Temperature and velocity distributions in an inductively coupled plasma

Spectr~himica Acta, Vol. 36B, PP.81 WJ101 @ Pergamon PressLtd.. 1981. Printed inGreatBritain

Temperatire and velocity distributions in an inductively coupled plasma RAMON M. BARNES and

ROBERT

G.

SCHLEICHER*

Department of Chemistry, GRC Towers, University of Massachusetts, Amherst, MA 01003,

(Received

4 August

U.S.A.

1980)

A~~~omputer simulations of inductively coupled plasma discharges (ICP) with flow patterns similar to those found in spectrochemical analysis were reported previously. In this investigation temperature and velocity distributions are measured under conditions which allow direct comparison with computer calculations for pure argon central gas flows without solution aerosols. Based upon these comparisons, a refined ICP gas flow model is proposed and its application provides agreement within experimental error between measured and calculated velocity and temperature profiles in most regions of the discharge.

1. INTRODUDION ABIL.ITY to model an inductively coupled plasma (ICP) discharge provides an efficient approach to the simulation of experimental conditions during the testing of new designs or evaluating of operating conditions for spectrochemical analysis. Models based upon early work of MILLER and AYEN [l] were described previously for argonand nitrogen-supported ICP discharges operating over a 15-70 MHz frequency range and 0.5-5 kW power domain with the injection of dried powder aluminum oxide sample into torch configurations commonly employed in spectrochemical analysis [2-51. At that time few experimental measurements of the temperature or velocity distributions in spectrochemical ICP discharges were available, and models of central stream flow were based upon empirical observations. In the meantime, spatial temperature and atom and electron number density distributions were reported by KALNICKY et al. [6,7], MERMET et al. [S-12], KORNBLUM and DE GALAN [13,14], and ALDER et al. [15]. Experimental velocity distributions, in contrast, have not been reported for a spectrochemical ICP, although KLUBNIKIN et al. [l&17] and others as cited in references [18] and [19] have reported velocity distributions in non-spectrochemical ICP discharges.

THE

*Present

address:

Instrumentation

Laboratory,

Jonspin

Road,

Wilmington,

MA

01887,

U.S.A.

[II R. C. MILLER and R. J. AYEN, J. appl. Phys. 40, 5260 (1969). t21 R. M. BARNES and R. G. SCHLEICHER,Spectrockim. Acta 30B, 109 (1975). c31R. M. BARNES and S. NIKDEL, 1. appf. Phys. 47, 3929 (1976). [41 R. M. BARNES and S. NIKDEL, Appf. Specfry. 30, 310 (1976). [a C. D. ALLEMAND and R. M. BARNES, Appl. Spectry. 31, 434 (1977). [61 D. J. KALNICKY, R. N. KNISELEY and V. A. FASSEL, Spectrochim. Acta 30B, 511 (1975). c71D. J. KALNICKY, V. A. FASSEL and R. N. KNISELEY, Appf. Spectry. 31, 137 (1977). Bl J. F. ALDER and J. M. MERMET, Spectrochim. Acta 28B, 421 (1973). [91 J. JAROSZ, J. M. MERMET and J. ROBIN, C.R. Acad. Sci, Ser B 278, 885 (1974). t101 J. M. MERMET, S~~tro~him. Acru 30B, 383 (1975). and C.TRASSY, [Ill M. H.ABDALLAH,R.DIEMIASZONEK,J.JAROSZ,J.M.MERMET,J.ROBIN

Anni. C&m. Acta 84, 271 (1976). [I21 J. JAROSZ, J. K. MERMET and J. P. ROBIN, Spectrochim. Acta 33B, 5.5 (1978). t131 G. R. KORNBLUM and L. DE GALAN, Spectrochim. Acta 29B, 249 (1974). [I41 G. R. KORNBLUM and L. DE GALAN, Spectrochim. Acta 32B, 71 (1977). El51J.F.ALDER, R. M. BOMBELKA and G. F.KIRKBRIGHT, Spectrochim. Acra 35B, I63 (1980). [lb1 A. A. VOROPAEV, S. V. DRESVIN and V. S. KLUBNIKIN, High Temp. 7, 580 (1969). r171 V. S. KLUBNIKIN, High Temp. 13, 439 (1975). PJusma. Iowa State University El81S. V. DRESVIN (Editor) Physics and Technology of Low-Temperature Press, Ames. IA (1971). [I91 V. KH. GOYKHMAN and V. M. GOL’DFARB, Plasma Chemical Reactions and Processes, (edited by L. S. POLAK ) Chapter

10. NAUKA

Publishing House,

ECKERT and TH. CHERON, fCP Inform.

Newlett.

Moscow

(1977);

4, 537 (1979);

translated into English by H. U.

5, 15 (1979).

R. M. BARNES and R. G. SCHLEICHER

82

Determination of radial temperatures profiles in argon discharges using both spectroscopic and enthalpy probes have been reviewed, however, all temperature diagnostics of spectroanalytical ICP discharges were made spectroscopically generally with the aid of spectroscopic tracer elements introduced as solution aerosols [12, 15,201 or molecular emission [8, 13, 21, 221. For the present study, spectroscopic tracer elements added as solution aerosols containing aqueous or organic solvents perturb the discharge temperature, electron number density, and plasma transport properties sufficiently to invalidate the present desired comparison with model calculations. Furthermore, the analyte injected in the aerosol gas flow is spatially confined and permits diagnostic measurements only near the center line of the discharge [7, 141, and the addition of water vapor from the aqueous aerosol increases the electron density and excitation and ionization temperatures in the central channel of the analytical observation region [ 15,231. This investigation requires the measurement of temperature distributions in pure argon to verify model calculations, which limits the choice of temperature diagnostic techniques. The experimental results obtained in a low-power, 27 MHz argon ICP by spectroscopic measurements using only argon species permit direct comparison with computer calculation of temperature and velocity distributions. 2. EXPERIMENTAL 2.1

Temperature

measurements

Three methods appear most suited for temperature determinations in a pure, atmospheric pressure argon ICP: (a) radiance of a single atomic line; (b) spectral radiance of the continuum; and (c) atomic line radiance ratio. Of these methods, the determination of absolute argon line or continuum intensities are used generally for non-spectrochemical ICP discharges [13, 19, 19, 24-281, whereas the atomic or ionic line radiance ratio “two-line” or “slope” methods are applied to both physical and analytical ICP discharges r&15,29]. Thermometric species, including iron [6, 10,151, titanium [lo, 12, 301, vanadium [12], hydrogen [31], and zinc [14, 231 are commonly employed, although ICP temperatures are also derived from relative argon line intensity measurements [ 10, 121. The atomic line radiance ratio approach in pure argon ICP discharges is sensitive to the accuracy of the measured line ratio or slope if the difference between the upper energy level is small. For most argon lines that can be measured practically, the energy difference in upper levels is less than 0.4 eV. This approach is also sensitive to uncertainties in argon transition probabilities which are usually not known to better than +15%. In a preliminary experiment with four argon lines measured in a 450 W discharge, temperatures varied between 4656 and 6760 K for different sets of transition probabilities. In agreement with a similar experiment performed by others [lo, 12, 141, we conclude that this technique is unsatisfactory when applied to the determination of temperatures in a pure argon ICP. MERMET showed that poor agreement among different sets of transition probabilities could lead to variations greater than 1000 K for [ZO] J. JAROSZ and J. M. MERMET, J. Quant. Spectrosc. Radiat. Tranfer 17, 237 (1977). [21] P. B. ZEEMAN, S. P. TERBLANCHE, K. VISSER and F. H. HAMM, Appl. Spectry. 32, 572 (1978). [22] M. H. ABDALLAH and J. M. MERMET, J. Quant. Spectrosc. Radiat. Transfer 19, 83 (1978). [23] P. W. J. M. BOUMANSand F. J. DE BOER, Specrrochim. Acra JlB, 355 (1976). [24] F. MOLINET, C.R. Acad. Sci. Paris, Ser. I? 262, 1377 (1966). [25] A. D. STOKES, Brir. J. appE. Phys. D., Appl. Phys. 4, 916 (1971). [26] P. D. SCHOLZ and T. P. ANDERSON,J. Quant Specrrosc. Radiar. Transfer 8, 1411 (1965). [27] S. L. LEONARD, J. Quanr. Specrrosc. Rudiar. Transfer 12, 619 (1972). [28] V. M. GOL’DFARB, A. V. DONSKOI, S. V. DRESVIN and V. S. KLUBNIKIN, Teplofiz. Vys. Temp. 5, 549 (1967). [29] K. S. .DRELLISHAK, C. F. KNOPP and A. B. CAMBEL, Phys. Fluids 6, 1280 (1963). [30] B. TALAYRACH, J. BESOMBES-VAILHE, and H. TRICHE, Analusis 1, 135 (1972). [31] K. VISSER, F. M. HAMM, and P. B. ZEEMAN, Appl. Specrry. 30, 34 (1976).

Temperature

and velocity

distributions

in an inductively

coupled

83

plasma

the determination of ICP temperatures using Ar I lines and the two-line This technique is also sensitive to errors introduced by the Abel inversion

technique. procedure

[W. Methods based upon the absolute measurement of the radiance of an atomic line [26,27] or the spectral radiance of the continuum [13,25] are less sensitive to measurement errors than the radiance ratio approach. They are not necessarily more accurate, because absolute transition probabilities are required in the atomic line approach, correction factors are needed for the continuum method, local thermodynamic equilibrium is assumed, and some error is introduced in the spectrometer calibration. Also temperatures calculated from the spectral radiance of the argon continuum are critically dependent upon the free electron number density. In this investigation, the single-line radiance method is employed and, for comparison purposes, some temperatures are also calculated from continuum intensity measurements. Radial temperature profiles are determined by measuring the absolute intensity of the Ar I 430.01 nm emission, and some temperature profiles are determined by measuring the absolute intensity of the continuum at 533.0 nm in the regions of the discharge near the induction coil. Beyond the coil region, the continuum is weak, and accurate measurements cannot be obtained. Total lateral profiles are determined for the Ar I 430.01 nm emission at several axial positions. At each position the corresponding lateral continuum radiance profile is also measured by resetting the wavelength slightly from the argon wavelength. Measurement of the background intensity at one wavelength, either above or below the 430.01 nm wavelength, was sufficient for background corrections, since the background is virtually unchanged over this small range of wavelengths. The continuum profile is subtracted from the total (i.e. line plus background) lateral profile to obtain net lateral line radiance profiles. Radial profiles are measured at different axial positions above the induction coil, and a single profile is acquired at the center of the discharge between the windings of the induction coil. The geometry of the induction coil and reference points used to fix axial and radial positions are indicated in Fig. 1. Continuum lateral radiance profiles at 533.0 nm are measured similarly. The net lateral radiance profiles are reduced to radial emission coefficient profiles using the Abel integral equation and the numerical method developed by NESTOR 9mm

0

9mm

Radial position

0 mm -7 mm

Fig. 1. Geometry

of induction

coil, plasma

torch,

and reference

points.

R. M.

84

BARNES and R. G. SCHLEICHER

and OLSEN [32] to integrate the inverted Abel equation. The experimental data are fitted by a least square curve technique prior to inversion to prevent magnification of data scatter by the numerical method [12]. Radial temperature profiles are calculated using the radial emission coefficient profiles by assuming LTE and equation (1)

in which h is Planck’s constant, c the speed of light, A the spectral transition wavelength, g4 the statistical weight of the upper state, A the transition probability, Zi the partition function of the jth species, fii the number density of species j, E, the energy level of the upper state, k the Boltzmann constant, and T the temperature. Equation (1) can be employed to determine the temperature of a plasma in LTE if the spectral line constants are known, and equilibrium values of 1~and Z as a function of temperature are utilized. The values of ADCOCKand PLUMTREE[33] used in the present study are in good agreement with more recent measurements made by MALONEand CORCORAN[34]. The continuum emission coefficient is also calculated [35) with the assumption that ion and electron number densities can be obtained as a function of temperature from tabulated equilibrium values [29]. Temperature profiles are reported for ICP discharges operated at 0.46 and 0.75 kW for central gas flow rates between 0 and 1.35 l/min. 2.2 Velocity determination Of the available approaches for the determination of ICP gas velocities [18], two techniques are employed in the present investigation: stagnation pressure measurement and photography. Impact (Pitot) tubes are commonly applied to obtain fluid velocities derived from measured stagnation pressure by means of the Bernoulli equation. CARLETONand KADLEC [36] developed a model to relate the pressure measured with a water-cooled impact tube in a plasma stream to the free-stream plasma velocity. Their model includes the effects of viscosity and heat transfer, and CARLETON[37] also showed for a plasma flowing around a hemispherical-tipped cylindrical probe that the difference between the measured impact pressure and the free-stream pressure can be expressed as correction terms in the Bernoulli relationship. Previously CHASE [38], DUNDAS[39], KLUBNIKIN1171, and others [18,19] measured stagnation pressures in induction discharges but generally without central argon carrier gas flow. This report provides data for the axial velocity distribution in a spectrochemical ICP discharge. At the temperatures encountered in the core of an ICP, an impact tube must be internally cooled to prevent its destruction. The probe applied in this investigation is illustrated schematically in Fig. 2 and consists of three concentric stainless steel tubes. The central tube permits pressure sensing, and the annulus between the outer two tubes provides a pathway for coolant circulation. Coolant water is supplied at the top of the probe through a brass manifold protected by a water cooled heat shield (not indicated in Fig. 2). The entire apparatus is electrically insulated to eliminate current paths to ground and prevent arcing. A hemispherical brass probe tip was silver soldered to the outer and inner stainless steel tubes. A second probe tip constructed to determine the [32] 0. H. NESTER and [3.5] [36] [37] [38] [39]

H. N.

Spectrosc. Radiat. Transfer 6, 443 (1966). J. F. Bon, Phys. Fluids 9, 1540 (1966). F. E. CARLETONand R. H. KADLEC,AIChE J; 18,1065 (1972). F. E. CARLETON,Ph.D. Thesis, University of Michigan, Ann Arbor (1970). J. D. CHASE, .I.appl. Plays. 42, 4870 (1971). P. H. DUNDAS, Induction Plasma Hearing: Measurement of Gas Concentrations, Temperatures, Stug~at~~~Heads in a Binary Plasma System, NASA ContractorReport, CR-1527 (1970).

and

Temperature

and velocity

distributions

in an inductively

coupled

plasma

85

To monometer

A-4 0.4 mm

I+-3.46mmc(

Fig.

2. Water-cooled

Pitot

tube.

Enlarged sections indicate sampling tip.

two version

of machined

brass

free-stream pressure (Fig. measures pressure perpendicular to direction of gas flow. these probes, and free-stream are measured radially different axial of the discharge by translating discharge relative the fixed position the probe. tube is to a manometer with tubing and pressure head measured with micrometer mounted above open end the U-tube. radial stagnation pressure profiles obtained different axial are converted to velocity profiles congruent temperature profiles are The two of data of using corrected Bernoulli relationship [37]. dependence the velocity calculation rather weak, a 1000 error in temperature approximately a error in errors not expected situations for which is a mismatch in axial position and pressure

2.3 Equipment Equipment employed in this investigation is listed in Table 1. A 1.5-m CzernyTurner spectrometer is calibrated using a tungsten lamp (Quartzline, 650 W, General Electric) which is placed in the optical path at the ICP torch position inside a section of quartz tubing to account for the transmission loss through the ICP torch wall. The tungsten filament temperature was determined by means of an optical pyrometer (Leeds and Northrup Model 8622C). A 1 : 1 image of the ICP discharge is formed at the entrance slit of the spectrometer by a quartz lens with 203-mm focal length and 30-mm diameter. The arrangement provides a small solid acceptance angle of 4 msr, so that orthogonal geometric projections, used to simplify the Abel inversion method, reliably approximate the optical projections.

86

R. M. BARNES and R. G.

SCHLEKHER

Table 1. Experimental facilities Spectrometer

Entrance optics Detection system ICP generator ICP torch Argon supply

1.5-m Czerny-Turner, f/27, Applied Research Laboratories Modet QSP-14, reciprocal linear dispersion 0.556 nm/mm (first order)? 100 micrometer entrance and exit slits, 1 mm entrance slit height Quartz lens, 203-mm focal length, 30-mm diameter, 1 : 1 magnification of source at entrance slit Photomultiplier tube (RCA lP28), high-speed picoammeter (Keithley Instruments, Model 417), X-Y recorder (Houston Instrument, Model 2000 Omnigraphic) Modified Forrest Electronic Corp., tuned plate-tuned grid oscillator, variable frequency operated at 26.5 MHz [41] Ail quartz construction [403 with outer tube extending 32 mm above the induction coil Compressed argon (99.99%), two-stage regulation (Airco), pIasma gas flowmeter (Brooks R-6-15-B), auxiliary gas flowmeter (Brooks R-2-15-C), aerosol carrier gas fowmeter (Brooks R-2-25-C)

The ICP torch configuration studied is similar to the one described by Scorr et al. [4OJ except the outer tube extends 32 mm above the induction coil to prevent air from mixing with the argon discharge in regions of interest downstream of the coil (Fig. 1). The discharge assembly is mounted on a movable stage allowing the image of the discharge to be translated in three dimensions with respect to the optical axis. 3. RESULTS

Radial temperature profiles at several axial positions are illustrated in Figs. 3-5 for power levels of 0.46 and 0.75 kW with central argon flow rates of 0 and 1.35 Urnin. In Fig. 3 temperature profiles are superimposed for short and extended confinement tube walls. Air entrainment downstream of the induction coil increases the axial temperature gradients as well as the radial temperature gradients at the edges of the discharge, and decreased temperatures at a position 20 mm above the induction coil is distinguishable In contrast, the shielded discharge temperature profiles fill the confining quartz tube, and only a 500 K decrease in axial temperature is detected between 20 and 30 mm above the coil. In the open tube the decrease found was greater than 3500 K (not shown in the figure). The introduction of argon central fIow in Figs. 4 and 56 reduces the centerline temperature. For the 0,75 kW discharge, the maximum temperature decreases by 400 K with increasing central gas ilow rate. Comparison of radial temperature profiles determined from both absolute Ar I line and ~nti~~um intensity profiles can be made with the assistance of Fig. 6. The two profiles exhibit the same shape, but the temperature values obtained from the argon line measurements are overall higher. Since the temperatures differ by less than 1% at the centerline, approximately 2% at a radius of 4.5 mm, and approximately 7% at 7 mm, the disagreement could be due to inaccuracies in the line transition probability and continuum coefficient or to non-LTE effects.

Radial velocity profiles at several corresponding axial positions for central argon flow rates from 0 to 1.35 l/min are presented in Fig. 7(a) for a 0.75 kW discharge and in Fig. 7(b) for a 0.46 kW plasma. The velocity profiles for zero central argon flow, illustrated in an enlarged view for both power levels in Fig.. 8, indicate a s~ila~ty in shape, although the magnitude of the velocities at 0.75 kW is higher than at 0.46 kW, as might be expected. The diameter of the Pitot probe prevented measurements within 1.73 mm of the confinement tube wall, but, higher velocities found near the walls in the coil region appear to decay downstream of the induction coil. [40f R_ H. Scorr,

V. A. FASSZ, R. N.

KMSELEY,

and D. E. NIXON, Anat. Chem. 46, 75 (1974).

Temperature

and velocity distributions in an inductively coupled plasma

___--__-

------

-

Z=l2

87

mm

56789

Radius,

mm

Fig. 3. Experimental ICP radial temperature profiles for power input, 0.75 kW, plasma gas flow, 10.0 Urnin, and central gas flow, 0 l/min. Dashed line indicates measurements made using a torch with short outer tube extending to 12 mm above the induction coil. The solid line represents measurements made with a long outer tube extending 32 mm above the induction coil.

As the central argon flow increases, the velocity profiles inside and just above the induction coil undergo marked changes (Fig. 7). In these regions, the velocities near the centerline increase rapidly with central argon flow rate, as indicated for two axial positions and power levels in Fig. 9. Well-defined radial velocity peaks grow along the discharge axis in the coil region as the central argon flow increases. Above the induction coil, the radial velocity profiles flatten as the central gas stream appears to spread and the plasma gas mixes with the central gas stream. As the gas streams mix, the peak velocity becomes proportional to the total flow at approximately 25 mm above the induction coil instead of the central argon flow rate. Similar trends are observed at both power levels, but higher overall velocities are observed at the higher plasma power level. Centerline gas velocities, plotted as function of axial position, are illustrated in Fig. 10 for the two discharges. For no central argon flow [Fig. 10(a)], the centerline velocity increases from approximately 5-20 m/s inside the coil for both power levels, and above the induction coil the centerline velocities remain relatively constant to an axial position of 20 mm. In this region, the velocities are higher for the 0.75 kW ICP, averaging

88

R. M. BARNES

I

and R. G. SCHLEICHER

I

I

1

I

/

9a-

IO

?-

Radius, mm

Fig. 4. Experimental

radial temperature profiles at input power, 0.75 kW, plasma 10.0 llmin, and central gas flow, 1.35I/min.

gas flow rate,

25 m/s, compared to an average of 22 m/s for the 0.46 kW ICP. At higher central flow rates [Fig. lO(b-d)], the centerline velocities are highest for axial positions near the injection orifice and decrease to approximately 20 m/s at 20 mm above the induction coil. As indicated, the axial velocities sustain their high values over a longer distance for the higher central argon gas flow rates.

N' c

bI B g

S8-

2

7-

73

4

5

Radius,

Fig. 5. Experimental

6 mm

7

I

--_-o 9-

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-7

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8

I

/

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9

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,

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radial temperature profiles at 0.46 kW for (a) no central flow, and (b) 1.35 Urnin central argon flow.

argon

mm

carrier

gas

Temperature

and velocity distributions in an inductively coupled ptasma

BOO0 Y

Continuum, ?1\

?ooom 2

0

3

4

Radius,

5

6

7

a

mm

Fig. 6. Comparison of experimental temperature profiles in 0.46-kW argon discharge with only plasma gas flow (lO.Ol/min) determined using the absolute intensity of the Ar I 430.01~nm wavelength and the absolute intensity of the argon continuum at 533.0 nm. Axial position is the center of the induction coil (-7 mm).

f

o3nhf 0 0

“i

- 30 ----A_ - 20

-

.

2

-

irllI II I (Af

(Bf

I

zt- Ik jIt I 0 I (Cf

I

(D)

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I

fR

(b)

Fig. 7. Experimental radial velocity profiles for (a) 0.75kW discharge, and (b) 0.46-kW discharge both with plasma flow rates of 10.0 l/min and variable central argon carrier gas flow rates. The central flow rates are: (A) 0 l/mm: (B) 0.46 I/min; (C) 0.90 I/min; (D) 1.35 I/mm; and (E) 1.80I/min. The axial positions are indicated to the right, and the zero velocity reference point is represented on the right-hand side for each figure.

89

90

R. M. BARNES and

R. G. SCHLEICHER

-I

Z,mm

so--

I

20lllh

T

0 0

Fig. 8. Experimental radial velocity profiles for (a) 0.46-kW and (b) 0.75kW discharges without central gas Row. Plasma flow, 10.0 I/min. Axial positions and zero velocity reference marks are indicated.

The range of ICP gas velocities determined by high-speed particle tracking photography in a 0.46 kW discharge is superimposed for axial positions between 20 and 40 mm above the coil in Fig. 10(d). Results from these particle tracking experiments provide an independent means to verify the accuracy of the Pitot tube measurements, however, only limited regions within the ICP were studied by both techniques. Particle track velocity data result in a velocity of approximately 181-t 3 m/s in the 0.46 kW discharge with a central argon flow carrying aluminum oxide particles at 1.35 l/min. When alumina particles were tracked photographically in the plasma rather than central argon stream, their velocities increased from approximately 7 m/s at the top of

150 -

. 0.75 kw ./

v) 100 > i * B J 8 (3

/

.

0.46

50 -

kw 9 /'

x;; ._____+:O_-I

0

.,' :,'

I

I 2.0

1.0 Aerosol carrier flow,

Fig. 9. Centerline gas velocity at axial position 2mm - 13 mm (solid line) and 25 mm (dashed line) as a function for 0 0.75-kW and 0 0.46-kW

l/min above the central injection nozzle of central argon carrier gas flow rate discharge.

I

I -10

0

I 0

!

IO Axiol positIon,

I

-IO

I

0

IO Axial position,

I 30

I

40

mm

1

1

I

20

30

40

30

40

I

IO Axial position,

0

I 20

mm

20 mm

Id)

Range of particle tmck

I

1

- 10

0

I IO

/ 20

Axial posltion,

mm

I

30

1 40

I

Fig. 10. Centerline gas velocity determined by Pitot tube measurements as a function of axial position for 0 0.75-kW and 0 0.46kW discharges with 10.0 lfmin plasma gas flow rate and central gas flows of (a) 0.0 Ilmin, (b) 0.46 ilmin, (cl 0.90 timin, (d) f .35 Urnin. The induction coiI extends between -15 and 0 mm.

R. M. BARNESand

92

R. G. SCHLEICHER

the induction coil to about 16 m/s at 40-50 mm above the induction coil as the gas streams mix and the particles appear to be entrained into the higher velocity central gas flow region. 4. COMPARISON OF EXPERIMENTAL Computed previously

results

for

the

[2] are compared

free

turbulent

in this section

AND

jet

COMPUTATIONAL RESULTS and

confined

with experimental

jet

models

temperature

described

and velocity

profiles.

Since the selection of an ICP flow model is a critical factor in the computer calculation, variations in the flow model are considered based upon these comparisons. An empirically modified flow model provides the best fit to the experimental data. 4.1

Temperature

Calculated and experimental ICP radial temperature are compared in Fig. 11 for central argon flow rates locations in the discharge.

profiles for a 0.75 kW discharge of 0 and 1.35 l/min at different

In its simplest form the ICP gas flow model used for this illustration assumes only plasma gas flow and gives calculated temperature profiles in good agreement with the experimental data, within 9%, over the body of the discharge inside the induction coil and 6-7 mm above it corresponding to the expectations of MILLER and AYEN [l]. Further downstream from the coil, however, the agreement become increasingly poorer as the calculated values drop more rapidly than the experimental values. At 20 mm above the induction coil, the experimental and calculated values differ by as much as 120%. This disagreement is not unexpected, because experimental gas velocities are low inside the induction coil and increase to approximately 20 m/s downstream of the coil (see Fig. 10). The original assumption that no flow occurs in the volume between the inner and intermediate tubes is invalid, especially downstream of the coil. The plasma gas from the outer annulus apparently begins to diffuse and/or mix with the discharge inside the energy addition region as demonstrated in experimental results obtained by KLUBNIKIN [17] zero

central

and computer

calculations

by DELETTREZ [42]

and BOULOS [43,44]

for

flow

in other ICP configurations. Above the induction coil, the mixing appears to increase rapidly as fully developed parabolic velocity profiles are observed. To take mixing into account, YOSHIDA and AKASHI [55] included mixing of two steady

turbulent

streams

with flat velocity

profiles

in their

modification

of the MILLER and

AYEN calculation, and they obtained improved agreement between experimental and calculated values. In the present effort, an arbitary fraction (e.g. 0.25%) of the plasma gas was subtracted from the outer gas stream in the calculation and added to the intermediate flow to test the influence of gas stream mixing. The same fraction of the plasma gas flow is subtracted from the outer flow at each axial position (i.e. every z = 2 mm) starting at the bottom edge of the induction coil, which leads to a two-step flow profile with the ratio of intermediate-to-outer gas flow increasing at each axial position. The computed temperature results for this flow model are presented as broken lines in Fig. 11. Little difference appears between the two flow models for axial positions less than 6 mm above the top of the induction coil. In these regions, the model without mixing gives slightly better agreement with the experimental data. Above 6 mm from the coil, however, the mixing model is more accurate by a factor of two to three. The results of this arbitrary adjustment of the flow model verifies the need to include gas mixing, especially for the regions downstream of the induction coil. Other factors, however, such as the actual magnetic field distribution of the induction

[41] R. G. SCHLEICHER and R. M. BARNES, Anal. Chem. 47, 724 (1975). [42] J. A. DELE-ITREZ, Ph.D. Dissertation, University of California, Davis 1974. [43] M. I. BOULOS,IEEE Trans. Plasma Sci. 4, 28 (1976). [44] R. GAGNE, M. I. BOULOS,and R. M. BARNES, Can. J. Chem. Engr. 58, 367 [45] T. YOSHIDA and K. AKASHI, J. appl. Phys. 48, 2252 (1977).

(1980).

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mm

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mm

-0

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00 Radius,

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=----..

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mm

*. ‘.

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00 Radius,

mm

Fig. 11. Comparison of experimentally determined and computed ICP radial temperature profiles for 0.75-kW discharge with 10.0 llmin plasma flow and no central argon flow. calculated with mixing - - - -. Axial Experimental M; calculated ~empirical model) -; positions are (al -7 nm (center of coil), (bl 2 mm, (c) 4 mm, (dl 6 mm, (el 8 mm, (f) 10 mm, (g) 14 mm, (h) 20 mm.

94

R. M. BARNES and R. G.

SCHLEICHER

coil or heating resulting from electron di~usion as suggested by be important. 4.2 Centrul

ECKERT f46],

may also

ftow

Experimental and calculated ICP temperature profiles for a 0.75 kW discharge are shown in Figs. 12-14 corresponding to central argon flaw rates of 0.46, 0.90, and 1.35 I/min. For the calculations at 1.35 I/min (Fig. 12), results for three models of the central gas flow are superimposed for comparison with experimentat data at different positions. Two of these models were described previously [2], and the empirical model represents a modi~cat~o~ derived during the present investigation illustrated in Fig, 15(a). Results from only the empirical model are compared in Figs. 13 and 14 for the 0.46 and 0.9 l/min central gas flow rates. None of these models includes mixing of plasma gas described in the previous section. In the previous calculations 1121,the central gas flow models included a freely expanding turbulent jet which spreads from the injection nazzle at a constant rate and a restrained or confined jet which continues from the injection nozzle throughout the discharge without spreading, Two variations of the empirical flow model are indicated in Fig. 15. The central gas stream is assumed to display a Gaussian velocity profile, with a specified initial width at half height at the inlet nozzle. The variation of half width with axial position is specified in the computer program, and any function may be used. For example, the half width was made to increase rapidly at axial position bt in Fig. 15(a) to sin-&ate the experimentally observed spreading and fattening of the velocity profiles downstream of the induction coil (Fig. 7). The calculated results shown in Figs. 11-14 are based on the empirical flow model illustrated in Fig. 15(a), for which the profile half width was maintained at 1.3 mm through the coil region and then allowed to expand beginning at axial position il. The value of 1.3 mm selected for the veiocity half width in the coil region was based upon experimentally determined velocity profiles inside the coil. The agreement between the calculated and experimental temperature profiles for the discharge with central argon flow rates is better than 15% if the data near the outer edge of the discharge, within approximately 2 mm of the torch Walt, are not considered. Near the wall, especially inside and just above the induction coil, the experimentally determined temperatures are often two to three times higher than the calcutated temperatures. Experimental results measured near the confinement tube walls are questionably for a number of reasons. First, non-LTE effects, such as electron diffusion across the temperature gradient [46], could cause high values for spectroscopically measured temperatures. Secondly, reflections from the torch walls, induction coil, or enclosure could be significant in spite of efforts to exclude them, when the low intensities at the edge of the discharge were measured. Thirdly, the regions near the edge of the discharge carry little weight in the Abel inversion procedure and may be biased by small errors in the measured lateral radiance profile, and fourthly, unrealistically high temperature gradients, on the order of 8000 K/mm, would have to exist if the experimental temperature profdes were correct at the discharge edges. fn view of these measurements, using a non-spectroscopic possible problems, more temperature method, are required before the accuracy of the calculated results near the wail can be detern~ined. Both the experimental and calculated temperature profiles have the same general shapes, with an off-axis maximum resulting from the cooling effect of the central argon gas stream. Similar reduction of central temperatures were reported by KALNIKY et al. [7], JAROSZet al. [$I], and KORNBLUM and DE GALAN [14] upon introduction of central ffow. The agreement in profile shape between experimental and calculated values is best for axial positions less than 8 mm above the induction coil. Above this axial 1461 H. U. ECKERT, lnrernutionaIWinter Conferersce1980 on Dewekytnents in Atomic S@?crrochemicd Analyses, San Juan, Puerto Rico 1980, Paper 3.

Radius,

mm

Radios, mm

00

Radius,

mm

9.0

Radius,

Radius,

mm

mm

Fig. 12. Comparison of experimentally determined and computed radial temperature profiles for 0.75-kW discharge with plasma flow rate 10.0 Ijmin, and central carrier argon flow rate of calculated (empirical model) ; - - - - calculated (free 1.3511min. 03 experimental: turbulent jet model); - . - . - * - s-c alculated (confined jet modeif. Axial positions are (a) -7 mm. (b) 2 mm. (cl 4 mm, (d) 6 mm, (e) 8 mm, Q 10 mm, (g) 12 mm.

Y 8000

Radius,

Radus,

mm

Radius2 mm

mm

Fig. 13. Comparison of experimentally determined and computed radial temperature profiles for 0.75kW discharge with central flow rate of 0.46 l/min. Axial positions are (a) -7 mm, (b) 2 mm, (c) 4 mm, (d) 6 mm, (e! 8 mm, (ff 10 mm, (g) 12 mm. M experimental; catculated jempiricai model],

0)

(bl

9000

l/*-• Y

6CCC

.’

.’

6000

\ %

q

\ I

I

/

1

,

I

/

I

9.0 Radius,

R&us,

mm

Radius,

mm

mm

Radius,

n-m

Radius,

mm

6CCO

Radius,

mm

I

I

I

I

,

I

00

I

90 Radius,

mm

Fig. 14. Comparison of experimentally determined and computed radial temperature profiles for 0.75kW discharge with 0.90I/min central argon flow rate. Positions are the same as indicated in Fig. 13. O---O experimental; calculated (empirical model).

R. M. BARNES and R. G. SCHLEICHER

-1Omm

-0

mm

--IOmm

(a)

(b)

Fig. 15. Gas flow models as explained in the text.

position, the calculated results give a nearly parabolic temperature profile while the experimental profiles retain the off-axis maximum and centerline low temperature characteristic of lower axial positions, as clearly indicated for the 0.9 and 1.35 l/min central flow rate results (Figs. 12 and 15). For the 1.35 l/min central flow rate {Fig. 12), calculated results for the free turbulent jet model [2] are also indicated. The calculated results do not agree as well in magnitude with the experimental data (Fig. 16) as the results obtained when the

01

I

I

I

I

-20

-IO

0

10

I

20

I

30

I

40

Axial position, mm Fig. 16. Experimental and calculated ICP centerline temperatures as a function of axial position for 0.75-kW discharge with plasma flow of 10.0 I/mm’ and central flow of 1.35 l/min. The dashed line corresponds to calculated results for the free turbulent jet flow model, the solid line represents the empirical flow model [Fig. 15(a)] and the solid line through the data points is the experimental curve. The induction coil is located between -15 and 0 mm.

Temperature

and velocity distributions

in an inductively

coupled plasma

99

empirical flow model is used, although the radial distribution shape corresponds more closely. In general, little difference exists between temperature profiles calculated using the empirical and confined jet models for the axial positions at which experimental profiles were determined. The centerline temperature dependence as a function of axial position in the 0.75 kW discharge with 1.35 l/min central gas flow rate is compared in Fig. 16 to both the free turbulent jet and empirical central flow models. The axial temperatures predicted by the empirical flow model correspond more closely to the experimental data, although the shape of the axial distribution appears closer to the free turbulent jet model. However, the final assessment of the most appropriate central flow model must be based upon comparison of other experimental results such as the velocity distributions. 4.3 Gas velocities Calculated and experimental centerline gas velocities are compared in Fig. 17 as a function of axial position in the 0.75 kW discharge for the 1.35 l/min central gas flow rate. The shape of the experimental velocity curve best agrees with the results for the free turbulent jet calculations, although the experimental values are higher than predicted as might be expected from the higher calculated compared to experimental temperatures. In contrast, the empirical model predicts a peak velocity near the top of the induction coil rather than near the central gas inlet as indicated by the experimental results. 4.4 Modified flow model These and the temperature results indicate that neither the empirical flow model in Fig. 15(a) nor the turbulent jet model [2] provide exact correlation with the experimental results. The empirical flow model is modified, then, to improve the correspondence between experimental and computed results. The first empirical model [Fig. 15(a)] was based upon measured half widths of ICP velocity profiles (Fig. 7). The results shown in Fig. 17 for this empirical model indicate that the central velocities predicted by this model are too low near the central gas inlet, which would result if the actual velocity profile half widths are smaller than those measured using the Pitot tube. Owing to the necessity for water cooling, the smallest Pitot tube available for this study had a radius of 1.75 mm, which is approximately the same as the half width of the velocity profiles determined. The ratio of probe diameter-to-jet diameter could potentially cause errors in the measured shape of the jet velocity profiles, and blockage of the

I

-20

-10

0

IO

Axial position,

20

30

40

mm

Fig. 17. Experimental and calculated ICP centerline gas velocities as a function of axial position under the same conditions as in Fig. 16. The dashed line corresponds to calculated results for the free turbulent jet gas flow model, the solid line represents the empirical flow model, and the solid line through the data points is the experimental curve.

100

R. M. BARNES and R. G. SCHLEICHER

Y

8000

0

I

-20

-10

/

/

I

I

I

0

IO

20

30

40

Axial position, mm Fig. 18. Experimental and calculated ICP centerline temperatures as a function of axial position under the same conditions as given in Figure 16. The dashed line corresponds to calculated results for the modified empirical model [Fig. 15(b)], and the solid line through the data points is the experimental curve.

jet flow pattern might tend to widen it. Secondly, the position of the Pitot tube tip in the cooler central channel created by the central gas stream in the coil region could not always be monitored optically, because the coil windings blocked the view. The temperature gradients in this region could cause the stainless steel tubing to bend the probe as the tip is moved across the central gas channel. This bending might tend to keep the probe tip in the channel even though the Pitot tube assembly was moved. This effect would also introduce an apparent velocity profile broadening. In view of these experimental uncertainties and the absence of a more accurate method for determining the shape of the velocity profiles inside the induction coil, the dInpiriC~ model in Fig. 15(a) was modified in the following ways. (i) The initial velocity profile half width at the inlet nozzle was reduced from 1.3 to 0.5 mm, which corresponds more closely to the actual dimension of the inlet nozzle (0.75 mm). (ii) The half width was increased gradually through the coil region with an included angle of four degrees as indicated in Fig. 15(b). A similar graduated increase was applied previously by BARNES and ALLEMAND 15) based upon photographic observations. (iii) The jet half width was increased at a faster rate starting at axial position h noted in Fig. 15(b). Calculated results for this modified empirical model are shown in Fig. 18 for the axial temperatures and in Fig. 19 for the axial velocities at the same conditions used

Axial

paatm,

mm

Fig. 19. Experimental and calculated centerline gas velocities for the same conditions as given in Fig. 16. The dashed line represents calculated results for the modified empirical model [Fig. 1 S(b)].

Temperature

and velocity distributions in an inductively coupied pfasma

101

previously in Figs. 16 and 17. This modification elevates the centerline temperatures throughout the discharge compared to the previous empirical model, but substantially reduces the centerline temperatures in the -15 to + IS mm positions and increases it somewhat above the coil compared to the free turbulent jet model. The calculated centerline gas velocities are in good agreement with the experimental data (Fig. 19) as the maximum axial centerline velocity shifts from approximately 2 mm above the coil to near the center of the coil.

The experimental temperature and gas velocity profiles obtained in this investigation provide new information needed to evaluate the spectrochemical ICP discharge. Prior to this report, no velocity measurements in the argon ICP used for analysis were available to test computer models of the discharge. The empirical adjustments of the flow models of the ICP discharge result in predicted temperature and velocity distributions which agree well with experimental results. The agreement between calculated and experimental temperature profiles are found to be better than 1tl5% inside the core of the discharge and up to 15 mm above the coil. Near the torch walls, however, the agreement is poor, and because of the high uncertainty of experimental measurements near the confinement wail, the accuracy of calculated results could not be evaluated in this region. Also, temperatures less than 6000 K cannot be determined spectroscopically in a pure argon ICP with sufficient -accuracy, because the argon line emission is too weak. Experimental velocity data also cannot be obtained near the walls, owing to the size of the Pitot tube. Prior to undertaking further intuitive alteration of the empirical central flow model, additional and improved spatial temperature and velocity djstributions are needed to define completely these parameters throughout the discharge under diverse operating conditions. Furthermore, all experimental and computed results presented are obtained for a pure argon discharge. Since ICP discharges commonly applied in spectrochemical analysis differ by the injection of analyte as aqueous or organic aerosols and the presence of air mixing with the discharge above the induction coil, the extension of these models to more complex discharges identical to those used in analysis requires detailed knowledge of the mixing patterns [44] as well as the mixed-gas transport property data. The diffusion of electrons from the discharge region and their influence on electron density and temperature distributions in the boundary regions [46] also need to be considered. Ackno~fedg~~~~~$-~~s work was completed by R.E.S in par&I fulfillment of the requirements for the Ph.D. degree in chemistry. Supported in part by Department of Energy (Office of Basic Energy Sciences) Contract DE-X302-77ER04471. The authors appreciate the helpful discussions with J. L. GENNA and F. AE~~CHI~MX.