Some fundamental considerations on analytical high-frequency plasmas

0039.9140iSl;oso629-07M)2.00/0

Tulonra. Vol 28.pp.629to635.19x1 Printed in Great Britam. All rights reserved

Copyright

8

1981 Pergamon Press Ltd

SOME FUNDAMENTAL CONSIDERATIONS ON ANALYTICAL HIGH-FREQUENCY PLASMAS P. F. E. VAN MONTFORT*and J. AGTERDENBOS Analytisch Chemisch Laboratorium der Rijksuniversiteit Utrecht, Croesestraat 77a, 3522 AD Utrecht, Netherlands (Received 3 September 1980. Revised 8 December 1980. Accepted 13 March 1981) Summary-Several possible models for plasmas, and their fundamental background, are discussed. The recent literature on investigations of fundamental plasma models and plasma parameters is reviewed.

A plasma can be defined as a gas or vapour in a partially ionized state, and thus is composed of atoms, molecules, ions and free electrons.’ Some of the atoms, ions and molecules of the plasma will be in the excited state. PLASMA MODELS

Thermal equilibrium (T.E.)

The simplest model for a plasma is that of thermal equilibrium. It is governed by the principle of microreversibility, which means that every energy-transfer process is exactly balanced by the reverse process2 For instance, the number of transitions per unit of time from a level p to a level q, by absorption of radiation, is exactly the same as the number of transitions per unit of time from level q to level p, with emission of radiation. The same holds for radiationless transitions between levels p and q, caused by collisions. When a plasma is in T.E. all microscopic states can be calculated from the temperature, which is the only variable. Thus we can deduce the following. (a) The number of particles dN with velocity between c and c + da is given by Maxwell’s law:

there is an infinite number of levels with finite, hardly differing energies before the ionization limit is reached. However, in practice Z(T) does not become infinite, because the electric field due to neighbouring particles reduces the ionization limit so that the number of energy levels becomes finite. (c) The degree of ionization is given by the Saha equation, which gives in principle the relation between the ionization equilibrium constant Ki( T), the ionization energy Ei and the temperature T: K,(T) =

(2nm)2’3(kT)5’2 22, h3

Z,e

_EI,kT (3)

where Zi and Z, are the partition functions for the ionic and atomic states respectively. (d) The emission intensity of a spectral line for the transition from level q to level p can be calculated from Einstein’s formula: I

4-p

(4)

where NO is the number of particles in the ground state, f is the oscillator strength, g,, is the statistical weight and E, the energy of level q, co the dielectric constant and 1 the wavelength. Local thermal equilibrium (LT.E)

where M is the atomic weight of the particles considered, N the number of those particles, and k Boltzmann’s constant. (b) The number of particles (NJ in a certain level p is calculated from -E,ikT

where Z(t) = 1 gp e-E@, Z(T) being the partition

function, gp the statistical weight and E, the energy of level p. Theoretically * Present address: T.N.O., Voedingsonderzoek,

Centraal Instituut voor Utrechtseweg 48, Zeist, Netherlands.

Perfect thermal equilibrium never exists in labora.ory plasmas, for two reasons. First, in a laboratory plasma, there is a clear temperature gradient, because the centre is at a temperature of, e.g., 4000 K, whereas a few mm or cm outside the centre of the plasma the temperature is room temperature. Therefore the plasma could be considered to be built up of volume elements at different temperatures,‘.’ each volume element being in thermal equilibrium. Secondly, as a consequence of the small dimensions of the plasma, a large part of the emitted radiation escapes without being reabsorbed. This causes a relative overpopulation of the ground state, because the emission process is not balanced by self-absorption. The extent of the deviation from Boltzmann’s law thus caused is determined by the ratio of radiative 629

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630

P. F. E. VAN MONTFORT and J. AGTERDENB~~

and collisional de-excitation processes. For sufficiently high particle concentrations (for which deexcitation is mainly collisional) the laws for thermal equilibrium still hold in good approximation. Partial local thermal equilibrium: the thermal limit

For some elements the radiative transition probability increases and the impact cross-section for collisions with electrons decreases for levels with low quantum numbers (i.e., near the ground state).3 With low electron densities, the radiative de-excitationswhich cause a further depopulation of the excited states--are so predominant for levels p with $rincipal quantum numbers below a certain level, the “thermal limit”, that these levels can no longer be considered to be in L.T.E. For levels q with principal quantum numbers above the thermal limit, the relations for L.T.E. still hold. Under these conditions a plasma can be considered to be in partial local thermal equilibrium (P.L.T.E.). In some of the following sections, methods are described for quantifying, for analytical plasmas, the degree of deviation from (P.L.)T.E.; these methods are only tentative, however. The corona model

At very low electron concentrations (n,), two energytransfer processes, not described above, take place to an increasing’extent. They are: (1) spontaneous emission of radiation; (2) radiative recombination of particles.4 For electron concentrations below 10”/cm3 and plasma temperatures above lo4 K, the so-called corona model can be formulated. Three-particle recombination : P_+l,p + e + e+P,,

+ e

(5)

(z is the charge of the particle P, and p and q are the energy levels) plays only a minor role in this model because of the low electron concentration. Much more important is radiative recombination: PI + I .p + e -

Pz,q+ hVcontinuum

(6)

The rate of this process is proportional to the electron concentration. The ionization equilibrium is therefore a balance between radiative recombination (6) and ionization by collisions of electrons with the atoms (P,., + e+PZ+l,Q + 2e). The ions are mainly in the ground state because their average excitation energy is larger than the energy of the electrons. The population of the excited levels is determined by a balance between the rate of collisional excitation from the ground state and the rate of spontaneous radiative decay.’ So far, plasmas conforming to the corona model have not been applied in analytical chemistry. Radiative ionization recombination (R.I.R.) model6

The R.I.R. model, applied to a low-pressure hydrogen radiofrequency plasma, postulates two groups of

electrons, i.e., one group with a relatively high density and low energy and the second group with a relatively low density and high energy. The total energy distribution of the electrons becomes the sum of two Maxwell distributions. In the case of a hydrogen plasma, the high kineticenergy electrons (e) cause ionization according to: H+e+H++e+e

(7)

For levels with principal quantum numbers below the thermal limit, recombination (and hence population of the excited atomic levels) is due to the low kineticenergy electrons (e) according to: Hi + e-+ H, + hvcontinuum

(8)

followed by: H4-+ H, + hv,,,

(9)

For levels with principal quantum numbers above the thermal limit the atoms are in thermal equilibrium with the ionization level, so the occupation of these levels is ruled by the reverse of reaction (7). For hydrogen (z = 1) the expression for the thermal limit given by Griem’ becomes n,,, = 126n;2/17~$~‘17exp[

&]

(10)

where Vi is the ionization energy for hydrogen, k is Boltzmann’s constant and n, and t, are the concentration and temperature of the low-energy electrons. Brassem et a1.7 give the same expression but with a printer’s error in the index to n,. RECENTPRACTICALINVESTIGATIONS ON THE PLASMAMODELS Several types of modern analytical plasmas can be distinguished. The radiofrequency plasma, which can be capacitively or inductively coupled, the plasma jet, which is a modified arc, and the microwave-induced plasma (M.I.P.) which is fed by a microwave field of 2450 MHz. The M.I.P. with working pressure 0.1-0.5 mmHg

Brassem et al.’ calculated, for a O.ZmmHg argon or helium M.I.P. to which 1% of hydrogen has been added, the H, and H, emission intensities according to the L.T.E. and R.I.R. models. To do this they had to calculate [H,] (the concentration of hydrogen atoms in the 9th level), from which the emission intensities can easily be found from I,, = A,, hv,, [Hs] (where A,, is the transition probability). For levels below the thermal limit, three possible R.I.R. reactions are assumed: H,+e+H++e+e Y

(11)

where e is-a high-energy electron and e is a lowenergy electron, kb is the rate constant for the ioniz-

631

Analytical high-frequency plasmas ation process, and k,” is the rate constant reverse process, H+ + e&

H, + hvconrinuum

where k; is the rate-constant combination, and H, A,,

for the

(12)

for this two-body

H, + hv,,

(13)

where A,, is the transition probability. The reactionrate constants can be calculated according to gchliiter’s expression.8 From these constants [H’] can be calculated, assuming that a steady state (d[H+]/dt = 0) exists. After substitution for [H’] in the reactions above, [H,] and hence I,, can be found. In order to calculate Schliiter’s reaction-rate constants, however, the four parameters N,, T,. n, and T, have to be known, where n and T are the population density and temperature, respectively, for the species indicated by subscript. T, and n, can be directly measured with the double-probe system and N, and T, have to be estimated. The experimentally measured H, and H, line intensities were higher by a factor of lo8 than the values calculated from the thermal models with an assumed electron temperature of about 4OOOK, and about higher by a factor of 10’ than the intensities calculated according to the R.I.R. model described above. The conclusion can be drawn that the thermal model does not hold for this plasma and that the R.I.R. model gives considerable improvement. It is noticed here that the deviation from linearity between the H concentration and the H, and H, emission intensities is more important than suggested by Brassem et al.’ Hence the value of the above-mentioned factors is questionable. The M.I.P. with working pressure l-25 mmHg

Busch and Vickers’ studied an argon and a helium M.I.P. (325 mmHg) and measured, inter ah, the following parameters. The electron temperature was measured with the double-probe system;“.” the spectroscopic temperature was determined by measuring the ratios of several line intensities; the electron density was determined by measuring positive currents ([e-l = [ions]) and finally the concentration of metastable argon atoms [Arm] was determined by atomic absorption. A very large discrepancy was found between the spectroscopic and electronic temperatures of the argon M.I.P. (4200K and 33,000 K respectively). The following explanation of this discrepancy was propose& The double-probe method gives the electron temperature of only the high kinetic-energy electrons, but the electron density measured was the sum for the low and high kinetic-energy electrons. The excited levels from the ionization limit down to the thermal limit are predominantly collisionally populated (by recombination) when the electron density is

low. This results in a Boltzmann partition corresponding to a temperature of about 4500K. The bound electrons are in equilibrium with the electrons of low kinetic energy (and at high density) and the high kinetic-energy electrons play no part in the recombination process. It was also found that the measured electron temperature increased with the ionization potential of the noble gas, because the plasma can only exist if sufficient ions are produced to balance the loss by recombination, etc. If the plasma gas has a high ionization potential, high kinetic-energy electrons, i.e., a high electron temperature will be required to maintain the plasma. Metastable argon atoms (Arm) were also found to play a part in the ionization process: Arm + X-+Ar + X+ + e

(14)

where X is an atom with a lower ionization potential than the excitation potential of the metastable argon. An increase of the line intensities with increased applied microwave-power, IV, was explained as due to the increase of the electron pressure with increasing W. Because of the electroneutrality law, the number of positive ions will also increase, SO the possibility for radiative recombination increases. When metal atoms (e.g., mercury) were added to the plasma, the atomic lines of the metal were emitted with high intensity. It was found that the intensity of the mercury lines in the argon plasma was greater than in the helium plasma. This is in agreement with the fact that n,(Ar) > n,(He) (n, is the sum of the low and high kinetic-energy electrons). Avni and Winefordner” performed double-probe measurements on pure argon, helium and nitrogen M.I.P.s, for a number of plasma parameters: the electric field (E), electron (i,) and ion (ii) current densities, electron density (n,), electron temperature (T,), electron conductivity (a,), ion density (ni), electron mean free path A,, electron (p,) and ion (hi) mobilities, and ion-diffusion coefficient (Q). These parameters could be either directly measured or calculated. The gas temperature of the plasma was determined by the line-reversal method directly from the intensities of the spectroscopic lines. The authors criticised Busch and Vickers for calculating the spectroscopic temperature from argon lines with levels far above the ground-state level. According to Avni and Winefordner a considerable part of the process of population of these levels takes place non-thermally e.g. by Ar+ + e+Ar*. The closer the energy level of the line involved to the ground-state level, the greater is the probability of thermal population. The mean electron density (E,) was not taken equal to the ion densitywhich can be easily measured-but was calculated from

&=-_

2p

dT -

eperE2 ’ dr

(15)

632

P. F. E. VAN MONTFORTand J. AGTERDENBOS

where e is the charge on the electron, p the thermal conductivity, and r the distance from the axis of the cylindrical plasma. In this way a discrepancy was found between q and n, (ni > n,); this would apparently result in a net space charge and thus in an electrical field. At low plasma pressures (< 4 mmHg) a very strong increase in the electron temperature was found when a few micrograms of metal were added. This was explained by the fact that the bombardment of the metal atoms by argon ions releases electrons of high kinetic energy. The gas temperatures measured according to the line-reversal method were in agreement with the gas temperatures found by Bu’sch and Vickers, and about one order of magnitude lower than the electron temperature, indicating non-L.T.E. behaviour. Avni and Winefordner further found an increase in the electron temperature with applied microwave power, in contradiction of the work of Busch and Vickers. However, when comparing different authors’ results it should be realized that the power values read on microwave generator meters may often be in error, as was shown by Jiitte and Agterdenbos.13 Also in contradistinction to Busch and Vickers, Avni and Winfordner found an increase in the electron concentration with the working pressure, but no increase of the ion concentration, the latter being explained by a decrease of the net (positive) electrical field. Finally” the mean electron density iic in the argon plasma was calculated from the Elenbaas-Heller energy-balance equation for steady-state plasma conditions: div (p grad T) + j,E = 0

Me+ + e + Me* + hv,,,, Ar”+Me-+Ar+Me++e

(17)

electrodeless discharge lamp

Cooke et al.” and Jansen et al.” have investigated the spectral line profiles in a closed M.I.P. (an EDL) at 2-15 mmHg argon pressure, with a few pg or mg of a volatile element, but have not considered the fundamental mechanism of the plasma. Browner and Winefordner” investigated EDLs with external heating of the quartz walls of the lamps. It was found that the spectral emission intensity was proportional to n,nL (n, = density of the radiating atoms in the ground state, n: = density of electrons with electron energies greater than the energy of the upper level of the transitions). Plots were made of the radial output l?,i3/gf (B, is the corrected radiance, g the statistical weight of the upper level and f the emission oscillator strength), us. upper energy level of the electronic transition. From these plots it appeared that the mean electron energy was below 3 eV. The M.I.P. at atmospheric pressure

Beenakker18 used a specially designed microwave cavity to create a helium plasma at atmospheric pressure. An important part in the excitation mechanism of this plasma is supposed to be played by the reactions of metastable atoms. Four types of reaction are suggested : Am+X+A+X++e (22) A” + X+-A

+ X2+* + e

(23)

A”+X-+A+X* A” + X+ +A

(24) + X+*

(25)

(A” is a metastable atom of the support gas A, and X is the analyte). Of course it is necessary that E(A”) > Ep for the ionization and E(A”) r Ezxc for the excitation. The low kinetic-energy electrons are especially effective for the recombination: e+A+X+-+A+X* The high plasma:

kinetic-energy

(26) electrons

sustain

e+A+A++2e

the (27)

or can give direct excitation such as

(18)

e+X--+X*+e

(1%

e + X+-+X+*

they now also proposed:

(28) + e

(2%

Ions can also be involved in the excitation process:

MeCl+e+Me++Cl+e+e

(20)

and He” + MeCl+

The sealed M.I.P.--the (ED4

(16)

No agreement was found between the value of n, calculated from equation (16) and the n, value from the double-probe measurements. This indicates that a steady state is not reached in the argon plasma. Kawaguchi et 01.‘~ studied a low-pressure helium M.I.P. into which metals (Me) were vaporized from a filament. From the analytical curves obtained from these metals when potassium chloride or other salts were added the authors gave a working hypothesis for the plasma mechanism which differed from the usual R.I.R. model as follows. In addition to the usual R.I.R. reactions: Me+e-+Me++e+e

lo4 K) electron temperature of the plasma (the energy of He” is much higher than that of Arm).

He + Me+ + Cl + e

(21)

The new (highly energy-consuming) reactions proposed are possible because of the very high (5 x

A+ + X-A Some characteristics M.I.P. are:

+ X+*

of this atmospheric

(30) helium

(1) line &ctra of all elements present are found (e.g., chlorine: Cl+ lines);

Analytical high-frequency plasmas (2) the same analysis lines occur at reduced pressure and at atmospheric pressure; (3) only the ion lines of S, P, Cl, Br and I with excitation energies in a limited range (12.3-15.9 eV) are found; (4) no ion lines for C, N, 0 and F are found (excitation energies > 20 eV). Considering the energies of the Hey metastable species (13.3-15.9 eV) Beenakker supposes that the principal excitation mechanism for ion-line emission is He? + X+ -+X+* + 2He

(31)

For the argon M.I.P. only the ion lines of C, P, S, and I are found, probably because the excitation energy of the ions is greater than the excitation energy of Arm. Of course recombination of X+ with low-energy electrons can be expected, resulting in atom-line emission. Other considerations on M.I.P.s and 1.C.P.s

Greenfield et al.19*2o measured different temperatures of an I.C.P., viz. kinetic gas temperature, electron temperature and excitation temperature. With increasing differences between the values of these temperatures an increased deviation from L.T.E. occurs. In plasmas with very high gas temperatures high continuum radiation I, is found because I, = Knz/Tf

(32)

and n, increases strongly with the temperature. Aldous et aL2’ found that for a metal introduced into an argon M.I.P. the metal signal increased with applied microwave power. They explained this as due to an increase in the plasma’dimensions and not an increase of plasma temperature and electron pressure. Eckert” studied a closed rf-I.C.P. and calculated the plasma temperature from the intensity of two lines (1 and 2) according to: (33)

where A = transition probability, V = excitation potential, e = electronic charge, and g is the usual statistical factor. From this formula it was found that the temperature in the plasma ranged from 6450 to 8740 K. It is remarked here that Eckert’s assumption of L.T.E. in this case’ seems doubtful. Eckert2j also calculated the radial temperature distribution in a closed atmospheric-pressure argon rf-I.C.P. with an rf power of 530W and 25 MHz, using the Elenbaas Heller energy-balance equation which in its general form is aE2 = V(KVT) = 0

(34)

where u = electrical conductivity, K = thermal conductivity and E = electrical field. The assumptions were made that the plasma is symmetric and in L.T.E., that radiation losses and flow circulation effects can be neglected, and that the entire rf power dissipated in

633

the plasma volume is lost by static heat conduction to the walls. From the calculations it appears that the temperature distribution in the plasma is not quite homogeneous. A hot spot (6000 K) is present in the plasma and in the region of the wall the temperature decreases to 1OOOK.Haarsma et a1.24 gave a critical review of the preparation and use of an electrodeless discharge lamp (EDL) but did not mention the fundamental aspects: they stated, however, that a plasma will be extinguished if the concentration of quenchers (e.g., H,O, O2 and N2) reaches a critical value. Kirkbright and Ward2’ calculated the number of particles to be expected in the viewing zone of an I.C.P., and thence the intensity to be expected for the analysis lines (they assumed L.T.E. to exist). They also discussed the background continuum radiation in the plasma. Three kinds of background radiation were considered: bremsstrahlung, cyclotron radiation and real blackbody radiation. Experimentally? it appeared that the background radiation of an I.C.P. with T = 8250 K (Tkin) mainly consists of bremsstrahlung (I#‘,). The following expression was found to hold:

where p = refractive index of the plasma (z l), G,,(T) = the Gaunt factor (z l), N, and Ni = electron and ion densities, Z = atomic number. For a plasma with a core volume of 8 cm3, T = 9000 K and N, = 2 x 10’5/cm3, it can be calculated from the formula that Wa reaches the considerable value of ca. I75 w. Henriksen et aLz6 gave a theoretical calculation of the electromagnetic fields involved in cylindrical electrodeless discharges (1.C.P.s). No conclusions about a discharge mechanism classification were given. Novak et al.” have considered the effect of pulsed rf-excited metal EDLs on ‘the radiant output, but drew no mechanistic conclusions. Eckert2s has given a theoretical treatment of the analytical properties of a sealed rf-argon-I.C.P. into which metals are introduced. The plasma was considered to be cylindrical and in L.T.E. With the temperature field of the plasma, as calculated before,22 the spatial distributions of trace element atoms and ions and the specific line intensity emitted from these particles were calculated. The number of metal atoms (Me) in a volume element was calculated from the ratio n(Me)/n(Ar) and the gas laws. The density of electrons, atoms and ions as a function of temperature was calculated by solving the combination of (1) the Saha equation, (2) the charge-balance equation for the plasma and (3) the mass-balance equation. From Einstein’s formula [equation (4)] the emission coefficients and thence the specific and total power emitted by the Me lines in the plasma were calculated for magnesium. It appeared that the emission coefficient of the Me ion-line increased monotonically with temperature, whereas the emission coefficient of an atomic

634

P. F. E. VAN MONTFORT and J. AGTERDENBOS

line passed through a maximum in the particular temperature range where the transition from metaldominated to gas-dominated ionization occurred. The temperatures associated with this maximum were called “norm temperatures”. It was noticeable that in certain cases the power emitted per particle could be even higher (8.4 x lo-” W) than the shot-noise level (- lo-i5 W) of a photoelectric detector. From the data obtained, analytical curves and detection limits could easily be calculated. Finally, it should be mentioned that no wall effects, i.e., absorption or release of analyte elements, were considered. Barnes et aLz9 have calculated temperature and velocity profiles for a nitrogen I.C.P., but drew no conclusions about the mechanism. Recent considerations on the I.C.P. The role of metastable helium and argon species in the excitation of atoms in an M.I.P. was described above. For an I.C.P. a similar excitation process had been suggested earlier by Mermet.30 The problem has been investigated in more detail by Boumans and de Boer.31 The reactions suggested as occurring in an argon I.C.P. are: Ar”‘+X+Ar+X++e

(36)

Arm + X--rAr + X+* + e

(37)

When L.T.E. is assumed, the intensity ratio of ion and atom lines (Zi/l,) can be calculated as follows.

0 Ii

I,

LTE

= 7-3'2 ~0-5040(V10"+V,I-

V,.)/T

where gp and V, (eV) are the statistical weight and excitation energy of the upper level of the transition q-p, A,, (set-‘) and &,, (A) are the corresponding transition probability and wavelength, and i and a refer to ions and atoms respectively. It is then possible to calculate (Ii/lakra and to formulate the ratio of the experimental and L.T.E. intensity ratios as the deviation from L.T.E. With n, = 1016/cm3 and Tki, = 5850 K the deviation reaches a value of lO-103. The following reaction is therefore supposed to take place Ar”’ + e+Ar+

+ 2e

(39)

This means that Ar’” also acts as an “ionizant”, so n, reaches a higher value than that calculated by assuming L.T.E. This is in agreement with the overpopulation of the excited levels. Furthermore it appeared that the introduction of an easily ionizable element M in the plasma caused only a small change in n, and in the concentration of Ar”. This can again be explained in terms of metastable species as follows. The system strongly acts as a buffer according to: M+Ar”‘-+M++Ar+e

(40)

and M+e+M++2e

(41)

giving Arm + eeAr+

+ 2e

(42)

The loss of metastable species through reaction (40) (and thereby increase in n,) is compensated by recombination of the liberated electrons with Ar+ to form new metastable species [reaction (42)]. The points mentioned above can be considered as a working hypothesis for explanation of the following facts: (i) the electron density is much higher than that calculated for L.T.E., (ii) n, and the concentration of Arm are only slightly influenced by easily ionizable matrices, (iii) the ratio of the intensity of the ion lines to the intensity of the atom lines is much higher than that calculated for L.T.E. [because of reaction (39)]. Kornblum and De Galan3’ have discussed the theoretical aspects of temperature measurement in plasmas (especially the I.C.P.). They have also given some theoretical criteria for classifying the excitation mechanisms in different plasmas. The criterion applied for the presence of T.E. in a d.c. arc was:

Tc - Tkin ----------= T,

M i,E
(43)

(1, = free path of the electron, m, = mass of the electron and M = mass of the atom involved). Substituting the values determined for 1 and E yields for an ICP T, - Tkin = 800 K (T, being 6500 K). This difference does not preclude T.E. The experimentally observed differences are much larger (4000 K), so this criterion is obviously not directly applicable to the I.C.P. The criterion for L.T.E., taken from Griem,33 was n, 2 ~.OJ’T,(AE)~

(44)

where AE is the energy-level difference (cm- ‘) for the line involved. This inequality holds if collisional deactivation exceeds radiative deactivation by an order of magnitude. The energy difference AE is decisive here. For instance, the excitation energy of the argon lines used, with respect to the ground state, was 124 x lo3 cm- ’ (1 eV = 8.7 x lo3 cm-‘), which would require a value of n, > 5 x 101’/cm3 in equation (44). This is much higher than was actually observed in the I.C.P. However, the energy difference between the upper argon levels was only 8 x lo3 cm-‘, corresponding to an electron density of only 1.3 x 1014/ cm3, which is even lower then actually measured. It was concluded that the transitions between the upper argon levels are likely to be in L.T.E. It is obvious that the criteria mentioned above do not show clearly the extent of T.E. to be expected in an I.C.P. Walters et al.34 reported measurements of excitation, ionization, electron temperatures and positive ion concentrations in a 144-MHz argon or neon I.C.P. In this plasma, the electron temperature T,, measured with Johnson and Malter’s probe system,”

Analytical high-frequency plasmas was again found to be much greater then the excitation temperature (T,) calculated according to:

where E = energy of an upper state level, A = Einstein’s coefficient of spontaneous emission, I = wavelength of the line involved and E = integrated spec-’ tral radiance. Also, the ionization temperature, calculated according to Saha, was found to be much lower than T,. Both facts indicate a serious deviation from L.T.E. for such an I.C.P. When a small amount of a metal (Tl) was added to the plasma, a significant increase in T, and the positive ion concentration was found; obviously the metal acts as a releasing agent. Finally it should be mentioned that there is a perfect analogy between the results of this work and the Busch and Vickers investigations’ on the M.I.P. REFERENCES

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