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Measurements of transition probabilities for two N I infrared transitions and their application for diagnostics of low temperature plasmas
Spectrochimica Acta Part B 65 (2010) 113–119
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Spectrochimica Acta Part B j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s a b
Measurements of transition probabilities for two N I infrared transitions and their application for diagnostics of low temperature plasmas A. Baclawski ⁎, J. Musielok Institute of Physics, Opole University, ul. Oleska 48, 45-052 Opole, Poland
a r t i c l e
i n f o
Article history: Received 24 August 2009 Accepted 27 October 2009 Available online 31 October 2009 Keywords: Plasma diagnostic Temperature determination Nitrogen spectrum Transition probabilities
a b s t r a c t Spectra emitted from a wall-stabilized arc, running in a gas mixture of helium, argon, nitrogen, oxygen and traces of hydrogen have been studied. Intensities of selected spectral transitions of neutral nitrogen and oxygen have been measured. Applying the Boltzmann plot method and using a reliable set of O I transition probabilities of spectral lines, originating from levels considerably spread in excitation energies, the temperatures of arc plasmas have been determined. Line intensities of two N I infrared transitions, originating from doubly excited terms 3p′ 2Fo and 3p′ 2G have been measured. In order to obtain the corresponding transition probabilities (Aki) for these lines, intensities of other N I infrared lines, with well known transition probabilities (taken from recently published data by Wiese and Fuhr [W.L. Wiese and J.R. Fuhr, Improved critical compilations of selected atomic transition probabilities for neutral and singly ionized carbon and nitrogen, J. Phys. Chem. Ref. Data 36 (2007) 1287–1345] from National Institute of Standards and Technology — NIST) have been measured. For evaluation of the transition probabilities the temperatures obtained from the above mentioned O I Boltzmann plots have been used. The results agree satisfactorily with older data found in literature. The new Aki values for transitions involving the doubly excited levels, together with Aki values taken from the above mentioned NIST source (used for determination of the new Aki values), are proposed as a convenient set for determining temperatures of plasmas containing nitrogen atoms. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Intensities of spectral lines are widely applied for diagnostic purposes of low temperature plasmas. In many plasma sources, ranging from flames and various types of electrical discharges to astrophysical objects, neutral (atomic) nitrogen is present. Therefore, the knowledge of reliable transition probabilities of neutral nitrogen (N I) suitable for temperature determination is strongly demanded. If the plasma is optically thin and its geometry is simple (homogeneous along the line of sight or revealing cylindrical symmetry) the so-called emission coefficient of spectral line can be easily derived from directly measured line intensities. The emission coefficient is proportional to the number density (population) of the upper energy level of the considered transition. By applying appropriate models describing the plasma state (usually Local Thermal Equilibrium — LTE, or partial LTE) the total densities of plasma components can be easily evaluated. In majority of laboratory and technical plasmas, the dominating processes leading to population of excited atomic levels are collisions between particles. Among them electron–atom (ion) collisions usually play the decisive role. As a rule, the efficiencies of these processes in plasmas depend on the excitation energy of the considered atomic ⁎ Corresponding author. E-mail address: [email protected] (A. Baclawski). 0584-8547/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2009.10.007
levels as well as on the electron density and the relative velocity of colliding particles. Therefore, the electron temperature may be determined from measured intensities of lines, originating from levels with significant different excitation energies. This method of temperature determination is known as the Boltzmann plot technique [1]. The great advantage of this method is that it does not require the knowledge of populations of excited levels in an absolute scale. The uncertainty of this method depends not only on accuracy of measurements of emission coefficients and on the quality of applied Aki data, but also on the energy difference between excited upper levels of transitions used for construction of the Boltzmann plot. The wider the energy gap, the more reliable the temperature determination. From a practical point of view, the wavelength interval where the applied spectral lines appear is also of great importance — the narrower the wavelength range, the easier it is to determine relative emission coefficients with reliable accuracy. Recent progress in construction of charge coupled devices made the detection of spectra significantly easier also in the infrared wavelength interval. Therefore, we decided to search for a suitable set of N I spectral lines for temperature determination in this spectral interval. 2. Selection of spectral transitions In Table 1, the atomic data characterizing the selected O I and N I transitions are listed. The transition probabilities for the “thermometric”
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Table 1 Atomic data for selected O I and N I spectral transitions are listed. No
Emitter
Transition
λki (nm)
gi
gk
Ei (eV)
Ek (eV)
Aki (107 s− 1)
Acc.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
OI
(4So)3s 5So–(4So)3p 5P (4So)3p 5P–(4So)3d 5Do (2Do)3s 1Do–(2Do)3p 1P (2Do)3p 3F–(2Do)3d 3Go (3P)3s 2P–(3P)3p 2Do
777.337 926.387 948.289 949.794 938.680 946.068 939.279 1071.35 1075.79 1065.30 1071.80 1062.32 1064.40 1051.34 1050.03 1052.06 1050.70 1054.96 1053.96 981.001 979.856 983.461 982.275 987.215 986.333
5 15 5 14 2 4 4 4 6 2 6 2 4 2 2 4 4 6 6 4 4 6 6 8 8
15 25 3 18 4 4 6 6 6 4 4 2 2 2 4 4 6 6 8 2 4 4 6 6 8
9.146 10.741 12.728 14.099 10.680 10.690 10.690 11.840 11.844 11.837 11.844 11.837 11.840 11.837 11.837 11.840 11.840 11.844 11.844 11.753 11.753 11.758 11.758 11.764 11.764
10.741 12.079 14.036 15.404 12.000 12.000 12.010 12.997 12.997 13.001 13.001 13.004 13.004 13.016 13.018 13.018 13.019 13.019 13.020 13.016 13.018 13.018 13.019 13.019 13.020
3.69 4.46 2.34 3.2 2.13 0.373 2.51 0.716 0.392 0.903 0.375 0.540 0.675 1.91 0.654 1.59 1.32 1.23 2.54 0.542 0.333 0.450 0.574 0.297 1.03
A A B C+ B B B B+ B+ B+ B+ B+ B+ B+ B+ B+ B+ B+ B+ B B B B B B
NI
(3P)3p 4Po–(3P)3d 4P
(3P)3p 4Po–(3P)3d 4D
(3P)3p 4Do–(3P)3d 4D
In the last column, the accuracies of Aki data are given using the convention introduced by NIST. All N I Aki values are taken from the recent compilation of Wiese and Fuhr [4]. The first three O I transition probabilities are taken from [2], the last (No. 4) is taken from our recent paper [3].
O I lines at λλ 777.337, 926.387, 948.289 nm, are taken from Wiese et al. [2]. The Aki value for the doubly excited O I triplet transition at 949.794 nm, which is based on the absolute scale of [2], is taken from our recent paper [3]. The N I spectral lines selected for the purpose of this work belong to 4 multiplets: 3s 2P–3p 2Do, 3p 4Do–3d 4D, 3p 4Po–3d 4D, and 3p 4Po– 3d 4P. The corresponding transition probabilities for these transitions are taken from the recent compilation of Wiese and Fuhr [4], where the N I data of Froese Fischer and Tachiev [5] are recommended as the most reliable ones. These spectral lines appear within the wavelength range from 938 to 1055 nm, which is of great advantage for accurate relative line intensity measurements. Unfortunately, also the maximum gap between excitation energies of the upper levels is narrow (ΔE = 1.16 eV), and thus possible uncertainties in temperature determination, based on measured line intensities and the Boltzmann plot method, are expected to be significant. Therefore, into the proposed nitrogen “thermometric” set we included two doubly excited N I transitions, which have not been calculated by Froese Fischer and Tachiev and, consequently are not listed in the compilation [4], namely the transitions 3s′ 2D–3p′ 2Fo and 3p′ 2Fo–3d′ 2G. The Aki data for both these transitions are reported in the old paper by Richter [6]. The Aki value for the transition at 904.76 nm (3s′ 2D–3p′ 2Fo) is also listed in the monograph by Wiese et al. [2]. In Fig. 1, the partial Grotrian diagram of the N I atomic system is presented showing all selected spectral transitions. In order to check how the old data of Richter agree with contemporary data reported by Wiese et al. [2] and Wiese and Fuhr [4], we compare the Aki data for selected N I multiplets in Table 2. The comparison reveals an overall good agreement between the data of Richter [6] and the data reported by Wiese et al. [2] as well as the very recent data of Froese Fischer and Tachiev [5] recommended by Wiese and Fuhr [4], with the exception of results for the multiplet 3s 2P–3p 2Do, where the discrepancies of about 20% are encountered. Even though the Aki value for the transition 3s′ 2D–3p′ 2Fo, recommended in the monograph [2] agrees well with the result of Richter [6], the new compilation [4] does not contain the Aki value for this transition. The discrepancy between both results taken from NIST
[2,4] in the case of the transition 3p 4Po–3d 4P is somewhat mysterious: the more recent result is a factor of 1.6 larger than the result given in the monograph [2]. Because of the above mentioned discrepancies, it seems to be somewhat risky to include the data of Richter [6] into the set of transition probabilities taken from recently critically evaluated data by Wiese and Fuhr [4], and proposing them for reliable temperature determination of plasmas without verifying the old measurements of Richter. Therefore, we decided to determine the transition probabilities for the two doubly excited multiplets and normalize them to the N I data reported by Froese Fischer and Tachiev [5] and recommended by Wiese and Fuhr [4].
Fig. 1. The partial Grotrian diagram of the N I atomic system is presented showing all studied spectral transitions. Emission coefficients for transitions between levels belonging to the excited atomic core configuration (1D) have been measured and the respective transition probabilities have been determined in this work.
A. Baclawski, J. Musielok / Spectrochimica Acta Part B 65 (2010) 113–119 Table 2 Comparison of selected multiplet transition probabilities determined by Richter [6] with results reported in two recent NIST publications [2] and [4] is presented. λki (nm)
Multiplet
3
2
3
2
o
( P)3 s P–( P)3p D (3P)3p 4Do–(3P)3d 4D (3P)3p 4Po–(3P)3d 4D (3P)3p 4Po–(3P)3d 4P (1D)3 s 2D–(1D)3d 2Fo (1D)3p 2Fo–(1D)3d 2G
939.53 983.06 1052.6 1070.7 904.76 1059.5
Aki (107 s− 1) Ref. [6]
Ref. [2]
Ref. [4]
2.14 1.00 2.47 1.11 2.74 3.58
2.63 0.937 2.43 0.718 2.80 –
2.51 1.02 2.57 1.18 – –
Aki [2]/ Aki [6]
Aki [4]/ Aki [6]
1.23 0.94 0.98 0.65 1.02 –
1.17 1.02 1.04 1.06 – –
115
For both experiments: A and B, the radiation from the arc in endon (axial) direction was registered several times in spectral intervals embracing all transitions (O I, N I) listed in Tables 1 and 2, and additionally also in the spectral range around the hydrogen Hβ line at 486.1 nm. We restricted our spectroscopic analysis to the arc radiation originating from plasma layers near the arc axis r ≤ 1.7 mm (the total arc radius was 2.5 mm). The radial gradients of the plasma parameters (electron density, atomic number density and temperature) are very weak up to the distance from the arc axis of 1.0 mm. The temperature gradients in this region are less than 300 K/mm, and the electron density gradients do not exceed 0.3 · 1016 cm− 3/mm. For distances larger than 1.0 mm from the axis, the mean gradients are around 1000 K/mm and 0.65 · 1016 cm− 3/mm respectively.
3. Experimental set-up and details of the measurements The spectroscopic instrumentation applied in this paper is described in detail in our recent paper devoted to a similar subject — the determination of transition probabilities in neutral oxygen suitable for temperature determination [3]. Also the registration of the spectra, including the intensity calibration procedure, self-absorption checks and evaluation of individual total line intensities were performed in the same manner as in the above mentioned paper. The wallstabilized high-current arc, operated at atmospheric pressure in a mixture of helium, argon, nitrogen, oxygen, and with some traces of hydrogen was applied as the excitation source. Oxygen was introduced into the plasma in order to measure the O I line intensities of the “thermometric” set proposed in our previous paper [3]. The presence of traces of hydrogen in the plasma allows the electron density to be determined on the basis of Stark broadening of the Hβ transition. For the purpose of this work, we used a gas cylinder with pure argon and prepared two other cylinders with the following gas compositions: (99.5% He + 0.5% H2) and (75% N2 + 25% O2). The arc was operated at d.c. current of 45 A and at two different gas compositions and gas flow rates. In both cases, helium is the dominant plasma component. By varying the argon flow rate the main plasma parameters temperature and electron density can be changed, particularly their radial distributions. Larger amount of argon causes an increase of electron density and the decrease of temperature at the arc axis. By changing the amount of the O2 + N2 gas mixture the intensities of selected O I and N I lines can be optimized for accurate line intensity measurements (albeit strongly enough and with negligible self-absorption). The operating conditions of the two experiments (A and B) are given in Table 3. In the last column of this table the electron densities at the arc axis, determined from measured Hβ line widths and applying theoretical broadening data of Gigosos and Cardeñoso [7], are listed. As mentioned earlier, in order to determine the electron density of the arc plasma, the hydrogen Balmer β line has been registered. From measured Full Widths at Half Maximum (FWHM) the electron densities have been deduced. The calculations of Gigosos and Cardeñoso [7] include the ion dynamic effects contributing to the measured line width. Other broadening mechanisms, such as instrumental and Doppler broadening, have also been taken into account while determining the pure Stark FWHM of the Hβ line. The plasma temperature values, needed for determining the electron densities, have been obtained from measured intensities of selected O I spectral lines (details of the temperature determination are given below). Table 3 Operating conditions of the arc source for both experiments A and B, together with the obtained electron densities at the arc axis are given. Expt.
A B
Flow rate from gas cylinder (cm3 s− 1) 99.5% He + 0.5% H2
Ar
75% N2 + 25% O2
20 20
3.4 4.4
0.13 0.21
Ne (1016 cm− 3) 1.5 ± 0.3 2.0 ± 0.4
4. Determination of transition probabilities for two doubly excited N I transitions Detailed elaboration of the measured spectra has been performed for selected plasma layers (of both experiments A and B) differing in the distance from the arc axis and covering the plasma electron density range from 5.3 · 1015 to 2.0 · 1016 cm− 3. By constructing Boltzmann plots on the basis of measured O I line intensities, the plasma temperatures for various plasma layers have been determined. In Fig. 2 such Boltzmann plots are shown for axial plasma layers (r ≤ 0.052 mm) corresponding to both experiments, A and B. The quantities ln (Iki · λki/gk · Aki), plotted in the upper part of the figure for three N I upper terms (3s 2Do, 3p 4P, 3p 4D), have been obtained by averaging the values ln (Iki · λki/gk · Aki), determined from measured intensities of individual spectral lines (listed in Table 1), originating from respective initial upper terms. For determination of transition probabilities of the two doubly excited multiplets, the radiation originating from on-axis plasma layers with the largest electron densities (experiment B) has been used. According to the pLTE criteria given by Griem [8], for temperatures around 10,000–11,000 K electron density of 1.7 · 1014 cm− 3 is sufficient for establishing Boltzmann-like population among excited levels with principal quantum numbers n = 3. The axial electron
Fig. 2. Boltzmann plots based on measured intensities of O I spectral transitions corresponding to axial plasma layers of experiments A and B are shown. The triangles above the two Boltzmann plots correspond to the averaged quantities ln (Iki · λki/gk · Aki) for three N I terms (3p 2Do, 3d 4P, 3d 4D) — for details see the text. The solid symbols correspond to the results of experiment B, the open ones to the results of experiment A. The arrows on the right hand side indicate the excitation energies of the two doubly excited terms 3p′ 2Fo and 3d′ 2G. For transitions originating from these terms new Aki values have been obtained in this work.
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tral instrumentation. Therefore, for these overlapping components individual transition probabilities could not be determined. The transition probabilities (Aki) for these two selected N I multiplets have been determined on the basis of measured total line intensities (Iki) of the studied fine structure components (or the sum of two fine structure components) and the intensity of a reference spectral line (IRmn) from the following formula: R
R
Aki = Amn ⋅
R
gm λki Iki E −Em ⋅ R ⋅exp k kT gk λRmn Imn
! ð1Þ
where: ARmn, λRmn, gRm and ERm are the transition probability, wavelength, statistical weight and excitation energy of the upper level of the reference line, λki, gk, and Ek are the wavelength, statistical weight and excitation energy of the upper level of the studied line, and kT = 0.9495 eV is the plasma temperature expressed in energy units (T(expt. B) = 11,020 K). The N I line intensities were determined by averaging data obtained from a few independent registrations of the plasma radiation. The transition probabilities for the two selected multiplets have been determined taking as a reference all N I transitions listed in Table 1, with quoted accuracies B + (i.e. with uncertainties ≤7%): 6 lines each, originating from the upper terms 3d 4P and 3d 4D. In Table 4, the averaged Aki values (in absolute scale) are compared with data available in literature [2,6,9,10]. In the right part of this table the corresponding line strengths, normalized to the sum of 100 within each multiplet, are compared. 5. Discussion of results
Fig. 3. The measured N I multiplets in the infrared part of the spectrum from the on-axis plasma layer of experiment B, obtained at plasma conditions Ne = 2 · 1016 cm− 3 and T = 11,020 K, are shown. In the case of both multiplets two fine structure components are not resolved by our instrumentation. The measured relative line intensities within each multiplet are in very good agreement with those resulting from the LS coupling scheme.
density of experiment B is 2 · 1016 cm− 3 and is about 120 times larger than the density required by the pLTE criteria. Examples of our measured spectra, comprising the two doubly excited N I infrared transitions, emitted from the on-axis plasma layer of experiment B, are presented in Fig. 3. As can be seen, in both cases two fine structure components are not resolved enough by our spec-
Our absolute transition probabilities, which are based on the absolute scale of Aki values for the N I multiplets 3p 4Po–3d 4P and 3p 4 o P –3d 4D, taken from [4,5], agree within the error limits with all results available in literature. The relative uncertainties of our Aki data as well as those of Richter [6] are the same — ±15%. Our Aki values are systematically somewhat larger than the data of Richter [6] (8–16%) as well as those of Kurucz and Bell [10] (13–18%). The transition probabilities for the multiplet 3s′ 2D–3p′ 2Fo could also be compared with results of the CIV3 calculations of Hibbert et al. [9] and with data reported in the monograph by Wiese et al. [2]. Our Aki data are about 6% and 12% larger than the results of Hibbert et al. [9] and Wiese et al. [2] respectively. The comparison of relative line strengths within both multiplets shows excellent agreement with all available data sources, including those resulting from the LS coupling scheme. The uncertainties given in the table arise from the accuracy of transition probabilities of the reference data (7%) and from uncertainties
Table 4 Comparison of absolute transition probabilities for two infrared N I multiplets obtained in this work with results taken from literature. Multiplet
λki (nm)
gi
gk
(1D)3 s 2D–(1D)3p 2Fo
904.759 904.5878 904.9690a 1059.54 1059.200 1059.690b
10 6 10 14 6 8
14 8 6 18 8 18
(1D)3 s 2Fo–(1D)3p 2G
Aki (107 s− 1)
Srel ki
This work
Ref. [6]
Ref. [2]
Ref. [9]
Ref. [10]
3.17 ± 0.48 3.16 ± 0.47 1.56 ± 0.24 3.93 ± 0.59 3.81 ± 0.57 2.24 ± 0.34
2.74 2.68 1.41 3.58 3.52 2.01
2.80 2.80 1.40 – – –
2.94 2.94 1.47 – – –
2.717 2.685 1.380 3.391 3.240 1.951
This work
LS
Ref. [6]
Ref. [10]
56.9 ± 2.0 43.1 ± 1.5
57.1 42.9
55.8 44.2
56.4 43.6
43.0 ± 1.5 57.0 ± 1.8
42.9 57.1
43.7 56.3
42.4 57.6
The transitions labeled with superscripts “a” and “b” consist of two blended fine structure components. In the right part of the table the corresponding relative line strengths, normalized to the sum of 100 within each multiplet, are given. In the case of the first multiplet (1D)3 s 2D–(1D)3p 2Fo, the relative line strengths resulting from the LS coupling scheme are identical with those reported by Wiese et al. [2] and Hibbert et al. [9], therefore we do not include these data in the comparison of relative line strengths. a Two lines: 904.9492 nm (6–6) + 904.9889 nm (4–6). b Two lines: 1059.686 nm (8–10) + 1059.696 nm (8–8).
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Fig. 4. The measured N I spectrum in the wavelength range 1053–1060 nm is shown. The spectrum illustrates the advantage of applying relative line intensity measurements for Aki determination. The studied and the reference lines are close in wavelength; the line to continuum ratios as well as the signal to noise ratios are favorable for accurate relative intensity measurements.
of our relative line intensity measurements (systematic and statistical origin). Since the determination of transition probabilities is based on relative line intensity measurements, the possible systematic errors are rather small. As can be seen from Fig. 4, the multiplet 3p′ 2Fo–3d′ 2G appears in the spectrum very close to the reference multiplet 4Po–4D. In the case of the transition 3s′ 2D–3p′ 2Fo the wavelength difference between the studied lines and the reference lines is in the range of 45– 71 nm. The largest possible systematic errors arise from: (i) the uncertainty of temperature determination of the plasma layer applied for evaluation of Aki, and (ii) the radiance calibration procedure. In the case of the multiplet 3p′ 2Fo–3d′ 2G, the possible error arising from source mentioned as (i) is larger than for the multiplet 3s′ 2D–3p′ 2Fo, because the excitation energy gap between the respective upper terms of the studied and reference transitions is larger (1.88 eV). However, even in this case the contribution to the uncertainty of Aki determination does not exceed 3%. On the other hand, the possible error arising from the source mentioned as (ii) is larger in the case of the multiplet 3s′ 2D– 3p′ 2Fo. Nevertheless, since the intensity of the radiation standard (tungsten strip lamp) in the wavelength range 900–1060 nm does not change substantially and the sensitivity of our registration system decreases monotonically with λ, these possible errors are small. The uncertainties of relative line intensity determination depend slightly on the selected line pairs and amount about 3% to 6%. The total relative uncertainties of our transition probabilities are ±15%. We are not able to decide if possible systematic errors, bound up with the determination procedure, may lead to final results which are higher or lower compared to the absolute scale proposed by the NIST team [4,5]. 6. Application of the proposed N I spectral line set for temperature determination of the off-axis arc plasma layers In order to check the usefulness of the proposed set of N I lines for diagnostic purposes, we have determined the radial temperature and electron density distributions in our arc for the conditions of experiment A. Knowing the temperature distribution, the electron density distribution has been obtained from measured FWHM of the Hβ line — the details are described in section: Experimental set-up and details of the measurements. The temperature was obtained from measured radial distributions of the respective O I and N I line intensities. In Fig. 5 we present four Boltzmann graphs based on both sets of “thermometric” lines: the O I and N I set, corresponding to
Fig. 5. Four Boltzmann plots constructed on the basis of measured intensities of O I (upper graphs) and N I (lower graphs) lines registered from different plasma layers are shown.
selected (different r) plasma layers. The plasma temperatures resulting from Boltzmann plots (slopes of the best fit straight lines) based on O I lines are systematically larger than those based on N I lines — the discrepancies, however, do not exceed 600 K (see Table 5). In Fig. 6 the electron density and temperature distributions in our arc discharge of experiment A are shown. For evaluations of radial temperature distributions three Aki sets have been applied: the O I set proposed in [3], our present N I set and the Aki values reported by Richter [6]. As mentioned above, the temperatures based on measured O I line intensities are systematically larger than those obtained using the N I data. On the other hand, the error bars are larger in case of
Table 5 Electron densities and temperatures determined for four selected plasma layers of the arc discharge are quoted. r (mm)
Ne (1015 cm− 3)
TOI (K)
TNI (K)
0 1.0 1.5 1.7
15 ± 3 11 ± 2 7.0 ± 1.6 5.3 ± 1.2
11,370 ± 110 10,940 ± 80 10,390 ± 160 9740 ± 330
10,780 ± 160 10,350 ± 180 9920 ± 290 9470 ± 330
The temperatures are determined from Boltzmann plots based on the O I and N I line sets. The quoted uncertainties of T-determination arise only from the best fit to the experimental points shown on the graph in Fig. 5, and do not include the contribution originating from uncertainties of applied (relative) transition probability values.
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Fig. 6. Radial distributions of temperature and electron density of the plasma generated in a wall-stabilized arc at working conditions of experiment A are shown. The temperatures have been obtained applying the Boltzmann plot method based on two sets of “thermometric” lines: the O I set (triangles) and the proposed N I set (squares). For evaluation of temperature distributions based on N I line intensities two sets of transition probabilities have been used: the data of Richter [6] (open squares) and our proposed Aki set (solid squares), consisting of the NIST data [4] and the new Aki values determined in this work. The error bars correspond to uncertainties of T-determination arising only from the best fit to the experimental points on the respective Boltzmann plots, and do not include the contribution originating from uncertainties of applied (relative) transition probability values.
using the N I sets, particularly if Richter's Aki data are applied. The smaller uncertainties in case of using the O I set are caused mainly by wider energy separation of upper levels of the transitions involved — in the case of O I ΔE = 4.66 eV, while in the case of N I this gap is significantly (1.6 times) smaller. The temperature values obtained by applying Richter's data are systematically somewhat smaller than those based on our proposed Aki set. This is not surprising since our Aki values are systematically slightly larger than Richter's data. The relative good agreement between these two radial temperature distributions, however, seems to be incidental. In Fig. 7 we show two N I Boltzmann plots, corresponding to the on-axis plasma layer of experiment A. For construction of the upper graph the Aki values of Richter [6] and for the lower our N I data set have been applied. Both Boltzmann plots lead to nearly the same temperatures, but the scatter of experimental points in the case of using Richter's data is significantly larger. This larger scatter explains also the respective larger error bars on the graph (in case of using Richter's data) shown on Fig. 7. It has to be emphasized that the uncertainties quoted in Table 5 and error bars shown on Fig. 6 result only from the fitting procedure, used for construction of the Boltzmann plots, and do not include possible contributions originating from uncertainties of applied (relative) transition probability values.
Fig. 7. Two N I Boltzmann plots, corresponding to the on-axis plasma layer of experiment A, are shown. For construction of the upper graph the Aki values of Richter [6] and for the lower graph our proposed N I data set have been applied. Both Boltzmann plots lead to nearly the same temperatures but the scatter of experimental points, in case of using our proposed Aki data set, is significantly smaller.
7. Conclusions Transition probabilities for two N I multiplets have been determined by emission spectroscopy method. The absolute scale of Aki values was established by comparing measured relative line intensities of the studied lines, with measured intensities for N I lines belonging to 2 multiplets 3p 4Po–3d 4D, 3p 4Po–3d 4P, and applying transition probabilities for these reference lines calculated by Froese Fischer and Tachiev [5] and recommended in the recent compilation by Wiese and Fuhr [4]. The new Aki data, together with those used as reference lines as well as the data for lines belonging to the multiplets 3s 2P–3p 2Do and 3p 4Do–3d 4D, form a suitable and convenient set of lines for temperature determination by applying the Boltzmann plot method. The proposed N I lines appear in a rather narrow spectral interval (130 nm), which is advantageous for performing relative line intensity measurements with good accuracy. The upper terms of the selected multiplets are spread in excitation energy by 2.9 eV, i.e. large enough for constructing reliable Boltzmann plots for low temperature plasmas.
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A. Baclawski, J. Musielok / Spectrochimica Acta Part B 65 (2010) 113–119 [2] W.L. Wiese, J.R. Fuhr, T.M. Deters, Atomic transition probabilities of carbon, nitrogen, and oxygen — a critical data compilation, J. Phys. Chem. Ref. Data Monogr. 7 (1996). [3] A. Bacławski, J. Musielok, Transition probabilities for some infrared O I spectral lines — application for determining excitation temperatures in low temperature plasmas, Spectrochim. Acta Part B 63 (2008) 1315–1319. [4] W.L. Wiese, J.R. Fuhr, Improved critical compilations of selected atomic transition probabilities for neutral and singly ionized carbon and nitrogen, J. Phys. Chem. Ref. Data 36 (2007) 1287–1345. [5] C. Froese Fischer, G. Tachiev, Breit–Pauli energy levels, lifetimes, and transition probabilities for the beryllium-like to neon-like sequences, At. Data Nucl. Data Tables 87 (2004) 1–184.
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[6] J. Richter, Über Oscillatorstärken von Multiplets des neutralen Stickstoffs, Z. Astrophys. 51 (1961) 177–186. [7] M.A. Gigosos, V. Cardeñoso, New plasma diagnosis tables of hydrogen Stark broadening including ion dynamics, J. Phys. B 29 (1996) 4795–4838. [8] H.R. Griem, Validity of local thermal equilibrium in plasma spectroscopy, Phys. Rev. 131 (1963) 1170–1176. [9] A. Hibbert, E. Biémont, M. Godefroid, N. Vaeck, New accurate transition probabilities for astrophysically important spectral lines of neutral nitrogen, Astron. Astrophys., Suppl. Ser. 88 (1991) 505–524. [10] R.L. Kurucz, B. Bell, Atomic Line Data Kurucz, Smithsonian Observatory, Cambridge, MA, 1995 CD-ROM no. 23.
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Spectrochimica Acta Part B j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s a b
Measurements of transition probabilities for two N I infrared transitions and their application for diagnostics of low temperature plasmas A. Baclawski ⁎, J. Musielok Institute of Physics, Opole University, ul. Oleska 48, 45-052 Opole, Poland
a r t i c l e
i n f o
Article history: Received 24 August 2009 Accepted 27 October 2009 Available online 31 October 2009 Keywords: Plasma diagnostic Temperature determination Nitrogen spectrum Transition probabilities
a b s t r a c t Spectra emitted from a wall-stabilized arc, running in a gas mixture of helium, argon, nitrogen, oxygen and traces of hydrogen have been studied. Intensities of selected spectral transitions of neutral nitrogen and oxygen have been measured. Applying the Boltzmann plot method and using a reliable set of O I transition probabilities of spectral lines, originating from levels considerably spread in excitation energies, the temperatures of arc plasmas have been determined. Line intensities of two N I infrared transitions, originating from doubly excited terms 3p′ 2Fo and 3p′ 2G have been measured. In order to obtain the corresponding transition probabilities (Aki) for these lines, intensities of other N I infrared lines, with well known transition probabilities (taken from recently published data by Wiese and Fuhr [W.L. Wiese and J.R. Fuhr, Improved critical compilations of selected atomic transition probabilities for neutral and singly ionized carbon and nitrogen, J. Phys. Chem. Ref. Data 36 (2007) 1287–1345] from National Institute of Standards and Technology — NIST) have been measured. For evaluation of the transition probabilities the temperatures obtained from the above mentioned O I Boltzmann plots have been used. The results agree satisfactorily with older data found in literature. The new Aki values for transitions involving the doubly excited levels, together with Aki values taken from the above mentioned NIST source (used for determination of the new Aki values), are proposed as a convenient set for determining temperatures of plasmas containing nitrogen atoms. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Intensities of spectral lines are widely applied for diagnostic purposes of low temperature plasmas. In many plasma sources, ranging from flames and various types of electrical discharges to astrophysical objects, neutral (atomic) nitrogen is present. Therefore, the knowledge of reliable transition probabilities of neutral nitrogen (N I) suitable for temperature determination is strongly demanded. If the plasma is optically thin and its geometry is simple (homogeneous along the line of sight or revealing cylindrical symmetry) the so-called emission coefficient of spectral line can be easily derived from directly measured line intensities. The emission coefficient is proportional to the number density (population) of the upper energy level of the considered transition. By applying appropriate models describing the plasma state (usually Local Thermal Equilibrium — LTE, or partial LTE) the total densities of plasma components can be easily evaluated. In majority of laboratory and technical plasmas, the dominating processes leading to population of excited atomic levels are collisions between particles. Among them electron–atom (ion) collisions usually play the decisive role. As a rule, the efficiencies of these processes in plasmas depend on the excitation energy of the considered atomic ⁎ Corresponding author. E-mail address: [email protected] (A. Baclawski). 0584-8547/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2009.10.007
levels as well as on the electron density and the relative velocity of colliding particles. Therefore, the electron temperature may be determined from measured intensities of lines, originating from levels with significant different excitation energies. This method of temperature determination is known as the Boltzmann plot technique [1]. The great advantage of this method is that it does not require the knowledge of populations of excited levels in an absolute scale. The uncertainty of this method depends not only on accuracy of measurements of emission coefficients and on the quality of applied Aki data, but also on the energy difference between excited upper levels of transitions used for construction of the Boltzmann plot. The wider the energy gap, the more reliable the temperature determination. From a practical point of view, the wavelength interval where the applied spectral lines appear is also of great importance — the narrower the wavelength range, the easier it is to determine relative emission coefficients with reliable accuracy. Recent progress in construction of charge coupled devices made the detection of spectra significantly easier also in the infrared wavelength interval. Therefore, we decided to search for a suitable set of N I spectral lines for temperature determination in this spectral interval. 2. Selection of spectral transitions In Table 1, the atomic data characterizing the selected O I and N I transitions are listed. The transition probabilities for the “thermometric”
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Table 1 Atomic data for selected O I and N I spectral transitions are listed. No
Emitter
Transition
λki (nm)
gi
gk
Ei (eV)
Ek (eV)
Aki (107 s− 1)
Acc.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
OI
(4So)3s 5So–(4So)3p 5P (4So)3p 5P–(4So)3d 5Do (2Do)3s 1Do–(2Do)3p 1P (2Do)3p 3F–(2Do)3d 3Go (3P)3s 2P–(3P)3p 2Do
777.337 926.387 948.289 949.794 938.680 946.068 939.279 1071.35 1075.79 1065.30 1071.80 1062.32 1064.40 1051.34 1050.03 1052.06 1050.70 1054.96 1053.96 981.001 979.856 983.461 982.275 987.215 986.333
5 15 5 14 2 4 4 4 6 2 6 2 4 2 2 4 4 6 6 4 4 6 6 8 8
15 25 3 18 4 4 6 6 6 4 4 2 2 2 4 4 6 6 8 2 4 4 6 6 8
9.146 10.741 12.728 14.099 10.680 10.690 10.690 11.840 11.844 11.837 11.844 11.837 11.840 11.837 11.837 11.840 11.840 11.844 11.844 11.753 11.753 11.758 11.758 11.764 11.764
10.741 12.079 14.036 15.404 12.000 12.000 12.010 12.997 12.997 13.001 13.001 13.004 13.004 13.016 13.018 13.018 13.019 13.019 13.020 13.016 13.018 13.018 13.019 13.019 13.020
3.69 4.46 2.34 3.2 2.13 0.373 2.51 0.716 0.392 0.903 0.375 0.540 0.675 1.91 0.654 1.59 1.32 1.23 2.54 0.542 0.333 0.450 0.574 0.297 1.03
A A B C+ B B B B+ B+ B+ B+ B+ B+ B+ B+ B+ B+ B+ B+ B B B B B B
NI
(3P)3p 4Po–(3P)3d 4P
(3P)3p 4Po–(3P)3d 4D
(3P)3p 4Do–(3P)3d 4D
In the last column, the accuracies of Aki data are given using the convention introduced by NIST. All N I Aki values are taken from the recent compilation of Wiese and Fuhr [4]. The first three O I transition probabilities are taken from [2], the last (No. 4) is taken from our recent paper [3].
O I lines at λλ 777.337, 926.387, 948.289 nm, are taken from Wiese et al. [2]. The Aki value for the doubly excited O I triplet transition at 949.794 nm, which is based on the absolute scale of [2], is taken from our recent paper [3]. The N I spectral lines selected for the purpose of this work belong to 4 multiplets: 3s 2P–3p 2Do, 3p 4Do–3d 4D, 3p 4Po–3d 4D, and 3p 4Po– 3d 4P. The corresponding transition probabilities for these transitions are taken from the recent compilation of Wiese and Fuhr [4], where the N I data of Froese Fischer and Tachiev [5] are recommended as the most reliable ones. These spectral lines appear within the wavelength range from 938 to 1055 nm, which is of great advantage for accurate relative line intensity measurements. Unfortunately, also the maximum gap between excitation energies of the upper levels is narrow (ΔE = 1.16 eV), and thus possible uncertainties in temperature determination, based on measured line intensities and the Boltzmann plot method, are expected to be significant. Therefore, into the proposed nitrogen “thermometric” set we included two doubly excited N I transitions, which have not been calculated by Froese Fischer and Tachiev and, consequently are not listed in the compilation [4], namely the transitions 3s′ 2D–3p′ 2Fo and 3p′ 2Fo–3d′ 2G. The Aki data for both these transitions are reported in the old paper by Richter [6]. The Aki value for the transition at 904.76 nm (3s′ 2D–3p′ 2Fo) is also listed in the monograph by Wiese et al. [2]. In Fig. 1, the partial Grotrian diagram of the N I atomic system is presented showing all selected spectral transitions. In order to check how the old data of Richter agree with contemporary data reported by Wiese et al. [2] and Wiese and Fuhr [4], we compare the Aki data for selected N I multiplets in Table 2. The comparison reveals an overall good agreement between the data of Richter [6] and the data reported by Wiese et al. [2] as well as the very recent data of Froese Fischer and Tachiev [5] recommended by Wiese and Fuhr [4], with the exception of results for the multiplet 3s 2P–3p 2Do, where the discrepancies of about 20% are encountered. Even though the Aki value for the transition 3s′ 2D–3p′ 2Fo, recommended in the monograph [2] agrees well with the result of Richter [6], the new compilation [4] does not contain the Aki value for this transition. The discrepancy between both results taken from NIST
[2,4] in the case of the transition 3p 4Po–3d 4P is somewhat mysterious: the more recent result is a factor of 1.6 larger than the result given in the monograph [2]. Because of the above mentioned discrepancies, it seems to be somewhat risky to include the data of Richter [6] into the set of transition probabilities taken from recently critically evaluated data by Wiese and Fuhr [4], and proposing them for reliable temperature determination of plasmas without verifying the old measurements of Richter. Therefore, we decided to determine the transition probabilities for the two doubly excited multiplets and normalize them to the N I data reported by Froese Fischer and Tachiev [5] and recommended by Wiese and Fuhr [4].
Fig. 1. The partial Grotrian diagram of the N I atomic system is presented showing all studied spectral transitions. Emission coefficients for transitions between levels belonging to the excited atomic core configuration (1D) have been measured and the respective transition probabilities have been determined in this work.
A. Baclawski, J. Musielok / Spectrochimica Acta Part B 65 (2010) 113–119 Table 2 Comparison of selected multiplet transition probabilities determined by Richter [6] with results reported in two recent NIST publications [2] and [4] is presented. λki (nm)
Multiplet
3
2
3
2
o
( P)3 s P–( P)3p D (3P)3p 4Do–(3P)3d 4D (3P)3p 4Po–(3P)3d 4D (3P)3p 4Po–(3P)3d 4P (1D)3 s 2D–(1D)3d 2Fo (1D)3p 2Fo–(1D)3d 2G
939.53 983.06 1052.6 1070.7 904.76 1059.5
Aki (107 s− 1) Ref. [6]
Ref. [2]
Ref. [4]
2.14 1.00 2.47 1.11 2.74 3.58
2.63 0.937 2.43 0.718 2.80 –
2.51 1.02 2.57 1.18 – –
Aki [2]/ Aki [6]
Aki [4]/ Aki [6]
1.23 0.94 0.98 0.65 1.02 –
1.17 1.02 1.04 1.06 – –
115
For both experiments: A and B, the radiation from the arc in endon (axial) direction was registered several times in spectral intervals embracing all transitions (O I, N I) listed in Tables 1 and 2, and additionally also in the spectral range around the hydrogen Hβ line at 486.1 nm. We restricted our spectroscopic analysis to the arc radiation originating from plasma layers near the arc axis r ≤ 1.7 mm (the total arc radius was 2.5 mm). The radial gradients of the plasma parameters (electron density, atomic number density and temperature) are very weak up to the distance from the arc axis of 1.0 mm. The temperature gradients in this region are less than 300 K/mm, and the electron density gradients do not exceed 0.3 · 1016 cm− 3/mm. For distances larger than 1.0 mm from the axis, the mean gradients are around 1000 K/mm and 0.65 · 1016 cm− 3/mm respectively.
3. Experimental set-up and details of the measurements The spectroscopic instrumentation applied in this paper is described in detail in our recent paper devoted to a similar subject — the determination of transition probabilities in neutral oxygen suitable for temperature determination [3]. Also the registration of the spectra, including the intensity calibration procedure, self-absorption checks and evaluation of individual total line intensities were performed in the same manner as in the above mentioned paper. The wallstabilized high-current arc, operated at atmospheric pressure in a mixture of helium, argon, nitrogen, oxygen, and with some traces of hydrogen was applied as the excitation source. Oxygen was introduced into the plasma in order to measure the O I line intensities of the “thermometric” set proposed in our previous paper [3]. The presence of traces of hydrogen in the plasma allows the electron density to be determined on the basis of Stark broadening of the Hβ transition. For the purpose of this work, we used a gas cylinder with pure argon and prepared two other cylinders with the following gas compositions: (99.5% He + 0.5% H2) and (75% N2 + 25% O2). The arc was operated at d.c. current of 45 A and at two different gas compositions and gas flow rates. In both cases, helium is the dominant plasma component. By varying the argon flow rate the main plasma parameters temperature and electron density can be changed, particularly their radial distributions. Larger amount of argon causes an increase of electron density and the decrease of temperature at the arc axis. By changing the amount of the O2 + N2 gas mixture the intensities of selected O I and N I lines can be optimized for accurate line intensity measurements (albeit strongly enough and with negligible self-absorption). The operating conditions of the two experiments (A and B) are given in Table 3. In the last column of this table the electron densities at the arc axis, determined from measured Hβ line widths and applying theoretical broadening data of Gigosos and Cardeñoso [7], are listed. As mentioned earlier, in order to determine the electron density of the arc plasma, the hydrogen Balmer β line has been registered. From measured Full Widths at Half Maximum (FWHM) the electron densities have been deduced. The calculations of Gigosos and Cardeñoso [7] include the ion dynamic effects contributing to the measured line width. Other broadening mechanisms, such as instrumental and Doppler broadening, have also been taken into account while determining the pure Stark FWHM of the Hβ line. The plasma temperature values, needed for determining the electron densities, have been obtained from measured intensities of selected O I spectral lines (details of the temperature determination are given below). Table 3 Operating conditions of the arc source for both experiments A and B, together with the obtained electron densities at the arc axis are given. Expt.
A B
Flow rate from gas cylinder (cm3 s− 1) 99.5% He + 0.5% H2
Ar
75% N2 + 25% O2
20 20
3.4 4.4
0.13 0.21
Ne (1016 cm− 3) 1.5 ± 0.3 2.0 ± 0.4
4. Determination of transition probabilities for two doubly excited N I transitions Detailed elaboration of the measured spectra has been performed for selected plasma layers (of both experiments A and B) differing in the distance from the arc axis and covering the plasma electron density range from 5.3 · 1015 to 2.0 · 1016 cm− 3. By constructing Boltzmann plots on the basis of measured O I line intensities, the plasma temperatures for various plasma layers have been determined. In Fig. 2 such Boltzmann plots are shown for axial plasma layers (r ≤ 0.052 mm) corresponding to both experiments, A and B. The quantities ln (Iki · λki/gk · Aki), plotted in the upper part of the figure for three N I upper terms (3s 2Do, 3p 4P, 3p 4D), have been obtained by averaging the values ln (Iki · λki/gk · Aki), determined from measured intensities of individual spectral lines (listed in Table 1), originating from respective initial upper terms. For determination of transition probabilities of the two doubly excited multiplets, the radiation originating from on-axis plasma layers with the largest electron densities (experiment B) has been used. According to the pLTE criteria given by Griem [8], for temperatures around 10,000–11,000 K electron density of 1.7 · 1014 cm− 3 is sufficient for establishing Boltzmann-like population among excited levels with principal quantum numbers n = 3. The axial electron
Fig. 2. Boltzmann plots based on measured intensities of O I spectral transitions corresponding to axial plasma layers of experiments A and B are shown. The triangles above the two Boltzmann plots correspond to the averaged quantities ln (Iki · λki/gk · Aki) for three N I terms (3p 2Do, 3d 4P, 3d 4D) — for details see the text. The solid symbols correspond to the results of experiment B, the open ones to the results of experiment A. The arrows on the right hand side indicate the excitation energies of the two doubly excited terms 3p′ 2Fo and 3d′ 2G. For transitions originating from these terms new Aki values have been obtained in this work.
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tral instrumentation. Therefore, for these overlapping components individual transition probabilities could not be determined. The transition probabilities (Aki) for these two selected N I multiplets have been determined on the basis of measured total line intensities (Iki) of the studied fine structure components (or the sum of two fine structure components) and the intensity of a reference spectral line (IRmn) from the following formula: R
R
Aki = Amn ⋅
R
gm λki Iki E −Em ⋅ R ⋅exp k kT gk λRmn Imn
! ð1Þ
where: ARmn, λRmn, gRm and ERm are the transition probability, wavelength, statistical weight and excitation energy of the upper level of the reference line, λki, gk, and Ek are the wavelength, statistical weight and excitation energy of the upper level of the studied line, and kT = 0.9495 eV is the plasma temperature expressed in energy units (T(expt. B) = 11,020 K). The N I line intensities were determined by averaging data obtained from a few independent registrations of the plasma radiation. The transition probabilities for the two selected multiplets have been determined taking as a reference all N I transitions listed in Table 1, with quoted accuracies B + (i.e. with uncertainties ≤7%): 6 lines each, originating from the upper terms 3d 4P and 3d 4D. In Table 4, the averaged Aki values (in absolute scale) are compared with data available in literature [2,6,9,10]. In the right part of this table the corresponding line strengths, normalized to the sum of 100 within each multiplet, are compared. 5. Discussion of results
Fig. 3. The measured N I multiplets in the infrared part of the spectrum from the on-axis plasma layer of experiment B, obtained at plasma conditions Ne = 2 · 1016 cm− 3 and T = 11,020 K, are shown. In the case of both multiplets two fine structure components are not resolved by our instrumentation. The measured relative line intensities within each multiplet are in very good agreement with those resulting from the LS coupling scheme.
density of experiment B is 2 · 1016 cm− 3 and is about 120 times larger than the density required by the pLTE criteria. Examples of our measured spectra, comprising the two doubly excited N I infrared transitions, emitted from the on-axis plasma layer of experiment B, are presented in Fig. 3. As can be seen, in both cases two fine structure components are not resolved enough by our spec-
Our absolute transition probabilities, which are based on the absolute scale of Aki values for the N I multiplets 3p 4Po–3d 4P and 3p 4 o P –3d 4D, taken from [4,5], agree within the error limits with all results available in literature. The relative uncertainties of our Aki data as well as those of Richter [6] are the same — ±15%. Our Aki values are systematically somewhat larger than the data of Richter [6] (8–16%) as well as those of Kurucz and Bell [10] (13–18%). The transition probabilities for the multiplet 3s′ 2D–3p′ 2Fo could also be compared with results of the CIV3 calculations of Hibbert et al. [9] and with data reported in the monograph by Wiese et al. [2]. Our Aki data are about 6% and 12% larger than the results of Hibbert et al. [9] and Wiese et al. [2] respectively. The comparison of relative line strengths within both multiplets shows excellent agreement with all available data sources, including those resulting from the LS coupling scheme. The uncertainties given in the table arise from the accuracy of transition probabilities of the reference data (7%) and from uncertainties
Table 4 Comparison of absolute transition probabilities for two infrared N I multiplets obtained in this work with results taken from literature. Multiplet
λki (nm)
gi
gk
(1D)3 s 2D–(1D)3p 2Fo
904.759 904.5878 904.9690a 1059.54 1059.200 1059.690b
10 6 10 14 6 8
14 8 6 18 8 18
(1D)3 s 2Fo–(1D)3p 2G
Aki (107 s− 1)
Srel ki
This work
Ref. [6]
Ref. [2]
Ref. [9]
Ref. [10]
3.17 ± 0.48 3.16 ± 0.47 1.56 ± 0.24 3.93 ± 0.59 3.81 ± 0.57 2.24 ± 0.34
2.74 2.68 1.41 3.58 3.52 2.01
2.80 2.80 1.40 – – –
2.94 2.94 1.47 – – –
2.717 2.685 1.380 3.391 3.240 1.951
This work
LS
Ref. [6]
Ref. [10]
56.9 ± 2.0 43.1 ± 1.5
57.1 42.9
55.8 44.2
56.4 43.6
43.0 ± 1.5 57.0 ± 1.8
42.9 57.1
43.7 56.3
42.4 57.6
The transitions labeled with superscripts “a” and “b” consist of two blended fine structure components. In the right part of the table the corresponding relative line strengths, normalized to the sum of 100 within each multiplet, are given. In the case of the first multiplet (1D)3 s 2D–(1D)3p 2Fo, the relative line strengths resulting from the LS coupling scheme are identical with those reported by Wiese et al. [2] and Hibbert et al. [9], therefore we do not include these data in the comparison of relative line strengths. a Two lines: 904.9492 nm (6–6) + 904.9889 nm (4–6). b Two lines: 1059.686 nm (8–10) + 1059.696 nm (8–8).
A. Baclawski, J. Musielok / Spectrochimica Acta Part B 65 (2010) 113–119
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Fig. 4. The measured N I spectrum in the wavelength range 1053–1060 nm is shown. The spectrum illustrates the advantage of applying relative line intensity measurements for Aki determination. The studied and the reference lines are close in wavelength; the line to continuum ratios as well as the signal to noise ratios are favorable for accurate relative intensity measurements.
of our relative line intensity measurements (systematic and statistical origin). Since the determination of transition probabilities is based on relative line intensity measurements, the possible systematic errors are rather small. As can be seen from Fig. 4, the multiplet 3p′ 2Fo–3d′ 2G appears in the spectrum very close to the reference multiplet 4Po–4D. In the case of the transition 3s′ 2D–3p′ 2Fo the wavelength difference between the studied lines and the reference lines is in the range of 45– 71 nm. The largest possible systematic errors arise from: (i) the uncertainty of temperature determination of the plasma layer applied for evaluation of Aki, and (ii) the radiance calibration procedure. In the case of the multiplet 3p′ 2Fo–3d′ 2G, the possible error arising from source mentioned as (i) is larger than for the multiplet 3s′ 2D–3p′ 2Fo, because the excitation energy gap between the respective upper terms of the studied and reference transitions is larger (1.88 eV). However, even in this case the contribution to the uncertainty of Aki determination does not exceed 3%. On the other hand, the possible error arising from the source mentioned as (ii) is larger in the case of the multiplet 3s′ 2D– 3p′ 2Fo. Nevertheless, since the intensity of the radiation standard (tungsten strip lamp) in the wavelength range 900–1060 nm does not change substantially and the sensitivity of our registration system decreases monotonically with λ, these possible errors are small. The uncertainties of relative line intensity determination depend slightly on the selected line pairs and amount about 3% to 6%. The total relative uncertainties of our transition probabilities are ±15%. We are not able to decide if possible systematic errors, bound up with the determination procedure, may lead to final results which are higher or lower compared to the absolute scale proposed by the NIST team [4,5]. 6. Application of the proposed N I spectral line set for temperature determination of the off-axis arc plasma layers In order to check the usefulness of the proposed set of N I lines for diagnostic purposes, we have determined the radial temperature and electron density distributions in our arc for the conditions of experiment A. Knowing the temperature distribution, the electron density distribution has been obtained from measured FWHM of the Hβ line — the details are described in section: Experimental set-up and details of the measurements. The temperature was obtained from measured radial distributions of the respective O I and N I line intensities. In Fig. 5 we present four Boltzmann graphs based on both sets of “thermometric” lines: the O I and N I set, corresponding to
Fig. 5. Four Boltzmann plots constructed on the basis of measured intensities of O I (upper graphs) and N I (lower graphs) lines registered from different plasma layers are shown.
selected (different r) plasma layers. The plasma temperatures resulting from Boltzmann plots (slopes of the best fit straight lines) based on O I lines are systematically larger than those based on N I lines — the discrepancies, however, do not exceed 600 K (see Table 5). In Fig. 6 the electron density and temperature distributions in our arc discharge of experiment A are shown. For evaluations of radial temperature distributions three Aki sets have been applied: the O I set proposed in [3], our present N I set and the Aki values reported by Richter [6]. As mentioned above, the temperatures based on measured O I line intensities are systematically larger than those obtained using the N I data. On the other hand, the error bars are larger in case of
Table 5 Electron densities and temperatures determined for four selected plasma layers of the arc discharge are quoted. r (mm)
Ne (1015 cm− 3)
TOI (K)
TNI (K)
0 1.0 1.5 1.7
15 ± 3 11 ± 2 7.0 ± 1.6 5.3 ± 1.2
11,370 ± 110 10,940 ± 80 10,390 ± 160 9740 ± 330
10,780 ± 160 10,350 ± 180 9920 ± 290 9470 ± 330
The temperatures are determined from Boltzmann plots based on the O I and N I line sets. The quoted uncertainties of T-determination arise only from the best fit to the experimental points shown on the graph in Fig. 5, and do not include the contribution originating from uncertainties of applied (relative) transition probability values.
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Fig. 6. Radial distributions of temperature and electron density of the plasma generated in a wall-stabilized arc at working conditions of experiment A are shown. The temperatures have been obtained applying the Boltzmann plot method based on two sets of “thermometric” lines: the O I set (triangles) and the proposed N I set (squares). For evaluation of temperature distributions based on N I line intensities two sets of transition probabilities have been used: the data of Richter [6] (open squares) and our proposed Aki set (solid squares), consisting of the NIST data [4] and the new Aki values determined in this work. The error bars correspond to uncertainties of T-determination arising only from the best fit to the experimental points on the respective Boltzmann plots, and do not include the contribution originating from uncertainties of applied (relative) transition probability values.
using the N I sets, particularly if Richter's Aki data are applied. The smaller uncertainties in case of using the O I set are caused mainly by wider energy separation of upper levels of the transitions involved — in the case of O I ΔE = 4.66 eV, while in the case of N I this gap is significantly (1.6 times) smaller. The temperature values obtained by applying Richter's data are systematically somewhat smaller than those based on our proposed Aki set. This is not surprising since our Aki values are systematically slightly larger than Richter's data. The relative good agreement between these two radial temperature distributions, however, seems to be incidental. In Fig. 7 we show two N I Boltzmann plots, corresponding to the on-axis plasma layer of experiment A. For construction of the upper graph the Aki values of Richter [6] and for the lower our N I data set have been applied. Both Boltzmann plots lead to nearly the same temperatures, but the scatter of experimental points in the case of using Richter's data is significantly larger. This larger scatter explains also the respective larger error bars on the graph (in case of using Richter's data) shown on Fig. 7. It has to be emphasized that the uncertainties quoted in Table 5 and error bars shown on Fig. 6 result only from the fitting procedure, used for construction of the Boltzmann plots, and do not include possible contributions originating from uncertainties of applied (relative) transition probability values.
Fig. 7. Two N I Boltzmann plots, corresponding to the on-axis plasma layer of experiment A, are shown. For construction of the upper graph the Aki values of Richter [6] and for the lower graph our proposed N I data set have been applied. Both Boltzmann plots lead to nearly the same temperatures but the scatter of experimental points, in case of using our proposed Aki data set, is significantly smaller.
7. Conclusions Transition probabilities for two N I multiplets have been determined by emission spectroscopy method. The absolute scale of Aki values was established by comparing measured relative line intensities of the studied lines, with measured intensities for N I lines belonging to 2 multiplets 3p 4Po–3d 4D, 3p 4Po–3d 4P, and applying transition probabilities for these reference lines calculated by Froese Fischer and Tachiev [5] and recommended in the recent compilation by Wiese and Fuhr [4]. The new Aki data, together with those used as reference lines as well as the data for lines belonging to the multiplets 3s 2P–3p 2Do and 3p 4Do–3d 4D, form a suitable and convenient set of lines for temperature determination by applying the Boltzmann plot method. The proposed N I lines appear in a rather narrow spectral interval (130 nm), which is advantageous for performing relative line intensity measurements with good accuracy. The upper terms of the selected multiplets are spread in excitation energy by 2.9 eV, i.e. large enough for constructing reliable Boltzmann plots for low temperature plasmas.
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