Plasma Science and Technology, Vol.14, No.8, Aug. 2012
Plasma Formed in Argon, Acid Nitric and Water Used in Industrial
ICP Torches
F. BENDJEBBAR1 , P. ANDRE2 , M. BENBAKKAR3 , D. ROCHETTE2 ,
S. FLAZI1 , D. VACHER2
1
LGEO, Oran University, BP1505, El Mnaouer ORAN, Algerie
Blaise Pascal University, LAEPT, BP 10448, F-63000 CLERMONT-FERRAND, France
3
Blaise Pascal University, LMV, BP 10448, F-63000 CLERMONT-FERRAND, France
2
Abstract
Inductively coupled plasmas (ICPs) are used in spectrochemical analyses. The introduction of the sample by means of an aerosol are widely used. The introduction and the total
evaporation of the aerosol is required in order to obtain a good repeatability and reproducibility of
analyses. To check whether the vaporization of the aerosol droplets inside the plasma is completed,
a solution could be used to compare the experimental results of the emission spectral lines with
theoretical results. An accurate calculation code to obtain monatomic spectral lines intensities
is therefore required, which is the purpose of the present paper. The mixtures of argon, water
and nitric acid are widely used in spectrochemical analyses with ICPs. With these mixtures, we
calculate the composition, thermodynamic functions and monatomic spectral lines intensities of
the plasma at thermodynamic equilibrium and at atmospheric pressure. To obtain a self sufficient
paper and also to allow other researchers to compare their results, all required data and a robust
accurate algorithm, which is simple and easy to compute, are given.
Keywords: inductively coupled plasmas, argon plasma, monatomic spectral lines, thermodynamic properties, thermal plasma
PACS: 52.25.Kn, 52.50.Qt, 52.70.Kz
DOI: 10.1088/1009-0630/14/8/01
1
Introduction
Inductively coupled plasmas (ICPs) are widely used
for spectrochemical analyses such as soil elements analysis and geological analysis through the dissolution of
the elements inside a liquid solution [1∼4] . The measurement techniques and sample introduction by means
of an aerosol are now widely used with a high accuracy but with a strong hypothesis: the droplet has
to be totally vaporized and the plasma has to stay
at a given thermodynamic state [1∼5] . As a matter
of fact, the chemistry and the transport of the liquid
droplets inside the plasma are not well understood. The
droplet injection influences thermodynamic state of the
plasma. When the aerosol is chosen with an appropriate droplet size, experimenters assume that the vaporization occurs quickly [6∼8] . The droplet vaporization
inside the plasma influences directly the composition
of the plasma. So the emission of spectral lines depends on the proportion of chemical species inside the
plasma. Knowing that many such parameters influence
the transport of the aerosol inside the plasma, such as
turbulence, gravitational loss, viscosity and also that
the solvents can reduce significantly the temperature
inside the plasma, the lowering of the intensities of spectral lines can be observed. Consequently analysts must
check their measurements and note the repeatability of
acquisitions of the monatomic spectral lines intensities.
To obtain the characterization of the plasma, a comparison of the experimental spectral intensity with a
monatomic spectral intensity calculation made at thermodynamic equilibrium with the assumption of optically thin plasma should be useful and easy to execute.
Unfortunately, although it is a mixture widely used in
geological and spectrochemical analyses, to our knowledge, no data on the composition, thermodynamic functions and monatomic spectral lines for argon, nitric acid
and water mixture have been published.
First, we have to obtain the plasma composition.
For this purpose, we can use mass action laws or use
the Gibbs free energy minimization principle. Several
numerical methods of resolution exist and numerous
papers have been written on this subject and various
algorithms presented [9∼13] (non exhaustive list). Recent papers have been published to describe the numerical methods: we can cite the work from GODIN et
al. [14] describing a method based on mass action laws
and also the fine and precise work from COUFAL et
al. [15,16] and the cited literature presenting a method
based on Gibbs free energy minimization. In this paper, we propose to use an approach using Lagrangian
multipliers to address the conservation of nuclei, the
electrical neutrality and Dalton’s law, and solve the system with a Newton-Raphson numerical method. This
Plasma Science and Technology, Vol.14, No.8, Aug. 2012
numerical method is easy to execute in any programming language or via mathematical software, allowing
one to code the program as a routine in the exploiting
code of industrial ICP torches. Furthermore, with the
proposed convergence test, it is accurate, and one can
even achieve better cpu time than with other numerical
methods [15,16] . We have also noticed that several free
calculation codes are available on websites [17∼19] (non
exhaustive list here).
To perform the calculation, we need all the chemical potentials of each chemical species to be taken into
account. Since polyatomic species appear at low temperature, only the low excitation quantum energy levels are populated. Consequently, their standard thermodynamic functions are given in databases [20∼22] can
be used in a valid way. Unlike the diatomic chemical species, which are present at a higher temperature (>6000 K) and consequently have their excited energy levels populated. Consequently, we need to take
into account higher excitational quantum levels. In
JANAF’s [21] table or in BARIN’s table [22] only the
ground state and lower energy state have been taken
into account. These data are available for temperatures
lower than 6000 K and 2000 K, respectively. The temperature of the plasma inside an ICP torch usually falls
between 4000 K and 15000 K. For higher temperature
the monatomic thermodynamic functions have to be
calculated at each temperature step to take the lowering
of ionization energy into account [23,24] . In this paper we
propose to calculate the monatomic standard thermodynamic functions taking into account only the energy
levels that are known and given in tables [25] . Then, we
supply fitting coefficients to get the monatomic species
thermodynamic functions. We compare and estimate
the difference of values for the monatomic spectral lines
intensities using these two methods in the temperature
range from 1000 K to 20,000 K.
In this paper, we provide the chemical composition
data of the plasma between 1000 K and 20,000 K for a
plasma composed of nitric acid, water and argon. The
two considered mixtures are composed of 99.90% Ar,
0.098% HNO3 , 0.002% H2 O in weight percentage for
mixture 1 and 99.50% Ar, 0.496% HNO3 , 0.004% H2 O
in weight percentage for mixture 2. In order to compare
the properties of these plasma mixtures, we have also
reported the classical pure argon plasma. These three
plasma types have been chosen since they are widely
used in spectrochemical analyses with ICP torches. We
chose to conduct the calculation with an assumption of
thermal and chemical equilibrium. As a matter of fact,
in industrial ICP torches, the spectral measurements
are always made in the warmest zone of the plasma,
which can be considered at chemical and thermal equilibrium [26∼28] . The internal and translational temperatures are consequently assumed to be the same for each
chemical species.
Firstly, we describe the calculation method. We provide all the data required to obtain the composition,
the thermodynamic functions and the intensities of the
monatomic spectral lines. Secondly, we compare and
684
discuss the results of heat capacity at constant pressure
and enthalpy versus temperature. Thirdly, the results
of the useful spectral intensities are discussed.
2
Calculation of plasma composition
The plasma chemical compositions at chemical and
thermal equilibrium can be stated by a thermodynamic
function. We use the minimization of Gibbs free energy
to determine the composition versus the temperature
at atmospheric pressure of the considered plasma. At
temperature T and pressure P , the Gibbs free energy
is written as:




µ ¶
N

 N 
X
P 
 0

i 
G=
Ni µi + RTi ln  N
,
 + RTi ln
0 
P
P




i=1
Nj
j=1
(1)
where Ni is the mole number of chemical species, N is
the number of different chemical species presented in
the plasma and gas, µ0i is the chemical potential of i
species at standard pressure P 0 (105 Pa), R is the molar gas constant. Ti is the temperature of each chemical
species i and is equal to the temperature T in the considered case since we assume thermal equilibrium.
To solve the system of equations, we need two other
physical equations:
1) The electrical neutrality and the nuclei conservation:
N
X
aij Ni = b j , j= 0, . . . , m;
(2)
i= 1
where m is the number of different nuclei equal to 4 in
our case (Ar, N, O, H). j = 0 is devoted to the electrical
neutrality. aij represents the nucleus number of type
j for particle i; bj is equal to the number of different
nucleus types in the initial mixture; ai0 represents the
number of elementary charge for particle i; so electrical
neutrality imposes b0 = 0 (see Table 1).
2) The Dalton law is written as:
P − ∆P =
N
X
Ni
i=1
V
RT =
N
X
ni R T ,
(3)
i=1
where ni is the molar density of the i chemical species,
V the considered volume and ∆P is the pressure correction due to the Coulomb interaction [23,24,29] .
By introducing Lagrange multipliers πk to take
the physical conditions (2) into account and using a
Newton-Raphson numerical method [30] , the solution of
the system given in appendix I is obtained.
In Table 1, we give the coefficients aij for the considered chemical species. The coefficients bi depend on
the initial weight percentages of the mixture. We obtain a linear system of N + 4 dimension, which can be
compared to the dimension of 5 obtained for the linear
F. BENDJEBBARR et al.: Plasma Formed in Argon, Acid Nitric and Water Used in Industrial ICP Torches
Table 1.
species
Species
Ar:
Ar+ :
Ar++ :
Ar+++ :
e− :
H:
H− :
H+ :
N:
N+ :
N++ :
N+++ :
O:
O− :
O+ :
O++ :
O+++ :
H2 :
H−
2 :
H+
2 :
N2 :
N−
2 :
Matrix aij and vector bi ; M and % denote the mass molar and the weight percentage of the initial chemical
aij
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
0
0
1
2
3
−1
0
−1
1
0
1
2
3
0
−1
1
2
3
0
−1
1
0
−1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
2
Species
N+
2 :
NH :
NH− :
NH+ :
NO:
NO− :
NO+ :
O2 :
O−
2 :
O+
2 :
OH:
OH− :
OH+ :
H2 N:
H2 N2 :
H2 O:
H3 N :
H 3 O+ :
H4 N2 :
HNO:
HNO2− C:
HNO2− T:
aij
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
0
1
0
−1
1
0
−1
1
0
−1
1
0
-1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
1
2
2
2
3
3
4
1
1
1
3
0
0
0
0
1
1
1
2
2
2
1
1
1
0
0
1
0
1
0
1
2
2
4
2
1
1
1
1
1
1
0
0
0
0
0
0
1
2
0
1
0
2
1
1
1
Species
HNO3 :
HO2 :
N2 O:
N2 O3 :
N2 O 4 :
N2 O5 :
N2 O + :
N3 :
NO2 :
NO−
2 :
NO3 :
O3 :
H+
3 :
HO−
2 :
H 2 O+ :
H2 O2 :
NO−
3 :
NH+
4 :
NH2 OH:
NH2 NO2 :
aij
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
0
0
0
0
0
0
0
1
0
0
−1
0
0
1
−1
1
0
−1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
4
3
2
3
3
2
1
3
4
5
1
0
2
2
3
3
0
2
1
2
3
0
1
2
4
1
0
2
2
2
2
2
3
1
1
1
0
0
0
0
0
1
1
1
2
Note: b0: 0; b1(Ar): %Ar /MAr ; b2(H): 2*%H2 O /MH2 O +%HNO3 /MHNO3 ; b3(O): %H2 O /MH2 O +3*%HNO3 / MHNO3 ;
b4(N): %HNO3 /MHNO3
system with the White et al method [9] . At the present
time, the computers and their memory size make it easy
to solve a large linear system. To resolve the system
(appendix I), we used a Gauss numerical method and
in our case a preconditioner is not needed but nevertheless can be used [31] .
For each chemical species, we have to determine the
chemical potential µ0i , 17 concerned monatomic chemical species: Ar, Ar+ , Ar++ , Ar+++ , e− , H, H− , H+ ,
N, N+ , N++ , N+++ , O, O− , O+ , O++ , O+++ ; 18 con+
−
cerned diatomic chemical species: H2 , H−
2 , H2 , N2 , N2 ,
+
−
N2 , NH, NH− , NH+ , NO, NO− , NO+ , O2 , O2 , O+
2,
OH, OH− , OH+ and 29 concerned polyatomic chemical
species: H2 N, H2 N2 , H2 O, H3 N, H3 O+ , H4 N2 , HNO,
HNO2 (Cys), HNO2 (Trans), HNO3 , HO2 , N2 O, N2 O3 ,
+
N2 O4 , N2 O5 , N2 O+ , N3 , NO2 , NO−
2 , NO3 , O3 , H3 ,
−
−
+
HO2 , H2 O+ , H2 O2 , NO3 , NH4 , NH2 OH, NH2 NO2 .
The electrical neutrality is obtained between charged
chemical species and electrons. For the monatomic
species, the partition function has to be calculated at
each temperature step. As described in Refs. [23,24],
we add artificially levels with a Ritz-Rytberg series,
which is called hydrogenoid approximation, to take into
account the lowering of the ionization energy due to the
electrical charges. The other way is to take only the
published excited energy levels into account. Anyway,
we calculate the partition function and provide the fitting coefficients in Table 2a. The sensitivity of both
calculations to spectral lines intensities will be tested
in section 3.2 and Table 4. In order to calculate the
partition functions for the diatomic species, we take all
the rotational, vibrational and excitational levels given
in tables [32,33] using the calculation method described
in Ref. [34]. As a matter of fact, the thermodynamic
functions given in such tables as the JANAF [21] and
BARIN [22] tables are calculated for temperature lower
than 6000 K and 2000 K, respectively. In this temperature range the higher excitational levels are not excited, for example the nitrogen oxide at the 2 Π levels
is taken into
table, and four states
Q account in JANAF
Q
X 2 Π, a4 , A2 Σ and B 2
in the GURVICH et al.
table. In the HUBER and HERZBERG [32,33] tables
15 states are given for NO. We calculate the partition
function with these 15 states. The fitting coefficients
are given in Table 2b. Since the polyatomic species appear at low temperature, the standard thermodynamic
functions are taken from tables [21,22,35] .
The values of new molar number and the Lagrangian
multipliers are calculated as
½
ni = ni + λ ∆ni ,
∀ i ∈ [1, N ];
(4)
πj = πj + λ ∆πj ,
∀j ∈ [0, 4].
The parameter λ is the highest value included between
0 and 1 that satisfies the following conditions:
ni + λ ∆ni > 0,
∀ i ∈ [1, N ].
(5)
This step avoids obtaining negative new molar numbers, which will appear when they are far from the solution. The new values of molar number and Lagrangian
multipliers are used for a new calculation cycle. The
convergence criterion is fixed as follows:
∆ ni < 10−15 ni , ∀i ∈ [1, N ].
(6)
685
Plasma Science and Technology, Vol.14, No.8, Aug. 2012
Table 2a. Fitting coefficients for the monatomic species; for each chemical species the first line corresponds to the temperatures
below 13000 K and second line to the temperatures above 13000 K
a
Ar
b
Er: -6196.5
c
d
e
f
g
h
i
j
J/mol
-3.60E+09 1.02E+07
-11100.5
8.51584
-0.00174424 2.72E-07
4.90E+16
-1.90E+13
3.10E+09
-275641
14.3942
-0.00044092 7.34E-09
-2.14E-11 6.63E-16
-5.12E-14 -2.80E+10
79819
2.65E+06
-42.7771
Ar+
Er: 1.5207e+006
J/mol
-2.98E+07 -348103
857.605
2.21027
5.40E-05
-5.52E-09
2.86E-13
-5.79E-18 -5899.26
8.57478
3.92E+13
-1.65E+10
2.97E+06
-295.603
0.0179439
-6.44E-07
1.26E-11
-9.89E-17 -2.65E+07
2828.32
Ar++
Er: 4.19263e+006 J/mol
1.68E+09
-5.38E+06
6728.69
-0.986936
0.00087478
-9.57E-08
4.99E-12
-1.02E-16 -47730.9
34.1888
1.98E+12
-8.43E+08
150968
-12.0519
0.00088761
-3.29E-08
6.60E-13
-4.93E-18 -1.35E+06
144.933
Ar+++
Er: 8.1288e+006
J/mol
-7.24E+08 3.27E+06
-5374.39
6.67249
-0.00162206 3.01E-07
-2.21E-11 5.68E-16
9.20E+12
-3.26E+09
425636
-22.2646
0.0008022
-1.48E-08
1.56E-13
e−
Er: -6196.5
J/mol
-1655.11
4.31223
36579.1
-6.70E-19 -3.98E+06
-25.5574
256.331
-0.00422969 2.5
-5.15E-10
7.02E-14
-4.84E-18 1.31E-22
0.0309688
-11.7208
-1.50E+10 5.52E+06
-859.974
2.57337
-3.70E-06
1.11E-10
-1.81E-15 1.25E-20
7816.63
-12.4279
H
J/mol
17913.1
-11.2783
Er: 211832
-7.85E+08 2.25E+06
-2498.38
3.88659
-0.0004146
6.72E-08
-5.54E-12 1.82E-16
1.83E+15
-6.40E+11
9.15E+07
-6833.05
0.280959
-6.06E-06
5.74E-11
H−
Er: 132835
J/mol
-269.701
0.753137
-0.00081016 2.5
-1.23E-10
1.84E-14
-1.39E-18 4.08E-23
9.29E+10
-3.43E+07
5365.09
2.32E-05
-6.94E-10
1.14E-14
H+
Er: 1.52992e+006 J/mol
-448.952
1.26914
2.04121
-1.05E-16 -8.41E+08
66990.5
0.00584843 -1.13899
-7.87E-20 -48752.5
3.28148
-0.00137261 2.5
-2.05E-10
2.99E-14
-2.17E-18 6.12E-23
0.00991686 -1.14063
-2.51E+09 926529
-144.886
2.51242
-6.30E-07
1.89E-11
-3.11E-16 2.16E-21
1316.34
-1.26023
N
Er: 466480
J/mol
8.58E+08
-729404
-1814.23
5.43343
-0.00156184 3.50E-07
-2.97E-11 8.75E-16
9970.68
-16.5659
5.21E+15
-1.95E+12
3.06E+08
-25927.4
1.27902
-3.66E-05
5.64E-10
-3.61E-15 -2.78E+09
250257
N+
Er: 1.8764e+006
J/mol
1.80E+09
-5.02E+06
5279.89
-0.0871583 0.00059291
-5.62E-08
2.54E-12
-4.35E-17 -38163.5
25.6762
8.59E+12
-3.39E+09
562046
-48.3417
0.00276038
-8.81E-08
1.54E-12
-1.08E-17 -5.07E+06
491.929
N++
Er: 4.4236e+006
J/mol
2.81E+08
-779873
869.311
2.03035
0.00013367
-1.97E-08
1.35E-12
-2.85E-17 -6082.65
8.2848
5.41E+12
-2.34E+09
424557
-38.3034
0.00214731
-5.88E-08
8.40E-13
-4.97E-18 -3.80E+06
394.178
N+++
Er: 9.3216e+006
J/mol
-1.21E+07 57783.9
-98.6448
2.58045
-3.43E-05
7.72E-09
-8.65E-13 3.79E-17
667.473
2.20863
4.96E+13
2.43E+06
-163.948
0.00529244
-3.78E-08
-1.34E-12 2.07E-17
-2.24E+07
1657.6
-1.74E+10
O
Er: 242470
J/mol
1.08E+09
-2.86E+06
2795.89
1.34269
0.0001573
1.33E-08
-2.98E-12 1.28E-16
-20468.6
14.7502
5.59E+14
-1.80E+11
2.24E+07
-1272.11
0.0237884
7.12E-07
-3.61E-11 4.12E-16
-2.10E+08
13009.1
O−
Er: 95189
J/mol
3.18E+09
-8.67E+06
8833.37
-1.6377
0.00088101
-7.07E-08
2.16E-12
-1.26E-17 -64303
38.0876
1.16E+12
-5.01E+08
79215.5
-2.84772
0.00022026
-5.55E-09
7.88E-14
-4.85E-19 -727649
58.2065
O+
Er: 1.5626e+006
J/mol
-3.69E+09 1.07E+07
-11923.2
9.03493
-0.00185012 2.58E-07
-1.51E-11 3.15E-16
85503.1
-46.8367
1.06E+13
-2.91E+09
243948
-0.356785
-0.00039554 2.14E-08
-4.75E-13 4.68E-18
-2.44E+06
47.4182
O++
Er: 4.9571e+006
J/mol
4.03E+08
-834819
520.24
2.53194
-0.00012212 3.51E-08
-2.91E-12 8.01E-17
-3937.26
5.3122
-107260
12.3164
-0.00047307 1.31E-08
-1.74E-13 8.75E-19
966517
-89.0291
-1.68E+12 6.43E+08
O+++
Er: 1.02637e+007 J/mol
-1.75E+07 133554
-66.9862
2.53781
-1.22E-05
2.21E-09
-2.10E-13 8.07E-18
851.833
4.50525
-5.46E+11 4.54E+08
-127926
20.1322
-0.00131364 5.20E-08
-9.65E-13 6.88E-18
1.10E+06
-157.461
686
F. BENDJEBBARR et al.: Plasma Formed in Argon, Acid Nitric and Water Used in Industrial ICP Torches
Table 2b. Fitting coefficients for the diatomic species; for each chemical species the first line corresponds to the temperatures
below 1500 K and second line to the temperatures above 1500 K
a
b
c
d
e
f
g
h
i
j
H2
Er: -8467
J/mol
3.87E+06
-92549.7
824.027
0
0.00782114
-9.33E-06
5.72E-09
-1.31E-12
-4243.5
16.0388
4.21E+10
-5.59E+07
22912.4
0
0.00078408
-8.50E-08
3.60E-12
-5.05E-17
-190876
27.4425
H−
2
Er: 226752
J/mol
2.57E+06
-71581.2
739.969
0
0.00765653
-6.53E-06
3.39E-09
-7.74E-13
-3692.7
17.3789
-1.38E+08
-1.01E+07
13473.9
0
0.00020634
-8.08E-09
1.38E-13
-6.80E-19
-99368.3
30.2946
H+
2
Er: 1.48609e+006
J/mol
4.53E+06
-107926
920.767
0
0.00606811
-4.28E-06
1.83E-09
-3.42E-13
-4785.75
18.0204
6.19E+10
-8.76E+07
37640.6
0
-2.46E-05
8.71E-09
-3.19E-13
3.66E-18
-314069
35.1164
N2
Er: -8670
J/mol
4.70E+06
-110617
930.811
0
0.00605245
-4.65E-06
2.14E-09
-4.37E-13
-4837.34
23.9891
1.02E+11
-1.39E+08
55825.1
0
-0.00141505
2.56E-07
-1.20E-11
1.73E-16
-471176
47.3843
N−
2
Er: 139941
J/mol
3.79E+06
-94603.3
857.995
0
0.0063634
-4.32E-06
1.47E-09
-2.00E-13
-4388.93
25.2754
1.37E+10
-2.41E+07
15088.7
0
0.00065638
-3.90E-08
9.01E-13
-7.10E-18
-118280
35.9172
N+
2
Er: 1.50083e+006
J/mol
4.53E+06
-107846
920.195
0
0.00600017
-4.21E-06
1.65E-09
-2.76E-13
-4769.11
24.6948
3.80E+10
-5.31E+07
23524.7
0
0.00067162
-3.33E-08
4.83E-13
2.90E-19
-194027
36.5307
NH
Er: 367943
J/mol
4.50E+06
-105452
892.82
0
0.00696919
-7.45E-06
4.51E-09
-1.06E-12
-4631.36
22.4726
2.12E+10
-2.97E+07
14508.1
0
0.00100622
-9.29E-08
3.34E-12
-4.22E-17
-116704
31.4547
NH−
Er: 331279
J/mol
4.34E+06
-102428
876.473
0
0.00717644
-7.93E-06
4.81E-09
-1.13E-12
-4534.62
22.6636
2.83E+10
-4.08E+07
19429.2
0
0.00060303
-5.42E-08
1.99E-12
-2.59E-17
-158170
33.7579
NH+
Er: 1.67199e+006
J/mol
9.04E+06
-190478
1298.6
0
0.00631598
-6.55E-06
4.20E-09
-1.07E-12
-7117.99
24.2394
5.67E+10
-7.08E+07
26800.2
0
0.00083762
-8.90E-08
3.61E-12
-4.99E-17
-225505
35.4677
NO
Er: 81099
J/mol
3.29E+06
-85688.7
857.201
0
0.00635036
-4.29E-06
1.44E-09
-1.94E-13
-4295.02
26.0683
1.22E+10
-2.29E+07
15291.3
0
0.00044493
6.59E-09
-1.46E-12
2.96E-17
-119013
37.2314
NO−
Er: 77958
J/mol
1.60E+06
-52172.5
632.147
0
0.00869671
-7.99E-06
3.63E-09
-6.50E-13
-3044.35
24.8676
1.33E+10
-2.19E+07
13607.8
0
0.00086157
-7.77E-08
2.76E-12
-3.47E-17
-106019
36.088
NO+
Er: 981515
J/mol
4.71E+06
-110813
931.506
0
0.00605887
-4.69E-06
2.18E-09
-4.49E-13
-4841.9
24.7874
1.26E+11
-1.71E+08
67874.5
0
-0.00210424
3.64E-07
-1.73E-11
2.54E-16
-574809
52.3313
O2
Er: -8683
J/mol
2.50E+06
-70199.2
733.196
0
0.00749215
-5.89E-06
2.26E-09
-3.29E-13
-3639.91
24.778
1.54E+10
-2.31E+07
13231.4
0
0.0009889
-8.51E-08
2.90E-12
-3.49E-17
-103866
34.847
O−
2
Er: -57345
J/mol
1.08E+06
-38582.1
533.275
0
0.0105313
-1.15E-05
6.09E-09
-1.25E-12
-2486.96
24.1117
6.51E+10
-6.20E+07
15233.2
0
0.00212841
-2.56E-07
1.09E-11
-1.54E-16
-134240
31.7919
O+
2
Er: 1.16221e+006
J/mol
3.03E+06
-88792.8
920.938
0
0.00596403
-3.56E-06
9.27E-10
-6.57E-14
-4641.19
25.6987
-2.11E+10
1.91E+07
988.048
0
0.00100503
-5.44E-08
7.63E-13
2.76E-18
5722.33
32.3951
OH
Er: 29815
J/mol
3.46E+06
-88053.7
860.755
0
0.00739482
-8.49E-06
5.23E-09
-1.23E-12
-4340.48
22.6585
1.53E+10
-2.33E+07
12796.6
0
0.00095591
-8.78E-08
3.17E-12
-4.01E-17
-101146
31.507
OH−
Er: -152201
J/mol
4.14E+06
-98591.4
855.713
0
0.00744482
-8.59E-06
5.30E-09
-1.25E-12
-4412.61
21.2493
9.48E+08
-5.05E+06
6540.82
0
0.00120253
-1.12E-07
4.03E-12
-5.05E-17
-46776.2
28.2459
OH+
Er: 1.30851e+006
J/mol
4.00E+06
-98202.9
872.987
0
0.00634891
-4.46E-06
1.75E-09
-3.03E-13
-4490.14
22.7009
-8.23E+09
1.10E+07
-422.708
0
0.0017502
-1.82E-07
7.00E-12
-9.27E-17
12629.5
27.1399
687
Plasma Science and Technology, Vol.14, No.8, Aug. 2012
The enthalpy is calculated by:
H=
N
X
ni (h0i + Eri ),
(7)
i=1
where h0i is the molar enthalpy of i species at reference pressure and Eri is the formation enthalpy of the
i chemical species (Table 2).
The heat capacity at fixed pressure is calculated by:
µ
¶
∂H
Cp =
.
(8)
∂T P
The intensities of the monatomic spectral lines can be
calculated with
Iλ =
1 hc
ni −(Em /kT )
Amn gm
e
,
4 π λmn
Zint
(9)
where Amn is the transition probability; λmn is the
wavelength between the upper level m and lower level
n; gm is the statistical weight; Em is the energy of the
upper level; ni is the total concentration of the specie i
and Zint is the internal partition function calculated at
temperature T (appendix II).
The chosen spectral lines are given in Table 3. These
lines are chosen since they have already been observed
Table 3.
in ICP torches or in thermal plasmas at the same temperature [27,36∼39] .
The Hα and Hβ spectral line intensities are determined by the intensities summation on the spectral
lines given in Ref. [35].
3
Results
3.1
Composition and thermodynamic
functions
To our knowledge, no composition curves and thermodynamic functions for the two considered mixtures
have been published previously. These curves are useful for analysts who use industrial ICP torches and help
them to save time in reproducing the proposal method
or using free software [17∼19] . In Fig. 1, we have plotted
the composition of the two considered mixtures versus temperature between 1000 K and 20000 K. We observe that the main chemical species are argon chemical
species until a temperature of 14500 K and the argon
ions and electrons for higher temperatures. The electrical neutrality is made mainly between argon ions and
Spectroscopic properties of the spectral lines studied in this paper
Species Wavelength Transition
[35]
Statistical weight Upper energy level Transition probability
(cm−1 )
(nm)
(s−1 )
Ar I
675.2834
3s2 3p5 (2 P03/2 )4p − 3s2 3p5 (2 P03/2 )4d
5
118906.6110
1.93e+06
Ar I
687.1289
3s2 3p5 (2 P03/2 )4p − 3s2 3p5 (2 P03/2 )4d
3
118651.3950
2.78e+06
3s 3p ( P01/2 )4p
3s2 3p5 (2 P03/2 )4p
3s2 3p5 (2 P01/2 )4p
2
3 4 0
3
107496.4166
6.39e+06
3
106087.2598
5.18e+06
3
107496.4166
1.17e+07
7
86631.454
3.69e+07
Ar I
696.5430
Ar I
772.3760
Ar I
772.4207
OI
777.1944
OI
777.4166
2
5 2
3s 3p ( P03/2 )4s
3s2 3p5 (2 P03/2 )4s
3s2 3p5 (2 P01/2 )4s
2
3 4 0
−
−
−
2
5 2
2s 2p ( S )3s − 2s 2p ( S )3p
2
3 4 0
2
3 4 0
5
86627.778
3.69e+07
2
3 4 0
2
3 4 0
2s 2p ( S )3s − 2s 2p ( S )3p
OI
777.5388
2s 2p ( S )3s − 2s 2p ( S )3p
3
86625.757
3.69e+07
NI
742.3641
2s2 2p2 (3 P)3s − 2s2 2p2 (3 P)3p
4
96750.840
5.95e+06
2
2 3
2
2 3
NI
744.2298
2s 2p ( P)3s − 2s 2p ( P)3p
4
96750.840
1.24e+07
NI
746.8312
2s2 2p2 (3 P)3s − 2s2 2p2 (3 P)3p
4
96750.840
1.93e+07
HIα
656.27096
2p − 3d
4
97492.3212
5.388e+07
HIα
656.27247
2s − 3p
4
97492.3214
2.245e+07
HIα
656.27517
2p − 3s
2
97492.2235
2.104e+06
HIα
656.27714
2s − 3p
2
97492.2130
2.245e+07
HIα
656.28516
2p − 3d
6
97492.3574
6.465e+07
HIα
656.28672
2p − 3d
4
97492.3212
1.078e+07
HIα
656.29093
2p − 3s
2
97492.2235
4.209e+06
HIβ
486.12785
2p − 4d
4
102823.8961
1.718e+07
HIβ
486.12869
2s − 4p
4
102823.8962
9.668e+06
HIβ
486.12883
2p − 4s
2
102823.8549
8.593e+05
HIβ
486.12977
2s − 4p
2
102823.8505
9.668e+06
HIβ
486.13614
2p − 4d
6
102823.9114
2.062e+07
HIβ
486.13650
2p − 4d
4
102823.8961
3.437e+06
HIβ
486.13748
2p − 4s
2
102823.8549
1.719e+06
688
F. BENDJEBBARR et al.: Plasma Formed in Argon, Acid Nitric and Water Used in Industrial ICP Torches
electrons in the considered temperature range. For the
second mixture (Fig. 1(b)), the electrical neutrality is
made between nitrogen oxide ions (NO+ ) and electrons
for temperature lower than 6000 K. For the temperature between 1000 K and 2000 K, the main chemical
species are argon Ar, nitrogen N2 , oxygen O2 and water H2 O. The N2 molecules dissociate in monatomic
nitrogen N around 4700 K for mixture 1 and around
5000 K for mixture 2. The O2 molecules dissociate in
monatomic oxygen O around 2600 K for mixture 1 and
around 2800 K for mixture 2. The H2 O molecules dissociate in hydroxyl OH and hydrogen H around a temperature of 2500 K for mixture 1 and around a temperature of 2700 K for mixture 2. For temperatures higher
than 6000 K all the monatomic species are ionized into
argon ions Ar+ , oxygen ions O+ , hydrogen ions H+ and
nitrogen ions N+ .
observe this step in the enthalpy between 11000 K and
16000 K. The heat capacity at constant pressure is the
sum of two terms [23] :
Cp = CpR + CpF .
(10)
The CpR is due to the variation of chemical species concentration and the other CpF is due to the variation of
the specific enthalpy of each chemical species. So we can
associate the peaks to the chemical reactions. By comparing the concentration (Fig. 1) and the heat capacity
at constant pressure (Fig. 2) we can determine them.
The first peak around 2700 K appearing for mixture 1
and 2900 K for mixture 2 is due to the dissociation of
H2 O into H and O2 and mainly due to the dissociation
of O2 into O, respectively. This peak does not appear
with argon plasma and appears at a higher temperature for mixture 2 since the proportion of addition in
argon is higher for mixture 2 than for mixture 1. The
second peak appearing for the both mixtures and for
argon plasma is due to the ionization of argon. Since
the main species Ar, Ar+ and e− are the main chemical
species (Fig. 1) they contribute mainly to the enthalpy
and consequently to the heat capacity at constant pressure. Owing to the chosen scales, they can hardly be
distinguished in Fig. 2. By a zoom we can highlight
the peak near 2900 K that is due to molecular chemical
species that are not presented in argon plasma.
Fig.1 (a) Plasma composition versus temperature for
mixture 1 [99.9% Ar-0.002% H2 O-and 0.098% HNO3 ] in
weight percentage at atmospheric pressure, (b) Plasma
composition versus temperature for mixture 2 [99.5% Ar0.004% H2 O-and 0.496% HNO3 ] in weight percentage at
atmospheric pressure
In Fig. 2, we give the enthalpy evolution versus the
temperature and the heat capacity at constant pressure
for the two considered mixtures and argon plasma. The
enthalpy is related to the power injected in the plasma
by ICP torch coils. Between 1000 K and 12000 K, the
enthalpy increases with slowly. Then, the increase
is faster when the ionization of monatomic argon occurs. As a matter of fact it is necessary to add energy,
15.76 eV per atom, to ionize argon. Consequently, we
Fig.2 (a) Enthalpy and heat capacity at constant pressure for argon, mixture 1 and mixture 2 plasmas at atmospheric pressure, (b) Zoom of heat capacity at pressure constant between 1000 K and 5000 K for the three considered
plasmas
689
Plasma Science and Technology, Vol.14, No.8, Aug. 2012
3
Table 4. Intensities of spectral lines (W/m /sr) calculated with hydrogenoid approximation and the lowering of the
ionization energy for the monatomic chemical species (denoted by With), and those calculated with the fitting specific
properties without hydrogenoid approximation and without the lowering of the ionization energy (denoted by Without)
Ar I 772.4207
O I 777.1944
N I 742.3641
HIα
3.2
With
Without
Error
With
Without
Error
With
Without
Error
With
Without
Error
5000 K
3.82603e-02
3.82453e-02
0.04%
1.21617e-01
1.21619e-01
0.002%
1.58396e-04
1.58409e-04
0.008%
2.94966e-02
2.94950e-02
0.005%
10000 K
9.55928e+04
9.55796e+04
0.01%
1.42488e+04
1.42490e+04
0.002%
2.09783e+02
2.09815e+02
0.02%
1.74483e+04
1.74482e+04
0.001%
15000 K
3.00051e+06
2.99938e+06
0.04%
2.29006e+05
2.29239e+05
0.10%
3.66452e+03
3.66998e+03
0.15%
4.96530e+05
4.97165e+05
0.13%
20000 K
1.19136e+06
1.19067e+06
0.06%
1.04954 e+05
1.05087e+05
0.13%
1.49694 e+03
1.49926e+03
0.15%
3.39435e+05
3.40050e+05
0.18%
Monatomic spectral lines
In Table 4, we give the monatomic spectral lines calculated with consideration of the lowering of the ionization potential and with the hydrogenoid approximation
of the upper levels and those obtained from the fitting
data given in Table 2a. The relative error between both
calculations is less than 0.2%. So the fitting coefficient
can be used to determine the spectral line intensities
of monatomic chemical species in our considered temperature range. In Fig. 3, the intensities of the chosen
spectral lines are plotted for both considered mixtures
and with argon plasma. The argon spectral lines have
the same intensities in the three cases. As a matter of
fact, since the argon is the main species it follows the
Dalton law in the three considered cases calculated at
the same pressure. Furthermore, the Boltzmann distribution on the quantum levels has been assumed, we do
not take into account the under-population of the low
lying state [40] since we assume the considered region to
be in the warmest zone of the plasma.
The proportion of nitric acid and water in mixture 2
is higher than that in mixture 1. The intensities of
the oxygen monatomic species, hydrogen monatomic
species and nitrogen monatomic species spectral lines
are higher.
The ratio of the spectral lines between argon lines
and oxygen monatomic species, hydrogen monatomic
species and nitrogen monatomic species depends directly on the proportion of the vaporized liquid inside
the plasma.
The crossing between OI 777.19 spectral lines and
Hα is made at 8800 K for mixture 1 and at 8900 K
for mixture 2. The ratio between these two lines is not
really sensitive to the proportion between water and nitric acid for the two considered mixtures. As a mater of
fact the nitric acid proportion is higher in both cases.
Nevertheless the intensities of nitrogen spectral lines
are rather low.
690
Fig.3 (a) Intensities of the chosen spectral lines (Table 3)
versus temperature for mixture 1 at atmospheric pressure,
(b) Intensities of the chosen spectral lines (Table 3) versus
temperature for mixture 2 at atmospheric pressure, Intensities of the chosen spectral lines (Table 3) versus temperature
for argon plasma at atmospheric pressure
F. BENDJEBBARR et al.: Plasma Formed in Argon, Acid Nitric and Water Used in Industrial ICP Torches
4
Conclusion
To obtain the plasma composition, we have described
a numerical method that is robust and easy to execute
for the Gibbs free energy minimization. The specific
thermodynamic of chemical species of diatomic species
has been calculated with a consideration of higher excitation energy levels, allowing us to use them in a
large temperature range from 1000 K to 20000 K. By
comparing the monatomic spectral lines intensities, we
show that we can use the partition function without hydrogenoid approximation and the lowering of ionization
potential in the temperature range between 1000 K and
20000 K for the two mixtures of nitric, water and argon widely used in ICP spectrochemical analyses. All
the data for obtaining the composition, the thermodynamic functions and monatomic spectral lines intensities are given, allowing one to reproduce such calculations. From the thermodynamic functions the main
chemical reactions are given, showing that the argon
plays the major role to the plasma thermodynamic
functions. Nevertheless, the loss of energy due to ra-
diation from atoms and molecules emissions has to be
studied carefully [41] . Concerning the spectral lines intensities, the argon lines are similar in the three considered cases so these lines can be used as reference
lines for the wavelength and the intensity calibrations.
The other lines depend directly on the proportion of
vaporized droplets inside the plasma and can be used
to characterize the plasma state. So the analyst can
compare the spectroscopic measurements experimentally obtained with those calculated, and check the repeatability. Any deviation from the calculation results
will give indication of the plasma state: thermal equilibrium, chemical equilibrium and total evaporation of
the droplet.
Acknowledgement
The authors would like to acknowledge both universities, Blaise PASCAL and MOHAMED Boudiaf, and the
three laboratories, LAEPT, LMV in Clermont-Ferrand
and LGEO in Oran, for their helps in this collaborative
work.
Appendix I
Numerical system resolved at each temperature step


RT
n1
 ...



 a
 1,0
 ...
a1,4
...
...
...
...
...
0
...
RT
nN
aN,0
...
aN,4
a1,0
...
aN,0
0
...
0
... a1,4
...
...
... aN,4
...
0
...
...
...
0











∆n1
...
∆nN
∆π0
...
∆π4



 


 
 
 
 
=
 
 
 
 






4
−µ01
X
n1
P
πj ai,j
− RT ln N
− RT ln 0 −
P
P
j=0
ni
i
...
4
−µ0N
−
...
−
N
P
i=1
N
P
i=1
X
nN
P
πj aN,j
− RT ln N
− RT ln 0 −
P
P
j=0
ni
i
ni ai,0 + b0
ni ai,4 + b4






















Appendix II
Fitting coefficients for the standard thermodynamic functions of i chemical species (heat capacity at constant
pressure, enthalpy, and entropy) [10,23] :
µ
¶
b
c
a
2
3
4
+
+
Cpi = R
+
d
+
e
∗
T
+
f
∗
T
+
g
∗
T
+
h
∗
T
(J/mol/K),
T3
T2
T
µ
¶
−b
ln(T )
−a
T
T2
T3
T4
0
+ 2 +c∗
hi = R ∗ T ∗
+d+e∗ +f ∗
+g∗
+h∗
+ R ∗ i (J/mol),
2 ∗ T3
T
T
2
3
4
5
µ
¶
−b
c
−a
T2
T3
T4
0
+
− + d ∗ ln(T ) + e ∗ T + f ∗
si = R ∗
+g∗
+h∗
+ j (J/mol/K).
3 ∗ T3
2T 2
T
2
3
4
The chemical potential is given by:
µ0i = h0i − T s0i + Eri .
Knowing the chemical potential µ0i of the i chemical species, we can deduce the internal partition function at
temperature T :
¶
µ
µ0i + RT ln(ztr ) − Eri
,
zint = exp −
RT
691
Plasma Science and Technology, Vol.14, No.8, Aug. 2012
where Eri is the formation enthalpy of the i chemical species (Table 2) and ztr the translational partition function:
¶
µ
2π mi k T kT
ztr =
,
h2
P0
where mi is the mass of particle of the i chemical species, h is the Planck constant, k is the Boltzmann constant
and P 0 the standard pressure.
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(Manuscript received 11 November 2010)
(Manuscript accepted 26 October 2011)
E-mail address of corresponding author P. ANDRE:
[email protected]