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Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma
Optics & Laser Technology 66 (2015) 138–145
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Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma Xiao Xiao a,b, Xueming Hua a,b,n, Yixiong Wu a,b a Welding Engineering Technology Research Institute of Materials Science and Engineering (Shanghai Jiao Tong University), Shanghai 200240, People's Republic of China b Shanghai Key Laboratory of Materials Laser Processing and Modification (Shanghai Jiao Tong University), Shanghai 200240, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 2 March 2014 Received in revised form 23 August 2014 Accepted 27 August 2014 Available online 21 September 2014
Three different spectroscopic methods were used to calculate the temperature and composition distribution of argon–helium arc plasma—the Fowler–Milne method, the two-line intensity correlation method and the Boltzmann plot method. Experimental errors, including random errors and systematic errors, were analyzed in detail to comparing the accuracy of different methods. Due to the large differences of physical characteristics between argon and helium, there were limited reports on the measurement of temperature and composition distribution in argon–helium arc plasma. To this end, The Fowler–Milne method and the Boltzmann plot method were modified in this paper. Three spectroscopic methods were compared with other's simulation result and showed good agreement with each other, except the Boltzmann plot method which had partly distinction. Through comparison and analysis of error bar in those methods, it was found that both the Fowler–Milne method and the two-line intensity correlation method had less error than the Boltzmann plot method, while the Fowler–Milne method, which is irrelevant to atomic transition probabilities and experimental apparatus calibration, had the minimum error. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Experimental error Spectroscopic measurement Argon–helium arc plasma
1. Introduction Emission spectroscopy, which does not disturb the arc plasma, is a very effective way to investigate the plasma property. And most of the spectral measurement techniques have been applied to determine the temperature in single gas arc plasma [1,2]. However, it seems that the temperature measurement of arc plasma presented by many researchers have mutually contradictory results, as indicated by Lancaster [3]. For example, the measured temperature using the Fowler–Milne method is higher than those using the Boltzmann plot method. Those groups using a relative or an absolute intensity method had considerable disagreement results, while the Fowler–Milne spectroscopic technique obtained consistent values [4]. Moreover, the presence of additional gas causes demixing in most cases, which means temperature and gas composition changes with position. The existence of demixing significantly complicates the measurement for multi-element arc plasma. Hence, most of the accepted methods need to be modified for applying in multi-element arc plasma. In this paper, different spectroscopic methods were n Corresponding author at: Welding Engineering Technology Research Institute of Materials Science and Engineering (Shanghai Jiao Tong University), Shanghai 200240, People's Republic of China. Tel.: þ 86 21 54748940 8009. E-mail address: [email protected] (X. Hua).
http://dx.doi.org/10.1016/j.optlastec.2014.08.017 0030-3992/& 2014 Elsevier Ltd. All rights reserved.
introduced and then the temperature and gas composition (mole fraction of argon in arc plasma) distribution were compared among those methods in the mixture of argon–helium arc plasma. Due to the complexity of measurement in multi-element arc plasma, only few researchers measured its temperature and gas composition distribution in gas tungsten arc welding (GTAW) using mixed gas. Song et al. [5,6] used absolute intensity of Ar I, Hα and N I line, to determine temperature and gas composition in argon–hydrogen arc plasma and argon–nitrogen arc plasma. The result showed that hydrogen concentrate in the center of the arc plasma. Hiraoka [7,8] used a two-line intensity correlation method to measure temperature and composition distribution in the multi-element arc plasma. It involved the measurement of the relative intensity of Ar I and Ar II lines or Ar I and H I lines to obtain temperature distribution of Ar–He or Ar–H2 mixed-gas tungsten arc plasma, and find the helium concentrate on the axis of arc. Murphy [9] used a modified Fowler–Milne method to measure the radial profiles of temperature and gas composition of free-burning arcs in mixtures of argon and nitrogen. The results demonstrate that the occurrence of demixing depending on the relative concentration of argon and nitrogen. These methods are used in different gas mixtures in different experimental conditions, so they are difficult to compare with each other. Due to the physical characteristic between argon and helium differs largely, i.e., the first ionization energy of helium is much
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larger than that of argon, the density of helium is much lighter than that of argon, there exist large differences in ionization degree and complicate spectra chosen. There are thus limited reports on measuring the temperature and composition for the mixture of argon and helium. Only Hiraoka [7,10] used the twoline intensity correlation method to measure the temperature and composition distributions in the argon–helium arc plasma of 100 A. It is interesting to compare with other spectroscopic methods and analyze the error distribution. In this study, we will use a spectrometer system to measure spectral intensity distribution, and then use three different spectroscopic methods to obtain the temperature and composition of arc plasma with the mixture of argon–helium in GTAW. Firstly, the Fowler–Milne method was applied in the mixture of argon–helium arc plasma. Though Murphy [9] used this method in argon and nitrogen mixtures, they have similar physical property and got the similar normal temperature. However, there were problems existing in argon–helium gas mixture. From the perspective of first ionization energy and density, there are wide gap between argon and helium, as a result, their normal temperatures are quite different. In fact, the normal temperature of He I is above the temperature of arc plasma, and the maximum emission coefficient could not be measured. Nevertheless, the Fowler–Milne method requires that value, we chose Ar I and Ar II spectral lines in the study since their maximum emission coefficient could be obtained. Then, the two-line intensity correlation method and the Boltzmann plot method were used for temperature and composition measurement under the identical conditions. Meanwhile the experimental errors, including random errors and systematic errors, were thoroughly analyzed for each method. Furthermore, a comparative investigation was carried out for their respective temperature and composition results between the following spectroscopic methods: a) the Fowler–Milne method; b) the two-line intensity correlation method; c) the Boltzmann plot method, and others' simulation result [11], and they are also analyzed according to their error distribution.
2. Experimental system The experimental system mainly contains two parts. One is arc plasma source, which is used to produce arc plasma; the other is a spectrum acquisition system, which is used to obtain spectral intensity of arc plasma. 2.1. Arc plasma source In the experiment, a direct current (DC) arc was generated in the gas mixture of argon and helium at atmospheric pressure by welding power supply (DA300P-type, OTC Corporation, Japan). The arc freely burned between a tungsten cathode and a stationary water-cooled copper plate anode. A 2.4-mm-diameter tungsten electrode adding 2% ThO2 with a cone angle of 601 was employed as cathode. A water-cooled copper-plate vertically located below the cathode was employed as anode. Arc distance, defined as the distance from the tungsten electrode tip to copper-plate surface, is 5 mm. The mixture of argon (50% in volume) and helium (50% in volume) was used as the shielding gas feeding from the cathode nozzle with a flow rate of 10 L min i, and the current was set at 200 A. 2.2. Spectrum acquisition system The spectrum acquisition system consists of a single lens system, a motion control device and a spectrometer. Radiation from the arc plasma was imaged by a single lens system onto an
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Fig. 1. Spectroscopic acquisition system for arc plasma.
imaging screen at a magnification of 2:1. The convex lens (focal length is 0.3 m) was fixed 0.45 m away from the arc, thus the parallel-ray projection condition assumed in the Abel inversion can be approximately satisfied. A light aperture was employed to limit light from the arc for obtaining adequate spatial resolution. In the image screen which was places 0.9 m away from the lens, an optical fiber (P400-UV-SR, Ocean Optics, USA) was mounted on a motion control device which can be moved in both horizontal and vertical directions. The internal diameter of the optical fiber is 0.4 mm and thus the scanning step along the horizontal direction was determined as 0.4 mm. Light along the chord of arc 1 mm below the cathode tip was transmitted by the optical fiber to the spectrometer (HR-4000UV-NIR, Ocean Optics, USA) of 3648 pixels with a spectral range from 200 to 1100 nm. The spectroscopic acquisition system is schematically shown in Fig. 1.
3. Measurement of temperature and composition distribution by different methods Since temperature and gas composition could not be measured directly, they are derived from different spectroscopic methods which need the value of emission coefficient, and the measurements are line-of-sight integrated intensities, the distribution of emission coefficients must be reconstructed. This is accomplished by means of an Abel inversion, provided the plasma is cylindrically symmetric and optically thin. For Abel inversion, the measured intensity of the spectral line was corrected by subtracting the corresponding continuum radiation intensity first. Then, the sideon measured spectral line intensity profiles were symmetrized, noise filtered, and the Bockasten method [12,13] was used to convert intensity to emission coefficient. Since this experimental system was not calibrated to the absolute intensity, this emission coefficient is relevant to the experimental system. Hence, it is a relative emission coefficient. The line emission coefficient εnm of a transition from level m to lower level n of species j in plasma is given by [3] nj ðT Þ hc Em exp ð1Þ εnm ¼ g m Anm kT U j ðT Þ 4πλnm where nj (T) and Uj (T) are respectively the number density and the partition function of the species j, Em and gm are the energy and statistical weight of the upper level, Anm is the transition probability, λnm is the wavelength of the radiation emitted, and c, h, and k are respectively the speed of light in a vacuum, Planck's constant, and Boltzmann's constant. Hence, the intensity of emission from a single spectral line depends on the temperature T and the number density nj of the emitting species. If the plasma is in local thermal equilibrium (LTE), and only one chemical element is present in the
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plasma, the relationship between T and nj could be calculated from Saha equilibrium. Thus, it is sufficient to determine both T and nj from single spectrum radiation intensity. However, if two or more chemical elements are present in the plasma, nj dependents on both temperature T and the mole fraction YJ of the chemical element J, from which the specie j is derived. Because of demixing, YJ usually strongly depends on position. Therefore, it is insufficient to obtain T or nj only from single spectrum. To determine these values requires at least k species, where k is the number of chemical elements being present. For the mixture of argon–helium arc plasma, two species of spectral line are needed. The emission coefficient was obtained through spectral intensity. Fig. 2 shows the arc spectra in the wavelength range from 450 nm to 810 nm measured in the column region of the arc at a distance of 1 mm from the cathode tip, which contains the Ar I, Ar II and He I spectral lines. Table 1 contains spectral parameters used in this measurement. For the Fowler–Milne method, the emission coefficients have to be normalized to their respective maximum values in pure arc plasma. Ar I 696.5 nm and Ar II 480.6 nm lines were used to characterize the argon–helium plasma properties. The reason we chose these lines was that they are well separated from other lines and the line intensity is not weak. Although the He I 587.6 nm spectral line is also strong, the normal temperature of He I 587.6 nm spectrum is too high (24,300 K) for pure helium arc plasma to reach, the maximum value of εHeI could not be measured. Since the Fowler–Milne method need to normalize the emission coefficient, He I spectrum could not be chosen. The normal temperature of Ar II is 25,600 K, the maximum value of εArII could not be measured, either. However, in pure argon arc plasma, that value could be calculated through the Olsen–Richter method [14]. As a result, it is reasonable and rational to choose 696.5 nm Ar I and 480.6 nm Ar II spectral lines to measure temperature and gas composition distribution in the argon– helium arc plasma. For the two-line intensity correlation method, Ar I 696.5 nm and Ar II 480.6 nm lines were also used to measure temperature
and gas composition distribution in the argon–helium arc plasma. For the Boltzmann plot method, since it is irrelevant to composition of arc plasma, a group of Ar II lines was used to measure the temperature distribution, gas composition was calculated from Saha equation which needs temperature and electron density. Temperature is measured by the Boltzmann plot method, while electron density is acquired through 480.6 nm Ar II spectrum broadening. The experiment was repeated three times, and the results were given in average value with its error bar. 3.1. Temperature and composition distribution measured by the Fowler–Milne method The Fowler–Milne method relies on the fact that for plasma in LTE and at constant pressure, εnm has a maximum εcnm at a welldefined temperature Tc, known as the normal temperature. Provided that the maximum temperature of the plasma exceeds Tc, those positions at which the emission coefficient is maximum can be assumed at temperature Tc. If εJnc is a relative emission coefficient in our experiment system at the normal temperature T cJ of chemical element J in an arc containing only that element, then we can define the normalized emission coefficient εnJ using Eq. (1). For the Ar I and Ar II lines c1 εnArI nArI ðT; Y Ar ÞU ArI T c ε EArI EArI exp ð2Þ εnArI ¼ ArI ¼ ¼ nc εcArI c1 εArI kT c kT nArI T c U ArI ðT; Y Ar Þ
εnArII ¼
εArII c2 εnArII nArII ðT; Y Ar ÞU ArII T c E E exp ArIIc ArII ¼ ¼ nc εcArII c2 εArII kT kT nArII T c U ArII ðT; Y Ar Þ
ð3Þ
where c1 and c2 are constants that relate to the emission coefficient and the measured relative emission coefficient. For mixtures of argon and helium arc plasma, the normalized emission coefficient of an Ar I 696.5 nm line and an Ar II 480.6 nm line depend both on temperature and the composition; it could be calculated from Eqs. (2) and (3) at different ratios, and normalized to their respective maximum values in pure argon arc. The relationship
Fig. 2. Emission spectra distribution between 450 nm and 810 nm in a 200-A freeburning arc with input gas 50% Arþ 50% He.
Table 1 Spectral characteristic of major spectral lines in the measurement. Lines (nm)
Type
Transition probabilities
Normal temperature (K)
696.5 480.6 587.6
Ar I Ar II He I
6.39e þ 06 7.80e þ 07 5.31e þ 07a
14,700 25,000 24,300
a
Indicates one value of the transition probabilities.
Fig. 3. Dependence on temperature of the emission coefficient of a) the 696.5 nm Ar I line and b) the 480.6 nm Ar II line, normalized to its maximum value in pure argon, for different mixtures of argon and helium.
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between temperature and normalized emission coefficient of Ar I and Ar II are shown in Fig. 3. However, a value of the emission coefficient of either the Ar I 696.5 nm line or the Ar II 480.6 nm line corresponds to an infinite number of mole fraction–temperature pairs. Hence, each value of the normalized emission coefficient εArI for the Ar I 696.5 nm line corresponds to a curve Y(T, εArI), where Y is the mole fraction of argon; likewise, each value of εArII for the Ar II 480.6 nm line corresponds to a curve Y(T, εArII). These dependencies are shown in Fig. 4, which shows the relationship between Y and T for different values of εArI and εArII. In addition, it is demonstrated in Fig. 4 that if both εArI and εArII are known, the number of corresponding mole fraction–temperature pairs is, at most, one. In this experimental system, the norm relative emission coefficient of 696.5 nm line corresponded to the highest observed value of the off-axis maximum in pure argon arc plasma in the LTE state at atmospheric pressure. To determine the maximum relative emission coefficient value of Ar II 480.6 nm, the measured radial distributions of emission coefficients for the 696.5 nm and 480.6 nm lines were marked as points in the Olsen–Richter diagram [14]. These emission coefficients are below the cathode tip 2 mm in 100% Ar which are in the LTE state [15]. To superpose the experimental values on the theoretical graph, two constants are needed. In our case the norm relative emission coefficient of 696.5 nm line was acquired above. Taking into account remarks concerning the Boltzmann–Saha equilibrium for Ar II levels, the norm relative emission coefficient of 480.6 Ar II line could be determined through the Olsen–Richter diagram. The results of Fig. 6. Radial dependence of intensity for a) εArI 794.8 nm Ar I line, b) εArII 487.98 nm Ar II line, measured 1 mm below the cathode with the input gas of 50% Arþ 50% He in a 200-A free-burning arc.
Fig. 4. Relation between the mole fraction of argon and temperature for different normalized emission coefficients.
these procedures are shown in Fig. 5. It can be seen that the experimental data for Ar II and Ar I lines can be well superposed on the curve. The error of norm relative emission coefficient of 480.6 Ar II line comes from the relative emission coefficient in experiment and the fitting error, the calculated error is 4%. Fig. 6a and b shows the radial dependence of intensity with their error bar at a position 1 mm below the cathode in an argon– helium arc. The solid line represents the intensity distribution of Ar I 794.8 nm spectral line, and dotted line represents that of Ar II 487.98 nm spectral line. The intensity was the mean value of three times measurement, and the error was calculated from standard deviations of the mean value. The corresponding normalized emission coefficients with their error bar are shown in Fig. 7a and b. The error comes from the measurement of intensity, the Olsen–Richter diagram and the method of Abel inversion whose error was calculated according to Ref. [12]. Then, using the data depicted in Fig. 4, these normalized emission coefficients are transformed to temperature–mole fraction pairs. Fig. 8a and b shows the temperature and mole fraction of gas composition distribution with their error bar at 1 mm below the cathode. This error is relevant to emission coefficient and the Fowler–Milne method, the deduced error propagation formula is
ΔT T
¼
ΔY Y
¼
ΔðεArI =εArII Þ kT U εArI =εArII EArII þ EAr1 EArI
ð4Þ
where EAr1 is the ionization energy of argon atom, the meaning of other parameters are the same as mentioned above. 3.2. Temperature and composition distribution measured by the two-line intensity correlation method Fig. 5. Pair of the Olsen–Richter diagram for 100% Ar arc plasma at 2 mm below the cathode tip. (– – –) LTE isobars at atmospheric pressure, () temperature marks with 1000 K increments. ( ) Experimental points.
The two-line intensity correlation method is similar to the Fowler–Milne method. The only difference is the way to obtain
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line is higher than the maximum temperature in the arc plasma, εnArII cannot be measured by Ar II line. Instead, εnArII is normalized c to εnArI (the norm relative emission coefficient of Ar I line) by the following equation [7]:
εnArII ¼
nArII ðT; Y Ar ÞU ArII T c εnArII c2 εArII E E exp ArIc ArII ¼ ¼ C ArII nc c εArI c1 εArI kT kT nArI T c U ArI ðT; Y Ar Þ
ð5Þ
Fig. 7. Radial dependence of normalized emission coefficient for a) εArI 794.8 nm Ar I line, b) εArII 487.98 nm Ar II line, measured 1 mm below the cathode with the input gas of 50% Arþ 50% He in a 200-A free-burning arc.
CArII is the calibration factor related to the experiment system and atomic properties of the radiation. For the determination of unknown calibration factor CArII, the Ar I 696.5 nm and Ar II 480.6 nm emission coefficients are measured below the cathode tip 2 mm in pure argon when these are in the LTE state. The resulting data with circular marks are shown in Fig. 9. When the theoretical relationship between the Ar I and Ar II line emission coefficients was calculated as a function of temperature from both Saha relation and Eq. (5), the factor CArI which shows best fitting with experimental data could be determined. The error of CArII comes from the relative emission coefficient in experiment, transition probability of spectrum and the fitting error, the calculated error is 21%. Since Ar I 696.5 nm and Ar II 480.6 nm lines are also used in this method, the intensity distributions at a position 1 mm below the cathode in an argon–helium arc are identical with Fig. 5a and b. The relative emission coefficient of Ar I 696.5 nm is normalized to the maximum emission coefficient of 696.5 nm, it is the same as in Fig. 6a. While, the relative emission coefficient Ar II 480.6 nm is also normalized to the maximum emission coefficient of 696.5 nm, these values with their error bar are shown in Fig. 10. The corresponding emission coefficient of Ar I and Ar II in theoretical isogram is shown in Fig. 11 with circles, solid line and broken line depict theoretical emission coefficient relations and isotherms,
Fig. 9. Pair of the Olsen–Richter diagram for 100% Ar arc plasma at 2 mm below the cathode tip. (– – –) LTE isobars at atmospheric pressure, ( ) Experimental points.
Fig. 8. a) Temperature and b) composition distribution measured by the Fowler– Milne method in the line 1 mm below the cathode with the input gas of 50% Arþ 50% He in a 200-A free-burning arc.
εnArII. The two-line intensity correlation method also requires to measure the emission coefficient of εnArI and εnArII respectively. Ar I 696.5 nm and Ar II 480.6 nm spectra were chosen for the twoline intensity correlation method. εnArI is determined by the norm relative emission coefficient of Ar I line, which is the same as the Fowler–Milne method. Since the normal temperature of the Ar II
Fig. 10. Radial dependence of normalized emission coefficients for εArII 480.6 nm Ar II line, measured 1 mm below the cathode with the input gas of 50% Ar þ 50% He in a 200-A free-burning arc.
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plot equation ln
Fig. 11. Relationship between Ar I and Ar II emission coefficient in Ar–He mixed arc plasma.
εnm λnm
g m Anm c
¼
hnj ðT Þ Em þ ln kT 4π U j ðT Þ
ð7Þ
Thus, the temperature T is determined by the line slope ( 1/kT). In addition, this method is irrelevant to particle density nj(T) and is not affected by the atmospheric gas composition since nj(T) is in the constant term. In order to improve the accuracy, the wavelength range of these lines should be as small as possible to help reduce the influence of spectrometer's sensitivity to different wavelength; and the range of Em should be as wide as possible to help separate these points. In this experimental system, Em of Ar I lines are in small-scope and are not separated enough. Only Ar II between 450 nm and 500 nm meet the requirement of wavelength and Em. Fig. 13 shows Ar II spectra group usually employed in the Boltzmann plot method. A typical Boltzmann plot is shown in Fig. 14. All the points are fitted with the least-square method. However, some of the points are away from the line and temperature may vary depended on that line. After calculate point by point, the temperature distribution with its error bar is shown in Fig. 15a. Spectrum width includes equipment line width, Doppler broadening width, Stark broadening width, nature line width and so on, the first three items dominate the line width of spectrum, and other width could be ignored. Equipment line width and Doppler broadening width are of Gauss distribution, Stark broadening width is of Lorentz distribution, while the detected spectral line width is of Voigt distribution, it is the convolution of Gauss and Lorentz distribution. Then, the Fourier transform method was applied to these spectral widths to obtain Stark broadening width [17]. The electron density could be calculated since the relationship between Stark width and electron
Fig. 12. a) Temperature and b) composition distribution measured by the two-line intensity correlation method 1 mm below the cathode with the input gas 50% Ar þ50% He in a 200-A free-burning arc.
isoconcentration which are calculated from Eqs. (2) and (5). The transferred temperature and composition distribution are shown in Fig. 12. This error is relevant to emission coefficient, transition probability of spectrum and the two-line intensity correlation method, the deduced error propagation formula is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ΔT ΔY ΔðεArI =εArII Þ 2 ΔA 2 kT ¼ ¼ þ ð6Þ T Y A EArII þ EAr1 EArI εArI =εArII According to Wiese et al. [16],
Fig. 13. Emission spectra between 450 nm and 500 nm used in the Boltzmann plot method, at the axial position of 1 mm below the cathode in a 200-A free-burning arc with the input gas 50% Ar þ50% He.
ΔA/A is assigned to be 20%.
3.3. Temperature and composition distribution measured by the Boltzmann plot method In the Boltzmann plot method, the temperatures were calculated from the spectral intensity ratio of the particles in a similar state. By simple algebra, Eq. (1) is transformed into the Boltzmann
Fig. 14. Boltzmann plot data for the axial position of 1 mm below the cathode.
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Fig. 16. Electron density distribution with different methods of 1 mm below the cathode tip in a 200-A free-burning arc with input gas 50% Arþ 50% He.
Table 2 Electron population of argon and helium. Element
50% Ar þ50% He
ne 10,000 K
15,000 K
20,000 K
4.3 1022
5.32 1022
6.0 1022
Fig. 15. a) Temperature and b) composition distribution measured by the Boltzmann plot method at 1 mm below the cathode with the input gas 50% Ar þ 50% He in a 200-A free-burning arc.
density had been derived. Ar II 480.6 nm spectrum was chosen for calculating electron density. After the temperature and electron density were obtained, composition could be calculated through Saha equation. The composition distribution with its error bar is shown in Fig. 15b. Assume there is no error in electron density calculation. Then, the error of temperature and composition are relevant to emission coefficient, transition probability of spectrum and the slope fitting error, the deduced error propagation formula is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 7 ΔT ΔY u ΔεiArII 2 ΔA 2 ΔS t1 ¼ ¼ ð8Þ þ þ ∑ T Y 7 i ¼ 1 εiArII A S where S is the slope of fitted curve, the slope.
ΔS is the standard error of
Fig. 17. a) Temperature and b) composition distribution measured by different methods for 1 mm below cathode with the input gas 50% Arþ 50% He in a 200-A free-burning arc.
4. Discussion LTE is generally assumed in Ar–He arc plasma 1 mm below the cathode tip. The electron density was calculated above by the Stark broadening method, the result is shown in Fig. 16. To achieve LTE generally requires high enough electron density for collisional transitions to dominate radiate transitions between all states; otherwise, the absence of thermal radiation will cause deviations from the thermal equilibrium. The criterion given by Hutchinson [18] is adopted and applied for the present computations. ne c 1019 ðT=eÞ1=2 ðΔE=eÞ3 m 3
ð9Þ
where T/e and ΔE/e are the temperature and energy level difference in eV. The corresponding electron population is shown in Table 2. The electron density is higher than the limited value in
the mixture of argon and helium when not considering demixing. So the arc plasma is in LTE under this situation. Then, temperature and composition distribution are compared with kinds of methods. Temperature and composition distribution measured by different spectroscopic methods and the simulation result from Murphy [11] are shown in Fig. 17. The results of spectroscopic methods showed consistency with that of simulation. That means the spectroscopic methods in this paper had reasonable results. In the arc center, the temperature reaches approximately 20,000 K and the mole fraction of argon is about 20%. Temperature and composition measured by the Boltzmann plot method is lower
X. Xiao et al. / Optics & Laser Technology 66 (2015) 138–145
than those obtained by other methods. This phenomenon is similar to the result in pure argon arc plasma [19]. This is because Boltzmann temperature was largely affected by slope which has relatively high fitting error, meanwhile the uncertainties of transition probability cause errors either. All of these result in large error for Boltzmann plot. The Fowler–Milne method and the two-line intensity correlation method for Ar I 696.5 nm and Ar II 480.6 nm have good consistency in both temperature and composition distribution. However, the result of the two-line intensity correlation method has higher error than that of the Fowler–Milne method. When measured by the two-line intensity correlation method, the marked differences in the values of transition probability influence the normalized emission coefficient of Ar II and systematic error in the two-line intensity correlation method. And generate larger error in calculation results. While, for the Fowler–Milne method, neither the calibration of apparatus sensitivity nor the knowledge of the atomic transition probabilities is required. Hence, the error of the Fowler–Milne method is the lowest among those three methods. 5. Conclusions With three spectroscopic measurement methods, the temperature and composition distribution of the arc plasma of 200 A at 1 mm below the cathode with the mixture of 50% argon and 50% helium were obtained. These methods were the Fowler–Milne method, the two-line intensity correlation method and the Boltzmann plot method. And LTE was verified through electron density distribution in this experiment. The Ar I and Ar II spectra were applied to modify the Fowler– Milne method in this measurement. The maximum emission coefficient of Ar II was calculated through the Olsen–Richter diagram. When the spectroscopic methods were compared with Murphy's simulation result, they showed agreement with each other which indicate that the spectroscopic methods had reasonable results in this paper. Through comparison and analysis of the error bar in different methods, it showed that the calculated temperature and composition of the arc plasma are not always consistent. The Boltzmann plot method gave a lower temperature and composition distribution when compares with other methods. The differences between these methods are relevant to the error of slope fitting and uncertainties of transition probabilities. However, the Fowler–Milne method and the two-line intensity correlation method had good consistency in both temperature and composition distribution. The result of the two-line intensity correlation method had higher error than that of the Fowler–Milne method, it
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mainly caused by marked differences in the values of transition probability. The Fowler–Milne method, which was irrelevant to atomic transition probabilities and experimental apparatus calibration, had the minimum error.
Acknowledgment The authors acknowledge support from the National Natural Science Foundation of China under grant 51275299.
References [1] Haddad G, Farmer A. Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon. J Phys D: Appl Phys 1984;17:1189. [2] Ma S, Gao H, Zheng S, Wu L. Spectroscopic measurement of temperatures in pulsed TIG welding arcs. J Phys D: Appl Phys 2011;44:405202. [3] Lancaster JF. The physics of welding. Phys Technol 1984;15:73. [4] Thornton M. Spectroscopic determination of temperature distributions for a TIG arc. J Phys D: Appl Phys 1993;26:1432. [5] Li H, Li J, Li Y. High thermal characterictic of argon-nitrogen TIG arc. Weld J 1993;14:125–30. [6] Song Y. Research on spectroscopic diagnosis and application of welding arc plasma. Tianjin University. 1990. [7] K. Hiraoka, Demixing in Argon–Helium mixed gas tungsten welding arcs, in; Proceedings of the International Symposium on Plasma Chemistry 1; 1993, pp. 440–445. [8] Hiraoka K. Plasma structures of Ar-H2 mixed gas tungsten arcs determined by spectroscopic measurements. Weld Int 1998;12:186–94. [9] Murphy AB. Modified Fowler–Milne method for the spectroscopic measurement of temperature and composition of multielement thermal plasmas. Rev Sci Instrum 1994;65:3423. [10] Hiraoka K. Evaluation of local plasma composition and temperature in mixed gas tungsten arc plasma column by light spectroscopy-study on characteristics of gas tungsten arc shielded by mixed gases (Report 2). Q J Jpn Weld Soc 1993;11(1):68. [11] Murphy A. Demixing in free-burning arcs. Phys Rev E 1997;55:7473. [12] Ding P, Pan S. Error estimation and conversion coefficient of Bockasten method for Abel conversion in arc plasma spectra. J Jilin Univ (Sci) 1987;2:010. [13] Bockasten K. Transformation of observed radiances into radial distribution of the emission of a plasma. JOSA 1961;51:943–7. [14] Pokrzywka B, Musiol K, Pellerin S, Pawelec E, Chapelle J. Spectroscopic investigation of the equilibrium state in the electric arc cathode region. J Phys D: Appl Phys 1996;29:2644. [15] Olsen HN. Thermal and Electrical Properties of an Argon Plasma. Phys Fluids 1959;2:614. [16] Wiese W, Martin G. Wavelengths and transition probabilities for atoms and atomic ions: Part 2. Transition probabilities, 68. Gaithersburg, MD, U.S: NSRDS-NBS; 1980; 1. [17] Pan C, Hua X, Zhang W, Li F, Xiao X. Calculating the Stark broadening of welding arc spectra by Fourier transform method. Spectrosc Spectr Anal 2012;32:1739–43. [18] Hutchinson IH. Principles of plasma diagnostics. Cambridge university press; 2005. [19] Hiraoka K, Shiwaku T, Ohji T. Determining temperature distributions of gas tungsten arc (TIG) plasma by spectroscopic methods. Weld Int 1997;11:688–96.
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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Comparison of temperature and composition measurement by spectroscopic methods for argon–helium arc plasma Xiao Xiao a,b, Xueming Hua a,b,n, Yixiong Wu a,b a Welding Engineering Technology Research Institute of Materials Science and Engineering (Shanghai Jiao Tong University), Shanghai 200240, People's Republic of China b Shanghai Key Laboratory of Materials Laser Processing and Modification (Shanghai Jiao Tong University), Shanghai 200240, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 2 March 2014 Received in revised form 23 August 2014 Accepted 27 August 2014 Available online 21 September 2014
Three different spectroscopic methods were used to calculate the temperature and composition distribution of argon–helium arc plasma—the Fowler–Milne method, the two-line intensity correlation method and the Boltzmann plot method. Experimental errors, including random errors and systematic errors, were analyzed in detail to comparing the accuracy of different methods. Due to the large differences of physical characteristics between argon and helium, there were limited reports on the measurement of temperature and composition distribution in argon–helium arc plasma. To this end, The Fowler–Milne method and the Boltzmann plot method were modified in this paper. Three spectroscopic methods were compared with other's simulation result and showed good agreement with each other, except the Boltzmann plot method which had partly distinction. Through comparison and analysis of error bar in those methods, it was found that both the Fowler–Milne method and the two-line intensity correlation method had less error than the Boltzmann plot method, while the Fowler–Milne method, which is irrelevant to atomic transition probabilities and experimental apparatus calibration, had the minimum error. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Experimental error Spectroscopic measurement Argon–helium arc plasma
1. Introduction Emission spectroscopy, which does not disturb the arc plasma, is a very effective way to investigate the plasma property. And most of the spectral measurement techniques have been applied to determine the temperature in single gas arc plasma [1,2]. However, it seems that the temperature measurement of arc plasma presented by many researchers have mutually contradictory results, as indicated by Lancaster [3]. For example, the measured temperature using the Fowler–Milne method is higher than those using the Boltzmann plot method. Those groups using a relative or an absolute intensity method had considerable disagreement results, while the Fowler–Milne spectroscopic technique obtained consistent values [4]. Moreover, the presence of additional gas causes demixing in most cases, which means temperature and gas composition changes with position. The existence of demixing significantly complicates the measurement for multi-element arc plasma. Hence, most of the accepted methods need to be modified for applying in multi-element arc plasma. In this paper, different spectroscopic methods were n Corresponding author at: Welding Engineering Technology Research Institute of Materials Science and Engineering (Shanghai Jiao Tong University), Shanghai 200240, People's Republic of China. Tel.: þ 86 21 54748940 8009. E-mail address: [email protected] (X. Hua).
http://dx.doi.org/10.1016/j.optlastec.2014.08.017 0030-3992/& 2014 Elsevier Ltd. All rights reserved.
introduced and then the temperature and gas composition (mole fraction of argon in arc plasma) distribution were compared among those methods in the mixture of argon–helium arc plasma. Due to the complexity of measurement in multi-element arc plasma, only few researchers measured its temperature and gas composition distribution in gas tungsten arc welding (GTAW) using mixed gas. Song et al. [5,6] used absolute intensity of Ar I, Hα and N I line, to determine temperature and gas composition in argon–hydrogen arc plasma and argon–nitrogen arc plasma. The result showed that hydrogen concentrate in the center of the arc plasma. Hiraoka [7,8] used a two-line intensity correlation method to measure temperature and composition distribution in the multi-element arc plasma. It involved the measurement of the relative intensity of Ar I and Ar II lines or Ar I and H I lines to obtain temperature distribution of Ar–He or Ar–H2 mixed-gas tungsten arc plasma, and find the helium concentrate on the axis of arc. Murphy [9] used a modified Fowler–Milne method to measure the radial profiles of temperature and gas composition of free-burning arcs in mixtures of argon and nitrogen. The results demonstrate that the occurrence of demixing depending on the relative concentration of argon and nitrogen. These methods are used in different gas mixtures in different experimental conditions, so they are difficult to compare with each other. Due to the physical characteristic between argon and helium differs largely, i.e., the first ionization energy of helium is much
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larger than that of argon, the density of helium is much lighter than that of argon, there exist large differences in ionization degree and complicate spectra chosen. There are thus limited reports on measuring the temperature and composition for the mixture of argon and helium. Only Hiraoka [7,10] used the twoline intensity correlation method to measure the temperature and composition distributions in the argon–helium arc plasma of 100 A. It is interesting to compare with other spectroscopic methods and analyze the error distribution. In this study, we will use a spectrometer system to measure spectral intensity distribution, and then use three different spectroscopic methods to obtain the temperature and composition of arc plasma with the mixture of argon–helium in GTAW. Firstly, the Fowler–Milne method was applied in the mixture of argon–helium arc plasma. Though Murphy [9] used this method in argon and nitrogen mixtures, they have similar physical property and got the similar normal temperature. However, there were problems existing in argon–helium gas mixture. From the perspective of first ionization energy and density, there are wide gap between argon and helium, as a result, their normal temperatures are quite different. In fact, the normal temperature of He I is above the temperature of arc plasma, and the maximum emission coefficient could not be measured. Nevertheless, the Fowler–Milne method requires that value, we chose Ar I and Ar II spectral lines in the study since their maximum emission coefficient could be obtained. Then, the two-line intensity correlation method and the Boltzmann plot method were used for temperature and composition measurement under the identical conditions. Meanwhile the experimental errors, including random errors and systematic errors, were thoroughly analyzed for each method. Furthermore, a comparative investigation was carried out for their respective temperature and composition results between the following spectroscopic methods: a) the Fowler–Milne method; b) the two-line intensity correlation method; c) the Boltzmann plot method, and others' simulation result [11], and they are also analyzed according to their error distribution.
2. Experimental system The experimental system mainly contains two parts. One is arc plasma source, which is used to produce arc plasma; the other is a spectrum acquisition system, which is used to obtain spectral intensity of arc plasma. 2.1. Arc plasma source In the experiment, a direct current (DC) arc was generated in the gas mixture of argon and helium at atmospheric pressure by welding power supply (DA300P-type, OTC Corporation, Japan). The arc freely burned between a tungsten cathode and a stationary water-cooled copper plate anode. A 2.4-mm-diameter tungsten electrode adding 2% ThO2 with a cone angle of 601 was employed as cathode. A water-cooled copper-plate vertically located below the cathode was employed as anode. Arc distance, defined as the distance from the tungsten electrode tip to copper-plate surface, is 5 mm. The mixture of argon (50% in volume) and helium (50% in volume) was used as the shielding gas feeding from the cathode nozzle with a flow rate of 10 L min i, and the current was set at 200 A. 2.2. Spectrum acquisition system The spectrum acquisition system consists of a single lens system, a motion control device and a spectrometer. Radiation from the arc plasma was imaged by a single lens system onto an
139
Fig. 1. Spectroscopic acquisition system for arc plasma.
imaging screen at a magnification of 2:1. The convex lens (focal length is 0.3 m) was fixed 0.45 m away from the arc, thus the parallel-ray projection condition assumed in the Abel inversion can be approximately satisfied. A light aperture was employed to limit light from the arc for obtaining adequate spatial resolution. In the image screen which was places 0.9 m away from the lens, an optical fiber (P400-UV-SR, Ocean Optics, USA) was mounted on a motion control device which can be moved in both horizontal and vertical directions. The internal diameter of the optical fiber is 0.4 mm and thus the scanning step along the horizontal direction was determined as 0.4 mm. Light along the chord of arc 1 mm below the cathode tip was transmitted by the optical fiber to the spectrometer (HR-4000UV-NIR, Ocean Optics, USA) of 3648 pixels with a spectral range from 200 to 1100 nm. The spectroscopic acquisition system is schematically shown in Fig. 1.
3. Measurement of temperature and composition distribution by different methods Since temperature and gas composition could not be measured directly, they are derived from different spectroscopic methods which need the value of emission coefficient, and the measurements are line-of-sight integrated intensities, the distribution of emission coefficients must be reconstructed. This is accomplished by means of an Abel inversion, provided the plasma is cylindrically symmetric and optically thin. For Abel inversion, the measured intensity of the spectral line was corrected by subtracting the corresponding continuum radiation intensity first. Then, the sideon measured spectral line intensity profiles were symmetrized, noise filtered, and the Bockasten method [12,13] was used to convert intensity to emission coefficient. Since this experimental system was not calibrated to the absolute intensity, this emission coefficient is relevant to the experimental system. Hence, it is a relative emission coefficient. The line emission coefficient εnm of a transition from level m to lower level n of species j in plasma is given by [3] nj ðT Þ hc Em exp ð1Þ εnm ¼ g m Anm kT U j ðT Þ 4πλnm where nj (T) and Uj (T) are respectively the number density and the partition function of the species j, Em and gm are the energy and statistical weight of the upper level, Anm is the transition probability, λnm is the wavelength of the radiation emitted, and c, h, and k are respectively the speed of light in a vacuum, Planck's constant, and Boltzmann's constant. Hence, the intensity of emission from a single spectral line depends on the temperature T and the number density nj of the emitting species. If the plasma is in local thermal equilibrium (LTE), and only one chemical element is present in the
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plasma, the relationship between T and nj could be calculated from Saha equilibrium. Thus, it is sufficient to determine both T and nj from single spectrum radiation intensity. However, if two or more chemical elements are present in the plasma, nj dependents on both temperature T and the mole fraction YJ of the chemical element J, from which the specie j is derived. Because of demixing, YJ usually strongly depends on position. Therefore, it is insufficient to obtain T or nj only from single spectrum. To determine these values requires at least k species, where k is the number of chemical elements being present. For the mixture of argon–helium arc plasma, two species of spectral line are needed. The emission coefficient was obtained through spectral intensity. Fig. 2 shows the arc spectra in the wavelength range from 450 nm to 810 nm measured in the column region of the arc at a distance of 1 mm from the cathode tip, which contains the Ar I, Ar II and He I spectral lines. Table 1 contains spectral parameters used in this measurement. For the Fowler–Milne method, the emission coefficients have to be normalized to their respective maximum values in pure arc plasma. Ar I 696.5 nm and Ar II 480.6 nm lines were used to characterize the argon–helium plasma properties. The reason we chose these lines was that they are well separated from other lines and the line intensity is not weak. Although the He I 587.6 nm spectral line is also strong, the normal temperature of He I 587.6 nm spectrum is too high (24,300 K) for pure helium arc plasma to reach, the maximum value of εHeI could not be measured. Since the Fowler–Milne method need to normalize the emission coefficient, He I spectrum could not be chosen. The normal temperature of Ar II is 25,600 K, the maximum value of εArII could not be measured, either. However, in pure argon arc plasma, that value could be calculated through the Olsen–Richter method [14]. As a result, it is reasonable and rational to choose 696.5 nm Ar I and 480.6 nm Ar II spectral lines to measure temperature and gas composition distribution in the argon– helium arc plasma. For the two-line intensity correlation method, Ar I 696.5 nm and Ar II 480.6 nm lines were also used to measure temperature
and gas composition distribution in the argon–helium arc plasma. For the Boltzmann plot method, since it is irrelevant to composition of arc plasma, a group of Ar II lines was used to measure the temperature distribution, gas composition was calculated from Saha equation which needs temperature and electron density. Temperature is measured by the Boltzmann plot method, while electron density is acquired through 480.6 nm Ar II spectrum broadening. The experiment was repeated three times, and the results were given in average value with its error bar. 3.1. Temperature and composition distribution measured by the Fowler–Milne method The Fowler–Milne method relies on the fact that for plasma in LTE and at constant pressure, εnm has a maximum εcnm at a welldefined temperature Tc, known as the normal temperature. Provided that the maximum temperature of the plasma exceeds Tc, those positions at which the emission coefficient is maximum can be assumed at temperature Tc. If εJnc is a relative emission coefficient in our experiment system at the normal temperature T cJ of chemical element J in an arc containing only that element, then we can define the normalized emission coefficient εnJ using Eq. (1). For the Ar I and Ar II lines c1 εnArI nArI ðT; Y Ar ÞU ArI T c ε EArI EArI exp ð2Þ εnArI ¼ ArI ¼ ¼ nc εcArI c1 εArI kT c kT nArI T c U ArI ðT; Y Ar Þ
εnArII ¼
εArII c2 εnArII nArII ðT; Y Ar ÞU ArII T c E E exp ArIIc ArII ¼ ¼ nc εcArII c2 εArII kT kT nArII T c U ArII ðT; Y Ar Þ
ð3Þ
where c1 and c2 are constants that relate to the emission coefficient and the measured relative emission coefficient. For mixtures of argon and helium arc plasma, the normalized emission coefficient of an Ar I 696.5 nm line and an Ar II 480.6 nm line depend both on temperature and the composition; it could be calculated from Eqs. (2) and (3) at different ratios, and normalized to their respective maximum values in pure argon arc. The relationship
Fig. 2. Emission spectra distribution between 450 nm and 810 nm in a 200-A freeburning arc with input gas 50% Arþ 50% He.
Table 1 Spectral characteristic of major spectral lines in the measurement. Lines (nm)
Type
Transition probabilities
Normal temperature (K)
696.5 480.6 587.6
Ar I Ar II He I
6.39e þ 06 7.80e þ 07 5.31e þ 07a
14,700 25,000 24,300
a
Indicates one value of the transition probabilities.
Fig. 3. Dependence on temperature of the emission coefficient of a) the 696.5 nm Ar I line and b) the 480.6 nm Ar II line, normalized to its maximum value in pure argon, for different mixtures of argon and helium.
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between temperature and normalized emission coefficient of Ar I and Ar II are shown in Fig. 3. However, a value of the emission coefficient of either the Ar I 696.5 nm line or the Ar II 480.6 nm line corresponds to an infinite number of mole fraction–temperature pairs. Hence, each value of the normalized emission coefficient εArI for the Ar I 696.5 nm line corresponds to a curve Y(T, εArI), where Y is the mole fraction of argon; likewise, each value of εArII for the Ar II 480.6 nm line corresponds to a curve Y(T, εArII). These dependencies are shown in Fig. 4, which shows the relationship between Y and T for different values of εArI and εArII. In addition, it is demonstrated in Fig. 4 that if both εArI and εArII are known, the number of corresponding mole fraction–temperature pairs is, at most, one. In this experimental system, the norm relative emission coefficient of 696.5 nm line corresponded to the highest observed value of the off-axis maximum in pure argon arc plasma in the LTE state at atmospheric pressure. To determine the maximum relative emission coefficient value of Ar II 480.6 nm, the measured radial distributions of emission coefficients for the 696.5 nm and 480.6 nm lines were marked as points in the Olsen–Richter diagram [14]. These emission coefficients are below the cathode tip 2 mm in 100% Ar which are in the LTE state [15]. To superpose the experimental values on the theoretical graph, two constants are needed. In our case the norm relative emission coefficient of 696.5 nm line was acquired above. Taking into account remarks concerning the Boltzmann–Saha equilibrium for Ar II levels, the norm relative emission coefficient of 480.6 Ar II line could be determined through the Olsen–Richter diagram. The results of Fig. 6. Radial dependence of intensity for a) εArI 794.8 nm Ar I line, b) εArII 487.98 nm Ar II line, measured 1 mm below the cathode with the input gas of 50% Arþ 50% He in a 200-A free-burning arc.
Fig. 4. Relation between the mole fraction of argon and temperature for different normalized emission coefficients.
these procedures are shown in Fig. 5. It can be seen that the experimental data for Ar II and Ar I lines can be well superposed on the curve. The error of norm relative emission coefficient of 480.6 Ar II line comes from the relative emission coefficient in experiment and the fitting error, the calculated error is 4%. Fig. 6a and b shows the radial dependence of intensity with their error bar at a position 1 mm below the cathode in an argon– helium arc. The solid line represents the intensity distribution of Ar I 794.8 nm spectral line, and dotted line represents that of Ar II 487.98 nm spectral line. The intensity was the mean value of three times measurement, and the error was calculated from standard deviations of the mean value. The corresponding normalized emission coefficients with their error bar are shown in Fig. 7a and b. The error comes from the measurement of intensity, the Olsen–Richter diagram and the method of Abel inversion whose error was calculated according to Ref. [12]. Then, using the data depicted in Fig. 4, these normalized emission coefficients are transformed to temperature–mole fraction pairs. Fig. 8a and b shows the temperature and mole fraction of gas composition distribution with their error bar at 1 mm below the cathode. This error is relevant to emission coefficient and the Fowler–Milne method, the deduced error propagation formula is
ΔT T
¼
ΔY Y
¼
ΔðεArI =εArII Þ kT U εArI =εArII EArII þ EAr1 EArI
ð4Þ
where EAr1 is the ionization energy of argon atom, the meaning of other parameters are the same as mentioned above. 3.2. Temperature and composition distribution measured by the two-line intensity correlation method Fig. 5. Pair of the Olsen–Richter diagram for 100% Ar arc plasma at 2 mm below the cathode tip. (– – –) LTE isobars at atmospheric pressure, () temperature marks with 1000 K increments. ( ) Experimental points.
The two-line intensity correlation method is similar to the Fowler–Milne method. The only difference is the way to obtain
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line is higher than the maximum temperature in the arc plasma, εnArII cannot be measured by Ar II line. Instead, εnArII is normalized c to εnArI (the norm relative emission coefficient of Ar I line) by the following equation [7]:
εnArII ¼
nArII ðT; Y Ar ÞU ArII T c εnArII c2 εArII E E exp ArIc ArII ¼ ¼ C ArII nc c εArI c1 εArI kT kT nArI T c U ArI ðT; Y Ar Þ
ð5Þ
Fig. 7. Radial dependence of normalized emission coefficient for a) εArI 794.8 nm Ar I line, b) εArII 487.98 nm Ar II line, measured 1 mm below the cathode with the input gas of 50% Arþ 50% He in a 200-A free-burning arc.
CArII is the calibration factor related to the experiment system and atomic properties of the radiation. For the determination of unknown calibration factor CArII, the Ar I 696.5 nm and Ar II 480.6 nm emission coefficients are measured below the cathode tip 2 mm in pure argon when these are in the LTE state. The resulting data with circular marks are shown in Fig. 9. When the theoretical relationship between the Ar I and Ar II line emission coefficients was calculated as a function of temperature from both Saha relation and Eq. (5), the factor CArI which shows best fitting with experimental data could be determined. The error of CArII comes from the relative emission coefficient in experiment, transition probability of spectrum and the fitting error, the calculated error is 21%. Since Ar I 696.5 nm and Ar II 480.6 nm lines are also used in this method, the intensity distributions at a position 1 mm below the cathode in an argon–helium arc are identical with Fig. 5a and b. The relative emission coefficient of Ar I 696.5 nm is normalized to the maximum emission coefficient of 696.5 nm, it is the same as in Fig. 6a. While, the relative emission coefficient Ar II 480.6 nm is also normalized to the maximum emission coefficient of 696.5 nm, these values with their error bar are shown in Fig. 10. The corresponding emission coefficient of Ar I and Ar II in theoretical isogram is shown in Fig. 11 with circles, solid line and broken line depict theoretical emission coefficient relations and isotherms,
Fig. 9. Pair of the Olsen–Richter diagram for 100% Ar arc plasma at 2 mm below the cathode tip. (– – –) LTE isobars at atmospheric pressure, ( ) Experimental points.
Fig. 8. a) Temperature and b) composition distribution measured by the Fowler– Milne method in the line 1 mm below the cathode with the input gas of 50% Arþ 50% He in a 200-A free-burning arc.
εnArII. The two-line intensity correlation method also requires to measure the emission coefficient of εnArI and εnArII respectively. Ar I 696.5 nm and Ar II 480.6 nm spectra were chosen for the twoline intensity correlation method. εnArI is determined by the norm relative emission coefficient of Ar I line, which is the same as the Fowler–Milne method. Since the normal temperature of the Ar II
Fig. 10. Radial dependence of normalized emission coefficients for εArII 480.6 nm Ar II line, measured 1 mm below the cathode with the input gas of 50% Ar þ 50% He in a 200-A free-burning arc.
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143
plot equation ln
Fig. 11. Relationship between Ar I and Ar II emission coefficient in Ar–He mixed arc plasma.
εnm λnm
g m Anm c
¼
hnj ðT Þ Em þ ln kT 4π U j ðT Þ
ð7Þ
Thus, the temperature T is determined by the line slope ( 1/kT). In addition, this method is irrelevant to particle density nj(T) and is not affected by the atmospheric gas composition since nj(T) is in the constant term. In order to improve the accuracy, the wavelength range of these lines should be as small as possible to help reduce the influence of spectrometer's sensitivity to different wavelength; and the range of Em should be as wide as possible to help separate these points. In this experimental system, Em of Ar I lines are in small-scope and are not separated enough. Only Ar II between 450 nm and 500 nm meet the requirement of wavelength and Em. Fig. 13 shows Ar II spectra group usually employed in the Boltzmann plot method. A typical Boltzmann plot is shown in Fig. 14. All the points are fitted with the least-square method. However, some of the points are away from the line and temperature may vary depended on that line. After calculate point by point, the temperature distribution with its error bar is shown in Fig. 15a. Spectrum width includes equipment line width, Doppler broadening width, Stark broadening width, nature line width and so on, the first three items dominate the line width of spectrum, and other width could be ignored. Equipment line width and Doppler broadening width are of Gauss distribution, Stark broadening width is of Lorentz distribution, while the detected spectral line width is of Voigt distribution, it is the convolution of Gauss and Lorentz distribution. Then, the Fourier transform method was applied to these spectral widths to obtain Stark broadening width [17]. The electron density could be calculated since the relationship between Stark width and electron
Fig. 12. a) Temperature and b) composition distribution measured by the two-line intensity correlation method 1 mm below the cathode with the input gas 50% Ar þ50% He in a 200-A free-burning arc.
isoconcentration which are calculated from Eqs. (2) and (5). The transferred temperature and composition distribution are shown in Fig. 12. This error is relevant to emission coefficient, transition probability of spectrum and the two-line intensity correlation method, the deduced error propagation formula is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ΔT ΔY ΔðεArI =εArII Þ 2 ΔA 2 kT ¼ ¼ þ ð6Þ T Y A EArII þ EAr1 EArI εArI =εArII According to Wiese et al. [16],
Fig. 13. Emission spectra between 450 nm and 500 nm used in the Boltzmann plot method, at the axial position of 1 mm below the cathode in a 200-A free-burning arc with the input gas 50% Ar þ50% He.
ΔA/A is assigned to be 20%.
3.3. Temperature and composition distribution measured by the Boltzmann plot method In the Boltzmann plot method, the temperatures were calculated from the spectral intensity ratio of the particles in a similar state. By simple algebra, Eq. (1) is transformed into the Boltzmann
Fig. 14. Boltzmann plot data for the axial position of 1 mm below the cathode.
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Fig. 16. Electron density distribution with different methods of 1 mm below the cathode tip in a 200-A free-burning arc with input gas 50% Arþ 50% He.
Table 2 Electron population of argon and helium. Element
50% Ar þ50% He
ne 10,000 K
15,000 K
20,000 K
4.3 1022
5.32 1022
6.0 1022
Fig. 15. a) Temperature and b) composition distribution measured by the Boltzmann plot method at 1 mm below the cathode with the input gas 50% Ar þ 50% He in a 200-A free-burning arc.
density had been derived. Ar II 480.6 nm spectrum was chosen for calculating electron density. After the temperature and electron density were obtained, composition could be calculated through Saha equation. The composition distribution with its error bar is shown in Fig. 15b. Assume there is no error in electron density calculation. Then, the error of temperature and composition are relevant to emission coefficient, transition probability of spectrum and the slope fitting error, the deduced error propagation formula is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 7 ΔT ΔY u ΔεiArII 2 ΔA 2 ΔS t1 ¼ ¼ ð8Þ þ þ ∑ T Y 7 i ¼ 1 εiArII A S where S is the slope of fitted curve, the slope.
ΔS is the standard error of
Fig. 17. a) Temperature and b) composition distribution measured by different methods for 1 mm below cathode with the input gas 50% Arþ 50% He in a 200-A free-burning arc.
4. Discussion LTE is generally assumed in Ar–He arc plasma 1 mm below the cathode tip. The electron density was calculated above by the Stark broadening method, the result is shown in Fig. 16. To achieve LTE generally requires high enough electron density for collisional transitions to dominate radiate transitions between all states; otherwise, the absence of thermal radiation will cause deviations from the thermal equilibrium. The criterion given by Hutchinson [18] is adopted and applied for the present computations. ne c 1019 ðT=eÞ1=2 ðΔE=eÞ3 m 3
ð9Þ
where T/e and ΔE/e are the temperature and energy level difference in eV. The corresponding electron population is shown in Table 2. The electron density is higher than the limited value in
the mixture of argon and helium when not considering demixing. So the arc plasma is in LTE under this situation. Then, temperature and composition distribution are compared with kinds of methods. Temperature and composition distribution measured by different spectroscopic methods and the simulation result from Murphy [11] are shown in Fig. 17. The results of spectroscopic methods showed consistency with that of simulation. That means the spectroscopic methods in this paper had reasonable results. In the arc center, the temperature reaches approximately 20,000 K and the mole fraction of argon is about 20%. Temperature and composition measured by the Boltzmann plot method is lower
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than those obtained by other methods. This phenomenon is similar to the result in pure argon arc plasma [19]. This is because Boltzmann temperature was largely affected by slope which has relatively high fitting error, meanwhile the uncertainties of transition probability cause errors either. All of these result in large error for Boltzmann plot. The Fowler–Milne method and the two-line intensity correlation method for Ar I 696.5 nm and Ar II 480.6 nm have good consistency in both temperature and composition distribution. However, the result of the two-line intensity correlation method has higher error than that of the Fowler–Milne method. When measured by the two-line intensity correlation method, the marked differences in the values of transition probability influence the normalized emission coefficient of Ar II and systematic error in the two-line intensity correlation method. And generate larger error in calculation results. While, for the Fowler–Milne method, neither the calibration of apparatus sensitivity nor the knowledge of the atomic transition probabilities is required. Hence, the error of the Fowler–Milne method is the lowest among those three methods. 5. Conclusions With three spectroscopic measurement methods, the temperature and composition distribution of the arc plasma of 200 A at 1 mm below the cathode with the mixture of 50% argon and 50% helium were obtained. These methods were the Fowler–Milne method, the two-line intensity correlation method and the Boltzmann plot method. And LTE was verified through electron density distribution in this experiment. The Ar I and Ar II spectra were applied to modify the Fowler– Milne method in this measurement. The maximum emission coefficient of Ar II was calculated through the Olsen–Richter diagram. When the spectroscopic methods were compared with Murphy's simulation result, they showed agreement with each other which indicate that the spectroscopic methods had reasonable results in this paper. Through comparison and analysis of the error bar in different methods, it showed that the calculated temperature and composition of the arc plasma are not always consistent. The Boltzmann plot method gave a lower temperature and composition distribution when compares with other methods. The differences between these methods are relevant to the error of slope fitting and uncertainties of transition probabilities. However, the Fowler–Milne method and the two-line intensity correlation method had good consistency in both temperature and composition distribution. The result of the two-line intensity correlation method had higher error than that of the Fowler–Milne method, it
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mainly caused by marked differences in the values of transition probability. The Fowler–Milne method, which was irrelevant to atomic transition probabilities and experimental apparatus calibration, had the minimum error.
Acknowledgment The authors acknowledge support from the National Natural Science Foundation of China under grant 51275299.
References [1] Haddad G, Farmer A. Temperature determinations in a free-burning arc. I. Experimental techniques and results in argon. J Phys D: Appl Phys 1984;17:1189. [2] Ma S, Gao H, Zheng S, Wu L. Spectroscopic measurement of temperatures in pulsed TIG welding arcs. J Phys D: Appl Phys 2011;44:405202. [3] Lancaster JF. The physics of welding. Phys Technol 1984;15:73. [4] Thornton M. Spectroscopic determination of temperature distributions for a TIG arc. J Phys D: Appl Phys 1993;26:1432. [5] Li H, Li J, Li Y. High thermal characterictic of argon-nitrogen TIG arc. Weld J 1993;14:125–30. [6] Song Y. Research on spectroscopic diagnosis and application of welding arc plasma. Tianjin University. 1990. [7] K. Hiraoka, Demixing in Argon–Helium mixed gas tungsten welding arcs, in; Proceedings of the International Symposium on Plasma Chemistry 1; 1993, pp. 440–445. [8] Hiraoka K. Plasma structures of Ar-H2 mixed gas tungsten arcs determined by spectroscopic measurements. Weld Int 1998;12:186–94. [9] Murphy AB. Modified Fowler–Milne method for the spectroscopic measurement of temperature and composition of multielement thermal plasmas. Rev Sci Instrum 1994;65:3423. [10] Hiraoka K. Evaluation of local plasma composition and temperature in mixed gas tungsten arc plasma column by light spectroscopy-study on characteristics of gas tungsten arc shielded by mixed gases (Report 2). Q J Jpn Weld Soc 1993;11(1):68. [11] Murphy A. Demixing in free-burning arcs. Phys Rev E 1997;55:7473. [12] Ding P, Pan S. Error estimation and conversion coefficient of Bockasten method for Abel conversion in arc plasma spectra. J Jilin Univ (Sci) 1987;2:010. [13] Bockasten K. Transformation of observed radiances into radial distribution of the emission of a plasma. JOSA 1961;51:943–7. [14] Pokrzywka B, Musiol K, Pellerin S, Pawelec E, Chapelle J. Spectroscopic investigation of the equilibrium state in the electric arc cathode region. J Phys D: Appl Phys 1996;29:2644. [15] Olsen HN. Thermal and Electrical Properties of an Argon Plasma. Phys Fluids 1959;2:614. [16] Wiese W, Martin G. Wavelengths and transition probabilities for atoms and atomic ions: Part 2. Transition probabilities, 68. Gaithersburg, MD, U.S: NSRDS-NBS; 1980; 1. [17] Pan C, Hua X, Zhang W, Li F, Xiao X. Calculating the Stark broadening of welding arc spectra by Fourier transform method. Spectrosc Spectr Anal 2012;32:1739–43. [18] Hutchinson IH. Principles of plasma diagnostics. Cambridge university press; 2005. [19] Hiraoka K, Shiwaku T, Ohji T. Determining temperature distributions of gas tungsten arc (TIG) plasma by spectroscopic methods. Weld Int 1997;11:688–96.