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Flowing-afterglow measurements of collisional radiative recombination of argon ions
Chemical Physics 296 (2004) 23–27 www.elsevier.com/locate/chemphys
Flowing-afterglow measurements of collisional radiative recombination of argon ions M.P. Skrzypkowski a, R. Johnsen a
a,*
, R.E. Rosati a, M.F. Golde
b
Department of Physics and Astronomy, University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260, USA b Department of Chemistry, University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260, USA Received 8 September 2003; accepted 24 September 2003
Abstract Collisional-radiative recombination (CRR) of argon ions has been studied in the upstream region of a flowing-afterglow plasma. It is found that the recombination rate is accurately described by the CRR theory. In addition, the yield of metastable Ar(3 P2 ) and Ar(3 P0 ) atoms was determined by spectroscopic methods to be 35%, Ar(3 P2 ) being approximately six times more abundant than Ar(3 P0 ). The argon line spectrum produced by CRR consists largely of the near-infrared lines, belonging to 4p–4s and 4p0 –4s0 transitions. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Electron–ion recombination in ionized gases can occur by a variety of mechanisms. Dissociative recombination (DR) tends to be the fastest recombination mechanism whenever molecular ions are the dominant ion species, as is the case in many low-temperature plasmas. However, if the plasma contains atomic rather than molecular ions, DR is precluded and collisionalradiative recombination (CRR) e þ Aþ þ e ! A þ e
ð1Þ
becomes the principal volume loss process of free electrons. The importance of this process in electrical discharges and astrophysical plasmas has motivated extensive theoretical work on CRR, but only a limited number of experimental investigations have been carried out. The rate at which CRR occurs can be derived from relatively simple arguments. In his review of electron– ion recombination mechanisms, Flannery [1] gives a concise introduction to the theory and its historical development. Since the rate-limiting step in CRR involves
*
Corresponding author. Tel.: +1-4126249285; fax: +1-4126249163. E-mail address: [email protected] (R. Johnsen).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.09.032
radiative and collision-induced transitions between high-lying, hydrogenic Rydberg states, it is possible to derive a fairly accurate universal formula for the recombination coefficient aCRR that applies regardless of the chemical nature of the recombining ion. The ‘‘working formula’’ given by Stevefelt et al. [2] aCRR ¼ 3:8 109 Te4:5 ne þ 1:55 1010 Te0:63 þ 6 109 Te2:18 n0:37 ½cm3 =s e
ð2Þ
is based on earlier work by Bates et al. [3] and Mansbach and Keck [4]. In this formula, Te is the electron temperature in Kelvin and ne is the electron density in cm3 . The first term describes collisional recombination. It is proportional to the electron density and depends strongly on electron temperature. The second term describes radiative recombination and is independent of ne , while the third term is a correction that was introduced by Stevefelt et al. [2] to account for the competition between collisionally induced and radiative transitions among highly excited states of the product atom. In plasmas of low electron temperature the first term in the formula dominates even at moderate electron densities. For example, in the afterglow experiments that we carried out (Te 300 K and ne > 1010 cm3 ) collisional recombination accounts for >90% of the total rate. According to calculations by Byron et al. [5] for
24
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
Hþ recombination, at ne ¼ 5 1010 cm3 the rate of collisional de-excitation exceeds that of radiative deexcitation for principal quantum numbers n > 7. The theory owes its simplicity and universality to the fact that the rate-limiting steps occur between high-lying hydrogenic states. It provides little information on the rate of formation of specific lower radiating or metastable states, the spectra that are emitted by a particular recombining ion species, or the energy partitioning among the products. More elaborate models of the collisional-radiative processes plasmas are needed to answer such questions. The complexity of the task is demonstrated by the recent work by Bogaerts et al. [6,7] on collisional-radiative processes in argon glow discharges. With the exception of the early work by Veatch and Oskam [8], which showed that CRR occurs in Arþ afterglows, to our knowledge the only other relevant experimental work is the recent spectroscopic study of CRR by Tsuji et al. [9]. They studied the interesting question that arises when the recombining ions are present in two spin–orbit states, Arþ (2 P3=2 ) and Arþ (2 P1=2 ) in their case. One might surmise that CRR would leave the ion-core configuration intact but this does not always seem to be the case. Tsuji et al. analyzed the recombination spectra arising from Arþ (2 P3=2 ) and concluded that both term systems, those belonging to the 2 P3=2 and the 2 P1=2 cores, were excited. The authors proposed a tentative mechanism to explain this finding. In the following article we present results of a flowing-afterglow experiment on CRR of Arþ ions. Our study was motivated by two goals. Firstly, we wanted to test the validity of the formula for the CRR recombination coefficient under the conditions of a flowing-afterglow plasma. A second goal was to test if CRR
provided a plausible source of argon spectral emissions and of metastable argon atoms that we have often observed in our spectroscopic afterglow studies of the DR of molecular ions. In such experiments, the desired molecular ions are formed indirectly by further reactions of Arþ with reagents that are added through a gas inlet. It is important to know the flux of other reactive species (e.g. metastable Ar atoms) that enter the reaction zone along with the Arþ ions.
2. Experimental apparatus and methods Our flowing-afterglow system has the configuration shown in Fig. 1. It consists of two discharge sources (a microwave and a DC discharge), a mixing chamber, and the flow-tube proper (a stainless steel tube with an internal diameter of 6 cm and a length of 36 cm). The central flow velocity is typically 6000 cm/s. Diagnostic tools include the following: a quadrupole mass spectrometer, located at the downstream end of the flow tube analyzes the ion composition of the plasma. A movable Langmuir probe (diameter ¼ 25 lm, length ¼ 0.28 cm, used in the electron-collecting mode [10]) measures the electron densities at different points in the plasma. A movable monochromator/photomultiplier-tube assembly records optical emissions from the flow tube through two long quartz windows along the flow tube. In most experiments only the microwave discharge (in high-purity helium at a pressure of 1 Torr) is used. In that mode of operation, the active particles that emanate from the discharge are predominately metastable helium atoms He (a mixture of He(23 S) and He(21 S)). When argon gas is blended into the helium flow, Penning ionization
Fig. 1. Schematic diagram of the flow-tube apparatus (not to scale).
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
Heð23 S; 21 SÞ þ Ar ! He þ Arþ ð2 P3=2 Þ þ e
3. Measurements and results ð3Þ
converts He atoms to Arþ ions and electrons. Its rate coefficient (7 1011 cm3 /s) is sufficiently [11] large to remove He atoms in a time of a few ls. It is known that Penning ionization forms Arþ (2 P3=2 ) and Arþ (2 P1=2 ) ions in the 2:1 ratio of the statistical weights of the two states, and that the electrons are produced with energies near 4 eV [12]. Photoionization of argon by He resonance radiation from the discharge may provide a further source of argon ions, but the extent of the contribution is not known. Depending on the power of the microwave discharge and its position along the helium inlet tube, the ‘‘upstream’’ electron density ranges from 5 109 to 6 1010 cm3 . The region in which CRR of Arþ ions occurs extends from the mixing chamber to the movable gas inlet, located a few cm downstream. In the current set of experiments the movable gas inlet was used to admit nitrogen and nitric oxide for measurements of the density of argon metastables that are produced by CRR. Even though the microwave discharge operates in helium, Heþ ions constitute only a small part (1% of Arþ ) of the ion composition of the plasma, and those that are observed do not appear to be produced in the discharge. Their origin was investigated briefly. We monitored the Heþ ion signal using the mass spectrometer, or alternatively observed the emission inten2 þ 2 þ sity of the Nþ 2 ðC Ru X Rg Þ (3,9) band excited by the reaction of Heþ with N2 , in the presence or absence of argon. The tests indicated that addition of argon strongly suppressed the observed Heþ ion density. This suppression cannot be due to charge transfer Heþ + Ar ! He + Arþ ions with argon, which is a very slow process. Rather, the observed helium ions appear to be formed downstream from the discharge by the reaction He + He ! Heþ + He + e . Addition of argon quickly eliminates He and consequently suppresses this source of Heþ ions. Three different sets of experiments on CRR were carried out. In the first part, we used the Langmuir probe to measure the decay of the electron density in an Arþ afterglow for different initial electron densities. The results were compared to model calculations that incorporate diffusion and CRR. In the second part, we used a spectroscopic method to determine the density of metastable argon atoms that are produced by CRR. The third part of the experiment consisted of recording the argon line spectrum that is emitted by CRR of Arþ ions in the spectral range from 300 to 850 nm. Other methods of analyzing flow-tube data are very well known and will not be described here. Some details of these methods have been presented in a recent publication [13].
3.1. Langmuir probe measurements of the electron density In this part of the experiment, we measured the electron density as a function of the axial distance from a reference point z ¼ 0, located at the entrance of the flow tube. We varied the flux of metastable helium atoms entering from the microwave discharge by displacing the discharge cavity along the helium inlet glass tube. In this set of experiments the helium pressure was 0.721 Torr, the argon pressure was 0.159 Torr, and the central gas flow velocity in the flow tube was 5.76 103 cm/s. The measured electron densities are shown in Fig. 2 for four different initial electron densities, together with the results of model calculations. We used a simple bulkflow model that ignores the parabolic dependence of the gas flow velocity on radial distance. Adams et al. [14] have shown that such an approximation is reasonable if one uses an effective plasma flow velocity vp that is lower than the central gas flow velocity vc by factors from 0.66 to 0.79, the most appropriate value being dependent on the gas flow pattern and the radial distribution of the ions. Since neither the ion distribution nor the flow pattern are well known in the upstream region of the flow tube, we chose the plasma velocity that best reproduced
5E +10
4E +10 -3
! He þ Ar ð P1=2 Þ þ e
ne (cm )
þ 2
25
3E +10
2E +10
1E +10
0E +00
0
2
4
6
8
10
Fig. 2. Decay of the electron density ne in the Arþ /e plasma for four different initial electron densities. Solid squares: data points. Two lines are drawn through each data set. The upper line represents the calculated electron-density decay due to diffusion only, the lower represents the decay due to both diffusion and CRR.
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M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
the experimentally observed diffusion loss in the limit of small electron densities. The choice vp ¼ 0:66vc worked very well and was adopted. We treated the ambipolar diffusion loss of electrons and argon ions by assuming that the Arþ radial distribution is a fundamental diffusion mode in a cylinder. Needed diffusion constants were obtained from the zero-field limit of measured Arþ mobilities in helium [15] and argon [16], using BlancÕs law to obtain the diffusion constant in the gas mixture. The loss due to CRR was computed from Eq. (2). No other adjustable constants were used. Fig. 2 shows that the model calculations reproduce the data very well. At the lowest electron densities, CRR is negligible and the loss is entirely due to ambipolar diffusion. At higher electron densities both CRR and diffusion contribute to the loss. Since the CRR model is firmly based in theory, one may not be surprised to find such good agreement. If one accepts the CRR rate coefficient as valid, then the agreement between data and model calculations indicates that the electron temperature in that region of the flow-tube plasma is very close to that of the neutral gas. Since the CRR rate varies as Te4:5 , a 10% elevation of Te above room temperature (about 300 K) would reduce aCRR by a factor of 1.5 which would worsen the fit. The conclusion that the electrons are rapidly thermalized requires a brief consideration of the electroncooling mechanism since the He + Ar Penning ionization produces electrons with energies near 4 eV. In addition, the CRR process as such transfers heat to the electron gas. Plausible cooling mechanisms are diffusion cooling (preferential escape of fast electrons from the ambipolar potential well) and collisional energy transfer to helium atoms. The second mechanism suffices to thermalize the electrons. A simple estimate of the rate of energy transfer from electrons to helium atoms (see e.g., Dulaney et al. [17]) indicates that it takes about 2 104 electron–helium collisions (at pðHeÞ ¼ 0:72 Torr and 300 K) to reduce the electron energy from 4 eV to thermal energy, or a time of about 70 ls. This time is short compared to the average residence time of electrons in the flow tube which is on the order of 5 ms. Hence, collisional cooling due to electron– helium collisions is sufficiently rapid to ensure thermalization. It may be worth noting that a ‘‘hot electron’’ will diffuse a large distance (on the order of 20 cm) before being thermalized. Thus, even though the heat input to the electron gas is localized, one should not expect pronounced electron-temperature gradients in the flow-tube plasma. We note in passing that electron cooling in helium gas is particularly effective. By comparison, electron thermalization in argon is very slow, due to the larger mass of argon atoms and the deep Ramsauer minimum in the e /Ar momentum transfer cross-section (see e.g. Huxley and Crompton [18] for data on electron/rare-gas crosssections).
3.2. Determination of the Ar* yield from CRR of Arþ To determine the concentration of Ar* atoms produced by CRR, we added nitrogen through the movable gas inlet and recorded the intensity of the N2 ðC3 Pu B3 Pg Þð0; 0Þ band (k ¼ 337 nm) that is produced by the reaction [19,20] Ar þ N2 ! Ar þ N2 ðC3 Pu Þ:
ð4Þ
In a second step, the same band intensity was measured when Ar atoms were admitted to the flow tube from the DC discharge in argon which produces a higher flux of Ar* but a lower electron density than the microwave discharge. To improve the accuracy of this measurement, the axial dependence of the band intensities was recorded for several N2 densities and fitted to a reaction model. Examples of such data have been given in an earlier publication [13]. In the third step, the Ar* concentration obtained from the DC discharge source was inferred from Langmuir-probe measurements of the electron density increase when nitric oxide rather than nitrogen was added through the movable inlet. The Penning ionization of Ar* with nitric oxide, Ar þ NO ! Ar þ NOþ þ e
ð5Þ
has a known electron yield of (0.35 0.1) [21,22]. The addition of nitric oxide causes a sharp fourfold increase of the electron density. This method of relating densities of neutral recombination products to those of charged particles has been extensively employed in our other experiments [13] on recombination products of DR and has been found to give results consistent with other calibration methods. From measurements of this kind we concluded that the concentration of Ar* produced by CRR was (10 ± 3)% of the Arþ concentration at a distance z ¼ 4 cm, when the initial Arþ density at z ¼ 0 was 6 1010 cm3 . A simple model calculation shows that an Ar* yield (defined as the number of Ar* metastables obtained for each recombined Arþ ion) of 0.35 ± 0.1 is needed to reproduce the observed Ar* density. This yield may be slightly too large since the onset of CRR occurs a short distance upstream from the reference point. It should also be noted that the yield is an effective quantity that is the result of multiple collisions and radiative cascading, and that it may depend on the degree to which resonance radiation is ‘‘imprisoned’’. It would be wrong to view the yield as characterizing a simple three-body process, as might be suggested by Eq. (1). 3.3. Argon emissions from CRR of Arþ In our flow tube a bluish ‘‘flame’’, bright enough to be seen with the naked eye, is usually seen in the region
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
downstream from the point where argon is added. We investigated its spectral properties to learn if CRR is its origin, and perhaps to obtain additional information on recombination products. Spectral scans (from 300 to 850 nm) of the emissions from this region showed intense near-infrared Ar lines between 700 and 850 nm, originating from 4p–4s and 4p0 –4s0 transitions, and comparatively weak ‘‘blue’’ lines in the range from 400 to 600 nm, originating from 5p–4s, and 5p0 –4s0 transitions. We use the notation in which ‘‘primed’’ levels have the Arþ (2 P1=2 ) core while the unprimed levels have the Arþ (2 P3=2 ) core. The lower levels are the two 4s levels, 3 o P1 and 3 Po2 (metastable) and two 4s0 levels, 1 Po1 and 3 Po0 (metastable). We do not reproduce the spectrum here since its overall appearance is similar to that observed and calculated by Bogaerts et al. [7] for argon glow discharges. We verified that the spectrum was drastically reduced when an electron attaching gas (SF6 ) was added, indicating that electron–ion recombination was indeed the source of the observed argon emissions. The spectrum was analyzed with the goal of determining the relative yields of the two argon metastable states, Ar(3 P2 ), which has the 2 P3=2 ion core, and Ar(3 P0 ), which has the 2 P1=2 ion core. After correcting the spectrum for the spectral response of the photon counting system, we added the intensities of all observed 4p–4s and 4p0 –4s0 lines that terminate on either of the two metastable levels. One of the 4p–4s lines (912.29 nm) was beyond the range of the photo-detector and was not included in the summation. We found that the observed radiative transitions into Ar(3 P2 ) are more frequent than those into Ar(3 P0 ) by a ratio of about 6:1, quite close to the 5:1 ratio of statistical weights of the two states. If the intensity of the unobserved 912.29 nm line is substantial, the 6:1 ratio should be increased. A ratio of 5:1 would be expected if the recombining ion population consisted of Arþ (2 P3=2 ) and Arþ (2 P1=2 ) ions in the 2:1 abundance ratio of their statistical weights, and if those recombined without changing the core configuration. While the observed ratio is roughly compatible with the assumption that the ion core is preserved, it does not prove that this is true; electron collisions that randomly change the core configurations would give the same ratio. The finding that the observed ratio Ar(3 P2 )/Ar(3 P0 ) ¼ 6 is somewhat larger than the statistical ratio of 5 may simply mean that the abundance of Arþ (2 P3=2 ) is somewhat larger than twice that of Arþ (2 P1=2 ), perhaps due to electron quenching collisions that convert one state into the other. A further reduction of the Ar(3 P0 ) abundance may be caused by electron collisional de-excitation to Ar(3 P1 ). However, except for a rough estimate due to Phelps [23] (1 107 cm3 /s), its rate coefficient is not known.
27
4. Conclusions The experiments described here show that the recombination of atomic argon ions in the upstream region of a flowing afterglow is described quite accurately by the collisional-radiative model. It was one of our goals to provide a better characterization of the processes in the upstream region of a flowing afterglow which is often simply treated as ‘‘nonrecombining’’. This is an unnecessary and avoidable simplification. CRR produces results in radiating and metastable products which can affect measurements carried out further downstream, and hence should be taken into account in the analysis of the downstream reactions. Acknowledgements This work was, in part, supported by the NASA Planetary Atmospheres Program. References [1] M.R. Flannery, Adv. Atomic, Mol. Opt. Phys. 32 (1994) 117. [2] J. Stevefelt, J. Boulmer, J.-F. Delpech, Phys. Rev. A 12 (1975) 1246. [3] D.R. Bates, A.E. Kingston, R.W.P. McWhirter, Proc. Roy. Soc. A 267 (1962) 297. [4] P. Mansbach, J. Keck, Phys. Rev. 181 (1969) 275. [5] S. Byron, R.C. Stabler, P.I. Bortz, Phys. Rev. Lett. 8 (1962) 376. [6] A. Bogaerts, R. Gijbels, J. Appl. Phys. 84 (1998) 121. [7] A. Bogaerts, R. Gijbels, J. Vlcek, Spectrochim. Acta: Part B 53 (1998) 1517. [8] G.E. Veatch, H.J. Oskam, Phys. Rev. A 1 (1970) 1498. [9] M. Tsuji, T. Matsuzaki, T. Tsuji, Chem. Phys. 285 (2002) 335. [10] R. Johnsen, E.V. ShunÕko, T. Gougousi, M.F. Golde, Phys. Rev. E 50 (1994) 3994. [11] A.L. Schmeltekopf, F.C. Fehsenfeld, J. Chem. Phys. 53 (1970) 3173. [12] H. Hotop, E. Kolb, J. Lorenzen, J. Electron Spectrosc. Rel. Phenom. 16 (1979) 213. [13] M. Skrzypkowski, T. Gougousi, R. Johnsen, M.F. Golde, J. Chem. Phys. 108 (1998) 8400. [14] N.G. Adams, M.J. Church, D. Smith, J. Phys. D: Appl. Phys. 8 (1975) 1409. [15] L.A. Viehland, A.A. Viggiano,, E.A. Mason, J. Chem. Phys. 95 (1991) 7286. [16] H.W. Ellis, R.Y. Pai, E.W. McDaniel, E.A. Mason, L.A. Viehland, Atom. Data Nucl. Data Tables 17 (1976) 177. [17] J.L. Dulaney, M.A. Biondi, R. Johnsen, Phys. Rev. A 36 (1987) 1342. [18] L.G.H. Huxley, R.W. Crompton, The Diffusion and Drift of Electrons in Gases, John Wiley & Sons, New York, 1974. [19] J.H. Kolts, H.C. Brashears, D.W. Setser, J. Chem. Phys. 67 (1977) 2931. [20] N. Sadeghi, D.W. Setser, Chem. Phys. Lett. 82 (1981) 44. [21] M.F. Golde, Y.-S. Ho, H. Ogura, J. Chem. Phys. 76 (1982) 3535. [22] M.T. Jones, T.D. Dreiling, D.W. Setser, R.N. McDonald, J. Phys. Chem. 89 (1985) 4501, The authors have reanalyzed their data to give an NOþ yield of 0.34 0.15. [23] A.V. Phelps, Phys. Rev. 114 (1959) 1011.
Flowing-afterglow measurements of collisional radiative recombination of argon ions M.P. Skrzypkowski a, R. Johnsen a
a,*
, R.E. Rosati a, M.F. Golde
b
Department of Physics and Astronomy, University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260, USA b Department of Chemistry, University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260, USA Received 8 September 2003; accepted 24 September 2003
Abstract Collisional-radiative recombination (CRR) of argon ions has been studied in the upstream region of a flowing-afterglow plasma. It is found that the recombination rate is accurately described by the CRR theory. In addition, the yield of metastable Ar(3 P2 ) and Ar(3 P0 ) atoms was determined by spectroscopic methods to be 35%, Ar(3 P2 ) being approximately six times more abundant than Ar(3 P0 ). The argon line spectrum produced by CRR consists largely of the near-infrared lines, belonging to 4p–4s and 4p0 –4s0 transitions. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Electron–ion recombination in ionized gases can occur by a variety of mechanisms. Dissociative recombination (DR) tends to be the fastest recombination mechanism whenever molecular ions are the dominant ion species, as is the case in many low-temperature plasmas. However, if the plasma contains atomic rather than molecular ions, DR is precluded and collisionalradiative recombination (CRR) e þ Aþ þ e ! A þ e
ð1Þ
becomes the principal volume loss process of free electrons. The importance of this process in electrical discharges and astrophysical plasmas has motivated extensive theoretical work on CRR, but only a limited number of experimental investigations have been carried out. The rate at which CRR occurs can be derived from relatively simple arguments. In his review of electron– ion recombination mechanisms, Flannery [1] gives a concise introduction to the theory and its historical development. Since the rate-limiting step in CRR involves
*
Corresponding author. Tel.: +1-4126249285; fax: +1-4126249163. E-mail address: [email protected] (R. Johnsen).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.09.032
radiative and collision-induced transitions between high-lying, hydrogenic Rydberg states, it is possible to derive a fairly accurate universal formula for the recombination coefficient aCRR that applies regardless of the chemical nature of the recombining ion. The ‘‘working formula’’ given by Stevefelt et al. [2] aCRR ¼ 3:8 109 Te4:5 ne þ 1:55 1010 Te0:63 þ 6 109 Te2:18 n0:37 ½cm3 =s e
ð2Þ
is based on earlier work by Bates et al. [3] and Mansbach and Keck [4]. In this formula, Te is the electron temperature in Kelvin and ne is the electron density in cm3 . The first term describes collisional recombination. It is proportional to the electron density and depends strongly on electron temperature. The second term describes radiative recombination and is independent of ne , while the third term is a correction that was introduced by Stevefelt et al. [2] to account for the competition between collisionally induced and radiative transitions among highly excited states of the product atom. In plasmas of low electron temperature the first term in the formula dominates even at moderate electron densities. For example, in the afterglow experiments that we carried out (Te 300 K and ne > 1010 cm3 ) collisional recombination accounts for >90% of the total rate. According to calculations by Byron et al. [5] for
24
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
Hþ recombination, at ne ¼ 5 1010 cm3 the rate of collisional de-excitation exceeds that of radiative deexcitation for principal quantum numbers n > 7. The theory owes its simplicity and universality to the fact that the rate-limiting steps occur between high-lying hydrogenic states. It provides little information on the rate of formation of specific lower radiating or metastable states, the spectra that are emitted by a particular recombining ion species, or the energy partitioning among the products. More elaborate models of the collisional-radiative processes plasmas are needed to answer such questions. The complexity of the task is demonstrated by the recent work by Bogaerts et al. [6,7] on collisional-radiative processes in argon glow discharges. With the exception of the early work by Veatch and Oskam [8], which showed that CRR occurs in Arþ afterglows, to our knowledge the only other relevant experimental work is the recent spectroscopic study of CRR by Tsuji et al. [9]. They studied the interesting question that arises when the recombining ions are present in two spin–orbit states, Arþ (2 P3=2 ) and Arþ (2 P1=2 ) in their case. One might surmise that CRR would leave the ion-core configuration intact but this does not always seem to be the case. Tsuji et al. analyzed the recombination spectra arising from Arþ (2 P3=2 ) and concluded that both term systems, those belonging to the 2 P3=2 and the 2 P1=2 cores, were excited. The authors proposed a tentative mechanism to explain this finding. In the following article we present results of a flowing-afterglow experiment on CRR of Arþ ions. Our study was motivated by two goals. Firstly, we wanted to test the validity of the formula for the CRR recombination coefficient under the conditions of a flowing-afterglow plasma. A second goal was to test if CRR
provided a plausible source of argon spectral emissions and of metastable argon atoms that we have often observed in our spectroscopic afterglow studies of the DR of molecular ions. In such experiments, the desired molecular ions are formed indirectly by further reactions of Arþ with reagents that are added through a gas inlet. It is important to know the flux of other reactive species (e.g. metastable Ar atoms) that enter the reaction zone along with the Arþ ions.
2. Experimental apparatus and methods Our flowing-afterglow system has the configuration shown in Fig. 1. It consists of two discharge sources (a microwave and a DC discharge), a mixing chamber, and the flow-tube proper (a stainless steel tube with an internal diameter of 6 cm and a length of 36 cm). The central flow velocity is typically 6000 cm/s. Diagnostic tools include the following: a quadrupole mass spectrometer, located at the downstream end of the flow tube analyzes the ion composition of the plasma. A movable Langmuir probe (diameter ¼ 25 lm, length ¼ 0.28 cm, used in the electron-collecting mode [10]) measures the electron densities at different points in the plasma. A movable monochromator/photomultiplier-tube assembly records optical emissions from the flow tube through two long quartz windows along the flow tube. In most experiments only the microwave discharge (in high-purity helium at a pressure of 1 Torr) is used. In that mode of operation, the active particles that emanate from the discharge are predominately metastable helium atoms He (a mixture of He(23 S) and He(21 S)). When argon gas is blended into the helium flow, Penning ionization
Fig. 1. Schematic diagram of the flow-tube apparatus (not to scale).
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
Heð23 S; 21 SÞ þ Ar ! He þ Arþ ð2 P3=2 Þ þ e
3. Measurements and results ð3Þ
converts He atoms to Arþ ions and electrons. Its rate coefficient (7 1011 cm3 /s) is sufficiently [11] large to remove He atoms in a time of a few ls. It is known that Penning ionization forms Arþ (2 P3=2 ) and Arþ (2 P1=2 ) ions in the 2:1 ratio of the statistical weights of the two states, and that the electrons are produced with energies near 4 eV [12]. Photoionization of argon by He resonance radiation from the discharge may provide a further source of argon ions, but the extent of the contribution is not known. Depending on the power of the microwave discharge and its position along the helium inlet tube, the ‘‘upstream’’ electron density ranges from 5 109 to 6 1010 cm3 . The region in which CRR of Arþ ions occurs extends from the mixing chamber to the movable gas inlet, located a few cm downstream. In the current set of experiments the movable gas inlet was used to admit nitrogen and nitric oxide for measurements of the density of argon metastables that are produced by CRR. Even though the microwave discharge operates in helium, Heþ ions constitute only a small part (1% of Arþ ) of the ion composition of the plasma, and those that are observed do not appear to be produced in the discharge. Their origin was investigated briefly. We monitored the Heþ ion signal using the mass spectrometer, or alternatively observed the emission inten2 þ 2 þ sity of the Nþ 2 ðC Ru X Rg Þ (3,9) band excited by the reaction of Heþ with N2 , in the presence or absence of argon. The tests indicated that addition of argon strongly suppressed the observed Heþ ion density. This suppression cannot be due to charge transfer Heþ + Ar ! He + Arþ ions with argon, which is a very slow process. Rather, the observed helium ions appear to be formed downstream from the discharge by the reaction He + He ! Heþ + He + e . Addition of argon quickly eliminates He and consequently suppresses this source of Heþ ions. Three different sets of experiments on CRR were carried out. In the first part, we used the Langmuir probe to measure the decay of the electron density in an Arþ afterglow for different initial electron densities. The results were compared to model calculations that incorporate diffusion and CRR. In the second part, we used a spectroscopic method to determine the density of metastable argon atoms that are produced by CRR. The third part of the experiment consisted of recording the argon line spectrum that is emitted by CRR of Arþ ions in the spectral range from 300 to 850 nm. Other methods of analyzing flow-tube data are very well known and will not be described here. Some details of these methods have been presented in a recent publication [13].
3.1. Langmuir probe measurements of the electron density In this part of the experiment, we measured the electron density as a function of the axial distance from a reference point z ¼ 0, located at the entrance of the flow tube. We varied the flux of metastable helium atoms entering from the microwave discharge by displacing the discharge cavity along the helium inlet glass tube. In this set of experiments the helium pressure was 0.721 Torr, the argon pressure was 0.159 Torr, and the central gas flow velocity in the flow tube was 5.76 103 cm/s. The measured electron densities are shown in Fig. 2 for four different initial electron densities, together with the results of model calculations. We used a simple bulkflow model that ignores the parabolic dependence of the gas flow velocity on radial distance. Adams et al. [14] have shown that such an approximation is reasonable if one uses an effective plasma flow velocity vp that is lower than the central gas flow velocity vc by factors from 0.66 to 0.79, the most appropriate value being dependent on the gas flow pattern and the radial distribution of the ions. Since neither the ion distribution nor the flow pattern are well known in the upstream region of the flow tube, we chose the plasma velocity that best reproduced
5E +10
4E +10 -3
! He þ Ar ð P1=2 Þ þ e
ne (cm )
þ 2
25
3E +10
2E +10
1E +10
0E +00
0
2
4
6
8
10
Fig. 2. Decay of the electron density ne in the Arþ /e plasma for four different initial electron densities. Solid squares: data points. Two lines are drawn through each data set. The upper line represents the calculated electron-density decay due to diffusion only, the lower represents the decay due to both diffusion and CRR.
26
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
the experimentally observed diffusion loss in the limit of small electron densities. The choice vp ¼ 0:66vc worked very well and was adopted. We treated the ambipolar diffusion loss of electrons and argon ions by assuming that the Arþ radial distribution is a fundamental diffusion mode in a cylinder. Needed diffusion constants were obtained from the zero-field limit of measured Arþ mobilities in helium [15] and argon [16], using BlancÕs law to obtain the diffusion constant in the gas mixture. The loss due to CRR was computed from Eq. (2). No other adjustable constants were used. Fig. 2 shows that the model calculations reproduce the data very well. At the lowest electron densities, CRR is negligible and the loss is entirely due to ambipolar diffusion. At higher electron densities both CRR and diffusion contribute to the loss. Since the CRR model is firmly based in theory, one may not be surprised to find such good agreement. If one accepts the CRR rate coefficient as valid, then the agreement between data and model calculations indicates that the electron temperature in that region of the flow-tube plasma is very close to that of the neutral gas. Since the CRR rate varies as Te4:5 , a 10% elevation of Te above room temperature (about 300 K) would reduce aCRR by a factor of 1.5 which would worsen the fit. The conclusion that the electrons are rapidly thermalized requires a brief consideration of the electroncooling mechanism since the He + Ar Penning ionization produces electrons with energies near 4 eV. In addition, the CRR process as such transfers heat to the electron gas. Plausible cooling mechanisms are diffusion cooling (preferential escape of fast electrons from the ambipolar potential well) and collisional energy transfer to helium atoms. The second mechanism suffices to thermalize the electrons. A simple estimate of the rate of energy transfer from electrons to helium atoms (see e.g., Dulaney et al. [17]) indicates that it takes about 2 104 electron–helium collisions (at pðHeÞ ¼ 0:72 Torr and 300 K) to reduce the electron energy from 4 eV to thermal energy, or a time of about 70 ls. This time is short compared to the average residence time of electrons in the flow tube which is on the order of 5 ms. Hence, collisional cooling due to electron– helium collisions is sufficiently rapid to ensure thermalization. It may be worth noting that a ‘‘hot electron’’ will diffuse a large distance (on the order of 20 cm) before being thermalized. Thus, even though the heat input to the electron gas is localized, one should not expect pronounced electron-temperature gradients in the flow-tube plasma. We note in passing that electron cooling in helium gas is particularly effective. By comparison, electron thermalization in argon is very slow, due to the larger mass of argon atoms and the deep Ramsauer minimum in the e /Ar momentum transfer cross-section (see e.g. Huxley and Crompton [18] for data on electron/rare-gas crosssections).
3.2. Determination of the Ar* yield from CRR of Arþ To determine the concentration of Ar* atoms produced by CRR, we added nitrogen through the movable gas inlet and recorded the intensity of the N2 ðC3 Pu B3 Pg Þð0; 0Þ band (k ¼ 337 nm) that is produced by the reaction [19,20] Ar þ N2 ! Ar þ N2 ðC3 Pu Þ:
ð4Þ
In a second step, the same band intensity was measured when Ar atoms were admitted to the flow tube from the DC discharge in argon which produces a higher flux of Ar* but a lower electron density than the microwave discharge. To improve the accuracy of this measurement, the axial dependence of the band intensities was recorded for several N2 densities and fitted to a reaction model. Examples of such data have been given in an earlier publication [13]. In the third step, the Ar* concentration obtained from the DC discharge source was inferred from Langmuir-probe measurements of the electron density increase when nitric oxide rather than nitrogen was added through the movable inlet. The Penning ionization of Ar* with nitric oxide, Ar þ NO ! Ar þ NOþ þ e
ð5Þ
has a known electron yield of (0.35 0.1) [21,22]. The addition of nitric oxide causes a sharp fourfold increase of the electron density. This method of relating densities of neutral recombination products to those of charged particles has been extensively employed in our other experiments [13] on recombination products of DR and has been found to give results consistent with other calibration methods. From measurements of this kind we concluded that the concentration of Ar* produced by CRR was (10 ± 3)% of the Arþ concentration at a distance z ¼ 4 cm, when the initial Arþ density at z ¼ 0 was 6 1010 cm3 . A simple model calculation shows that an Ar* yield (defined as the number of Ar* metastables obtained for each recombined Arþ ion) of 0.35 ± 0.1 is needed to reproduce the observed Ar* density. This yield may be slightly too large since the onset of CRR occurs a short distance upstream from the reference point. It should also be noted that the yield is an effective quantity that is the result of multiple collisions and radiative cascading, and that it may depend on the degree to which resonance radiation is ‘‘imprisoned’’. It would be wrong to view the yield as characterizing a simple three-body process, as might be suggested by Eq. (1). 3.3. Argon emissions from CRR of Arþ In our flow tube a bluish ‘‘flame’’, bright enough to be seen with the naked eye, is usually seen in the region
M.P. Skrzypkowski et al. / Chemical Physics 296 (2004) 23–27
downstream from the point where argon is added. We investigated its spectral properties to learn if CRR is its origin, and perhaps to obtain additional information on recombination products. Spectral scans (from 300 to 850 nm) of the emissions from this region showed intense near-infrared Ar lines between 700 and 850 nm, originating from 4p–4s and 4p0 –4s0 transitions, and comparatively weak ‘‘blue’’ lines in the range from 400 to 600 nm, originating from 5p–4s, and 5p0 –4s0 transitions. We use the notation in which ‘‘primed’’ levels have the Arþ (2 P1=2 ) core while the unprimed levels have the Arþ (2 P3=2 ) core. The lower levels are the two 4s levels, 3 o P1 and 3 Po2 (metastable) and two 4s0 levels, 1 Po1 and 3 Po0 (metastable). We do not reproduce the spectrum here since its overall appearance is similar to that observed and calculated by Bogaerts et al. [7] for argon glow discharges. We verified that the spectrum was drastically reduced when an electron attaching gas (SF6 ) was added, indicating that electron–ion recombination was indeed the source of the observed argon emissions. The spectrum was analyzed with the goal of determining the relative yields of the two argon metastable states, Ar(3 P2 ), which has the 2 P3=2 ion core, and Ar(3 P0 ), which has the 2 P1=2 ion core. After correcting the spectrum for the spectral response of the photon counting system, we added the intensities of all observed 4p–4s and 4p0 –4s0 lines that terminate on either of the two metastable levels. One of the 4p–4s lines (912.29 nm) was beyond the range of the photo-detector and was not included in the summation. We found that the observed radiative transitions into Ar(3 P2 ) are more frequent than those into Ar(3 P0 ) by a ratio of about 6:1, quite close to the 5:1 ratio of statistical weights of the two states. If the intensity of the unobserved 912.29 nm line is substantial, the 6:1 ratio should be increased. A ratio of 5:1 would be expected if the recombining ion population consisted of Arþ (2 P3=2 ) and Arþ (2 P1=2 ) ions in the 2:1 abundance ratio of their statistical weights, and if those recombined without changing the core configuration. While the observed ratio is roughly compatible with the assumption that the ion core is preserved, it does not prove that this is true; electron collisions that randomly change the core configurations would give the same ratio. The finding that the observed ratio Ar(3 P2 )/Ar(3 P0 ) ¼ 6 is somewhat larger than the statistical ratio of 5 may simply mean that the abundance of Arþ (2 P3=2 ) is somewhat larger than twice that of Arþ (2 P1=2 ), perhaps due to electron quenching collisions that convert one state into the other. A further reduction of the Ar(3 P0 ) abundance may be caused by electron collisional de-excitation to Ar(3 P1 ). However, except for a rough estimate due to Phelps [23] (1 107 cm3 /s), its rate coefficient is not known.
27
4. Conclusions The experiments described here show that the recombination of atomic argon ions in the upstream region of a flowing afterglow is described quite accurately by the collisional-radiative model. It was one of our goals to provide a better characterization of the processes in the upstream region of a flowing afterglow which is often simply treated as ‘‘nonrecombining’’. This is an unnecessary and avoidable simplification. CRR produces results in radiating and metastable products which can affect measurements carried out further downstream, and hence should be taken into account in the analysis of the downstream reactions. Acknowledgements This work was, in part, supported by the NASA Planetary Atmospheres Program. References [1] M.R. Flannery, Adv. Atomic, Mol. Opt. Phys. 32 (1994) 117. [2] J. Stevefelt, J. Boulmer, J.-F. Delpech, Phys. Rev. A 12 (1975) 1246. [3] D.R. Bates, A.E. Kingston, R.W.P. McWhirter, Proc. Roy. Soc. A 267 (1962) 297. [4] P. Mansbach, J. Keck, Phys. Rev. 181 (1969) 275. [5] S. Byron, R.C. Stabler, P.I. Bortz, Phys. Rev. Lett. 8 (1962) 376. [6] A. Bogaerts, R. Gijbels, J. Appl. Phys. 84 (1998) 121. [7] A. Bogaerts, R. Gijbels, J. Vlcek, Spectrochim. Acta: Part B 53 (1998) 1517. [8] G.E. Veatch, H.J. Oskam, Phys. Rev. A 1 (1970) 1498. [9] M. Tsuji, T. Matsuzaki, T. Tsuji, Chem. Phys. 285 (2002) 335. [10] R. Johnsen, E.V. ShunÕko, T. Gougousi, M.F. Golde, Phys. Rev. E 50 (1994) 3994. [11] A.L. Schmeltekopf, F.C. Fehsenfeld, J. Chem. Phys. 53 (1970) 3173. [12] H. Hotop, E. Kolb, J. Lorenzen, J. Electron Spectrosc. Rel. Phenom. 16 (1979) 213. [13] M. Skrzypkowski, T. Gougousi, R. Johnsen, M.F. Golde, J. Chem. Phys. 108 (1998) 8400. [14] N.G. Adams, M.J. Church, D. Smith, J. Phys. D: Appl. Phys. 8 (1975) 1409. [15] L.A. Viehland, A.A. Viggiano,, E.A. Mason, J. Chem. Phys. 95 (1991) 7286. [16] H.W. Ellis, R.Y. Pai, E.W. McDaniel, E.A. Mason, L.A. Viehland, Atom. Data Nucl. Data Tables 17 (1976) 177. [17] J.L. Dulaney, M.A. Biondi, R. Johnsen, Phys. Rev. A 36 (1987) 1342. [18] L.G.H. Huxley, R.W. Crompton, The Diffusion and Drift of Electrons in Gases, John Wiley & Sons, New York, 1974. [19] J.H. Kolts, H.C. Brashears, D.W. Setser, J. Chem. Phys. 67 (1977) 2931. [20] N. Sadeghi, D.W. Setser, Chem. Phys. Lett. 82 (1981) 44. [21] M.F. Golde, Y.-S. Ho, H. Ogura, J. Chem. Phys. 76 (1982) 3535. [22] M.T. Jones, T.D. Dreiling, D.W. Setser, R.N. McDonald, J. Phys. Chem. 89 (1985) 4501, The authors have reanalyzed their data to give an NOþ yield of 0.34 0.15. [23] A.V. Phelps, Phys. Rev. 114 (1959) 1011.