.
Adding a plate of a given material in the reactor, modifies the spatial distribution of the [N]-atoms. Figure 5
(Fig. 5) shows the atomic concentration profiles calculated on the axis of the reactor between the plate and the
C point for various γN/plate values. It is clear that the recombination of atoms on the plate is able to change the
atomic density by almost one order of magnitude near the
plate without modifying the density at the C point.
15
10
-3
10
6.9
Profile calculated with γN/Pyrex = 10
0,2
[N]-atom density (cm )
5
5.2
Profile calculated with γN/Pyrex = 0
0,6
TALIF measurement points
Table 1 : Absolute [N]-atom concentrations measured at the
reactor inlet and at the intersection between the afterglow axis
and the reactor axis. Experimental and calculated density ratios
Rci = [N]centre / [N]inlet are also presented.
pN2 (torr)
[N]centre
(1014 cm-3)
[N]inlet
(1014 cm-3)
R exp
ci
C point
pN2 = 30 torr
γN = 10
γN = 10
14
γN = 10
10
γN = 10
γN = 10
γN = 10
γN = 10
0.55 0.46 0.40 0.34 0.30 0.26
-1
-2
-3
-4
-5
-6
-7
TALIF measurement zone
13
10
In the pressure range studied, [N]-atom concentrations
increase at the reactor entrance to reach a plateau between
20 and 30 torr, while a maximum density is observed in
the reactor around 15 torr.
At high pressure, experimental and calculated density
ratios and density profiles are in good agreement. It can
also be seen that the calculated axial density profiles are
uninfluenced by the chosen value of the recombination
probability on the Pyrex walls of the reactor. For lower
pressures, the influence of the γN/Pyrex value entered in the
model on the calculated [N]-atom axial distribution is
greater but, as TALIF measurements were performed far
from the walls, they do not conduce to accurate values. It
can only be concluded that the recombination probability
of the nitrogen atoms on the Pyrex walls of the reactor is
low, probably comprised between 10-4 and 10-5, in agree-
0,00
0,01
0,02
0,03
0,04
0,05
Distance from the plate (m)
Fig. 5 : [N]-atom density profiles calculated on the reactor axis
between the plate and the C point for different values of γN/plate.
(QN2 = 500 sccm, pN2 = 20 torr and γN/Pyrex = 10-5)
The diameter of the TALIF windows (20 mm) makes it
possible to obtain the density profiles on the first 15 mm
above the plates, where density variations are more pronounced. γN/plate were thus obtained by adjusting the calculated profiles with the measured ones (normalized at the
distance d = 15 mm above the plate, Fig. 6). Considering
the normalized calculated profiles shown Fig. 7, this
method presents an excellent sensitivity for materials
having recombination probabilities between 10-3 and 10-5.
that γN is a function of pressure and not of the flux of atoms to the surface. The obtained inverse pressure dependence is similar to the one previously deduced from measurements of the surface temperature of materials submitted to the afterglow flow [5]. The agreement between the
γN values given independently by the two methods is good
for brass and alumina and acceptable for aluminum. Table
2 compares the γN values here determined with typical
values of the literature (no data was found for brass).
1,0
[N]d / [N]d=15mm
0,8
0,6
5 torr
10 torr
15 torr
20 torr
30 torr
0,4
0,2
0,002
0,004
0,006
0,008
0,010
0,012
0,014
0,016
Distance from the plate (m)
Fig. 6 : Normalized [N]-atom density profiles measured by
TALIF on the reactor axis at the vicinity of a brass plate for
different pressures. (QN2 = 1000 sccm)
1,0
Table 2 : Nitrogen atoms heterogeneous recombination probabilities of the literature.
Material Reference p (torr)
γN
This work
Alumina
[2]
1.4-3.6
1.6 10-3
> 3.5 10-4
-3
Aluminium
[6]
5
1.0 10
5.5 10-4
-4
-6
Quartz
[12]
3-35
5 10 -7 10 8 10-5-2 10-5
Quartz
[3]
11.25
2.1 10-5
3 10-5
-4
Silica
[4]
0.2
2.0 10
> 8 10-5
-6
Pyrex
[1]
0.6-4.2
3.2 10
> 8 10-5
-5
Pyrex
[13]
3
1.0 10
> 8 10-5
[N]d / [N]d=15mm
0,8
0,6
-2
γN/brass = 10
-3
γN/brass = 10
-4
γN/brass = 10
0,4
-5
γN/brass = 10
TALIF
measurements
0,2
0,0
0,000
0,002
0,004
0,006
0,008
0,010
0,012
0,014
Distance from the plate (m)
Fig. 7 : Comparison between the normalized [N]-atom profiles
calculated close to the brass plate with different γN/brass values
and the TALIF measurements. (QN2 = 1000 sccm, pN2 = 20 torr
and γN/Pyrex = 10-5)
-2
10
Pyrex
Aluminium
Alumina
Brass
Aluminium, taken from [5]
Alumina, taken from [5]
Brass, taken from [5]
-3
γN
10
-4
10
-5
10
5
10
15
20
25
30
Pressure (torr)
Fig. 8 : Evolution with pressure of the N-atom recombination
probabilities γN obtained using TALIF profiles for Pyrex, aluminium, brass and alumina. Values previously obtained from surface temperature measurements [5] are also given for comparison.
Figure 8 shows the variation of γN with pressure for the
four materials studied (Pyrex, alumina, aluminium and
brass). The [N]-atom density in the reactor presenting a
maximum when the pressure increases, it is demonstrated
5. Conclusion
Nitrogen atoms wall recombination probabilities were
obtained in a Pyrex flowing afterglow reactor using
TALIF measurements of the [N]-atom density close to
surfaces of different materials.
For each of the studied materials, an inverse pressure
dependence was found, which is consistent with the heterogeneous recombination theory [4,5].
γN values are in correct agreement with the data available in the literature and in good agreement with already
published values obtained using the heat transferred to the
surface during wall recombination.
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