# Using the Pairs of Lines Broadened by Collisions with Neutral and Charged Particles for Gas Temperature Determination of Argon Non-Thermal Plasmas at Atmospheric Pressure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{g}) determination of plasmas at atmospheric pressure. The rotational temperature derived from them is considered as a good estimation of the kinetic temperature of the plasma heavy particles [1,2] thanks to the strong coupling between translational and rotational energy states under high-pressure conditions. The emissions of diatomic species, such as OH, N

_{2}, N

_{2}

^{+}, CN, ..., have been traditionally employed with this purpose [3,4,5,6,7,8,9,10], but the use of molecular emission spectroscopy is not always easy for gas temperature measurement in plasmas: overlapping of bands, rotational population distribution of levels having a non-Boltzmann nature, wake emission of rotational bands, among others, can make it difficult to obtain reliable values of gas temperature.

_{g}). It requires the use of additional techniques for simultaneous determination of the electron density [15], as these lines have a non-negligible Stark broadening for electron densities above 10

^{14}cm

^{−3}, which needs to be determined. Yubero et al. in [16] proposed a method to circumvent this dependence on electron density by considering pairs of these lines. This method allows for the determination of the gas temperature from the measurements of Lorentzian profiles of some pairs of argon atomic lines, and when applying it, no assumptions on the degree of thermodynamic equilibrium among excited states are needed (unlike methods based on rotational temperature determination).

## 2. Method

_{V}-resulting from the convolution of a Gaussian function (W

_{G}) with a Lorentzian function (W

_{L}) (see, e.g., [17,18]). Indeed, the profiles of atomic lines emitted by plasmas with no presence of magnetic fields result from different broadening mechanisms leading to Gaussian or Lorentzian profile shapes, briefly described below.

_{D}(in nm) given by

_{g}, and M are the wavelength (nm), the gas temperature (in K), and the mass of the radiating atom (in a.m.u.), respectively.

_{W}), according to the Lindholm–Foley theory [19].

_{R}.

_{S}) of a line is due to interactions of the emitter atom with the surrounding charged particles, perturbing the electric field it experiences. In the case of a non-hydrogenic atom, the profiles of isolated spectral lines broadened by collisions with electrons have a Lorentzian shape. For thermal plasmas with a gas temperature similar to the electron one, the mobility of ions is high and the impact approximation [21] is also valid for ions, being their contribution to the broadening also being Lorentzian. In the ion impact limit, line profiles are symmetric Lorentzian. On the contrary, for plasmas where the ion mobility is small (e.g., plasmas with gas temperature relatively low), a quasistatic approximation is often needed to model the ion broadening in order to explain the slightly asymmetric shape of the profiles. The less dynamical the ions are, the more asymmetric the lines are. The finite lifetime of the excited levels gives rise to natural broadening, which is typically very small (~0.00001 nm) and can be neglected in the case of atmospheric pressure plasma spectroscopy.

_{I}, as shown in the next section.

_{G}) given by

_{L}) given by

_{L}can be written as follows:

^{16}cm

^{−3}, and n

_{e}is the electron density.

_{g}is much lower than T

_{e}(electron temperature), the ionic contribution ${w}_{S}^{i}$ can be neglected. Additionally, W

_{S}can be considered to have a weak dependence on T

_{e}in the small range of electron temperature from 5000 to 10,000 K [22]. In this way, W

_{S}depends only on n

_{e}and Equation (5) can be approximated as follows:

_{W}in nm given by Griem [18], which, considering the ideal gas equation N = P/K

_{B}T

_{g}for the density of perturbers, and where K

_{B}is the Boltzmann constant and P is the pressure, can be written as

_{0}units) of the upper and lower level, λ is the wavelength of the observed line in nm, α is the polarizability of perturbers interacting with the excited radiator in cm

^{3}, T

_{g}is the temperature of the emitters (coincident with the gas temperature) in K, and µ is the reduced mass of the emitter–perturber pair in a.m.u.

^{−25}cm

^{3}), C can be written as [16]

_{L}given by Equation (3) can be approximately expressed as

_{L}for these lines allow us to obtain T

_{g}using Equation (14), provided the C coefficients and Stark broadening parameters are known. Table 1 includes values of the C coefficients calculated for these lines from Equation (8), and the Stark broadening parameters theoretically determined by Dimitrijević et al. [22] for an electron temperature of 10,000 K.

## 3. Experimental Set-Up

^{14}(cm

^{−3}). The electron temperature was estimated to be close to 10,000 K from observed relative populations of the argon excited levels assuming a partial local thermodynamic equilibrium [28].

_{I}= (0.032 ± 0.001) nm was measured when using slit widths of 100 µm.

`.`The Lorentzian contribution to the entire broadening in each case was obtained from the Voigt FWHM measured for each line using the formula [30,31]

_{G}≈ W

_{I}, since, according to Equation (2), the Doppler contribution can be considered as negligible when compared to the instrumental one under the experimental conditions in the plasma studied (T

_{g}≤ 2500 K, W

_{D}

^{ArI}≤ 0.003 nm).

## 4. Results

_{g}determination using Equation (14), provided C coefficients and Stark broadening parameters given in Table 1.

_{g}values obtained using these parameters for an electron temperature of 10,000 K. These values are also compared with the values obtained using OH ro-vibrational band [13]. Uncertainties in T

_{g}have been obtained from Equation (14) by considering C and W

_{S}as theoretical constants and only taking into account uncertainties in the broadenings experimentally measured and errors of approximations used in this method.

## 5. Discussion and Conclusions

_{g}values with higher uncertainty. They correspond to those cases in which the denominator in Equation (14) is very small, so gas temperature determination becomes very sensitive, giving rise to large errors. Examples of pairs of line giving large errors are Ar I 560.7 nm/Ar I 603.2 nm and Ar I 560.7 nm/Ar I 549.6 nm. This fact does not explain other values that are lower than those obtained from OH ro-vibrotional band. Examples of these pairs of lines are Ar I 518.8 nm/Ar I 603.2 nm, Ar I 518.8 nm/Ar I 549.6 nm, Ar I 518.8 nm/Ar I 522.1 nm, and Ar I 518.8 nm/Ar I 560.7 nm. This could be explained by errors in the theoretical broadening constants given in Table 1.

_{g}determination (see Equation (14)); this condition applies to plasmas with a relatively low gas temperature (van der Waals broadening not negligible) and moderate electron densities (significant Stark broadening).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Nassar, H.; Pellerin, S.; Mussiol, K.; Martinie, O.; Pellerin, M.N.; Cormier, J.M. N2(+)/N2 ratio and temperature 2 measurements based on the first negative N-2(+) and second positive N-2 overlapped molecular emission spectra. J. Phys. D Appl. Phys.
**2004**, 37, 1904. [Google Scholar] [CrossRef] - Britun, N.; Gaillard, M.; Ricard, A.; Kim, Y.M.; Kim, K.S.; Han, H.G. Determination of the vibrational, rotational and electron temperatures in N2 and Ar-N2 rf discharge. J. Phys. D Appl. Phys.
**2007**, 40, 1022. [Google Scholar] [CrossRef] - Zhu, X.M.; Chen, W.C.; Pu, Y.K. Gas temperature, electron density and electron temperature measurement in a microwave excited microplasma. J. Phys. D Appl. Phys.
**2008**, 41, 105212. [Google Scholar] [CrossRef] - Wang, Q.; Koleva, I.; Donnelly, V.M.; Economou, D.J. Spatially resolved diagnostics of an atmospheric pressure direct current helium microplasma. J. Phys. D Appl. Phys.
**2005**, 38, 1690. [Google Scholar] [CrossRef] - Abdallah, M.H.; Mermet, J.M. The Behavior of Nitrogen Excited in an Inductively Coupled Argon Plasma. J. Quant. Spectrosc. Radiat. Transf.
**1978**, 19, 83–91. [Google Scholar] [CrossRef] - Laux, C.O.; Spence, T.G.; Kruger, C.H.; Zare, R.N. Optical diagnostics of atmospheric pressure air plasmas. Plasma Sources Sci. Technol.
**2003**, 12, 125. [Google Scholar] [CrossRef] - Fantz, U. Emission spectroscopy of molecular low pressure plasmas. Contrib. Plasma Phys.
**2004**, 44, 508–515. [Google Scholar] [CrossRef] - Mora, M.; García, M.C.; Jiménez-Sanchidrián, C.; Romero-Salguero, F.J. Transformation of light paraffins in a microwave-induced plasma-based reactor at reduced pressure. Int. J. Hydrog. Energy
**2010**, 35, 4111–4122. [Google Scholar] [CrossRef] - Iza, F.; Hopwood, J.A. Rotational, vibrational, and excitation temperatures of a microwave-frequency microplasma. IEEE Trans. Plasma Sci.
**2004**, 32, 498–504. [Google Scholar] [CrossRef] - Lombardi, G.; Benedic, F.; Mohasseb, F.; Hassouni, K.; Gicquel, A. Determination of gas temperature and C-2 absolute density in Ar/H-2/CH4 microwave discharges used for nanocrystalline diamond deposition from the C-2 Mulliken system. Plasma Sources Sci. Technol.
**2004**, 13, 375. [Google Scholar] [CrossRef] - Christova, M.; Castaños-Martínez, E.; Calzada, M.D.; Kabouzi, Y.; Luque, J.M.; Moisan, M. Electron density and gas temperature from line broadening in an argon surface-wave-sustained discharge at atmospheric pressure. Appl. Spectrosc.
**2004**, 58, 1032–1037. [Google Scholar] [CrossRef] [PubMed] - Christova, M.; Gagov, V.; Koleva, I. Analysis of the profiles of the argon 696.5 nm spectral line excited in non-stationary wave-guided discharges. Spectrochim. Acta B
**2000**, 55, 815–822. [Google Scholar] [CrossRef] - Yubero, C.; Dimitrijevic, M.S.; García, M.C.; Calzada, M.D. Using the van der Waals broadening of the spectral atomic lines to measure the gas temperature of an argon microwave plasma at atmospheric pressure. Spectrochim. Acta B
**2007**, 62, 169–176. [Google Scholar] [CrossRef] - Muñoz, J.; Dimitrijevic, M.S.; Yubero, C.; Calzada, M.D. Using the van der Waals broadening of spectral atomic lines to measure the gas temperature of an argon-helium microwave plasma at atmospheric pressure. Spectrochim. Acta B
**2009**, 64, 167–172. [Google Scholar] [CrossRef] - Gigosos, M.A.; Cardeñoso, V. New plasma diagnosis tables of hydrogen Stark broadening including ion dynamics. J. Phys. B At. Mol. Opt. Phys.
**1996**, 29, 4795. [Google Scholar] [CrossRef] - Yubero, C.; Rodero, A.; Dimitrijevic, M.; Gamero, A.; García, M.C. Gas temperature determination in an argon non-thermal plasma at atmospheric pressure from broadenings of atomic emission lines. Spectrochim. Acta Part B
**2017**, 129, 14–20. [Google Scholar] [CrossRef] - Zaghloul, M.R. On the calculation of the Voigt line profile: A single proper integral with a damped sine integrand MNRAS. Mon. Not. R. Astron. Soc.
**2007**, 375, 1043–1048. [Google Scholar] [CrossRef] - Griem, H.R. Spectral Line Broadening by Plasmas; Academic Press: New York, NY, USA, 1974. [Google Scholar]
- Allard, N.; Kielkopf, J. The effect of neutral non resonant collisions on atomic spectral lines. Rev. Mod. Phys.
**1982**, 54, 1103. [Google Scholar] [CrossRef] - Griem, H.R. Stark broadening of isolated spectral lines from heavy elements in a plasma. Phys. Rev.
**1962**, 128, 515–531. [Google Scholar] [CrossRef] - Konjevic, N. Plasma broadening and shifting of non-hydrogenic spectral lines: Present status and applications. Phys. Rep.
**1999**, 316, 339–401. [Google Scholar] [CrossRef] - Dimitrijević, M.S.; Konjević, N. Stark broadenings of isolated spectral-lines of heavy-elements in plasmas. J. Quant. Spectrosc. Radiat. Transf.
**1983**, 30, 45–54. [Google Scholar] [CrossRef] - Dimitrijević, M.S.; Christova, M.; Sahal-Bréchot, S. Stark broadening of visible Ar I spectral lines. Phys. Scr.
**2007**, 75, 809–819. [Google Scholar] [CrossRef] - Christova, M.; Dimitrijević, M.S.; Sahal-Bréchot, S. Stark broadening of Ar I spectral lines emitted in surface wave sustained discharges. Mem. Della Soc. Astron. Ital. Suppl.
**2005**, 7, 238. [Google Scholar] - Dimitrijević, M.S. A programme to provide Stark broadening data for stellar and laboratory plasma investigations. Zh. Prikl. Spektrosk.
**1996**, 63, 810. [Google Scholar] - Sahal-Bréchot, S. Théorie de l’élargissement et du déplacement des raies spectrales sous l’effect des chocs avec les électrons et les ions dans l’approximation des impacts. Astron. Astrophys.
**1959**, 1, 91–123. [Google Scholar] - Moisan, M.; Etermandi, E.; Rostaing, J.C. Excitation System for a Gas Plasma Surface Wave, and Associated Gas Processing System—Has Electromagnetic Material Sleeve Surrounding Gas Circulating Tube (European Patent EP 0874 537 A1). French Patent N. 2,762,748, 1998. [Google Scholar]
- García, M.C.; Rodero, A.; Sola, A.; Gamero, A. Spectroscopic study of a stationary surface-wave sustained argon plasma column at atmospheric pressure. Spectrochim. Acta Part B
**2000**, 55, 1733–1745. [Google Scholar] [CrossRef] - Santiago, I.; Christova, M.; García, M.C.; Calzada, M.D. Self-absorbing method to determine the population of the metastable levels in an argon microwave plasma at atmospheric pressure. Eur. Phys. J. Appl. Phys.
**2004**, 28, 325–330. [Google Scholar] [CrossRef] - Temme, N.M. Voigt function. In NIST Handbook of Mathematical Functions; Olver Frank, W.J., Lozier, D.M., Boisvert, R.F., Eds.; Cambridge University Press: New York, NY, USA, 2010; ISBN 978-0521192255. [Google Scholar]
- Olivero, J.J.; Longbothum, R.L. Empirical fits to the Voigt line width: A brief review. J. Quant. Spectrosc. Radiat. Transf.
**1977**, 17, 233–236. [Google Scholar] [CrossRef] - Ali, A.W.; Giem, H.R. Theory of Resonance Broadening of Spectral Lines by Atom-Atom Impacts. Phys. Rev.
**1965**, 140, 1044. [Google Scholar] [CrossRef] - Ali, A.W.; Giem, H.R. Theory of Resonance Broadening of Spectral Lines by Atom-Atom Impacts (ERRATA). Phys. Rev.
**1966**, 144, 366. [Google Scholar] [CrossRef]

**Table 1.**C coefficients calculated from Equation (8), and the Stark broadening parameters due to electron impacts theoretically determined by Dimitrijević et al. [22] for an electron temperature of 10,000 K and an electron density of 10

^{16}cm

^{−3}.

Ar I Line (nm) | C | ${\mathit{w}}_{\mathit{S}}={\mathit{w}}_{\mathit{S}}^{\mathit{e}}$ (nm) |
---|---|---|

603.2 | 4.2 | 0.149 |

549.6 | 4.9 | 0.305 |

522.1 | 5.9 | 0.588 |

560.7 | 3.6 | 0.145 |

518.8 | 4.1 | 0.104 |

**Table 2.**Lorentzian FWHM of lines Ar I 603.2 nm, Ar I 549.6 nm, Ar I 522.1 nm, Ar I 560.7 nm, and Ar I 518.8 nm measured at different axial plasma positions.

z (cm) | z = 4 cm | z = 8 cm | z = 12 cm |
---|---|---|---|

W _{L}^{603} (nm) | 0.0411 ± 0.0014 | 0.0437 ± 0.0016 | 0.0459 ± 0.0014 |

W _{L}^{549} (nm) | 0.0594 ± 0.0019 | 0.0626 ± 0.0016 | 0.0731 ± 0.0012 |

W _{L}^{522} (nm) | 0.0958 ± 0.0024 | 0.1020 ± 0.0019 | 0.122 ± 0.002 |

W _{L}^{560} (nm) | 0.0342 ± 0.0024 | 0.0377 ± 0.0024 | 0.0429 ± 0.0012 |

W _{L}^{518} (nm) | 0.0372 ± 0.0021 | 0.0418 ± 0.0016 | 0.0472 ± 0.0018 |

**Table 3.**Gas temperature obtained using Equation (14) with theoretical Stark broadening parameters at electron temperatures of 10,000 K, and comparison with the one obtained from OH ro-vibrational bands, using the well known Boltzmann plot technique.

z = 4 cm T^{BP}_{g} (K) = 1390 ± 70 | Ar I 549 nm | Ar I 522 nm | Ar I 560 nm | Ar I 518 nm |

Ar I 603 nm | 1300 ± 300 | 1420 ± 180 | 570 ± 240 | 1100 ± 500 |

Ar I 549 nm | - | 1800 ± 900 | 2200 ± 1300 | 1200 ± 230 |

Ar I 522 nm | - | 2000 ± 700 | 1300 ± 200 | |

Ar I 560 nm | - | 900 ± 300 | ||

z = 8 cm T^{BP}_{g} (K) = 1330 ± 70 | Ar I 549 nm | Ar I 522 nm | Ar I 560 nm | Ar I 518 nm |

Ar I 603 nm | 1100 ± 220 | 1300 ± 200 | 700 ± 600 | 760 ± 220 |

Ar I 549 nm | - | 1700 ± 500 | 1400 ± 500 | 920 ± 120 |

Ar I 522 nm | - | 1600 ± 500 | 1030 ± 110 | |

Ar I 560 nm | - | 800 ± 300 | ||

z = 12 cm T^{BP}_{g} (K) = 1520 ± 70 | Ar I 549 nm | Ar I 522 nm | Ar I 560 nm | Ar I 518 nm |

Ar I 603 nm | 1600 ± 400 | 1680 ± 220 | 3000 ± 3000 | 500 ± 130 |

Ar I 549 nm | - | 1800 ± 500 | 1400 ± 400 | 810 ± 110 |

Ar I 522 nm | - | 1500 ± 300 | 930 ± 110 | |

Ar I 560 nm | - | 640 ± 130 |

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**MDPI and ACS Style**

Yubero, C.; Rodero, A.; Dimitrijevic, M.S.; Gamero, A.; García, M.D.C. Using the Pairs of Lines Broadened by Collisions with Neutral and Charged Particles for Gas Temperature Determination of Argon Non-Thermal Plasmas at Atmospheric Pressure. *Atoms* **2017**, *5*, 41.
https://doi.org/10.3390/atoms5040041

**AMA Style**

Yubero C, Rodero A, Dimitrijevic MS, Gamero A, García MDC. Using the Pairs of Lines Broadened by Collisions with Neutral and Charged Particles for Gas Temperature Determination of Argon Non-Thermal Plasmas at Atmospheric Pressure. *Atoms*. 2017; 5(4):41.
https://doi.org/10.3390/atoms5040041

**Chicago/Turabian Style**

Yubero, Cristina, Antonio Rodero, Milan S. Dimitrijevic, Antonio Gamero, and Maria Del Carmen García. 2017. "Using the Pairs of Lines Broadened by Collisions with Neutral and Charged Particles for Gas Temperature Determination of Argon Non-Thermal Plasmas at Atmospheric Pressure" *Atoms* 5, no. 4: 41.
https://doi.org/10.3390/atoms5040041