31st ICPIG, July 14-19, 2013, Granada, Spain
Topic No:-1
Ionization cross sections and rate coefficients for CF2Cl2 molecule by
electron impact
Neeraj Kumar, Satyendra Pal
Department of Physics, M.M.H. College, Ghaziabad- 201001 INDIA
We have employed the revisited Jain-Khare semi-empirical formulation for the calculation of
partial single differential cross sections for CF2Cl2 molecule through direct and dissociative
ionization processes at fixed incident electron energy of 100 eV. The corresponding derived
integral cross sections in terms of the partial and total ionization cross section of CF2Cl2 molecule
by electron impact, in the energy range varying from ionization threshold to 1000 eV, revealed a
reasonably good agreement with the available experimental and theoretical data. The ionization
rate coefficients are also evaluated using the partial and total ionization cross sections and the
Maxwell-Boltzmann distribution of energies of electrons.
1. Introduction
CF2Cl2 molecule is of considerable interest
because of its role in the catalytic decomposition of
atmospheric ozone in the stratosphere [1]. In this
process, CF2Cl2, which is widely used in the
semiconductor industry for cleaning chemical
vapour deposition chambers and also have
applications as solvents, aerosol propellants and
refrigerants in industries, dissociates by solar UV
radiations in the stratosphere to release chlorine
atoms. This in turn sets off a chain reaction that
results in the net conversion of ozone into oxygen.
The present work reports the calculations for
single differential cross sections as a function of
secondary/ ejected electron energy in the ionization
of CF2Cl2 molecule by electron collision leading to
the production of various cations viz. singly charged
ions CFCl2+ , CF2Cl+ , CCl2+ , CFCl+ , CF2+ , CCl+ ,
Cl+ , CF+ , F+ and C+ and doubly charged ion
CF2Cl+2 through direct and dissociative ionization
processes at a fixed incident electron energy of 100
eV. A modified Jain-Khare semi-empirical
formalism [2] based on oscillator strength has been
employed. To the best of our knowledge, no
experimental and/or theoretical data is available for
comparison of the present results for differential
cross sections. The corresponding derived integral
cross sections in terms of the partial and total
ionization cross sections corresponding for these
cations, in the energy range varying from ionization
threshold to 1000 eV, revealed a reasonably good
agreement with the experimental [3-6] and
theoretical data [7-9], wherever available. In
addition to the differential and integral ionization
cross sections, we have also calculated the ionization
rate coefficients using the evaluated partial
ionization cross sections and the Maxwell-
Boltzmann distribution as a function of electron
energy [10].
2. Theoretical
The present calculations are carried out
using the modified semi-empirical formalism
developed by Khare and co-workers (see for
discussion in Refs. [2]). In brief, the single
differential cross sections in the complete solid angle
Ω as a function of secondary electron energy ε
corresponding to the production of ith type of ion in
the ionization of a molecule by incident electron of
energy E is given by
(1   ) R dfi ( W,0) ln[ 1  Ci ( E  I i )]  
( E  Ii ) W dW

a 02 R 
Qi E, W  
 R ( E  Ii ) 
 d
2
3



E  S
  ( E ) 

2
3
3 
(
E


)
E


( 0  i )



where the various variables used have their usual
meanings. In the present formulation, the dipole
oscillator strengths dfi/dW are the key parameters. In
the present study, we have used the partial oscillator
strength data in the energy range from ionization
threshold to 70 eV provided by Brion et al. [11]. In
the photon energy range 70-200 eV, we have used
their measured total valence photoabsorption
oscillator strength data and above 200 eV the same
was extrapolated by Thomas-Reiche-Kuhn sum rule
within ±10% uncertainty (see for instance reference
[11]). Thus the derived total oscillator strength cross
sections have been distributed into ionic fragments
using the constant ionization efficiency above the
dipole breakdown limit of 17.5 eV. The collision
parameter Ci and energy parameter ε0 were evaluated
as for other polyatomic molecules/CCl4 [2]. The
vertical onsets or the ionization potentials
corresponding to the various cations are given
elsewhere [11]. In the present evaluations of cross
sections, the estimated uncertainty is more or less
31st ICPIG, July 14-19, 2013, Granada, Spain
the same as for the measurement of the oscillator
strength cross sections.
The partial ionization cross section is obtained by
the integration of the energy dependent single
differential cross sections over the entire energy loss
W,
experimental data sets of Leiter et. al [3], Bart et. al
[4], Sierra et. al [5] Beran et. al [6] along with the
theoretical data sets of BEB [7], DM and MAR [89] in the complete energy range covered in the
present calculations.
12
Q i E  
 Q (E, W)dW
i
Ii
and the total ionization cross section is obtained by
QiT (E) 
Qi (E)

i
In plasma processes, the ionization rate coefficients
are important quantities which are determined by
using our calculated partial and total ionization cross
sections and the Maxwell-Boltzmann distribution of
temperature/energy given by
Total Ionization Cross Sections
E
9
6
3
0
10
where kB, T and μ are the Botlzmann constant,
absolute temperature and mass of the electron,
respectively [12].
3. Results and Discussion
The partial single differential cross sections as a
function of secondary electron energy have been
calculated in terms of energy loss W (sum of
ionization threshold and the secondary electron
energy) at fixed incident electron energy of 100 eV
will be shown in the full length paper. To the best of
our knowledge, no experimental data is available to
compare the present results for the differential cross
sections. However, the qualitative behaviour of the
cross sections are the same as for other molecules
investigated. The energy dependent cross sections
are symmetric at W/2 where the energies of primary
and the secondary electrons are almost equal. The
present calculations account the exchange effects
through the non-dipole cross section term (second
part) of the formulation at about W/2. The
differential cross section profiles clearly show the
weight contribution of the molecular and atomic
cations. The atomic photoionization cross sections
include the contribution of the structures and many
body states produced near onsets which are
speculated in the present calculations for the energy
dependent differential cross sections [11].
In case of the non-availability of the experimental
data for differential cross sections, the corresponding
derived sum of the partial ionization cross sections
from ionization threshold to 1000 eV, become
important. Figure 1 shows the comparison of our
calculated partial ionization cross sections when
added up to a total cross section with the
100
E (eV)
1000
Figure 1: Total ionization cross sections (10-16 cm2)
for electron impact ionization of CF2Cl2 molecule
alongwith the data: ∆ – Ref. [3], ● – Ref. [4], X –
Ref. [5], Ο – Ref. [6], ■ – Ref. [7], and * – Ref. [89].
The present calculations for the partial and the total
ionization cross sections satisfy the necessary
consistency checks to access their consistency and
reliability. The consistency checks derived from the
fact that the total electron impact ionization cross
sections (i) is equal to the sum of the partial
ionization cross sections and (ii) is obtained by
integration of
differential cross sections over
secondary electron energies and angles. Both
relationships allow one to check the reliability of the
absolute magnitude and the energy dependence of
ionization cross sections under consideration. The
precise shape of the cross section in the low energy
limit close to the onset of ionization is especially
important in determination (by extrapolation) of
respective ionization thresholds, to compare with
those derived by other means [13].
In relation to the applications, in particularly to
plasma processes, ionization rate coefficients are
rather more desirable than ionization cross sections.
We have evaluated the ionization rate coefficients as
a function of electron temperature for the individual
cations produced in electron collision with the
CF2Cl2 molecule. The calculations are made using
the calculated ionization cross sections and
Maxwell-Boltzmann energy distributions and the
results are presented in Figure 2.
31st ICPIG, July 14-19, 2013, Granada, Spain
Ionization Rate Coefficients (cm3/sec)
1E-15
1E-17
total
CF2Cl+
2xCF2+
CF+
CFCl+
CCl+
CF2Cl++
1E-19
C+/25
F+/30
CCl2+
Cl+/2000
1E-21
CFCl2+/5000
1E-23
0
200
400
600
800
1000
1200
Temperature/Energy (eV)
Figure 2: Ionization rate coefficients as a function
of the electron energy for CF2Cl2 molecule.
4. Conclusion
The calculations for the differential cross
sections as a function of secondary electron energy
at fixed incident electron energy, corresponding to
the formation of various singly and doubly charged
cations in electron impact dissociative ionization of
the CF2Cl2 molecule have been carried out by
employing a semiempirical formalism based on the
Jain-Khare approach. In absence of any data for the
differential cross sections, the corresponding derived
partial and total ionization cross sections were
calculated. The total ionization cross sections are in
satisfactory agreement with the experimental and
theoretical data. The ionization rate coefficients, a
key parameter in plasma modelling, have been
evaluated using Maxwell-Boltzmann energy
distribution. The present calculations for electron
ionization cross sections and rate coefficients
provide a contribution to the knowledge of various
plasma processes.
Acknowledgements
S.Pal acknowledges the support from
Department of Science and Technology DST, New
Delhi, India.
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