The electron drift velocity, density-normalized
ongitudinal coefficient, and density-normalized effective
onization coefficient in the binary mixtures in CF3I with
Ar and Kr gases are calculated using a two-term
approximation of the Boltzmann equation for the energy in
the E/N range of 10 - 1000 Td for the first time. The NDC
phenomena in these binary gas mixtures are suggested. The
electron transport calculated coefficients are also
compared with those of the pure SF6 gas in experiments.
The limiting field strength values of E/N for the binary
mixtures of 70% CF3I gas with Ar and Kr gases are
determined and greater than those of the pure SF6 gas.
Therefore, these binary mixtures with CF3I concentration
equal to about 65 - 75% are considered for use in high
voltage and many industries. For the purposes of
justification of the accuracy of our results, more
experimental data for electron transport coefficients for the
binary mixtures of CF3I with these gases need to be
performed over a wide range of E/N
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ISSN 1859-1531 - THE UNIVERSITY OF DANANG, JOURNAL OF SCIENCE AND TECHNOLOGY, NO. 6(127).2018 17
A STUDY ON CF3I-Ar AND CF3I-Kr MIXTURE GASES SUBSTITUTING SF6
IN HIGH VOLTAGE EQUIPMENTS
Tran Thanh Son1, Do Anh Tuan2
1Electric Power University; sontt@epu.edu.vn
2Hung Yen University of Technology and Education; tuandoanh@utehy.edu.vn
Abstract - The present binary mixtures of the SF6 gas with Ar and
Kr gases have not been used in many industries as long-term
measures for totally eliminating the potential contribution of SF6
to global warming. In order to gain more insight into electron
transport coefficients in mixture gases as substitutes for SF6 in
high voltage equipment, transport coefficients such as electron
drift velocity, density-normalized longitudinal diffusion coefficient,
ratio of the longitudinal diffusion coefficient to the electron
mobility, Townsend first ionization coefficient, electron
attachment coefficient, and density-normalized effective
ionization coefficient in CF3I-Ar and CF3I-Kr mixture gases are
calculated and analyzed in the wide E/N range of 0.01 – 1000 Td
using a two-term approximation of the Boltzmann equation for the
energy. These calculated coefficients are analyzed and
compared to those in pure SF6 gas. The limiting field strength
values of E/N, (E/N)lim, of these mixture gases are also derived
and compared with those of the pure SF6 gas at different
percentages of CF3I and SF6. The mixture gases of 70% CF3I with
Ar and Kr have (E/N)lim values greater than those of the pure SF6
gas. Therefore, these mixture gases could be considered to
substitute SF6 gas in high voltage equipment.
Key words - Trifluoroiodomethane; CF3I; SF6; Boltzmann equation
analysis; electron transport coefficients; gas mixture
1. Introduction
Sulfur hexafluoride (SF6) has been widely used as an
isolated gas in high voltage equipment. The Kyoto
Protocol, however, has listed the greenhouse gases as CO2,
CH4, N2O, hydrofluorocarbons (HFCs), perfluorocarbons
(PFCs) and SF6, and we need to regulate the emissions and
the utilizations of those gases in the many industries [1]. In
recent decades, the conventional gases such as N2, CO2,
and air and the rare gases such as Ar, Kr, Xe, He, and Ne
have been considered to mix with the SF6 gas as a potential
to reach those attempts [2]. However, the present binary
mixtures of the SF6 gas with other gases have not been used
in many industries as long-term measures for totally
eliminating the potential contribution of SF6 to global
warming [2].
Recently, much research has been concentrated on
trifluoroidomethane (CF3I) gas because of its low global
warming potential, very short atmospheric lifetime and
relatively low toxicity gas [3]-[5]. It is a gas that is a
substitution candidate for the SF6 gas and as a candidate to
the replacement of potent greenhouse affects. This gas has
also been considered to be a candidate replacement for
bromotrifluoromethane (CF3Br), which is used in aircraft
for fuel inertness and for fire-fighting [3]. The boiling point
of CF3I gas is higher than that of the SF6 gas [4]. At an
absolute pressure of 0.5 MPa, CF3I becomes liquids at
about 260C, whereas the SF6 gas becomes liquids at about
-300C [4]. On the other hand, the SF6 gas is used in gas
circuit breakers at 0.5 to 0.6 MPa. Therefore, it is
impossible to use CF3I gas if this gas is used at this pressure
level [4]. However, in order to reduce the liquefaction
temperature of CF3I gas, Taki et al. [4] decreased partial
pressure by mixing it with other gases such as N2 and CO2.
For example, the boiling point can be reduced from about
260C (pure CF3I) to about -120C at 0.5 MPa by using a 30%
CF3I-CO2 mixture [5]. Therefore, it is necessary to mix the
CF3I gas with different buffer gases.
Moreover, the sets of electron collision cross sections
and electron transport coefficients for atoms, molecules,
and binary mixture gases are necessary for quantitative
understanding of plasma phenomena. Some gases, such as
rare gases (Ar, Kr, Xe, Ne, and He), N2, CO2, air, and O2
mixed with each of F2, Cl2, and SF6, are also necessary for
many applications, such as rare-gas halide laser, plasma
etching, and gaseous dielectric materials [2]. On the other
hand, the collision processes and electron transport
coefficients of the binary mixtures of CF3I gas with other
gases have been scarce so far. To the best of our
knowledge, neither measurements nor calculations of the
electron transport coefficients in the binary mixtures of the
CF3I gas with the Kr gas with the entire CF3I concentration
range have been performed previously.
In the present study, in order to gain more insight into
the electron transport coefficients, the electron transport
coefficients (electron drift velocity, density-normalized
longitudinal coefficient, and density-normalized effective
ionization coefficient) in the E/N range(ratio of the electric
field E to the neutral number density N) of 10 - 1000 Td
and the limiting field strength of E/N, (E/N)lim, for the
CF3I-Ar and CF3I-Kr mixtures are calculated by a two-term
approximation of the Boltzmann equation for the energy.
The negative differential conductivity (NDC) phenomena,
that is, decreasing electron drift velocity with increasing
electric field strength, in these binary gas mixtures are
suggested. The electron transport coefficients calculated
are also compared with those of pure SF6 gas and the
(E/N)lim values in those mixtures are also compared
respectively with those of SF6 mixtures with correlative
gases (Ar and Kr) in the experiments. The binary mixtures
of CF3I gas with Ar and Kr gases with CF3I concentration
equal to about 65 - 75%, are considered for use in high
voltage and many industries.
2. Calculation method of electron transport coefficients
in CF3I-Ar and CF3I-Kr mixtures
The electron transport coefficients are calculated by
sets of electron collision cross sections for gases and a two-
term approximation of the Boltzmann equation for the
18 Tran Thanh Son, Do Anh Tuan
energy given by Tagashira et al. [6]. The accurate electron
collision cross section sets for each gas in mixture are
chosen for calculation to obtain the reliable electron
transport coefficients. The electron energy distribution
function (EEDF) can be computed by solving the
Boltzmann equation. In this study, a two-term
approximation is applied as successfully used in our
previous article [7]. Based on the EEDF, f(ε, E/N), the
electron drift velocity, W, the density-normalized
longitudinal diffusion coefficient, NDL, the Townsend first
ionization, α, and the electron attachment coefficient, η,
can be calculated as following equations:
1/2
m0
1 2 eE df ( ,E / N)
W d .
3 m N q ( ) d
= −
(1)
where ε is the electron energy, m is the electron mass, e is
the elementary charge, and qm(ε) is the momentum-transfer
cross section.
( )
1
21
1 2
L 1 0
0 0
T T
0 2 1 1 02
V
ND E (F )d F d
3N q q
A A .
−
= +
− − −
(2)
where V1 is the speed of electron, qT is the total cross
section. Fn and n (n = 0, 1, 2) are respectively the electron
energy distributions of various orders and their
eigenvalues.V1, n , 0n , and An are given by
1/2
1
2e
V
m
=
;
1
2
0 1 i 0
0
V N q F d
= ;
1
1 2
1 0 0 1 01
0
T
V E
(F )d ( A )
3N q
−
= − + −
;
1
2
0n 1 i n
0
V N q F d
= ; n n0A F d .
=
where qi is the ionization cross section.
1/2
1/2
i
I
1 2
/ N f ( ,E / N) q ( )d .
W m
=
(3)
where I is the ionization onset energy and qi(ε) is the
ionization cross section.
1/2
1/2
a
0
1 2
/ N f ( ,E / N) q ( )d .
W m
=
(4)
where qa(ε) is the attachment cross section.
The electron collision cross sections for CF3I
determined by Kimura and Nakamura [8], Ar determined
by Nakamura and Kurachi [9], and Kr determined by
Hayashi [10] are used throughout the present study. The set
of electron collision cross sections for the CF3I molecule
[8] includes one momentum transfer, one attachment, three
vibrational excitations (threshold energies of 0.032 -
0.134 eV), five electronic excitations (threshold energies
of 4.7 - 9.6 eV), and one total ionization (threshold energy
of 10.2 eV) cross sections.
The set of electron collision cross sections for Ar atom
[9] includes one momentum transfer, five electronic
excitations (threshold energies of 11.6 - 13.9 eV), and one
total ionization (threshold energy of 15.69 eV) cross
sections. The set of electron collision cross sections for Kr
atom [10] includes one momentum transfer, fourteen
electronic excitations (threshold energies of 9.915 -
13.437 eV), and one total ionization (threshold energy of
14 eV) cross sections. The accuracy of the electron collision
cross section set for each gas is confirmed to be consistent
with all electron transport coefficients in each pure gas.
3. Results and discussions
The results for the electron drift velocities, W, as
functions of E/N for the binary mixtures of CF3I gas with
Ar and Kr gases calculated in the E/N range 10 < E/N <
1000 Td by a two-term approximation of the Boltzmann
equation are shown in Figures 1-2, respectively. Slight
regions of the NDC phenomena in these gas mixtures are
observed in the E/N range 15 < E/N < 170 Td. The NDC is
relatively shallow for all mixtures. The occurrences of
these phenomena are due to the Ramsauer-Townsend
minimum (RTM) of the elastic momentum transfer cross
sections of the Ar and Kr atoms, and the CF3I molecule.
These suggestions are analyzed and explained thoroughly
by Chiflikian [11]. In the binary mixtures of the CF3I gas
with the Ar and Kr gases, the values of W are suggested to
be between those of the pure gases over E/N > 100 Td and
these values grow linearly over E/N > 200 Td. For the sake
of comparison, the electron drift velocity obtained by
Aschwanden [12] for the pure SF6 gas is shown in Figures
1-2. The calculated electron drift velocities in 70%
CF3I-Ar in the E/N ranges of E/N < 600 Td are very close
to those of the pure SF6 gas.
Figure 1. Electron drift velocity, W, as functions of E/N for the
CF3I-Ar mixtures with 10%, 30%, 50%, and 70% CF3I.
The solid line and symbols show present W values calculated using
a two-term approximation of the Boltzmann equation for the CF3I-
Ar mixtures. The solid curves show present W values calculated for
the pure CF3I molecule and pure Ar atom. The star symbol shows
the measurement value of the pure SF6 [12]. The inset figure shows
these results calculated in the E/N range of 200 - 1000 Td
ISSN 1859-1531 - THE UNIVERSITY OF DANANG, JOURNAL OF SCIENCE AND TECHNOLOGY, NO. 6(127).2018 19
Figure 2. Electron drift velocity, W, as functions of E/N for the
CF3I-Kr mixtures with 10%, 30%, 50%, and 70% CF3I. The solid
line and symbols show present W values calculated using a two-
term approximation of the Boltzmann equation for the CF3I-Kr
mixtures. The solid curves show present W values calculated for
the pure CF3I molecule and pure Kr atom. The star symbol shows
the measurement value of the pure SF6 [12]. The inset figure
shows these results calculated in the E/N range of 200 - 1000 Td
The results for the density-normalized longitudinal
coefficients, NDL, as functions of E/N for the binary
mixtures of CF3I gas with Ar and Kr gases calculated in the
E/N range 10 < E/N < 1000 Td by a two-term
approximation of the Boltzmann equation are shown in
Figures 3-4, respectively.
For each E/N value, the NDL values of the binary
mixtures of the CF3I gas with Ar and Kr gases decrease with
the increase in the CF3Icontent in the mixture. This behavior
is due to the growing influence of the electron-CF3I
interaction as the CF3Icontent increases. In these figures, on
the other hand, these NDL curves have minima in the E/N
range of 15 - 170 Td for these binary mixtures. The same
process responsible for the NDC region in the electron drift
velocity curves in these binary mixtures caused the
occurrence of these minima. Urquijo et al. [13] also
observed the similar behavior for the C2F6-Ar mixtures. The
density-normalized longitudinal coefficient for the pure SF6
obtained by Aschwanden [12] is also shown in Figures 3-4
for the sake of comparison. The NDL values of the pure SF6
are greater than those of these binary mixtures.
The results for the density-normalized effective
ionization coefficients, (α - η)/N, as functions of E/N for the
binary mixtures of CF3I gas with Ar and Kr gases calculated
by a two-term approximation of the Boltzmann equation are
shown in Figures 5-6, respectively. In the binary mixtures of
the CF3I with the Ar and Kr gases, the values of (α - η)/N are
also suggested to be between those of the pure gases,
respectively. For the sake of comparison, the density-
normalized effective ionization coefficient obtained by
Aschwanden [12] for the pure SF6 gas is also shown in
Figures 5-6. The (α - η)/N values for 70% CF3I mixtures
with the Ar and Kr gases are very close to those of the pure
SF6 gas over E/N < 450 Td and E/N < 470 Td, respectively.
Because of the accuracy of the electron collision cross
sections for the present gases and the validity of the
Boltzmann equation, the present calculated results are
reliable. More experiments of the electron transport
coefficients for the binary mixtures of the CF3I gas with
these buffer gases need to be performed over the wide
range of E/N in the future. In general, when the percentage
ratio of the CF3I gas in binary mixtures increases, the
values of the electron transport coefficients increase
progressively to those of the pure CF3I.
The limiting field strength values of E/N, (E/N)lim, at
which α = η for the binary mixtures of CF3I gas with Ar
and Kr gases are derived at 133.322 Pa and shown in Figure
7. These values are also compared respectively with those
of the binary mixtures of the SF6 gas with the Ar [14] and
Kr [15] gases shown in Figure 7. The (E/N)lim value
calculated for the pure CF3I gas is equal to 437 Td greater
than the (E/N)lim of the pure SF6 gas (361 Td) [12]. It can
be considered as a prospective substitute for the SF6 gas. In
Figure 7, the CF3I concentration in the binary mixtures of
CF3I gas with Ar and Kr gases equal to about 65 - 75%, is
considered for use in high voltage and many industries if
other chemical, physical, electrical, thermal, and
economical studies are considered thoroughly.
Figure 3. Density-normalized longitudinal coefficient, NDL, as
functions of E/N for the CF3I-Ar mixtures with 10%, 30%, 50%, and
70% CF3I. The solid line and symbols show present NDL values
calculated using a two-term approximation of the Boltzmann
equation for the CF3I-Ar mixtures. The solid curves show present
NDL values calculated for the pure CF3I molecule and pure Ar atom.
The star symbol shows the measurement value of the pure SF6 [12]
Figure 4. Density-normalized longitudinal coefficient, NDL, as
functions of E/N for the CF3I-Kr mixtures with 10%, 30%,
50%, and 70% CF3I. The solid line and symbols show present
NDL values calculated using a two-term approximation of the
Boltzmann equation for the CF3I-Kr mixtures. The solid curves
show present NDL values calculated for the pure CF3I molecule
and pure Kr atom. The star symbol shows the measurement
value of the pure SF6 [12]
20 Tran Thanh Son, Do Anh Tuan
Figure 5. Density normalized effective ionization coefficient,
(α - η)/N, as functions of E/N for the CF3I-Ar mixtures with
10%, 30%, 50%, and 70% CF3I. The solid line and symbols
show present (α - η)/N values calculated using a two-term
approximation of the Boltzmann equation for the CF3I-Ar
mixtures. The solid curves show present (α - η)/N values
calculated for the pure CF3I molecule and pure Ar atom. The
star symbol shows the measurement value of the pure SF6 [12]
Figure 6. Density normalized effective ionization coefficient,
(α - η)/N, as functions of E/N for the CF3I-Kr mixtures with
10%, 30%, 50%, and 70% CF3I. The solid line and symbols
show present (α - η)/N values calculated using a two-term
approximation of the Boltzmann equation for the CF3I-Kr
mixtures. The solid curves show present (α - η)/N values
calculated for the pure CF3I molecule and pure Kr atom. The
star symbol shows the measurement value of the pure SF6 [12]
Figure 7. Limiting field strength values of E/N, (E/N)lim, as
functions of the percentage of CF3I gas for the binary mixtures
CF3I-Ar and CF3I-Kr. The solid line and solid symbols show
present (E/N)lim values for these binary mixtures calculated
using a two-term approximation of the Boltzmann equation.
The dotted curves and the open symbols show (E/N)lim values for
the binary mixtures SF6-Ar [14] and SF6-Kr [15]
4. Conclusion
The electron drift velocity, density-normalized
longitudinal coefficient, and density-normalized effective
ionization coefficient in the binary mixtures in CF3I with
Ar and Kr gases are calculated using a two-term
approximation of the Boltzmann equation for the energy in
the E/N range of 10 - 1000 Td for the first time. The NDC
phenomena in these binary gas mixtures are suggested. The
electron transport calculated coefficients are also
compared with those of the pure SF6 gas in experiments.
The limiting field strength values of E/N for the binary
mixtures of 70% CF3I gas with Ar and Kr gases are
determined and greater than those of the pure SF6 gas.
Therefore, these binary mixtures with CF3I concentration
equal to about 65 - 75% are considered for use in high
voltage and many industries. For the purposes of
justification of the accuracy of our results, more
experimental data for electron transport coefficients for the
binary mixtures of CF3I with these gases need to be
performed over a wide range of E/N.
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(The Board of Editors received the paper on 27/02/2018, its review was completed on 14/3/2018)
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