Consideration of norm temperature and local thermodynamic equilibrium models for emission and ionization in inductively coupled plasmas

Spectrochmwa

Acfa Vol 448, No

6, pp 625438,

1989

mntsd111 GreatBntam

0

0584~8547/89 $3 @I+ 00 1989 Pcrgamon Press plc

Consideration of norm temperature and local thermodynamic equilibrium models for emission and ionization in inductively coupled plasmas JOHN W. OLES~K

Department of Chemistry, Venable and Kenan Laboratories, CB No 3290, Umverslty of North Carohna, Chapel I-W, NC 27599-3290, U S A (Receaed

20 August 1988, in final form 4 January 1989)

Ahtract-Norm temperature and local thermodynamic eqmhbnum (LTE) models of ernlsSlon intensity and lomzatton m ICPs are &cussed Based on each of the two models, detuled predictions of emlSSionmtensltles and total atom, singly charged ion and doubly charged ton fractions are presented The predicted behanor 1scompared to pre~ously published expenmental data. The norm temperature model results appear to be consistent wraththe expenmentally observed behavior of the peak m emission mtenslty as a function of height m the plasma However, assumptions made m the norm temperature model are inconsistent with LTE LTE model predictions do not match experimentally observed data as a function of temperature.The LTE model results do not show a peak m ermsslon Intensity or ton to atom intensity ratlo as a function of temperature from 3000 to 10000 K The LTE model predicts that analytes m He ICPs should be more highly iomzed than m LTE Ar plasmas. However, expenmentally, He plasmas should be further from LTE. Possible causes of the disagreement between model predictions and expenmental data include radiative deexatation, non-LTE electron temperatures, mass transport effects, slow vaponzation or lomzation kinetics and non steady-state conditions

1. INTRODUCTION

MANYdifferent models of mductlvely coupled plasma excitation and iomzatlon have been proposed. The development of a model has two purposes. By comparing model predictions to expenmental data, the validity of the model and its fundamental chemical and physical basis can be tested. In this way, model testing leads to further understandmg of the chemical and physical processes controlling emlsslon from the plasma If the models are correct, they can be used to predict or explain observations. Adequate models could be used to predict emission or iomzatlon behavior as a function of experimental conditions such as power or flow rate. In combination with experimentally measured diagnostic signals, a working model could be used to mamtam constant excitation conditions from day to day, independently of the sample introduced into the plasma Two different, relatively simple models will be reviewed. The norm temperature model for ICP emlsslon was developed by BOUMANS Cl-43 A local thermodynamic equilibrium (LTE) model based on electron concentration [S-S] has gamed favor more recently The norm temperature model has been apphed to explain expenmentally observed signals as a function of expenmental conditions such as height in the plasma [9]. Based on the norm temperature model, analyte emission low m the plasma has been described as “thermal”. Conditions m the norinal analytical zone, where ion emlsslon peaks, has been described as “nonthermal”. This explanation is still used, although the inconsistency of the norm temperature model with local thermodynamic equilibrium has been exposed [S-S]. One may be tempted to use the LTE model m a predictive manner as well At first look the ICP may appear to be “close enough” to LTE for the LTE model to apply. However, trends m observed emlsslon as a function of electron number density do not agree with the LTE model prediction. Also, as discussed herein, Ion/atom population measurements made via laser fluorescence or atomic absorption appear to conflict with the emlsslon and model data. In this paper the strengths and weaknesses of the two models are first compared m some detail. Assumptions made in each model are evaluated. Model predictions are compared with expenmental data. Previously published results using the LTE model [S-S] included only atoms and singly charged ions. Here, the “electron based LTE” approach is extended to include doubly ionized species. The fraction of analyte existing as doubly lomzed species under LTE condltlons is much larger than the fraction existing as atoms for many elements. Little 625

JOHN W OLESIK

626

emission is observed from doubly charged ions, mainly because the excited states typically have high excitation potentials. However, doubly ionized species are detected in ICP-MS. Finally, the electron-based LTE model predictions will be briefly considered for hehum ICPS. 2. EXPERIMENTAL 2.1 sofiwure Norm temperature and LTE model simulation programs were written in either ASYST (Macmtllan Software Company) or Eureka (Borland Corporatron) and run on an IBM PC/AT

2.2 Data Partition functions were calculated from polynomial coefficients reported by DE GALAN et

al [lo]

for temperatures between 3000 and 7000 K and TAMAKIand KURODA[l l] for temperatures between 7000 and 10000 K Calculated partitron functions at 7000 K from the two references were not equal (Table 1).Therefore, a WI order polynomial was fitted to the partition functions calculated over the range of 3000 to 10000 K combinmg data from the two references The fifth order polynomtals fit the published data well from 3000 to 6000 K and from 8000 to 10000 K, while providing a smooth, contmuous transition from 6000 to 8000 K.

3. RESULTSAND DISCUSSION The models are both based on the Boltzmann equation describing the relative populations of energy levels and the Saha equation relating ion to atom populations. Therefore, both models assume the analyte species are m equilibrium. Using either model to describe the plasma requires that it be m a steady-state. The intensity of a spectral line is given by:

F,,, is the fraction as atom (ion). FE,, IS the fraction of atoms (tons) m excited state 1 A,, , is the transition probability for a spectroscopic transition from state i toj. C is a constant @*c/4@. n,,,,, is the total number of atoms and ions per cubic centimeter. A,,, is the wavelength of the observed spectral line. The fraction of analyte existing as atoms, singly charged ions and doubly charged ions can be calculated, using the Saha equations for the ionization of M and the ionization of M+, respectively:

&+,dU=

vh+

-

nM

Table 1 Calculated partltlon functions at 7000 K Partltlon function value DE

Species

Ar Ar+ Ca Ca+ Mg Mg+ Nl NI+ Zn Zn+

GALAN

TAMAKI

Ref [11]

Ref [lo] loo0

5 842 1707 2635 1 103 2000 34 23 14 02 1000 2000

,

1000 5 487 1966 2 639 1 181 2005 34 75 14 17 1031 2005

Emwon

SM+,M( T)=4.83

SM++,M+(T)=

x 10’5 z-3/2 3

and tomzatlon m ICPs

MIO-

c-Gi

627

1

n,nM++

(4)

h+

SM++,M+(T)=4.83

x 1Ol5 T 3’2 F

IOM+

IPl and ZP2 are the first and second ionization potentials, respectively, in electron volts n,, nM, nM+p nM + + are the number of electrons, atoms, singly charged ions and doubly charged ions per cubic centimeter. ZM, ZM+ and ZM++ are the partition functions for atom, singly charged ion and doubly charged ion species. The fraction of a species existing as atoms is given by: fraction atom, FM=

nM n,,$+n,+ +nM+ +

(6)

Here it is assumed that the number density of triply or more highly ionized species is small. The fraction as atoms can be calculated from equations (2) through (6):

F,=

1 -+l+ SM+/M

*es

.

M++/M+

(7)

n,

n,

Similar expressions can be written to describe the fraction as singly or doubly charged ions. The fraction of atoms (ions) m a particular excited state IS given by: 10- [ SW:

FE,,= 5 M

1

09

g, is the degeneracy of the upper state involved m the transition. EP IS the excitation potential of the upper state m electron volts. Input data dependent on plasma conditions includes the electron concentration and the temperature. The difference between the norm temperature and LTE models lies in the relationship between temperature and electron number density.

3.1. Norm temperature model The norm temperature model assumes that the electron concentration is constant while the temperature is variable. For example, BLADES and HORLICK[9] assumed a constant electron concentration of 10’ 3 5 cm - 3. Calculated intensrties were then compared to observed intensities as a function of height m the plasma. Plots of calculated relative intensity vs temperature appeared to be similar to plots of measured intensity vs height above the load coil. The observed atomic emission intensity is a function of the fraction of species existing as atoms, the fraction of atoms m the excited state and the transition probability. The calculated fractions, FM, of Ca as atom, ion and doubly charged ion are shown in Fig. la-c. An electron concentration of 1 x lOi cmH3 was used. The fractions of each species in the excited state, FE, for particular Ca I, Ca II and Ca III lines are shown m Fig. Id-f, respectively. The calculated relative emission intensities as a function of temperature are shown m Fig. lg-i. Both Ca atom and Ca ion emission show a peak at characteristic temperatures (called their norm temperatures). The peak in Ca atom emission results from a loss of atoms due to ionization coupled with an increase m the fraction of atoms in the excited state as the temperature increases Similarly, the peak in Ca II emission results from a loss of Ca+

JOHNW OLESIK

628

through iomzatton to Ca+ + All elements show similar behavior. The norm temperature is dependent on the ionization and excitation energies. The norm temperature model is appealing mainly because it appears to be able to explain the behavior of atom lines with low excitation potentials and ionization potentials (“soft” lines [9, 121) BLADESand HORLICK [9] found good correlation between the norm temperature of atom lines and the position above the load coil where the emission from each line peaked. BOUMANS calculated the distribution of Ca, Ti and Cd species as a function of temperature [l, 31 As one might intuitively expect, the fraction as atoms decreases as the temperature increases from 3000 to 10000 K while tbfraction as ions increases. (Fig. la-c). As will be seen below, this is in contrast to the LTE model predictions. There are two problems with the norm temperature approach. First, experimental data shows that the electron concentration 1s not constant as a function of height in the center of the plasma [ 131. Secondly, under LTE conditions there should be unique combinations of electron concentration and temperature One cannot be varied while the other remains constant [S-7] Based on the LTE model, a small change in temperature results in a large change m electron number density (Fig. 2).

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Tempera fure Fig 1 Norm temperature model based calculated values assummg a constant electron number density of 1 x 10” cmT3 Temperature dependent fraction ofcalcmm (FM) as Ca atom (a), Ca+ (b), Ca+ + (c). Temperature dependent fraction of Ca atoms (d), Ca+ (e), Ca+ + (f) m the excited state (FE) Involved m Ca 1422 7 nm, Ca II 393 6 nm, Ca III 357 9 nm spectral hnes. Relatwe mtenslty (I)of the Ca I (g), Ca II (h) and Ca III (I)lmes as a function of temperature

3000

6500 Tempera twe

10000

fKI

Fig 2 LTE electron number density (cmw3) m an Ar plasma as a function of temperature

Emlsslon and lomzatlon m ICPs

629

3.2. LTE model The LTE model derives all of its results from a single, experimentally measurable parameter. Either electron number density or temperature may be used. However, spectroscopic means of determining temperature require the assumption that the system is m LTE. In contrast, measurement of electron number density via Stark lme broadening does not require an assumption of LTE. Beginning from electron concentration; the LTE temperature can be calculated. Dalton’s law describes the number density of Ar species as a function of pressure and temperature The Saha equation is used to determim’the fraction of Ar which exists as singly charged ions. The number of argon atoms per cm3 based on Dalton’s law is: nAr

=

7.34 x 102’ P T

(9)

The pressure, P, is assumed to be one atmosphere. It is assumed that all argon exists as argon atoms (i.e. the degree of ionization is small). The Saha equation for the ionization of argon 1s S,,(T)=4.83 S,,(T)=

x lOi T’ 5 +

10 atam

F.

(10) (11)

If one assumes that all electrons come from the ionization of argon, the electron number density is equal to the argon ion number density. Then ‘b =@A,(

T hr)” ‘.

(12)

Given n,, the unknowns are T, S(T) and n&. Using Eqns (9), (10) and (12), one can solve for the three unknowns. This provides the link between temperature and electron concentration. Here it is assumed that practically all of the argon exists as argon atoms The argon is calculated to be less than 2.2% ionized at temperatures below 10000 K and less than 0.2% ionized at temperatures below 8000 K. While this assumption is consistent with the calculated results, it is not essential. Doubly charged Ar ions could be included using the Saha equation relating singly and doubly charged species. Electrons produced from sources other than lomzation of argon are assumed to be insignificant in number. Other potential sources of electrons are ionization of analyte, particularly easily ionizable elements and solvent products A rough calculation of the number of electrons produced by analyte shows that a large concentration would be required to produce a number of electrons similar to that from ionization of argon Assume that a solution of 10000 pg/ml Na is mtroduced at a rate of 10 ml/min with a transport efficiency of 1% The analyte appears to be confined to the central channel of the plasma. Therefore, the sample will be assumed to be in 1 l/mm of cold Ar If the argon IS at approximately 290 K before entering the plasma and the gas temperature m the plasma is about 2900 K, the gas will expand by a factor of 10 So, there would be 100 pg Na m 10 1of Ar m the plasma. If Na is completely iomzed, 4.3 x 10e6 moles of electrons will be produced. The resulting electron number density is 2.6 x 1014 electrons per cubic centimeter Electron concentrations measured m a 1 25 kW, low flow torch are typically 1 x 1015 cmm3 m the analytical zone [7, 131. If the Na concentration m the original sample was 1000 pg/ml, the number of electrons produced from Na iomzatlon (2.6 x 1013 cme3) would be a factor of about 50 less than that due to Ar ionization m the analytical zone The assumptions that: (1) all of the Na remains m the central channel and (2) the gas temperature is only 2900 K probably lead to an overestimation of the electron concentration from Na ionization. This IS supported by experimental measurements of the ground state number densities of Ca atoms and singly charged ions NOJIRIet al. [14] measured a total number density of Ca atoms and Ca+ of approximately 2 x lo’* cm-3 when a 1000 ppm solution was introduced

630

JOHN W

OLESIK

Another potential source of electrons is the ionization of H and 0 followmg atomization of water vapor and droplets. It has been observed that small amounts of water result in an increase in excitation temperatures and electron number density [15]. Therefore, one might conclude that the production of electrons from ionization of H and 0 produces a significant number of electrons. Typical rates of water vapor and aerosol entermg an analytical argon ICP are 23 and 10 mg/min, respectively. Therefore, 1.1 x 1021 H20 molecules enter the plasma per minute. Assuming virtually all of the water exists as H and 0 atoms m the plasma (reasonable above 6000 K), 2.2 x 102’ H atoms per minute and 1.1 x 10” 0 atoms per minute enter the plasma. If one assumes a total AK flow rate of 15 l/mm, 4 x 10” Ar atoms enter the plasma per minute So, the ratio of total number of H and 0 atoms to Ar atoms IS approximately 1 to 100. H and 0 have smaller ionization potentials than Ar (13.6 eV vs 15.75 eV). The fraction of H and 0 that is ionized is larger than the fraction of Ar which is ionized. By simultaneously solving the set of Saha equations for Ar, H and 0 and assummg that the total number density is based on an argon pressure of one atmosphere, one can calculate the number of electrons from ionization of Ar, H and 0, respectively. The LTE calculated total electron number density increases by only 0.8, 1.9 and 4.6% at 10000,8000 and 6000 K respectively when H and 0 ionization are Included. Therefore, at temperatures above 6000 K (electron number densities above 3 x lOi cmv3), electrons from H and 0 ionization should make a minimal contribution to the electron number density. Small amounts of H or 0 could affect the thermal conductivity of the plasma, resulting m changes in the plasma temperature 3.2.1 lonrzat~on. The two main factors control the fractions of atoms and singly charged ions as a function of temperature* first ionization potential and electron concentration. The fraction of calcium and zinc as atoms, singly charged ions and doubly charged ions for temperatures from 3000 to 10000 K are shown m Fig. 3. By comparmg Fig. la-c and Fig. 3a-c one can see that the norm temperature and LTE models predict very different behavior for calcium. The behavior of Ca is characteristtc of species with a first ionization potential less than 7 eV In contrast to the norm temperature model, the fraction of Ca atoms increases with increasing temperature The fraction of calcmm as Ca+ decreases with temperature. The decrease m the fraction of calcium as Ca+ is due to increases m both the fraction of Ca atoms and Ca++. The changes m electron concentrationdominate the behavior for the equilibrium between Ca and Ca+. Even though the equilibrium constant, SCa,ca+ , increases with temperature, the electron concentration increases rapidly enough to shift the equilibrium back toward atoms. Ca*Ca+

+e-

a,sCa/Ca += -.nca+ nca

(13)

The fraction of Ca and Ca+ + mcreases with temperature. The mcrease in the equilibrium constant, Sc, +,ca++, dominates over increases m the electron number density produced by ionization of Ar. The predicted fraction as Ca atoms and Ca ions are vastly different using the norm temperature and LTE models (Table 2). The LTE model predicts that the dominant species is the singly charged ion. Greater than 90% of the calcium IS predicted to exist as Ca’ for temperatures between 3000 and 10000 K. The distribution of zinc among atoms, tons and doubly charged ions as a function of temperature is characteristic of elements with a first ionization potential greater than 9 eV. The fraction of zinc as Zn atom decreases with increasing temperature, while the fraction of zinc as Zn+ increases. For species with large ionizatron potentials, the dominant species changes from atom to singly charged ion as the temperature is increased. The temperature where the dominant species changes increases with increasing first ionization potential. The trends in the fractions of atoms and ions for species with first ionization potentials between 7 and 9 eV as a function of temperature is dependent on the ratio of partition

Emlsslon and lomzatlon m ICPs

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x 10-4 10

f 05

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Rg 3 LTE model calculated fraction of calcmm as Ca atoms (a), Ca+ (b) and Ca+ + (c) Calculated fraction of zmc as Zn atoms (d), Zn + (e) and Zn + + (f)

Table 2 Comparison of norm temperature and LTE model predicted fraction of Ca as atom, smgly charged Ion and doubly charged Ion 3000K

Ca Ca+ Ca++

6500 K

1OOOOK

norm

LTE

norm

LTE

norm

LTE

100 0000085 7x lo-‘9

000007 100 7x 1o-7

0015 098 0 00072

000163 099 0 0062

0 00024 040 060

00083 091 0082

functions. If the ratio of partition functions was constant, species with a first ionization potential of 7.98 eV would show a peak in the fraction of ions as a function of temperature rather than continuously increasing or decreasing. The first ionization potential for Ni (7.633 eV) is smaller than that for Mg (7.644 eV). However, the fraction of nickel as Ni atoms is larger than the fraction of magnesium as Mg atoms (Fig. 4a, d). The fraction of nickel as Ni+ continuously increases with temperature (Fig. 4e, Fig. 5f). Zinc shows similar behavior, although the change is larger. In contrast, the Mg+ fraction peaks near 8200 K (Fig. 4b, Fig. SC). The seemingly anomalous behavior of Ni with respect to Mg is due to the ratio of ion to atom partition functions. The Saha constants for Ni and Mg, without including the ratio of partition functions (S’) divided by electron number density ([e-l) are nearly identical (Fig. 5a, d). However, the ratio of ion to atom partition functions (Z,,,/Z,,,,) for magnesium decreases with increasing temperature (Fig. 5b). As a result, the fraction of magnesium as Mg+ (Fig. 5c) varies only between 0.973 and 0.983. Zion/Zatom for nickel increases with SAIS)

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Fig 4 LTE model calculated fraction of magnesmm as Mg atoms (a), Mg” (b) and Mg’ + (c) Fraction of mckel as NI atoms (d), NI’ (e) and NI++ (f)

temperature (Fig. 5e) Therefore, the fraction of nickel as Ni+ (Fig. Sf) increases with increasing temperature. The ratio of ton to atom partition functions is less than one for Ni and greater than one for Mg. As a result, the fraction of Ni as Nt+ is smaller than the fraction of Mg as Mg+, even though Mg has a larger tomzation potential The fraction of magnesium as Mg+ + (Fig. 4c) is larger than the fraction of Nt as Ni+ + (Fig 4f), as one would expect based only on the difference m second tomzation potentials 3 2.2. Emzsslon mtensltles. Atom emission mtenstties peaked as a function of temperature m the norm temperature model (Fig 1) In contrast, the LTE model calculattons predict that the atom emission intensity contmuously increases with temperature (Fig. 6). There is no “norm temperature” where atom emisston is maxtmum. Also, the LTE model predicts no peak m the ion to atom intensity ratto as a function of temperature (Fig. 6c, f). CAUGHLIN and BLADES have measured ion to atom intensity ratios and electron number densities in ICPs [7] The ratios for calcium are close to the calculated LTE values m the normal analytical zone of a 2 kW plasma. However, direction of the change m the ratio with temperature (or electron concentration) is different, as shown m Fig. 7a Experimental data and LTE calculations show an increase m the Zn ion to atom mtenstty ratio (Fig. 7b) with temperature. However, the experimentally observed ratto is much lower than the LTE value C7, 81 3 2 3. Ground state popuhons. LTE and emission-based measurements [8,16] of ion to atom ratios indicate that elements with tomzatron potentials less than 8 eV should be more than 90% ionized m the analytical zone of the plasma However, other measurements indicate that the population of ground state atoms is similar to that of ground state tons in the center of the plasma m the normal analytical zone [14, 171.

Emlsslon and lomzatlon m ICPs

050

633

e

0.40

0.99

loo0

F ;:

Ni’

f

0.925

0.97

0850

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Fig 5 Factors other than Z,,,/Z,,,,, m determmmg the fraction of Mg and Nl as a function of temperature Saha constant wlthout mcluslon of the ratlo of partltlon functions (S’) dlvlded by electron concentration ([e-l) for Mg (a) and NI (d) Ratro of Ion partltlon function (Z,+) to atom partltlon functions (Z,) for Mg (b) and Nl (e) Fraction of magnesmm as Mg+ (c) and mckel as NI+ (f)

The ratio of the absolute ground state number densities of Ca ion to Ca atom measured by NOJIRIet al. [14] was approximately 2 The measurement was made in the center of a 1.5 kW plasma at a height of 15 mm above the load coil. The measured electron number density was approximately 4.5 x 10I5 . The LTE predicted ratio of Ca ion to Ca atom is 220. Interestingly, NORJIRI[14] measured much larger values of Ca ion to Ca atom ground state species off axis. The Ca ion to Ca atom ground state ratios were approximately 55 and 360 at 1.0 and 2.0 mm off axis, respectively. One must be cautious in comparing ion to atom ratios obtained by absorption or fluorescence and calculated total ion to atom ratios. The absorption and fluorescence measurements provide data on the ground state ion and atom populations. The fraction of atoms and ions in the ground state may not be identical For example, using the Boltzmann equation and a temperature of 8850 K, 63% of Ca ions are m the ground state, but only 20% of Ca atoms are m the ground state. So, the LTE calculated ratio of ground state ion to atom population is about 70. However, this does not explam the discrepancy between the LTE and experimental values. TURKet al. Cl73 used a laser ioruzatlon, laser fluorescence technique to study recombination of strontium ions and electrons. The observed Sr+ signal increased from 5.3 to 7.5 due to the laser ionization If one assumes that the laser caused complete ionization of Sr atoms to Sr+, the ratio of Sr+ to Sr atoms without laser ionization would be 5.3-2.2 giving a result of 2 4. The measurements were made in a 1.0 kW plasma at a height of 15 mm above the load coil. Further, the authors found that the laser-induced lomzation yield is only 14% and the ratio of Sr+ to Sr atoms was approximately one.

634

JOHN W OLESIK

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Fig 6 LTE model calculated relative mtensltles of Ca I 422 7 nm (a), Ca II 393 6 nm (b), Zn I 213 9 nm (d) and Zn II 202 5 nm (e) as a function of temperature Ion to atom mtenslty ratios for Ca (c) and Zn (f)

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Frg 7 Comparison of Ion to atom Intensity ratios calculated under LTE condltlons and experImentally observed [7] for Ca (a) and Zn (b) (Spectral lines are bsted m caption for Fig 6)

3 2 4 Potential sources ofdlsagreement between electron based LTE and observatrons. The

key to explaining emlsslon behavior as a function of experimental condltlons such as power or flow rates appears to be the departure from LTE condltlons. WALKER and BLADES [183 have shown that the low energy states of atoms are overpopulated compared to the electron-

Emlsslon and lonlzatlon m ICPs

635

based LTE conditions. The departure from LTE has been postulated to be due to radiative deexcitation competing with collisional deexcitation via electrons [8, 193. If the situation was that simple, the departure from LTE should be dependent only on the electron number density for a particular species and excited state. Experimental data from both CAUGHLINand BLADES[7] and FURUTAet al. [20] showed a height dependent relationship between electron concentration and closeness to LTE. The spatial location of maximum electron concentration did not necessarily correspond to the position where the ion to atom emission intensity ratio is closest to LTE. The deviation from LTE is larger in a 125 kW plasma than m a 1.75 kW plasma when ion to atom intensity ratios from regions of the plasmas with equal electron concentrations are compared, using data from Ref. [73. It is possible that these observations could be explained by different electron temperatures. WALKERand BLADES[18] and SCHRAMet al. [6] found thaf low energy atom states were overpopulated relative to LTE. Therefore, one would expect the ground state atom to be the most overpopulated. However, the overpopulation of the atom ground state would need to be much larger than the 6% figure calculated by Lov~rr [19] in order to explain the absorption and fluorescence data. The plasma is assumed to be in a steady-state condition. However, OLESIKet al. [21-241 and FARNSWORTH [25] have observed large fluctuations in the emission signals (Fig. 8). In particular, atom emission signals appear to be made up of large spikes on top of a low intensity steady-state signal. The spikes contribute significantly to a time-averaged signal. In contrast, ion emission is typically more normally distributed about a mean (although large time-dependent changes are observed). Below the analytical zone in the plasma, dips in the ion emission intensity correlate with spikes in the atom emission data [23,24]. Ion to atom intensity ratios vary wildly when viewed on a submillisecond time scale. High in the plasma, spikes m atom emission data are followed by spikes in ion emission [23, 241. The results of a series of emission and laser scattering experiments strongly support the hypothesis that the intensity fluctuations are due to individual aerosol droplets [23,24]. The

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Time fsl Rg 8 Ca I 422 7 nm (a) and Ca II 393 6 nm (b)ermsslonas a function of time at 15 mm above the load cod m a 1 kW plasma [21]

636

JOHN W OLESIK

behavior is not umque to calcmm We have observed similar behavior for Ba and Mg. Therefore, use of the time-averaged signal to describe plasma conditions may not be valid. In order for the LTE models to be valid, kinetic processes must be rapid compared to the time a particular volume of gas remains in the observation zone. The observed fluctuations may indicate that the vaporization, atomization or iomzation processes may be too slow to allow assumption of steady-state. If this was the case, mass transport and kinetic rate equations would be essential to explain the observed emission and fluorescence signals. Also, vanations in gas temperature will result in changes in gas density and velocity. Both will affect measured emission and fluorescence signals. 3.25 Helrum plasmas. The calculated LTE electron number density is lower for He plasmas than Ar plasmas at the corresponding temperatures (Table 3). This is due to the higher ionization potential of He compared to Ar. As a result, more highly ionized analyte Table 3 Companson of calculated electron number dens&es as a function of temperature m LTE argon and hehum plasmas Electron number density (cm-j) Temperature (K) 5000 6000 7000 8000 9000 10000

x

Ar plasma

He plasma

153 x lOI 3 33 x 10’3 3 02 x lOi 1 58 x lOI 578~10’~ 163 x 10’”

356x10’ 4 19 x lo9 127 x 10” 164x10’* 121x10’3 5 98 x 1013

106

x

I.37

Fz.

a Ca

I

10-4

3.5

I/

1.7

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Zn

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MI x 10-z

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Rg. 9 Calculated fraction of calcmm as Ca atoms (a), Ca+ (b) and Ca+ + (c) m an LTE hehum plasma Calculated fraction of zmc as Zn atoms (d), Zn+ (e) and Zn+ + (f)

631

Emlsslon and lomzatlon m ICPs Table 4 Comparwon of estimated (calculated) number of colhslonal deexatatlons m the radlatlve hfetlme of Ca and Zn speckes m Ar and He LTE plasmas Temperature (K) 7500 7500 9000 9000

Plasma

Ar He Ar He

CaI

Ca II

048 0 00034 348 00077

194 00014 14 1 0031

ZnI

0031 0 WOO23 0 228 0 00050

Zn II

0 246 000019 193 00043

species are predicted to be dominant For example, Ca+ + is calculated to be the dominant calcium species throughout the 3OOG10 000 K temperature range under LTE conditions m a He plasma (Fig. 9). In contrast, Ca+ predominates m an LTE Ar plasma. Zmc would exist mainly as Zn+ m the LTE He plasma, even at low temperatures In practice, one would expect that the LTE model for He plasmas would be less hkely to be valid than that for Ar because of the much lower electron concentration. Radratrve processes will compete more effectively with electron colhsional processes because there are fewer electrons, leadmg to non-LTE behavior. The number of de-excitations that occur m one radiative lifetime, N(p), can be estimated by: &K(P)

N(P)= ~

A(P)

(14)

as was done by BLADES et al. [S]. K(p), the de-excitation rate due to collisions with electrons was approximated as described by YASUDA and SEKIGUCHI [26]. A(p) 1s the total radiative de-excitation rate (transition probabihty) and n, is the electron number density. The results for Ca I, Ca II, Zn I and Zn II lmes m Ar and He plasmas at 7500 and 9000 K are listed in Table 4. Values of N(p) less than one indicate that de-excitation is radiatively dominated. Values of N(p) greater than 10 mdicate that the p level is in equihbrium with excited state levels above it. In the Ar plasma, the dominant de-excitation is different for atom lines than ion lines and is dependent on the temperature, Radiative de-excitation is dominant for all four of the excited species considered m the He plasma. Electrons produced from species other than He (such as analyte m high concentrations, or products from water) will be more important in the He plasma than the Ar plasma. 4. CONCLUSIONS Norm temperature and electron based LTE models are inadequate to describe the behavior of emission intensities and ionization m the ICP. The fraction of singly ionized species predicted by the LTE model is close to the experimentally measured values usmg emission intensity measurements. However, the LTE predicted fraction of smgly charged species is not a strong function of temperature, particularly for species with ionization potentials less than 9 eV. The fraction of singly charged species is much less dependent on temperature m the LTE model than the norm temperature model. The trend with changing electron concentration predicted by the LTE model is often not in agreement with experimental data. The LTE predicted trends are especially different from experimental results for elements with low ionization potentials. Further, as BLADES data showed [7,8], the zone of the plasma called “thermal” by BLADES and HORLICK IS m fact farthest from LTE, while the “nonthermal” norm analytical zone is close to LTE. The fact that all “hard” lines peak m the same location is consistent with the LTE model No peak m emission intensity is predicted over the range of temperatures from 3000 to 10 000 K. The ion to atom Intensity ratio also does not peak as a function of temperature in the LTE model. The peak behavior demonstrated experimentally by “soft” lines must be due to mass transport, kinetic or non-LTE effects.

638

JOHNW OLESIK

Departures from LTE or unfulfilled assumptions appear to be key in describing the plasma as experimental condltlons are changed A two temperature model such as the norm temperature model 1s inconsistent with LTE. However, it 1s apparent that at least a two temperature model may be needed to predict emlsslon behavior m the ICP. It may also be necessary to consider mass transport m and out of each observation zone. Large fluctuations in the ion to atom lqtenslty ratio occur on a submillisecond time scale. It may not be appropriate to develop models that attempt to predict the time-averaged behavior. Hehum plasmas should be further from equilibrium than Ar plasmas at similar temperatures. Electron number densities are lower m He plasmas. As a result, ionization should be more extensive. Radiative de-excitation should compete effectively with collisional de-exatatlon m He plasmas Acknowledgements-Support for this work was provided by a DuPont Young Faculty Grant and the Department of Chemistry, Umversity of North Carolina at Chapel I-Id1

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