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Temperature measurement of an N2 glow discharge by emission spectroscopy
Volume 95A, number 5
PHYSICS LETTERS
2 May 1983
TEMPERATURE MEASUREMENT OF AN N 2 GLOW DISCHARGE BY EMISSION SPECTROSCOPY A. PLAIN and A. RICARD Laboratoire de Physique des Gaz et des Plasmas l, Bdt. 212, UniversitE Paris-Sud, 91405 Orsay, France Received 1 July 1982 Revised manuscript received 24 February 1983
The rotational temperature (T R) o f a cold N 2 glow discharge was deduced from the intensity distribution o f the
N~(C 3flu, u' ---0 -, B 3rig, u" = 0) ~.= 337.1 nm R-branch. Likewise, the neutral temperature (Tg) was measured with a thermocouple located on the axis of the discharge. It is shown that TR = Tg for 300 < Tg < 700 K.
1. Introduction. The temperature of molecular gases in glow discharges is one of the parameters defining the nature and reactivity of the plasma. We therefore analyse a method for measuring the temperature of nitrogen by emission spectroscopy. Nitrogen is used in reactive plasma for: metal surface treatment [ 1] ; synthesis of nitrogen oxydes [2] ; CO, CO 2 and gas lasers [3]. Many of these applications are obtained by lowtemperature discharges where it is interesting to know the kinetic temperature which in such discharges may vary from 300 to 700 K. The gas temperature is a function of discharge parameters such as current discharge and gas pressure. The emission of the N 2 first positive, N 2 second positive and N 2 first negative are well separated in the spectral range 0.3-1 wn. Accordingly, the second positive N2(C 3 I I u - B 3IIg) was chosen to measure the temperature by analysis of the resolved rotational structure of this transition. We must take care in analyzing the results obtained by this spectroscopic method because rotational levels may be affected by transfers. The gas temperature Tg in the N 2 discharge was also determined by means of a thermocouple located on the discharge axis as in ref. [4]. The purpose of this work was to compare Tg with the temperature obtained by the spectroscopic method. 1 Associated with the CNRS.
0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
2. Measurement o f kinetic temperature. An electrical discharge was set up in a pyrex tube of inner diameter 2 cm and length 130 era. As shown in fig. 1, the discharge may be switched on between either electrodes I and II (130 cm apart) or electrodes I and III (20 cm apart). Hollow nickel electrodes of diameter 1 cm were used. The nitrogen pressure (N 2 purity 99.9999%) of 1 - 2 Torr was measured by a Pirani gauge (Alcatel A.P.I.). Gas velocities were in the 1 to 10 m s -1 range. Experiments were conducted with the following discharge currents: 25, 50, 75, 100 and 130 mA. A Cr-A1 thermocouple was used to determine the N 2 gas temperature. When the discharge was taking place between I and II the thermocouple was placed in a capillary pyrex tube sealed in the middle of the discharge tube (fig. 1). This capillary tube must both ensure vacuum tightness and electrically insulate the thermocouple from the discharge. However, the introduction of this capillary tube leads to temperature
~"*" ~ i
to pump
Fig. 1. ~xperirnental arrangement (I anode - II, III cathodes d(I, II) = 130 cm - d(I, l i d = 20 cm).
235
Volume 95A, number 5
PHYSICS LETTERS
values which are underestimated. To assess the importance of such a temperature shift the following sequence of measurements was carried out. The discharge is made between electrodes I and III, and the gas temperature is measured in post-discharge. In the first part of the test, the thermocouple is inside the capillary tube, while in the second part it is directly in the gas flow. Precautions must be taken, so that no charged particles can interact with the thermocouple. This experimental arrangement permits a determination of the thermal conduction of the capillary tube for the discharge conditions presently used. For currents varying from 25 to 130 mA, true temperatures ranging between 400 and 550 K at a pressure of 1 Torr and between 450 and 700 K at a pressure of 2 Torr, were measured in the discharge. In these temperature ranges the correction due to the emissivity of the thermocouple varies between 5 and 25 K [5].
3. Determination of the rotational temperature of N2(C3IIu}. The vibrorotational spectra of the N2(C 3 l-lu_B 3 IIg) transition were analysed by a SOPRA spectrometer ( f = 150 cm) coupled with a Hamamatsu photomultiplier (R 585). The more intense transition between C 3II u (o' = 0) and B 31]g (v" = 0) was used. The R-branch ( A N = N ' - N " = 1) of the rotational structure of this band is degraded towards the violet. In this experiment the intensities of 3 H1 rotational lines were selected to determine the rotational temperature of N2(C 3 IIu)" An example of the C 311u B 3 lag rotational spectrum obtained with a resolution 6X = 0.05 )k is given in fig. 2 for a discharge pressure of 1 Torr and a current of 50 mA. 3
,
3
~j
N2(CrIu,v=o~Brrg,v :o)
I
-
[I
-
29 2'5 2'0 3' Fig. 2. Emission rotational spectra of the N 2 second positive system C 3FIu-B 311g(u' = 0, J' ~ o" = 0, J") for p = 1 Torr and i = 50 mA. -
236
2 May 1983
For rotational levels populated according to a Boltzmann distribution with a temperature T R the Rbranch intensity is given by
IR(J' ) = const X SR(J')N 0 X exp [ - B 0 J ' ( J ' + 1)hc]kT R ],
(1)
where N O is the N2(C 3IIu, u' = 0) density, B 0 is the rotational constant, Bohc/k is equal to 2.6 K and J ' refers to rotational levels of C 31]u, v' = 0. The H 6 n l London factor SR(J ) for a 3 i]_3 II transition (Hund's b case) [6] and for high rotational levels ( J > 10) can be expressed by the following relation [7] : SR(J ) = [J(J + 2)] 2[3(J + 1)3 ,
(2)
where J refers to the lower rotational levels of B 31]g. As has been postulated previously [8,9] the high rotational levels of N2(C 3IIu, u = 0) are populated by excitation transfers such as the following process: N2(E 3~,~) + N2(X lZg ) N2(C 3Ilu, o = 0, J ' ) + N2(X l~g) .
(3)
Ochkin et al. [10] have shown that the population of levels J ' ~> 15 are perturbed by this process so that temperatures determined directly by application of (1) are too high. If we postulate, following ref. [10], that hot molecules produced by the transfer reaction (3) have a Boltzmann distribution with a temperature T b, expression (1) may be rewrit{en as I R ( J ' ) = const × S R ( J ' )
× (N O expl-~BoJ'(J' + 1)hc/kTR] +N h exp[-BoJ'(J' + 1)hc/kTh] ,
(4)
where N h is the hot-molecule density produced by reaction (3). The variation of log IR(J')/SR(J' ) obtained at p = 1 Torr and i = 50 mA is given in fig. 3. The solid line in fig. 3 fits the experimental result by using eq. (4) with the following values: T R = 425 K, T h ~ 2000 K and Nh/N 0 = 3%. For the other experimental conditions the rotational temperatures are reported in figs. 4a and 4b. The temperatures Th of hot molecules are in all cases about 2000 K and their density Nh/N 0 is a few percents. An approximate rotational temperature may
Volume 95A, n u m b e r 5
PHYSICS LETTERS
be calculated from eq. (1) (which supposes that there are no transfers) for 16 ~< J ' ~< 22. This temperature is deduced from the broken curve in fig. 3 which gives a value of about 450 K. This value is nearly equal to the accurate value deduced from eq. (4).
to rr~(J')] ~
-
-
,
r
,
~'o
4
x° o">~
I -
-
L
l
200
a
I
400
__~
I
600
800 J'(J'+l )
Fig. 3. Experimental plot o f loglIR(J')/SR(J')I as a function ofJ'(J' + 1) f o r P N 2 = 1 Torr and i = 50 mA. o experimental results; the solid line is calculated with TR = 425 K, Th = 2000 K andNh[No = 0.03. From the broken line, TR = 4 5 0 K . TR(K)
a
//
6oc /
/
/
/
P= 1 Torr Tg(K'
30C 300
4&~
TR(K)
.4o -
o~o
b
70C
6OO
2 May 1983
4. Comparison of temperature obtained by the two experimental methods. The rotational temperature T R determined by using eq. (4) is shown in figs. 4a, 4b, as a function of the gas temperature Tg measured by the thermocouple as described in section 2. The temperature variations were produced by varying the discharge current between 25 and 130 mA for two gas pressures: 1 Tort (fig. 4a) and 2 Torr (fig. 4b). The estimated accuracy is about 2% for Tg and 5% for T R. It can be concluded that a good correlation has been obtained between T R determined with rotational levels of N2(C 3IIu - B 3Ilg) and Tg measured with a thermocouple. 5. Conclusion. The rotational structure of bands emitted by excited molecules in electrical discharges enables a rotational temperature T R to be obtained when the population of the emitting levels obeys a Boltzmann distribution. However, one should be circumspect about concluding that this temperature T R is identical to the kinetic temperature. In the present study we have considered the peculiar case of nitrogen in low-temperature discharges (300 < T < 700 K). It has been shown that for the well-known transition (u' = 0 ~ o" = 0, ~, = 337.1 nm) of the second positive N2(C 3/I u - B 3IIg) the rotational temperature T R is identical to the gas temperature Tg. But to obtain the true temperature (TR) we must take into account the fact that rotational levels are perturbed by excitation transfers, mainly from the gas, for J ' > 22. Levels with J ' < 15 are difficult to resolve because of the overlapping of rotational lines near the head of the band. A fast method to obtain T R is to consider rotational levels with 16 ~< J ' ~< 22. Then we have found that T R is only overestimated by about 10%.
500 /~/~ /
40o/~ 500 400
P= 2T0rr
Tg(K~
6b0
Fig. 4. Rotational temperature T R o f N2(C 3Ilu, o = 0) as a function of gas temperature Tg for p = 1 Torr (a) and p = 2 Torr (b).
237
Volume 95A, number 5
PHYSICS LETTERS
References [ 1] H. Michel and M. Gantois, 18th Int. Conf. on Heat treatment of materials, Detroit (1980). [2] J.M. Baronnet et al., I.S.P.C. 4, Zurich (1979) 341; M. Locqueneux, F. Etile and R. Ben Aim, I.S.P.C. 4, Zurich (1979) 366. [3] A.G. Svindon, N.N. Sobolev and G.C. Tselikov, Zh. Eksp. Teor. Fiz. Pis'ma 6 (1967) 542. [4] L.S. Polak, P.A. Sergeev and D.I. Slovetsky, High Temp. 15 (1977) 13.
238
2 May 1983
[5] K.G. Enoh, Thesis M.I.T. (June 1976). [6] G. Herzberg, Molecular spectra and molecular structure (Van Nostrand, New York, 1950). [7] A. Schadee, Bull. Astron. Inst. Neth. 17 (1964) 311. [8] V.N. Ochkin, S.Yu. Savinov and N.N. Sobolev, Soy. Phys. JETP 48 (1978) 232. [9] D.J. Burns, D.E. Golden and D.W. GoUiard, J. Chem. Phys. 65 (1976) 2616. [ 10] V.N. Ochkin and S.Yu. Savinov, Zh. Prikl. Spektrosk. 28 (1978) 408.
PHYSICS LETTERS
2 May 1983
TEMPERATURE MEASUREMENT OF AN N 2 GLOW DISCHARGE BY EMISSION SPECTROSCOPY A. PLAIN and A. RICARD Laboratoire de Physique des Gaz et des Plasmas l, Bdt. 212, UniversitE Paris-Sud, 91405 Orsay, France Received 1 July 1982 Revised manuscript received 24 February 1983
The rotational temperature (T R) o f a cold N 2 glow discharge was deduced from the intensity distribution o f the
N~(C 3flu, u' ---0 -, B 3rig, u" = 0) ~.= 337.1 nm R-branch. Likewise, the neutral temperature (Tg) was measured with a thermocouple located on the axis of the discharge. It is shown that TR = Tg for 300 < Tg < 700 K.
1. Introduction. The temperature of molecular gases in glow discharges is one of the parameters defining the nature and reactivity of the plasma. We therefore analyse a method for measuring the temperature of nitrogen by emission spectroscopy. Nitrogen is used in reactive plasma for: metal surface treatment [ 1] ; synthesis of nitrogen oxydes [2] ; CO, CO 2 and gas lasers [3]. Many of these applications are obtained by lowtemperature discharges where it is interesting to know the kinetic temperature which in such discharges may vary from 300 to 700 K. The gas temperature is a function of discharge parameters such as current discharge and gas pressure. The emission of the N 2 first positive, N 2 second positive and N 2 first negative are well separated in the spectral range 0.3-1 wn. Accordingly, the second positive N2(C 3 I I u - B 3IIg) was chosen to measure the temperature by analysis of the resolved rotational structure of this transition. We must take care in analyzing the results obtained by this spectroscopic method because rotational levels may be affected by transfers. The gas temperature Tg in the N 2 discharge was also determined by means of a thermocouple located on the discharge axis as in ref. [4]. The purpose of this work was to compare Tg with the temperature obtained by the spectroscopic method. 1 Associated with the CNRS.
0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
2. Measurement o f kinetic temperature. An electrical discharge was set up in a pyrex tube of inner diameter 2 cm and length 130 era. As shown in fig. 1, the discharge may be switched on between either electrodes I and II (130 cm apart) or electrodes I and III (20 cm apart). Hollow nickel electrodes of diameter 1 cm were used. The nitrogen pressure (N 2 purity 99.9999%) of 1 - 2 Torr was measured by a Pirani gauge (Alcatel A.P.I.). Gas velocities were in the 1 to 10 m s -1 range. Experiments were conducted with the following discharge currents: 25, 50, 75, 100 and 130 mA. A Cr-A1 thermocouple was used to determine the N 2 gas temperature. When the discharge was taking place between I and II the thermocouple was placed in a capillary pyrex tube sealed in the middle of the discharge tube (fig. 1). This capillary tube must both ensure vacuum tightness and electrically insulate the thermocouple from the discharge. However, the introduction of this capillary tube leads to temperature
~"*" ~ i
to pump
Fig. 1. ~xperirnental arrangement (I anode - II, III cathodes d(I, II) = 130 cm - d(I, l i d = 20 cm).
235
Volume 95A, number 5
PHYSICS LETTERS
values which are underestimated. To assess the importance of such a temperature shift the following sequence of measurements was carried out. The discharge is made between electrodes I and III, and the gas temperature is measured in post-discharge. In the first part of the test, the thermocouple is inside the capillary tube, while in the second part it is directly in the gas flow. Precautions must be taken, so that no charged particles can interact with the thermocouple. This experimental arrangement permits a determination of the thermal conduction of the capillary tube for the discharge conditions presently used. For currents varying from 25 to 130 mA, true temperatures ranging between 400 and 550 K at a pressure of 1 Torr and between 450 and 700 K at a pressure of 2 Torr, were measured in the discharge. In these temperature ranges the correction due to the emissivity of the thermocouple varies between 5 and 25 K [5].
3. Determination of the rotational temperature of N2(C3IIu}. The vibrorotational spectra of the N2(C 3 l-lu_B 3 IIg) transition were analysed by a SOPRA spectrometer ( f = 150 cm) coupled with a Hamamatsu photomultiplier (R 585). The more intense transition between C 3II u (o' = 0) and B 31]g (v" = 0) was used. The R-branch ( A N = N ' - N " = 1) of the rotational structure of this band is degraded towards the violet. In this experiment the intensities of 3 H1 rotational lines were selected to determine the rotational temperature of N2(C 3 IIu)" An example of the C 311u B 3 lag rotational spectrum obtained with a resolution 6X = 0.05 )k is given in fig. 2 for a discharge pressure of 1 Torr and a current of 50 mA. 3
,
3
~j
N2(CrIu,v=o~Brrg,v :o)
I
-
[I
-
29 2'5 2'0 3' Fig. 2. Emission rotational spectra of the N 2 second positive system C 3FIu-B 311g(u' = 0, J' ~ o" = 0, J") for p = 1 Torr and i = 50 mA. -
236
2 May 1983
For rotational levels populated according to a Boltzmann distribution with a temperature T R the Rbranch intensity is given by
IR(J' ) = const X SR(J')N 0 X exp [ - B 0 J ' ( J ' + 1)hc]kT R ],
(1)
where N O is the N2(C 3IIu, u' = 0) density, B 0 is the rotational constant, Bohc/k is equal to 2.6 K and J ' refers to rotational levels of C 31]u, v' = 0. The H 6 n l London factor SR(J ) for a 3 i]_3 II transition (Hund's b case) [6] and for high rotational levels ( J > 10) can be expressed by the following relation [7] : SR(J ) = [J(J + 2)] 2[3(J + 1)3 ,
(2)
where J refers to the lower rotational levels of B 31]g. As has been postulated previously [8,9] the high rotational levels of N2(C 3IIu, u = 0) are populated by excitation transfers such as the following process: N2(E 3~,~) + N2(X lZg ) N2(C 3Ilu, o = 0, J ' ) + N2(X l~g) .
(3)
Ochkin et al. [10] have shown that the population of levels J ' ~> 15 are perturbed by this process so that temperatures determined directly by application of (1) are too high. If we postulate, following ref. [10], that hot molecules produced by the transfer reaction (3) have a Boltzmann distribution with a temperature T b, expression (1) may be rewrit{en as I R ( J ' ) = const × S R ( J ' )
× (N O expl-~BoJ'(J' + 1)hc/kTR] +N h exp[-BoJ'(J' + 1)hc/kTh] ,
(4)
where N h is the hot-molecule density produced by reaction (3). The variation of log IR(J')/SR(J' ) obtained at p = 1 Torr and i = 50 mA is given in fig. 3. The solid line in fig. 3 fits the experimental result by using eq. (4) with the following values: T R = 425 K, T h ~ 2000 K and Nh/N 0 = 3%. For the other experimental conditions the rotational temperatures are reported in figs. 4a and 4b. The temperatures Th of hot molecules are in all cases about 2000 K and their density Nh/N 0 is a few percents. An approximate rotational temperature may
Volume 95A, n u m b e r 5
PHYSICS LETTERS
be calculated from eq. (1) (which supposes that there are no transfers) for 16 ~< J ' ~< 22. This temperature is deduced from the broken curve in fig. 3 which gives a value of about 450 K. This value is nearly equal to the accurate value deduced from eq. (4).
to rr~(J')] ~
-
-
,
r
,
~'o
4
x° o">~
I -
-
L
l
200
a
I
400
__~
I
600
800 J'(J'+l )
Fig. 3. Experimental plot o f loglIR(J')/SR(J')I as a function ofJ'(J' + 1) f o r P N 2 = 1 Torr and i = 50 mA. o experimental results; the solid line is calculated with TR = 425 K, Th = 2000 K andNh[No = 0.03. From the broken line, TR = 4 5 0 K . TR(K)
a
//
6oc /
/
/
/
P= 1 Torr Tg(K'
30C 300
4&~
TR(K)
.4o -
o~o
b
70C
6OO
2 May 1983
4. Comparison of temperature obtained by the two experimental methods. The rotational temperature T R determined by using eq. (4) is shown in figs. 4a, 4b, as a function of the gas temperature Tg measured by the thermocouple as described in section 2. The temperature variations were produced by varying the discharge current between 25 and 130 mA for two gas pressures: 1 Tort (fig. 4a) and 2 Torr (fig. 4b). The estimated accuracy is about 2% for Tg and 5% for T R. It can be concluded that a good correlation has been obtained between T R determined with rotational levels of N2(C 3IIu - B 3Ilg) and Tg measured with a thermocouple. 5. Conclusion. The rotational structure of bands emitted by excited molecules in electrical discharges enables a rotational temperature T R to be obtained when the population of the emitting levels obeys a Boltzmann distribution. However, one should be circumspect about concluding that this temperature T R is identical to the kinetic temperature. In the present study we have considered the peculiar case of nitrogen in low-temperature discharges (300 < T < 700 K). It has been shown that for the well-known transition (u' = 0 ~ o" = 0, ~, = 337.1 nm) of the second positive N2(C 3/I u - B 3IIg) the rotational temperature T R is identical to the gas temperature Tg. But to obtain the true temperature (TR) we must take into account the fact that rotational levels are perturbed by excitation transfers, mainly from the gas, for J ' > 22. Levels with J ' < 15 are difficult to resolve because of the overlapping of rotational lines near the head of the band. A fast method to obtain T R is to consider rotational levels with 16 ~< J ' ~< 22. Then we have found that T R is only overestimated by about 10%.
500 /~/~ /
40o/~ 500 400
P= 2T0rr
Tg(K~
6b0
Fig. 4. Rotational temperature T R o f N2(C 3Ilu, o = 0) as a function of gas temperature Tg for p = 1 Torr (a) and p = 2 Torr (b).
237
Volume 95A, number 5
PHYSICS LETTERS
References [ 1] H. Michel and M. Gantois, 18th Int. Conf. on Heat treatment of materials, Detroit (1980). [2] J.M. Baronnet et al., I.S.P.C. 4, Zurich (1979) 341; M. Locqueneux, F. Etile and R. Ben Aim, I.S.P.C. 4, Zurich (1979) 366. [3] A.G. Svindon, N.N. Sobolev and G.C. Tselikov, Zh. Eksp. Teor. Fiz. Pis'ma 6 (1967) 542. [4] L.S. Polak, P.A. Sergeev and D.I. Slovetsky, High Temp. 15 (1977) 13.
238
2 May 1983
[5] K.G. Enoh, Thesis M.I.T. (June 1976). [6] G. Herzberg, Molecular spectra and molecular structure (Van Nostrand, New York, 1950). [7] A. Schadee, Bull. Astron. Inst. Neth. 17 (1964) 311. [8] V.N. Ochkin, S.Yu. Savinov and N.N. Sobolev, Soy. Phys. JETP 48 (1978) 232. [9] D.J. Burns, D.E. Golden and D.W. GoUiard, J. Chem. Phys. 65 (1976) 2616. [ 10] V.N. Ochkin and S.Yu. Savinov, Zh. Prikl. Spektrosk. 28 (1978) 408.