# Electron Density from Balmer Series Hydrogen Lines and Ionization Temperatures in Inductively Coupled Argon Plasma Supplied by Aerosol and Volatile Species

Authors: Jolanta Borkowska-Burnecka; Wiesław Żyrnicki; Maja Wełna; Piotr Jamróz
Journal: International Journal of Spectroscopy
 (2016)

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## Abstract

Electron density and ionization temperatures were measured for inductively coupled argon plasma at atmospheric pressure. Different sample introduction systems were investigated. Samples containing Sn, Hg, Mg, and Fe and acidified with hydrochloric or acetic acids were introduced into plasma in the form of aerosol, gaseous mixture produced in the reaction of these solutions with NaBH4 and the mixture of the aerosol and chemically generated gases. The electron densities measured from Hα, Hβ, Hγ, and Hδ lines on the base of Stark broadening were compared. The study of the H Balmer series line profiles showed that the ne values from Hγ and Hδ were well consistent with those obtained from Hβ which was considered as a common standard line for spectroscopic measurement of electron density. The ne values varied from 0.56·1015 to 1.32·1015 cm−3 and were the highest at loading mixture of chemically generated gases. The ionization temperatures of plasma, determined on the base of the Saha approach from ion-to-atom line intensity ratios, were lower for Sn and Hg (6500–7200 K) than those from Fe and Mg lines (7000–7800 K). The Sn II/Sn I and Hg II/Hg I, Fe II/Fe I, and Mg II/Mg I intensity ratios and the electron densities (ne) were dependent on experimental conditions of plasma generation. Experimental and theoretically calculated ionization degrees were compared.


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## Body

## 1. Introduction

Inductively coupled plasma (ICP) generated at atmospheric pressure has been recognized as a one of the most commonly applied techniques for both analytical purposes and spectrochemical investigations, including diagnostic studies. It has become attractive for simultaneous determination of several elements in a great variety of samples, namely, environmental, industrial, geological, biological, clinical, and food materials [1–3]. Additionally, although the method requires as a rule the liquid samples for measurements, the ability of hyphenation of the ICP with electrothermal vaporization or laser ablation allows analysis of the samples in their solid state [4, 5]. On the other hand, plasma discharge appears as an interesting tool enabling us to get knowledge and to understand the processes occurring in the plasma source [6–9].Typically, solutions are introduced into the plasma by means of pneumatic (PN) or ultrasonic nebulization(USN), while chemical vapour generation (CVG) based on the reduction of the element ions with NaBH4 in acidic medium has been widely employed to derivate elements into the form of volatile hydrides (e.g., As, Bi, Sb, Se, and Sn) or into cold vapours (Hg, Cd) [3, 10]. Systems without phase separation, that is, allowing the simultaneous introduction of volatile species and sample aerosol using pneumatic nebulization, can also be used to determine both hydride and nonhydride elements [3, 11–13].Experimental conditions have effects on ICP parameters, for example, electron density (ne), plasma temperatures (Texc, Tion, and Tgas), or plasma robustness employing the ion-to-atom intensity ratios (M II/M I). For the latter, the Mg II 280.3/Mg I 285.2 nm intensity ratio is usually considered. Determination of ne is commonly carried out using the Hβ line profile. Excitation temperature is typically derived from atomic iron lines and the OH A-X 0-0 band serves usually for gas plasma temperature measurements. A number of papers have been devoted to ICP spectral diagnostics; however, nebulization systems have been predominantly investigated [6–9, 14–16] in comparison to the reports concerning CVG [11, 17–19]. In the case of PN, the effect of hydrogen in addition to the argon or combined effect with a desolvation step was also discussed [19–21].Studies analysing the influence of CVG, PN, and combined PN + CVG systems on ICP characteristic are relatively rare and not consisted. Grotti et al. [18] investigated effect of operating conditions (power, carrier gas flow, and HCl and NaBH4 concentrations) on Texc, ne, and Pb II/Pb I ratio in an axially viewed ICP coupled with pneumatic nebulization and ultrasonic nebulization associated with desolvation and with chemical vapour generation. At robust conditions and the CVG system, the electron number density was about 8% higher than at the PN system. Batistoni et al. [19] determined ne and the H excitation temperature for the plasma with hydrogen from acidic NaBH4 hydrolysis and compared obtained values with those determined for PN and dry plasma. The increase in ne during NaBH4 hydrolysis with reference to the dry plasma and PN was about 50% and 40%, respectively [19]. In the other work [17], the ne values were above 70% higher at the CVG system than for dry plasma. Recently, spectroscopic and analytical characteristics of ICP with hydride generation with or without simultaneous introduction of the sample aerosol were presented by Pohl and Broekaert [11]. In this paper, the Tex values determined from Ar I, Au I, Bi I, and Fe I were found to be close together for the sample introduction systems studied although differences for particular species were noted. The highest ne values were obtained for the combined PN and CVG system while the ne values at CVG and PN mode were comparable [11].In the last years, attention has been paid to the use of other than Hβ hydrogen lines for the electron density determination [19, 22–32] in various plasma. Konjević et al. [23] discussed difficulties appearing during experimental line profile analysis for higher members of Balmer series and compared theory versus experiments for low ne plasma diagnostics. Mijatović et al. [24] tested the applicability of the Hγ line as a diagnostic tool at moderately low plasma densities using a low-pressure pulsed arc operating in a H2:He gas mixture as a plasma source. Nikiforov et al. [29] discussed applications of Stark broadening hydrogenated (and nonhydrogenated) atomic lines for determination of ne in atmospheric pressure plasma and presented equations for ne estimation based on measured broadening of hydrogen Balmer series (Hα, Hβ, and Hγ). For helium atmospheric pressure microwave induced plasma, the similar values of the electron density were obtained from the Hβ and Hδ lines [28]. Recently, many works are devoted to determination of ne from various hydrogen lines in laser-induced plasma [27, 30–32] due to very dynamic expansion and applications of such plasma. Pardini et al. [27] evaluated the plasma electron density through the measurements of the Stark broadening of the first-five members of the hydrogen Balmer series and compared experimental results with the predictions of three theories that described laser-induced breakdown plasma. The electron densities calculated from various H lines (with the exception of Hα) were comparable. The other works on laser-induced plasma diagnostics concern mainly exploration of the first-two Balmer series lines. For ICP only Batistoni et al. [19] measured the electron density in Ar-ICP for PN, CVG, and dry plasma by means of Hδ and Hγ lines and the results obtained from the two lines were not consisted.The objective of the present study was determination and comparison of spectroscopic parameters of the inductively coupled plasma operating with pneumatic nebulization (aerosol), chemical vapour generation (gas mixture), and pneumatic nebulization combined with CVG. For the electron density determination, the usage of the first-four hydrogen lines of the Balmer series was tested. Atomic and ionic lines of Fe, Mg, Sn, and Hg served as thermometric species. In considerations, effects of sample introduction systems and related to the water, hydrogen, and mixture of hydrogen and water loading into the plasma were analysed. In addition, influence of the matrix of HCl and CH3COOH on spectroscopic parameters was examined.


## 2. Materials and Methods

### 2.1. Instrumentation

All measurements were performed with the use of a Jobin Yvon sequential ICP-OES spectrometer (JY 38S) with a 1 m Czerny-Turner monochromator and two holographic gratings (4320 and 2400 grooves/mm). Spectra were recorded at the resolution of 0.01 nm in a sequential mode. Additionally, the image system for quick data acquisition in the range of 190–780 nm was used. Working parameters for the ICP-OES measurements are given in Table1. The recorded line intensities were background corrected and expressed as net signals. The mean values from three repeated measurements were used in all investigations. The precision of the signal measurements expressed as the relative standard deviation (RSD) ranged, depending on the experimental conditions, from 1 to 6%.Table 1
ICP operating parameters.
Generator
40.68 MHz
Monochromator
1 m with 4320/2400 grooves/mm grating
Photomultipliers Hamamatsu R106 and R955
Rf power
1000 W and 1200 W
Injector i.d.
2.5 mm
Observation zone
12 mm above load coil
Ar flow rates:
plasma gas
13–15 L min−1
sheath gas
0.2 L min−1
carrier gas
0.3 L min−1
Solution uptake:
acidified sample
1.0 mL min−1
reductant
1.0 mL min−1
Line wavelength (nm)
Sn II (189.9), Sn I (235.5), Hg II (194.2), Hg I (253.6), Mg II (280.3), Mg I (285.2), Hα (656.3), Hβ (486.1) Hγ (434.0 ), and Hδ (410.2)
Lines of Fe I (356–388 nm range) and Fe II (258–276 nm range)
Chemical vapour generation condition
NaBH4 concentration
0.75% (m/V) in 0.25 mol L−1 NaOH
HCl or CH3COOH concentration
1.0 mol L−1


### 2.2. Sample Introduction Systems

The ICP spectrometer, equipped with a modified cyclonic spray chamber and a parallel pneumatic nebulizer (Burgener), allowed nebulizing solutions (PN) as well as attaining chemical vapour generation (CVG) both separately and simultaneously with sample aerosol (PN + CVG). Solutions containing Sn(II), Hg(II), Mg(II), and Fe(II) at concentrations in the range of 5–50μg mL−1 were used. The solutions were acidified to final concentration of 1 mol L−1 with HCl or CH3COOH (HAc). In the case of phase separation (the CVG system only), volatile species of mercury and tin (vapours and hydrides) were generated in a continuous flow system. In the manifold applied, an acidified sample and reductant (NaBH4) solutions were continuously pumped in two separate streams to Y-junction where they mixed and the CVG reaction occurred. Then, through 5 cm reaction coil, the reaction mixture was introduced at the bottom of the chamber (acting as a gas-liquid phase separator). Volatile species and other gaseous by-products (mainly hydrogen) were swept by the stream of argon introduced through nebulizer and carried to the plasma torch. Conditions of the CVG mode are shown in Table 1.For the simultaneous chemical vapour generation and pneumatic nebulization (the PN + CVG system), the acidified sample solution was aspirated into the chamber by pneumatic nebulizer and the NaBH4 solution was introduced at the bottom of the chamber. Larger aerosol droplets deposited on the wall of the chamber dropped down to the bottom, where they reacted with incoming NaBH4. Formed gaseous products as well as the sample aerosol were carried by a stream of the nebulizer argon into the plasma.


### 2.3. Plasma Parameters Calculations

The electron density was determined from Stark broadening of the Hα, Hβ, and Hγ lines using tables obtained by computer simulation technique [33] assuming the electron temperature equal to 7500 K and a reduced mass of the emitter-perturber pair μ=1. Additionally, for the Hδ line, Griem’s approximation [34, 35] was also applied.For the extraction of the Stark broadening components from experimentally measured half widths of the hydrogen lines, the procedure described in work [26] and considering Doppler broadening and instrumental broadening was employed. The van der Waals and resonance broadening effects could be omitted. The instrumental line width was evaluated with the aid of the Ar lines lying in a neighbourhood of the hydrogen lines. The broadening caused by Doppler effect was calculated using common known expression at the assumption of the gas kinetic temperature equal to 4000 K. In the deconvolution, the GRAMS software and mixed Gaussian + Lorentz algorithm were used.Spectroscopic temperatures and ionization degree were calculated at an assumption of partial thermal equilibrium. Ionization temperatures (Tion) were calculated from the slope of the linearized form of the Saha-Boltzmann distribution [16, 36]:(1)ln⁡IigaAaλiIagiAiλa=-Eion+Ei-EakT+ln⁡22πmekT3/2neh3,where I is the line intensity, g is the statistical weight, A is the transition probability, λ is the line wavelength, E is the energy of the upper state, Eion is the first ionization potential, T is the ionization temperature, and ne is the electron density. Subscripts “i” and “a” refer to ions and atoms, respectively.At assumption of LTE, this method allows for the determination of theTion values independently of the ne measurements. Plotting the ln⁡IigaAaλi/IagiAiλa versus the energy sum (Eion+Ei-Ea) yields the straight line with the slope equal to -1/kTion. Ionization temperatures (Tion) were calculated using fourteen atomic iron lines (Fe I) with excitation energies from 3.21 to 4.72 eV and fifteen ionic iron lines (Fe II) with excitation energies from 4.77 to 8.04 eV (Table 1). The Fe transition probabilities were taken from the NIST Atomic Spectra Database [37]. Additionally, the ionization temperatures were calculated using two-line method [36, 38] and the Mg II/Mg I, Hg II/Hg I, and Sn II/Sn I intensity ratios. The Hg, Sn, and Mg line transition probabilities were taken from the Kurucz database [39].The ionization degrees (αion) were determined from the Saha ionization equation at assumption of plasma equilibrium:(2)KjT=neN+N=22πmekT3/2h3U+TUTexp⁡-Eion-ΔEionkT,where Kj(T) is equilibrium constant, N, N+, and ne are number of atoms, ions, and electrons, respectively, U+T and U(T) are partition functions for atom and ion of the elements, and ΔEion is lowering of the ionization energy due to effect of the plasma on atoms and ions. In ICP, a contribution of multiple charged ions is negligible and hence αion may be determined using (2) as (3)αionA+=NA+NA+NA+=NA+/NA1+NA+/NA. The partition functions for the atom and ion of the Mg, Fe, Sn, and Hg species were calculated from Irwin tables [40].


## 2.1. Instrumentation

All measurements were performed with the use of a Jobin Yvon sequential ICP-OES spectrometer (JY 38S) with a 1 m Czerny-Turner monochromator and two holographic gratings (4320 and 2400 grooves/mm). Spectra were recorded at the resolution of 0.01 nm in a sequential mode. Additionally, the image system for quick data acquisition in the range of 190–780 nm was used. Working parameters for the ICP-OES measurements are given in Table1. The recorded line intensities were background corrected and expressed as net signals. The mean values from three repeated measurements were used in all investigations. The precision of the signal measurements expressed as the relative standard deviation (RSD) ranged, depending on the experimental conditions, from 1 to 6%.Table 1
ICP operating parameters.
Generator
40.68 MHz
Monochromator
1 m with 4320/2400 grooves/mm grating
Photomultipliers Hamamatsu R106 and R955
Rf power
1000 W and 1200 W
Injector i.d.
2.5 mm
Observation zone
12 mm above load coil
Ar flow rates:
plasma gas
13–15 L min−1
sheath gas
0.2 L min−1
carrier gas
0.3 L min−1
Solution uptake:
acidified sample
1.0 mL min−1
reductant
1.0 mL min−1
Line wavelength (nm)
Sn II (189.9), Sn I (235.5), Hg II (194.2), Hg I (253.6), Mg II (280.3), Mg I (285.2), Hα (656.3), Hβ (486.1) Hγ (434.0 ), and Hδ (410.2)
Lines of Fe I (356–388 nm range) and Fe II (258–276 nm range)
Chemical vapour generation condition
NaBH4 concentration
0.75% (m/V) in 0.25 mol L−1 NaOH
HCl or CH3COOH concentration
1.0 mol L−1


## 2.2. Sample Introduction Systems

The ICP spectrometer, equipped with a modified cyclonic spray chamber and a parallel pneumatic nebulizer (Burgener), allowed nebulizing solutions (PN) as well as attaining chemical vapour generation (CVG) both separately and simultaneously with sample aerosol (PN + CVG). Solutions containing Sn(II), Hg(II), Mg(II), and Fe(II) at concentrations in the range of 5–50μg mL−1 were used. The solutions were acidified to final concentration of 1 mol L−1 with HCl or CH3COOH (HAc). In the case of phase separation (the CVG system only), volatile species of mercury and tin (vapours and hydrides) were generated in a continuous flow system. In the manifold applied, an acidified sample and reductant (NaBH4) solutions were continuously pumped in two separate streams to Y-junction where they mixed and the CVG reaction occurred. Then, through 5 cm reaction coil, the reaction mixture was introduced at the bottom of the chamber (acting as a gas-liquid phase separator). Volatile species and other gaseous by-products (mainly hydrogen) were swept by the stream of argon introduced through nebulizer and carried to the plasma torch. Conditions of the CVG mode are shown in Table 1.For the simultaneous chemical vapour generation and pneumatic nebulization (the PN + CVG system), the acidified sample solution was aspirated into the chamber by pneumatic nebulizer and the NaBH4 solution was introduced at the bottom of the chamber. Larger aerosol droplets deposited on the wall of the chamber dropped down to the bottom, where they reacted with incoming NaBH4. Formed gaseous products as well as the sample aerosol were carried by a stream of the nebulizer argon into the plasma.


## 2.3. Plasma Parameters Calculations

The electron density was determined from Stark broadening of the Hα, Hβ, and Hγ lines using tables obtained by computer simulation technique [33] assuming the electron temperature equal to 7500 K and a reduced mass of the emitter-perturber pair μ=1. Additionally, for the Hδ line, Griem’s approximation [34, 35] was also applied.For the extraction of the Stark broadening components from experimentally measured half widths of the hydrogen lines, the procedure described in work [26] and considering Doppler broadening and instrumental broadening was employed. The van der Waals and resonance broadening effects could be omitted. The instrumental line width was evaluated with the aid of the Ar lines lying in a neighbourhood of the hydrogen lines. The broadening caused by Doppler effect was calculated using common known expression at the assumption of the gas kinetic temperature equal to 4000 K. In the deconvolution, the GRAMS software and mixed Gaussian + Lorentz algorithm were used.Spectroscopic temperatures and ionization degree were calculated at an assumption of partial thermal equilibrium. Ionization temperatures (Tion) were calculated from the slope of the linearized form of the Saha-Boltzmann distribution [16, 36]:(1)ln⁡IigaAaλiIagiAiλa=-Eion+Ei-EakT+ln⁡22πmekT3/2neh3,where I is the line intensity, g is the statistical weight, A is the transition probability, λ is the line wavelength, E is the energy of the upper state, Eion is the first ionization potential, T is the ionization temperature, and ne is the electron density. Subscripts “i” and “a” refer to ions and atoms, respectively.At assumption of LTE, this method allows for the determination of theTion values independently of the ne measurements. Plotting the ln⁡IigaAaλi/IagiAiλa versus the energy sum (Eion+Ei-Ea) yields the straight line with the slope equal to -1/kTion. Ionization temperatures (Tion) were calculated using fourteen atomic iron lines (Fe I) with excitation energies from 3.21 to 4.72 eV and fifteen ionic iron lines (Fe II) with excitation energies from 4.77 to 8.04 eV (Table 1). The Fe transition probabilities were taken from the NIST Atomic Spectra Database [37]. Additionally, the ionization temperatures were calculated using two-line method [36, 38] and the Mg II/Mg I, Hg II/Hg I, and Sn II/Sn I intensity ratios. The Hg, Sn, and Mg line transition probabilities were taken from the Kurucz database [39].The ionization degrees (αion) were determined from the Saha ionization equation at assumption of plasma equilibrium:(2)KjT=neN+N=22πmekT3/2h3U+TUTexp⁡-Eion-ΔEionkT,where Kj(T) is equilibrium constant, N, N+, and ne are number of atoms, ions, and electrons, respectively, U+T and U(T) are partition functions for atom and ion of the elements, and ΔEion is lowering of the ionization energy due to effect of the plasma on atoms and ions. In ICP, a contribution of multiple charged ions is negligible and hence αion may be determined using (2) as (3)αionA+=NA+NA+NA+=NA+/NA1+NA+/NA. The partition functions for the atom and ion of the Mg, Fe, Sn, and Hg species were calculated from Irwin tables [40].


## 3. Results and Discussion

For the studied sample introduction systems emission spectra of Sn, Hg, H, Ar, Mg, OH, and CN were recorded while Fe lines were observed only if the PN and PN + CVG systems were used. At the condition of CVG in this study, intensities of the Fe lines were too low for reliable measurements, although the formation of volatile Fe compounds in the reaction with NaBH4 was indicated [41, 42]. Unlike Sn and Hg that both easily form volatile species in the reaction with NaBH4, the signals derived from Mg at the CVG mode were observed due to the transport of a fine aerosol [17].At PN and PN + CVG modes, the Mg II/Mg I ratio was 8.5–9.0 and 10-11 for 1000 W and 1200 W, respectively, showing that the plasma was in robust conditions. During chemical vapour generation, the ratio increased to about 10.5 (1000 W) and 13 (1200 W) probably due to higher energy of plasma without water aerosol. The ratio was slightly higher with CH3COOH than with HCl; however, these differences were in the standard deviation uncertainties.


### 3.1. Electron Density

The electron density was determined using hydrogen lines of the Balmer series. The H line profiles (both maximum intensities and half widths) depended significantly on the sample introduction system. All the Hα, Hβ, Hγ, and Hδ lines were observed here with a sufficiently high intensity to be exactly measured. The Hβ line intensities shown in Figure 1 well illustrate high sensitivity of H lines to changes in the plasma composition.Figure 1
The Hβ line intensities for various sample introduction systems.The contributions of H2 originating from NaBH4 hydrolysis (CVG) at the assumption of 100% efficiency of the reaction and from water dissociation (PN) were about 0.8 mmol/min and 1.0 mmol/min, respectively. The H line intensities at PN and CVG were close together and were approximately two times lower than it was observed for the mixture of the aerosol and products of chemical vapour generation (the combined PN + CVG system).At PN and at PN + CVG, the H line intensities were higher with the use of CH3COOH than HCl by about 20–30%, while, for the system with CVG only, the effect of the acid was not essential (differences within the SDs). It confirms the role of a presence of the CH3COOH matrix and H2 in the plasma. With an increase in the rf power, the H signals were nearly 40, 30, and 20% higher for PN, PN + CVG, and CVG systems, respectively, independently of the kind of acid.In plasma of moderately low electron density, the higher members of the Balmer series could be very useful forne determination since they are not self-absorbed and are considerably more Stark broadened [23, 24]. This means that the contribution of the Stark effect to overall broadening is significantly more pronounced in the case of Hγ and Hδ than in the case of Hα and Hβ. Consequently, instrumental broadening and Doppler broadening contribute less to the Hγ and Hδ overall widths, what decreases an error in the Stark originated broadening measurements. In our spectra, the following relationship between experimental values of the full width at half maximum, FWHM (Δλ1/2), was observed: Hα : Hβ : Hγ : Hδ = 1.0 : 2.9 : 4.4 : 6.0. The Hε line is often overlapped by the wing of a very intensive Ca II line at 396.8 nm. Taking into account that ICP serves mainly for analysis of water solutions with detectable Ca concentration even in the deionized water, the Hε line was excluded and not considered. Hence, ne was evaluated based on the Hα, Hβ, Hγ, and Hδ lines. Because the tables given in [33] concern only first-three lines of Balmer series, for estimation of ne from Hδ, broadening Griem’s approximation [34, 35] was applied. The ne values obtained from the Hα, Hβ, Hγ, and Hδ lines at loading chemical vapour generation products into plasma are presented in Figure 2.Figure 2
Values ofne derived from various H lines (CVG).A very good agreement was observed between thene values derived from the Hβ, Hγ, and Hδ lines; the same was observed for all systems. The ne results based on Hγ were quite well consistent with the values obtained from the Hβ and Hδ lines, despite overlapping of the Hγ line at the wings by three relatively intense Ar I lines at 433.36, 433.53, and 434.52 nm, which can distort the Hγ line profile. Application of Griem’s approximation led to slightly higher values (about 13%) of ne when the Hβ line was considered and the results obtained using Hβ and Hδ were close together.The Hα line is the narrowest (Δλ1/2~0.08–0.09 nm), only a few times broader than argon lines (Δλ1/2~0.02 nm) and with the relatively high contribution of the Doppler broadening (Δλ1/2~0.03 nm). The use of the Hα line led to the overestimation of ne (up to 35%) in reference to the other H lines.It may result from high contribution of other broadening effects [23, 29, 43] which are missed in calculations of the ne values from Hα in an approach typical for atmospheric pressure argon plasma and not based on sophisticated procedure applied for example, for laser plasma.If we take into account an effect of the van der Waals broadening and we employed the Voigt function for line profile [22], the electron density from the Hα line for the CVG mode and HCl was equal to 1.14·1015 cm−3 what was in an agreement with the values obtained from the other hydrogen lines.Nevertheless, FWHM of Hα is a few times smaller than FWHMs of the next hydrogen lines in the Balmer series, so uncertainty of ne measurements from the Hα line is much higher. What is more, the Hα line is lying far from typical analytical range (200–460 nm) used for trace element determination by ICP-OES.In spite of a large number of papers devoted to usage of higher members of hydrogen Balmer series lines, it is difficult to find a comparison between thene values experimentally determined from Stark broadening of different H lines. The electron density in Ar-ICP derived from the Hδ line by Batistoni et al. [19] was about twofold higher than the value calculated from the Hγ line. The authors suggested also spectral interferences in the case of the Hδ line (with nitrogen lines) but any interferences for Hγ were noted. In our opinion, in the case of Ar-ICP only the results obtained using Hα seem to be not reliable. This line could be useful for diagnostics of higher electron density plasma provided insignificant contribution of self-absorption and considering ion dynamic effects [32].The electron density values based on the broadening of the Hβ line for studied sample introduction systems are listed in Table 2. At the power of 1000 and 1200 W, the following relation was observed: ne(PN)≤ne(PN+CVG)<ne(CVG). It indicates that the addition of H2 to the wet plasma (the PN + CVG system) does not change the ne values, in practice. Some authors reported that at nonrobust conditions even a small amount of H2 added to a sheathing or carrier gas resulted in an increase in ne while at robust conditions such effect of hydrogen addition for dry plasma was found [20, 44]. It confirms our results. For the CVG system, ne was about 40% (1000 W) and 20% (1200 W) higher than in the case of the PN and PN + CVG systems. Slightly higher ne values were noted at the power of 1000 W for the PN and PN + CVG systems, in the presence of HCl than CH3COOH. With an increase in power, the ne values were comparable in the limits of standard deviation uncertainties for both acids.Table 2
Electron densities (ne/1015 cm−3) with their standard deviations (n=3).
Matrix
PN
PN + CVG
CVG
1000 W
1200 W
1000 W
1200 W
1000 W
1200 W
HCl
0.69 ± 0.03
1.05 ± 0.02
0.72 ± 0.01
1.09 ± 0.03
1.08 ± 0.02
1.27 ± 0.04
CH3COOH
0.56 ± 0.02
1.07 ± 0.03
0.63 ± 0.04
1.10 ± 0.01
1.09 ± 0.03
1.32 ± 0.06Our previous work indicated [16] that for plasma loaded by a low solvent amount (more dried plasma), the electron number density was reduced. Similar effects were observed for Ar, He, and Ar + He microwave plasma—the electron number density was evidently higher for wet plasma (solution nebulization) [45]. It may be concluded that the increase in ne is mainly related to a much better thermal conductivity of the dry plasma with hydrogen than the plasma loaded with water.


### 3.2. Ionization Temperatures and Degrees

The ionization temperatures obtained using (1) were calculated from Fe, Mg, Sn, and Hg ion-to-atom line intensity ratios and were presented for various experimental conditions in Figure 3.Figure 3
Ionization temperatures derived from the Sn, Hg, Fe, and Mg ion-to-atom intensity ratios measured at 1000 W (a) and 1200 W (b).
(a)
(b)Generally, the ionization temperatures did not show any significant changes with the experimental conditions and for all elements slightly increased with power (up to about 10%).At lower power, the highest ionization temperatures were observed if only the gas mixture generated by chemical reaction with NaBH4 (CVG) was introduced to plasma.At higher power, theTion values were comparable if the CVG products or the mixture of the aerosol and CVG products (PN + CVG) was supplied into plasma and higher than those found in the case of aerosol introduction (PN).At lower power, if aerosol was loaded to plasma (PN and PN + CVG), a weak influence of matrix on the ionization temperature was observed. For such conditions, theTion values were higher up to 700 K when HCl instead of CH3COOH was employed. It confirms that introduction of acetic acid to the plasma at relatively low power results in decrease of plasma energy. An increase of power (for PN and PN + CVG) caused that the differences in Tion values for both acids were insignificant. The Hg and Sn ionization temperatures were lower (by about 800–1800 K) than those from the Fe and Mg line intensity ratios. Generally, the changes in Tion along with plasma conditions showed the same tendency as it was noted for the ne values. However, the ionization temperature was found to be considerably less sensitive plasma parameter than the electron density.The atomic (Fe I) and ionic (Fe II) excitation temperatures determined from (3) varied from 5400 to 6300 K and from 7100 to 8000 K, respectively, and showed similar changes with experimental conditions as those observed for the ionization temperatures. The ionization temperatures were higher than the Fe I temperatures and lower than the Fe II temperatures.Investigation of the Hα, Hβ, Hγ, and Hδ lines emitted by ICP indicated that their intensities did not correspond to the Boltzmann distributions. The excitation temperatures obtained from the Hγ and Hδ lines were from 4500 to 5500 K. So generally the LTE or pLTE conditions were not accomplished for H atoms, while it was observed for heavy atoms and ions present in atmospheric argon pressure ICP. The kinetic (plasma gas) temperature evaluated by comparison of simulated and experimental rotational intensity distribution measured from the A2Π - X2Σ+ 0-0 band of the OH spectrum was between 3500 K and 4000 K.In addition to the temperatures, the ionization degrees were determined experimentally and theoretically. The calculations were performed from the Saha formulae (equation (1)), under assumption that Te is comparable to Tion and equal to 8000 K. The very satisfactory agreement between experimental ionization degrees (from M II/M I ratios) and theoretically calculated ones was observed for Fe and Mg (the differences did not exceed 2%) but for Sn and Hg the experimental αion values (78% and 20%) were lower than the ionization degrees from the Saha formula (86% and 30%). The αion and Tion values suggest that populations of atom and ion levels of Sn and Hg are much far from thermodynamic equilibrium than it takes a place in the case of Mg and Fe.The ion-to-atom intensity ratios measured from Sn, Hg, and Mg lines were plotted against thene values determined at various experimental conditions (see Figure 4). The correlation coefficients R for Hg, Sn, and, Mg were calculated to be 0.9, 0.8, and 0.7, respectively. The slope coefficients for Sn and Hg (0.55 and 0.33, resp.) were considerably higher than that for Mg (0.13). It means the ion-to-atom intensity ratios measured here from Sn and Hg lines were significantly more sensitive to changes in plasma characteristics and conditions than the Mg II/Mg I ratio.Figure 4
The ion-to-atom intensity ratio for Sn, Hg (left axis), and Mg (right axis) versus the electron density (in 1015 cm−3).


## 3.1. Electron Density

The electron density was determined using hydrogen lines of the Balmer series. The H line profiles (both maximum intensities and half widths) depended significantly on the sample introduction system. All the Hα, Hβ, Hγ, and Hδ lines were observed here with a sufficiently high intensity to be exactly measured. The Hβ line intensities shown in Figure 1 well illustrate high sensitivity of H lines to changes in the plasma composition.Figure 1
The Hβ line intensities for various sample introduction systems.The contributions of H2 originating from NaBH4 hydrolysis (CVG) at the assumption of 100% efficiency of the reaction and from water dissociation (PN) were about 0.8 mmol/min and 1.0 mmol/min, respectively. The H line intensities at PN and CVG were close together and were approximately two times lower than it was observed for the mixture of the aerosol and products of chemical vapour generation (the combined PN + CVG system).At PN and at PN + CVG, the H line intensities were higher with the use of CH3COOH than HCl by about 20–30%, while, for the system with CVG only, the effect of the acid was not essential (differences within the SDs). It confirms the role of a presence of the CH3COOH matrix and H2 in the plasma. With an increase in the rf power, the H signals were nearly 40, 30, and 20% higher for PN, PN + CVG, and CVG systems, respectively, independently of the kind of acid.In plasma of moderately low electron density, the higher members of the Balmer series could be very useful forne determination since they are not self-absorbed and are considerably more Stark broadened [23, 24]. This means that the contribution of the Stark effect to overall broadening is significantly more pronounced in the case of Hγ and Hδ than in the case of Hα and Hβ. Consequently, instrumental broadening and Doppler broadening contribute less to the Hγ and Hδ overall widths, what decreases an error in the Stark originated broadening measurements. In our spectra, the following relationship between experimental values of the full width at half maximum, FWHM (Δλ1/2), was observed: Hα : Hβ : Hγ : Hδ = 1.0 : 2.9 : 4.4 : 6.0. The Hε line is often overlapped by the wing of a very intensive Ca II line at 396.8 nm. Taking into account that ICP serves mainly for analysis of water solutions with detectable Ca concentration even in the deionized water, the Hε line was excluded and not considered. Hence, ne was evaluated based on the Hα, Hβ, Hγ, and Hδ lines. Because the tables given in [33] concern only first-three lines of Balmer series, for estimation of ne from Hδ, broadening Griem’s approximation [34, 35] was applied. The ne values obtained from the Hα, Hβ, Hγ, and Hδ lines at loading chemical vapour generation products into plasma are presented in Figure 2.Figure 2
Values ofne derived from various H lines (CVG).A very good agreement was observed between thene values derived from the Hβ, Hγ, and Hδ lines; the same was observed for all systems. The ne results based on Hγ were quite well consistent with the values obtained from the Hβ and Hδ lines, despite overlapping of the Hγ line at the wings by three relatively intense Ar I lines at 433.36, 433.53, and 434.52 nm, which can distort the Hγ line profile. Application of Griem’s approximation led to slightly higher values (about 13%) of ne when the Hβ line was considered and the results obtained using Hβ and Hδ were close together.The Hα line is the narrowest (Δλ1/2~0.08–0.09 nm), only a few times broader than argon lines (Δλ1/2~0.02 nm) and with the relatively high contribution of the Doppler broadening (Δλ1/2~0.03 nm). The use of the Hα line led to the overestimation of ne (up to 35%) in reference to the other H lines.It may result from high contribution of other broadening effects [23, 29, 43] which are missed in calculations of the ne values from Hα in an approach typical for atmospheric pressure argon plasma and not based on sophisticated procedure applied for example, for laser plasma.If we take into account an effect of the van der Waals broadening and we employed the Voigt function for line profile [22], the electron density from the Hα line for the CVG mode and HCl was equal to 1.14·1015 cm−3 what was in an agreement with the values obtained from the other hydrogen lines.Nevertheless, FWHM of Hα is a few times smaller than FWHMs of the next hydrogen lines in the Balmer series, so uncertainty of ne measurements from the Hα line is much higher. What is more, the Hα line is lying far from typical analytical range (200–460 nm) used for trace element determination by ICP-OES.In spite of a large number of papers devoted to usage of higher members of hydrogen Balmer series lines, it is difficult to find a comparison between thene values experimentally determined from Stark broadening of different H lines. The electron density in Ar-ICP derived from the Hδ line by Batistoni et al. [19] was about twofold higher than the value calculated from the Hγ line. The authors suggested also spectral interferences in the case of the Hδ line (with nitrogen lines) but any interferences for Hγ were noted. In our opinion, in the case of Ar-ICP only the results obtained using Hα seem to be not reliable. This line could be useful for diagnostics of higher electron density plasma provided insignificant contribution of self-absorption and considering ion dynamic effects [32].The electron density values based on the broadening of the Hβ line for studied sample introduction systems are listed in Table 2. At the power of 1000 and 1200 W, the following relation was observed: ne(PN)≤ne(PN+CVG)<ne(CVG). It indicates that the addition of H2 to the wet plasma (the PN + CVG system) does not change the ne values, in practice. Some authors reported that at nonrobust conditions even a small amount of H2 added to a sheathing or carrier gas resulted in an increase in ne while at robust conditions such effect of hydrogen addition for dry plasma was found [20, 44]. It confirms our results. For the CVG system, ne was about 40% (1000 W) and 20% (1200 W) higher than in the case of the PN and PN + CVG systems. Slightly higher ne values were noted at the power of 1000 W for the PN and PN + CVG systems, in the presence of HCl than CH3COOH. With an increase in power, the ne values were comparable in the limits of standard deviation uncertainties for both acids.Table 2
Electron densities (ne/1015 cm−3) with their standard deviations (n=3).
Matrix
PN
PN + CVG
CVG
1000 W
1200 W
1000 W
1200 W
1000 W
1200 W
HCl
0.69 ± 0.03
1.05 ± 0.02
0.72 ± 0.01
1.09 ± 0.03
1.08 ± 0.02
1.27 ± 0.04
CH3COOH
0.56 ± 0.02
1.07 ± 0.03
0.63 ± 0.04
1.10 ± 0.01
1.09 ± 0.03
1.32 ± 0.06Our previous work indicated [16] that for plasma loaded by a low solvent amount (more dried plasma), the electron number density was reduced. Similar effects were observed for Ar, He, and Ar + He microwave plasma—the electron number density was evidently higher for wet plasma (solution nebulization) [45]. It may be concluded that the increase in ne is mainly related to a much better thermal conductivity of the dry plasma with hydrogen than the plasma loaded with water.


## 3.2. Ionization Temperatures and Degrees

The ionization temperatures obtained using (1) were calculated from Fe, Mg, Sn, and Hg ion-to-atom line intensity ratios and were presented for various experimental conditions in Figure 3.Figure 3
Ionization temperatures derived from the Sn, Hg, Fe, and Mg ion-to-atom intensity ratios measured at 1000 W (a) and 1200 W (b).
(a)
(b)Generally, the ionization temperatures did not show any significant changes with the experimental conditions and for all elements slightly increased with power (up to about 10%).At lower power, the highest ionization temperatures were observed if only the gas mixture generated by chemical reaction with NaBH4 (CVG) was introduced to plasma.At higher power, theTion values were comparable if the CVG products or the mixture of the aerosol and CVG products (PN + CVG) was supplied into plasma and higher than those found in the case of aerosol introduction (PN).At lower power, if aerosol was loaded to plasma (PN and PN + CVG), a weak influence of matrix on the ionization temperature was observed. For such conditions, theTion values were higher up to 700 K when HCl instead of CH3COOH was employed. It confirms that introduction of acetic acid to the plasma at relatively low power results in decrease of plasma energy. An increase of power (for PN and PN + CVG) caused that the differences in Tion values for both acids were insignificant. The Hg and Sn ionization temperatures were lower (by about 800–1800 K) than those from the Fe and Mg line intensity ratios. Generally, the changes in Tion along with plasma conditions showed the same tendency as it was noted for the ne values. However, the ionization temperature was found to be considerably less sensitive plasma parameter than the electron density.The atomic (Fe I) and ionic (Fe II) excitation temperatures determined from (3) varied from 5400 to 6300 K and from 7100 to 8000 K, respectively, and showed similar changes with experimental conditions as those observed for the ionization temperatures. The ionization temperatures were higher than the Fe I temperatures and lower than the Fe II temperatures.Investigation of the Hα, Hβ, Hγ, and Hδ lines emitted by ICP indicated that their intensities did not correspond to the Boltzmann distributions. The excitation temperatures obtained from the Hγ and Hδ lines were from 4500 to 5500 K. So generally the LTE or pLTE conditions were not accomplished for H atoms, while it was observed for heavy atoms and ions present in atmospheric argon pressure ICP. The kinetic (plasma gas) temperature evaluated by comparison of simulated and experimental rotational intensity distribution measured from the A2Π - X2Σ+ 0-0 band of the OH spectrum was between 3500 K and 4000 K.In addition to the temperatures, the ionization degrees were determined experimentally and theoretically. The calculations were performed from the Saha formulae (equation (1)), under assumption that Te is comparable to Tion and equal to 8000 K. The very satisfactory agreement between experimental ionization degrees (from M II/M I ratios) and theoretically calculated ones was observed for Fe and Mg (the differences did not exceed 2%) but for Sn and Hg the experimental αion values (78% and 20%) were lower than the ionization degrees from the Saha formula (86% and 30%). The αion and Tion values suggest that populations of atom and ion levels of Sn and Hg are much far from thermodynamic equilibrium than it takes a place in the case of Mg and Fe.The ion-to-atom intensity ratios measured from Sn, Hg, and Mg lines were plotted against thene values determined at various experimental conditions (see Figure 4). The correlation coefficients R for Hg, Sn, and, Mg were calculated to be 0.9, 0.8, and 0.7, respectively. The slope coefficients for Sn and Hg (0.55 and 0.33, resp.) were considerably higher than that for Mg (0.13). It means the ion-to-atom intensity ratios measured here from Sn and Hg lines were significantly more sensitive to changes in plasma characteristics and conditions than the Mg II/Mg I ratio.Figure 4
The ion-to-atom intensity ratio for Sn, Hg (left axis), and Mg (right axis) versus the electron density (in 1015 cm−3).


## 4. Conclusions

Spectroscopic investigations of the most prominent hydrogen lines belonging to the Balmer series in point of view their application for determination of electron density in Ar-ICP were carried out. The Hβ, Hγ, and Hδ lines were suitable for accurate measurements of the Stark broadening effect and appropriate for determination of ne. The ne values obtained from the Hγ and Hδ line were in a very good agreement with those from the Hβ line at the all experimental conditions, while ne from the Hα line was significantly higher. It indicates that both the Hγ and Hδ line profiles can be alternatively used for electron density measurements. However, if the effect of the van der Waals broadening was taken into account and the Voigt function was used for line profile fitting, the agreement between the electron density from the Hα and from the other hydrogen lines could be achieved.The electron density was found to be the plasma parameter sensitive and reacting for changes in experimental conditions. For the dry plasma supplied by hydrogen, thene values were higher by a factor of 1.2–1.9 in dependence of the power than those obtained at pneumatic nebulization. In the case of mixed gas-liquid system, the plasma parameters are comparable to those observed for pneumatic nebulization.The ionization temperatures determined from Fe, Mg, Sn, and Hg were different and not too much sensitive for variation of experimental conditions. The following dependence was observed for the temperatures derived from Fe I and Fe II lines:(4)TexcFeI<TionFe≤TexcFeII.Intensity distributions of the Hα, Hβ, Hγ, and Hδ lines were not in a satisfactory agreement with the Boltzmann distributions characteristic for LTE or pLTE conditions. The plasma gas temperature evaluated from rotational line intensities of the OH A-X 0-0 spectrum was between 3500 K and 4000 K.At lower power, the plasma was less resistant to matrix effects and an influence of hydrogen. The Fe, Mg, Sn, and Hg ion-to-atom intensity ratios were observed to be dependent on experimental conditions. The correlation plots between the M II/M I ratios andne could be quite well approximated by linear equations and the R coefficients were 0.9, 0.8, and 0.7 for Hg II/Hg I, Sn II/Sn I, and Mg II/Mg I, respectively. The Hg II/Hg I and Sn II/Sn I ratios were more sensitive for ne changes than the Mg II/Mg I ratio.



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*Source: 7521050-2016-03-22.xml*