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Microwave plasma processing of unique ceramic particulate materials

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The Pennsylvania State University
The Graduate School
Department o f Chemical Engineering
MICROWAVE PLASM A PROCESSING OF UNIQUE CERAMIC
PARTICULATE MATERIALS
A Thesis in
Chemical Engineering
by
Chun-Ku Chen
© 2001 Chun-Ku Chen
Submitted in Partial Fulfillment
o f the Requirements
for the Degree of
Doctor of Philosophy
August 2001
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UMI Number 3020430
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We approve the thesis o f Chun-Ku Chen.
Date o f Signature
dak
TSM, Los Alamos Natic
Distinguished National La6“
Thesis Co-Adviser
Co-Chair o f Committee
Special Member
essor / UNM
L ( t4( B /
Lance R. Collins
Associate Professor o f Chemical Engineering
Thesis Co-Adviser
Co-Chair o f Committee
& /& < £//
Alfred Carlson
Associate Professor o f Chemical Engineering
Themis Matsoukas
Associate Professor o f Chemical Engineering
Stephen f. Fona^h
Bayard D. Kunkle Professor o f Engineering Sciences
W e>/
Hefiry C. Fol^y
Professor o f Chemical Engineering
Head o f the Department o f Chemical Engineering
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Abstract
A novel technology for generating specifically particulate materials was
developed. We have shown that the microwave generated atmospheric pressure plasma
can be employed to create novel particulate materials. Yet, in our initial work we were
only able to make simple correlation between operating param eters and material
characteristics. Direct correlation between material modification and measured plasma
characterization would enable the process to be scaled. In brief, the three stages of this
thesis were: U nderstanding novel particulate generation technology, thorough
characterization of the afterglow region of the plasma, and finally developing a model of
the coupler region of a low pressure plasma.
The material processing focused on developing a new technique for generating
spherical alumina particles of controlled size. This development led to a patent. In brief,
we showed that passing an aerosol containing irregularly shaped precursor particles,
could be controlled to generate spherical ceramic particles of selected size. A mechanistic
model of growth successfully explained observations. First, particles melt in the plasma
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hot zone, next they collide with others to form larger agglomerates and finally they are
quenched to form the solid spherical particles in the afterglow region.
A thorough and system atic investigation of the afterglow region o f an
atmospheric pressure argon plasma under various operating conditions was performed. It
was shown that the plasma is not in an equilibrium state. That is, the gas, electron and
excitation temperatures of the plasma are greatly different. This points out that a multi­
tem perature model is more appropriate than the one-temperature model. This
experimental data is valuable for future modeling work, as well as possible processing
optimization strategies.
Finally, a novel multi-temperature model of a low-pressure microwave plasma
was developed. We successfully solved the Boltzmann equation for a low pressure
microwave generated hydrogen plasma. Taken together with an appropriate set of
reactions and iteration procedure this has enabled us to determine the electron energy
distribution function as well as the density and temperature of all the other species
present. The model developed was not for the plasma employed in material modification.
It is a simpler system, and hence represents a step along the path toward modeling a high
pressure, multi-temperature microwave generated plasma.
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V
TABLE OF CONTENTS
LIST OF FIGURES................................................................................................................... ix
LIST OF TA B L E S....................................................................................................................xv
ACKNOWLEDGEMENTS...................................................................................................xvii
Chapter 1.
INTRODUCTION............................................................................................. 1
References ..............................................................................................................................5
Chapter 2.
LOW POWER PLASMA TORCH METHOD FOR THE PRODUCTION
OF CRYSTALLINE SPHERICAL CERAMIC PARTICLES......................8
2.1
Abstract................................................................................................................ 8
2.2
Introduction..........................................................................................................9
2.3
Experimental.................................................................................................... 13
2.3.1
Atmospheric microwave plasma torch system ........................................... 13
2.3.2
Precursor.......................................................................................................... 18
2.4
R esults............................................................................................................... 22
2.5
Discussion..........................................................................................................38
2.6
Conclusion........................................................................................................ 52
References ........................................................................................................................... 53
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Chapter 3.
PLASMA CHARACTERIZATION - SPECTROSCOPIC METHOD
58
3.1
Abstract............................................................................................................. 58
3.2
Introduction...................................................................................................... 59
3.3
Experimental.................................................................................................... 62
3.3.1
Instrumentation.............................................................................................. 62
3.3.1.1 Microwave plasma torch system ................................................................... 65
3.3.1.2 The optical arrangement.................................................................................66
3.3.1.3 The detection system and spectra analysis...................................................68
3.3.2
Experimental Procedure.................................................................................69
3.3.2.1 Position of focus and line of sight alignment............................................... 69
3.3.2.2 Experimental conditions.................................................................................70
3.4
Characterization of Plasma Param eters........................................................ 81
3.4.1
Gas tem perature.............................................................................................. 81
3.4.2
Excitation Tem perature.................................................................................. 87
3.4.3
Electron Tem perature..................................................................................... 93
3.4.4
Electron Number D ensity.............................................................................101
3.5
Results and Discussion..................................................................................109
Part I.
Thermodynamic Equilibrium in Plasma.................................................... I l l
1.1
Complete Thermodynamic Equilibrium (CTE)......................................... I l l
1.2
Local Thermodynamic Equilibrium (LTE)................................................. 114
1.3
Criteria for existence of Local Thermodynamic Equilibrium (LTE)
Part n .
116
Characterization of the plasma torch with the aerosol containing alumina
particles........................................................................................................... 118
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II.
1
H.2
Gas Temperature (Rotational Temperature)..............................................121
n .3
Excitation Temperature...............................................................................138
H.4
Electron Density........................................................................................... 142
H.5
Metallic Aluminium Emission Line Intensity........................................... 147
Part HI.
Non-Equilibrium Plasmas (Departure from L T E )....................................154
Part IV.
Two Flow Streams Effect on the Plasma Parameters................................ 160
IV. 1
Effect on electron temperature....................................................................160
IV.2.
Effect on electron density........................................................................... 161
P artV .
Data Summary and Comparison................................................................ 167
3.6
Electron Temperature........................................................................ 118
Conclusions...................................................................................................169
References .........................................................................................................................172
Chapter 4
MODELING THE DISCHARGE REGION OF A MICROWAVE
GENERATED HYDROGEN PLASMA..................................................... 178
4.1
Abstract......................................................................................................... 178
4.2
Introduction...................................................................................................179
4.3
Experimental Apparatus..............................................................................183
4.4
Model.............................................................................................................185
4.4.1
Boltzmann Equation.................................................................................... 187
4.4.2
Species balances........................................................................................... 188
4.4.2.1 Rate constants.............................................................................................. 194
4.4.2.2 Wall recombination..................................................................................... 195
4.4.3
Energy and power balance.......................................................................... 198
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v iii
4.4.3.1.
Power balance......................................................................................... 199
4.4.3.2.
Energy balance on neutral species...........................................................202
4.4.4
4.5
Method of solution........................................................................................205
Results and discussion.................................................................................. 208
4.5.1
Pressure...........................................................................................................209
4.5.1.1 Gas Temperature: p < 15 T o rr.....................................................................209
4.5.1.2 Gas Temperature: p > 15Torr.....................................................................212
4.5.1.3 Species density.............................................................................................. 214
4.5.1.4E/N ...................................................................................................................216
4.5.2
Microwave power.........................................................................................221
4.5.3.
Wall recombination coefficient....................................................................222
4.5.4
Feed flow rate.................................................................................................228
4.5.5
Comparison with prior experimental studies............................................. 229
4.6
Summary.........................................................................................................231
References ......................................................................................................................... 233
Chapter 5.
CONCLUSIONS AND RECOMMENDED FUTURE W O R K ............... 238
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LIST OF FIGURES
Figure 2.1
Schematic drawing of the coupler region of the microwave plasma
torch system ...................................................................................................14
Figure 2.2 Schematic drawing of novel particle feeder system....................................16
Figure 2.3 Example of plasma plume in chimney under three different operating
conditions....................................................................................................... 19
Figure 2.4 Schematic drawing of particle collection system which is secured to
the waveguide............................................................................................... 20
Figure 2.5 Scanning electron micrograph (SEM ) of a-alum ina precursor
particles.......................................................................................................... 21
Figure 2.6a Representative SEM of treated a-alum ina particles which have
overwhelmingly been spheroidized.............................................................23
Figure 2.6b Spheroidized a-alumina smaple collected from the trap ...........................24
Figure 2.6c
Spheroidized a-alumina smaple collected from the collar region of
the apparatus................................................................................................ 25
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X
Figure 2.6d Singular example o f sphere which has not completely melted to
form smooth surface....................................................................................26
Figure 2.6e
SEM image o f particles which provides evidence that particles
might becom e agglom erated at some point during plasm a
processing.....................................................................................................27
Figure 2.7
Characteristics o f treated particles as a function o f operating
conditions..................................................................................................... 29
Figure 2.8
Example of partially fused but not fully melted precursor particles
Figure 2.9
Average spherical particle size (by volume) as a function of mass
30
density travelling through the torch.......................................................... 31
Figure 2.10
Figure 2.1 la
SEM of air plasma treated particles.......................................................... 34
Particle size distribution for spherical a-alumina particles formed
in an argon plasma, mean particle size = 4.43 Jim.................................35
Figure 2.1 lb
Particle size distribution for spherical a-alumina particles formed
in an argon plasma, mean particle size = 8.56 pm .................................36
Figure 2.1 lc
Particle size distribution for spherical a-alumina particles formed
in a dry air plasma......................................................................................37
Figure 2.12a
Ratio of kinetic energy to electrostatic repulsion energy as a
function o f particle size and electron temperature o f the plasma
(aerosol flow rates = 0.2 L/m in............................................................... 47
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Figure 2.12b Ratio o f kinetic energy to electrostatic repulsion energy as a
function o f particle size and aerosol flow rates (Te =4 e V ) .................48
Figure 3.1
Schematic drawing of the experimental set-up........................................ 63
Figure 3.2
Spatial distribution o f the probe spots in the afterglow of the
plasma torch...............................................................................................72
Figure 3.3
A typical spectrum of the OH band, used in determining rotation
(gas) temperature......................................................................................85
Figure 3.4
Line profile with definition of line intensity Imax, and continuum
intensity Ic, and full width at half maximum (FWHM)........................ 95
Figure 3.5
2D Spatially resolved maps of electron temperature as a function
of applied microwave power, plasma gas: 1.17 L/min, aerosol gas
with alumina : 0.36 L /m in ...................................................................... 119
Figure 3.6
Spectrums of Q, branch of the OH (0-0) band observed at two gas
temperatures, (a)2951°K, (b) 3346°K...................................................... 122
Figure 3.7
2D Spatially resolved maps of gas temperature as a function of
applied microwave power, plasma gas: 1.17 L/min, aerosol gas
with alumina : 0.36 L /m in ........................................................................126
Figure 3.8
2D spatially resolved maps of the gas temperature as a function of
flow rates, plasma gas:1.17L/min, aerosol gas :0.36,0.72,1.06
L /m in...........................................................................................................131
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Figure 3.9
2D spatially resolved mapping of the gas temperature as a function
o f flow rates, plasma gas:0.81,1.17,2.5 L/min, aerosol gas :0.36
L /m in........................................................................................................... 132
Figure 3.10
Investigation of the influence of the plasma gas flow rates. Shown
are gas temperatures as a function of applied power and gas flow
rates.............................................................................................................. 134
Figure 3.11
Gas temperature as a function o f probe concentrations and applied
power. Plasma gas: 1.17 L/min, aerosol gas with alumina : 0.36
L/min, measured at (x,z)=(0,0)...................................................................137
Figure 3.12
2D Spatially resolved maps of excitation temperature as a function
o f applied microwave power, plasma gas: 1.17 L/min, aerosol gas
with alum ina: 0.36 L /m in...........................................................................141
Figure 3.13
Electron density measured from the Hp line as a function of probe
concentartions and applied p o w er............................................................. 144
Figure 3.14
2D Spatially resolved maps of electron density as a function of
applied microwave power, plasma gas: 1.17 L/min, aerosol gas with
alumina : 0.36 L/min....................................................................................145
Figure 3.15
Intensity in argon plasma of the metallic aluminium emission line
(394.4032nm) as a function of particle density and applied power
Figure 3.16
150
Intensity in air plasma o f the metallic aluminium emission line
(394.4032nm) as a function of particle density and applied power
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151
Figure 3.17
2D Spatially resolved maps of the intensity of metallic aluminium
emission line as a function of applied microwave pow er....................... 153
Figure 3.18
A com parison o f the calculated theoretical value of T lte to
measured gas, excitation and electron temperatures as a function of
applied power and position, (a) Z=0, (b) Z=8...........................................159
Figure 3.19
2D Spatially resolved maps of electron temperature as a function of
applied microwave power, plasma gas: 1.17 L/min without aerosol
gas .................................................................................................................163
Figure 3.20
2D Spatially resolved maps of electron temperature as a function
of applied microwave power, plasma gas: 1.17 L/min, aerosol gas
without alumina : 0.36 L/min....................................................................164
Figure 3.21
2D Spatially resolved maps of electron density as a function of
applied microwave power, plasma gas: 1.17 L/min without aerosol
gas .................................................................................................................165
Figure 3.22
2D Spatially resolved maps of electron density as a function of
applied microwave power, plasma gas: 1.17 L/min, aerosol gas
without alumina : 0.36 L/m in..................................................................... 166
Figure 4.1
Schem atic diagram o f experim ental apparatus; low-pressure
microwave plasma system.......................................................................... 184
Figure 4.2
Algorithm of the modeling in a fashion of flow chart...............................207
Figure 4.3
Gas temperature as a function of pressure..................................................210
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xiv
Figure 4.4
Power transfer. As pressure increases, the major channel for power
transfer from electrons to neutrals from dissociation to vibrational
excitation......................................................................................................211
Figure 4.5
Electron temperature and density as a function of pressure.....................213
Figure 4.6
Ion density as a function of pressure. H3ion isthe dominant ionic
species over the entire pressure range...................................................... 217
Figure 4.7
Fractional hydrogen dissociation. Fractional hydrogen dissociation
decreases with pressure.............................................................................. 218
Figure 4.8(a) E/N as a function of gas density............................................................... 219
Figure 4.8(b) E/N as a function of microwave power.................................................... 220
Figure 4.9
Electron temperature and electron density as a function o f
microwave power........................................................................................224
Figure 4.10
H-atom density and fractional dissociation as a function of
microwave power........................................................................................ 225
Figure 4.11
Gas temperature as a function o f microwave power................................ 226
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XV
LIST OF TABLES
Table 2.1
Monotonic increase o f precursor mass flow rate with increasing
aerosol gas flow rate......................................................................................17
Table 3.1
Description and specification of the experimental instrumentation
64
Table 3.2(a) Experiment conditions for spatially resolved maps o f plasm a
parameters......................................................................................................75
Table 3.2(b) Experim ent conditions for spatially resolved maps o f gas
temperature in different flow rates..............................................................77
Table 3.2(c) Experiment conditions for m easuring the gas tem peratures in
different applied powers, plasma gas and aerosol gas flow rate s
78
Table 3.2(d) Experiment conditions for m easuring the metallic alum inium
emission line intensity..................................................................................79
Table 3.2(e) Experim ent condition for determ ining the effect o f probe
concentrations on gas temperature and electron density.......................... 80
Table 3.3
Assignment, wavelengths, energies and transition probabilities for
the Q, branch of the OH (0-0) band ........................................................... 86
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Table 3.4
Wavelengths, energies, statistical weights and transition probabilities
of the argon em ission lines used in determining the excitation
tem perature...................................................................................................
Table 3.5
92
Param eters of A r (430 nm) for the calculation of electron
tem perature...................................................................................................
99
Table 3.6
Comparison of the line broadening from various sources...................... 108
Table 3.7
Comparison of plasma parameters between current work and data in
literature.......................................................................................................... 168
Table 4.1
Rate processes in a Hydrogen plasma.......................................................... 190
Table 4.2
Electron-neutral collisions in a Hydrogen plasma...................................... 191
Table 4.3
The impact of wall recombination coefficient on model results
Table 4.4
Comparison between model results and experimental measurements .. 230
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227
ACKNOWLEDGEMENTS
Many people have contributed to my endeavor of pursuing a Ph.D and completing this
dissertation. Those people listed below make my completion of a doctoral degree and
dissertation possible.
Sincere thanks to my advisors, Dr. Jonathan Phillips and Dr. Lance Collins, who
provide extraordinary support, guidance, and encouragement throughout this
process. In particular, I would like to show my greatest gratitude to Dr. Phillips
for being a wonderful mentor and friend.
To members of my committee, who assure that I successfully fulfilled my
requirements as a Ph.D.
To Dr. Ta-Chin Wei, for his selfless advice and assistance.
Deepest thanks to my parents, for their love, support, and faith in my abilities.
Special thanks to my lovely fiancee, Liting, for her love, support, and sacrifice
during this journey.
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1
Chapter 1
INTRODUCTION
Plasm a were employed to spheroidize ceramics [1-27] for many decades.
However, there is no record of efforts were reported to correlate the particles size, yield
and particle characteristics to operating parameters. In this work, a low power,
atmospheric plasma torch was used to make spherical alumina particles of controlled
size. In order to successfully generate desired properties of materials by this technique, it
is necessary to study the fundamental parameters o f the atmospheric plasma, such as
tem perature and species concentration profile for a better understanding o f the
relationship between operating characteristics and material properties. Characterization
studies are also important for developing a modeling strategy. Since the measurement of
plasma parameters is complex and plasma characteristics are easily changed, an accurate
model predicting changes with various operating parameters will greatly simplify the
process for searching the optimized conditions.
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2
There are three stages in this thesis. First, in Chapter 2, a pantented particulate
generation technology developed in our lab is discussed. We showed that passing an
aerosol containing irregularly shaped alum ina particles through an atmospheric
microwave generated plasma torch, could be controlled to generate spherical alumina
particles of selected sizes by carefully adjusting applied microwave power, gas flow rates
and gas identity. A simple three-stage collisional model of growth of spherical particles
successfully explained most aspects of the observed behavior. In the first stage, particles
melt in the plasma hot zone (above 3000 °K), next they collide with others to form larger
agglomerates and finally they are quenched to form the solid spherical particles in the
afterglow region. The impact of particle charging on the process is also considered.
Second, in Chapter 3, a thorough and systematic investigation of the afterglow
region of an atmospheric pressure argon plasma under various operating conditions was
performed. In this study, a non-intrusive spectroscopic method was used to develop twodimensional spatially resolved mappings of gas, electron and excitation temperatures and
electron densities as a function of operating conditions during material processing. It was
shown that the passage of an aerosol dramatically changes the structure of the afterglow.
Also, the non-equilibrium nature of the plasma was revealed. That is, the gas, electron
and excitation temperatures of the plasma are greatly different, Te > Texc > Tgas. This
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3
suggests that the LTE model is not an applicable approach and only a multi-temperature
model is capable of modeling this region of the plasma.
Third, in Chapter 4, a unique m ulti-tem perature model of a low pressure
microwave generated hydrogen plasma was developed. The unique feature of this model
is that it separates the plasma into charged and neutral species with different temperatures
but coupled through the power balance equation. The Boltzmann equation was first
solved to generate the electron energy distribution function for calculating the rate
constants of reactions and average electron temperature in plasma. Next, the energy
balances and species balances were solved simultaneously in order to obtain the gas
tem perature and the species concentrations. Finally, the power terms are directly
computed from the temperature and species concentration determined. These power
values are used in the power balance to test for self-consistency. The total power in this
balance must equal the total experimental power applied to the system.
This model enables us to predict the temperature of the neutral species (Tgas) and
electron temperature (Te) as well as the species concentrations in various operating
conditions. The dependence of the gas tem perature with operating pressure and
microwave power was computed and compared to experimental measurements. In both
cases, the agreement between model and experiment was very good. Although the model
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4
developed here was not for the plasma employed in material modification, it represents a
step along the path toward modeling a more complicated high pressure (one atmosphere),
multi-temperature microwave generated plasma.
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5
References
1.
T. Ishigaki, Y. Bando, Y. Morioshi and M. Boalos, J. Mater. Sci. 28, 4223 (1993).
2.
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(1986).
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E.Pfender, Plasma Chem. and Plasma Proc. 19, 1 (1999).
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B.H. Kear, W. Chang, G. Skandan, and H. W. Hahn, U.S. Patent No. 5,514,350
(1996).
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M. I. Boulos, IEEE Trans. Plasma Sci. 19, 1078 (1991).
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P. M. Kumar, C. Balasumramanian, N.D. Sali, S.V. Bhoraskar, V. K. Rohtgi, S.
Badrinarayanan, Mat. Sci. and Engr. B63, 215 (1999).
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S. Koura, H. Tanizaki, M. Niiyama and K. Iwasaki, Mat. Sci. Eng. A208, 69
(1996).
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H. Tanizaki, A. Otsuka, M. Niiyama and K. Iwasaki, Mat. Sci. Eng. A215, 157
(1996).
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P. Fauchais and A. Vardelle, IEEE Trans. Plasma Sci. 25, 1258 (1997).
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P. Fauchais, A. Vardelle and A. Denoiijean, Surf. Coat. Tech. 97, 66 (1997).
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S-M. Oh and D-W. Park, Thin Solid Films 316, 189 (1998).
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P. B. Pavlovic, Z. G. Kostic and P. Lj. Stefanovic, Mat. Sci. Forum 214, 205
(1996).
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X. Fan, F. Gitzhofer and M. Boulos, J. Therm. Spray Tech. 7, 247 (1998).
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M. F. Besser and D. J. Sordelet, J. Mat. Synth. Proc. 3, 223 (1995).
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J. R. Fincke, W. D. Swank, and D. C. Haggard, Plasma Chem. Plasma Proc. 13,
579 (1993).
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M. Vardelle, A. Vardelle, P. Fauchais, and M. I. Boulos, AIChE J. 29, 236 (1983).
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I. Bica, Mat. Sci. Eng B68, 5 (1999).
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R. Westhoff, G. Trapaga, and J. Szekely, Metallurg. Trans B, 23B, 683 (1992).
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G. Trapaga, R. Westhoff, J. Szekely, J. Finske, and W. D. Swank, Mat. Res. Soc.
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8
Chapter 2
LOW POW ER PLASMA TORCH METHOD FOR THE PRODUCTION OF
CRYSTALLINE SPHERICAL CERAMIC PARTICLES
The following is based on an article written by C. K. Chen, S. Gleiman and
J. Phillips. The article was published in the Journal of Material Research, 16, pp 12561265 (2001).
2.1
Abstract
A low power, atmospheric pressure, microwave plasma torch was used to make
spherical alumina particles of controlled size from irregularly shaped precursor powders.
Detailed studies of the impact of operating parameters, particularly gas identity (argon or
air), gas flow rates and applied power, showed that particle size changed in a predictable
fashion. The most important factor in controlling particle size appears to be precursor
particle density in the aerosol stream that enters the plasma hot zone. A simple
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9
calculation of the impact of particle charging indicated that in most of our experimental
conditions, the repulsion force generated by the negative potential created by net negative
charging o f the particles would not significantly change collision rates. Thus, it strongly
suggests that particle collision rate is primarily responsible for determining ultimate
particle size. Reproducible volume average particle sizes ranging from 97 pm 3 to 1150
pm3 were formed from precursor particles of order 14 pm 3. Moreover, for the first time
we report the creation of an atmospheric pressure low power air plasma (< 1 kW).
2.2
Introduction
Recent published work from our laboratory was the first indication that smooth,
spherical, crystalline, particles of alumina can be made by passing irregularly shaped,
largely amorphous particles of alumina through an atmospheric plasma generated with a
microwave source [1,2]. In that first example of the use of a low power microwave
plasma to generate spherical particles the final particle size was directly related to the size
of the input particles. An analysis of the particle size distribution of the input and output
particles indicated that each final particle was formed from the melting and subsequent
spheroidization of a single input particle. In this present investigation, it is shown that
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10
spherical particles o f a controlled size can be made from the collision of many input
particles. Moreover, we show there are clear relations between operating parameters and
the number o f particles which sinter together to form the final spherical particles.
Adjusting these operating parameters is a mechanism for control of the ultimate particle
size distribution. Thus, the primary focus of the present work is to study the relationship
between operating parameters and both particle size and yield. Also, a simple model
considering particle charging and agglomeration showed that the particle size can be
controlled by adjusting experimental conditions.
There is a long list of studies in which plasmas were used to spheroidize ceramics
[3-29], but in virtually all those earlier studies far higher power systems were employed.
Also, although some efforts were made to understand factors influencing spherodization
efficiency [18] at high power, there is no record of efforts to control particle size, or to
relate particle characteristics or yield to operating parameters. In fact the mechanism of
particle generation in those earlier works designed to generate particles (as opposed to
films) did so via the initial creation of atomic species and subsequent nucleation and
growth [11,12,16,17,22,30]. That approach is not compatible with particle size control.
At best using some of the earlier strategies, sphere size can be ‘predicted’ if it is assumed
(or found) that each output particle forms from the spheroidization of a single input
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11
particle [1,2,18]. In fact, most studies are focused on the use of plasma torches to create
protective films from the “splatting” o f input ceramic particles. These processes are
fundamentally different from the current work in several fashions: the range of power
used (>20 kW), the point of ceramic particle injection (into the ‘afterglow’), and the
intended product (films).
Several recent experimental studies have demonstrated the need to consider
additional factors in modeling plasma-particle interactions. For example, most recent
studies show that atmospheric plasmas are not equilibrium systems. Particle temperatures
are significantly different than ‘average’ plasma temperatures [20,21,29], and rotation,
excitation, and electron temperatures are all significantly different from each other and
from any ‘average’. It has also been suggested that particle injection into an afterglow
creates ‘bubbles’ of low-temperature gas in the plasma flow [20]. Some work clearly
shows the need to consider particle ablation to understand particle flow and temperature
[23,24,26]. The present work suggests one more fundamental aspect of particle behavior
which must be considered. In previous experimental and modeling studies [4-6, 9 and
references therein] particle growth by agglomeration was not considered. This is the first
work to demonstrate that particle agglomeration, even at relatively low temperatures and
particle densities (<1%), significantly impacts ultimate particle structure. Agglomeration
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12
may also impact film formation as the present work suggests it is likely to occur prior to
‘splatting’ in many systems. There is also evidence that in argon plasmas growth by
atomic addition (‘Ostwald ripening’) is occurring as well.
There are many applications of spherical ceramic particles, particularly as
polymer filler. At present this market is almost entirely for spherical silica particles as
relatively inexpensive silica spheres are available in a wide variety of sizes. A market for
small spheres of other ceramics is growing, as the characteristics of silica are not optimal
for many applications. However for most applications appropriate alternatives are too
expensive or not available. For example, it is widely understood by those familiar with
the technology, that spherical alumina or boron nitride (BN) particles in the 10-200
micron size range would be far superior than silica as filler in filled polymer ‘packages’
used for integrated circuits [31-33]. These high thermal conductivity/low electrical
conductivity ceramics would probably replace silica, if spherical particles could be
inexpensively produced. Present techniques for the generation of spherical alumina are
expensive such that, despite the preferred characteristics of alumina, it cannot compete
with silica in this and other applications.
Spherical, crystalline BN is simply not
available commercially. Thus, there is a m arket for a new low cost method for the
generation o f micron scale spherical ceramics.
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13
2.3
Experimental
2.3.1
Atmospheric microwave plasma torch system
There are two key components to the system employed in the present work: a low
power, atmospheric pressure, gas-flow microwave plasma, and a particle feeder of novel
design.
To generate the plasma two feed streams are fed to a quartz torch (cylinder, 19
mm ID) which passes through a microwave (2.45 GHz) waveguide (TE10) (see Figure
2.1). One of the streams (‘plasma gas’) is passed through the main body of the torch, and
the second stream ( ‘aerosol gas’ - contains particles) passes through a co-axial central
alumina tube (3mm ID) which terminates within the torch. Using a three stub tuner,
power is coupled into the gas (actually only the electrons [34], which are generated by
ionization processes) as it passes through the waveguide, hence creating an atmospheric
pressure plasma.
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14
Center Flam e
A rgo i Plasm a
M icrowave
Q uartz Tube
A lum ina Tixbe
Plasma
Gas Inlet
C arrier Gas Inlet
Figure 2.1
Schematic drawing of the coupler region of the microwave plasma torch
system.
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15
An important innovation in the present system is the aerosol generator. Creating a
high solid concentration dry particle aerosol with small particles (e.g. <10 micron) is still
an art. Using the system (no moving parts) shown in Figure 2.2 we were able to feed
small (<5 micron), dry, irregularly shaped alumina particles through the torch at rates as
high as 48 mg/hr.
The key component of the system is a 3mm ID x 25cm cylindrical tube perforated
with 3mm holes. The aerosol gas flows through the center of this tube. Particles in a
reservoir on the outside of the perforated tube fali into the plasma gas stream, pulled by
gravity, and possibly suction as well. Surprisingly, the particle density in the plasma gas
increases monotonically with increasing plasma gas flow rate as shown in Table 2.1. The
basis for this behavior is not clear. For example, calculations indicate that the pressure
drop resulting from the Bernoulli effect is insignificant. One possible explanation relates
to changes in the upstream pressure as a function of flow rate. Indeed, particle mass flow
rate is far faster with the plasma ignited. This suggests that the rapid heating of the gas
creates a pressure drop that can pull particles into the aerosol gas stream. Moreover, the
shape of the plasma hot zone is a function of flow rate.
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16
Figure 2.2
Schematic drawing of novel particle feeder system. Legend: A) precursor
particle reservoir; B) perforated feed tube —key dimensions: 3mm ID x 25
cm length; C) aerosol gas inlet; D) magnetic stir plate; E) to plasma.
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17
Table 2.1
Monotonic increase o f precursor mass flow rate with increasing aerosol
gas flow rate.
Aerosol Gas Flow Rate
Mass Flow Rate of Alumina
(slpm)
Precursor (mg/hr)
0.186
1.54
0.357
7.20
0.529
19.80
0.701
48.00
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18
Higher aerosol gas flow rates clearly increase the length of the central plume (see Figure
2.3). The impact of these effects on pressure gradients, velocity fields, and residence
time in the plasma hot zone (region with temperature higher than the melting temperature
of alumina) is not clear. Further study is planned.
After passage through the waveguide/coupler region the gas with treated particles
enters into a chimney (ID 10cm and height 20cm), and from there into a particle trap
which is approximately 95% effective at recovering the treated particles (see Figure 2.4).
No filter system was employed. Notably, a small fraction of the particles (approximately
10% by weight) do not make it to the chimney, but rather fall out of the aerosol stream
and are caught on a small region called the ‘collar’ between the bottom of the chimney
and the top of the quartz torch.
2.3.2
Precursor
The input particles are somewhat agglomerated, high-purity a-alum ina supplied
by a commercial vendor with an average diameter size of less than 2 microns (see Figure
2.5). This was determined using ImageSXM software [35].
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Figure 2.3(a)~(c)
2.3 (c)
Example of plasma plume in chimney under the following
operating conditions:
applied power = 500 watts; gas identity: argon;
(a) plasma gas = 1.544 slpm; aerosol gas = 0.3567 slpm.
(b) plasma gas = 1.544 slpm; aerosol gas = 0.5287 slpm.
(c) plasma gas = 1.544 slpm; aerosol gas = 0.7013 slpm.
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20
Particle Trap
Chimney
Top of
quartz
torch
Collar region
Waveguide
Figure 2.4
microwaves
Schematic drawing of particle collection system which is secured to the
waveguide. Critical chimney dimensions: 20cm height x 10 cm diameter.
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21
Figure 2.5
Scanning electron micrograph (SEM) of a-alum ina precursor particles.
Notice agglomerated, platelet-like shapes.
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22
2.4
Results
Several examples of the treated, spheroidized, non-agglomerated particles are
shown in Figure 2.6. It is clear that the particles are remarkably spherical. A simple
visual inspection o f the trap contents during processing indicates that particle
agglomeration is negligible: the treated particles are observed to be free-flowing and
statically charged. This is a reasonable assumption because the particles collect negative
charge as they are transported through the plasma; the negatively charged spheres tend to
repel each other. Comparing the spheres in Figures 2.6a and 2.6b shows that increasing
the applied power while keeping all other operating conditions constant, increases the
final particle size of the particles caught in the trap. Note that particles in the collar
(<10% by mass) are far larger than those found in the trap. This appears to result from a
longer residence time in the plasma. Interestingly the spheres in Figure 2.6e, under close
inspection, appear to be somewhat agglomerated. The reasons for this are unclear.
Obviously, this type of observed behavior requires further study. From this point forward
all comments, unless otherwise noted, refer to particles caught in the trap.
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Figure 2.6a
Representative SEM of treated a-a lu m in a particles which have
overwhelmingly been spheroidized. This sample was collected from the
trap. Operating conditions: applied power = 500 watts; gas identity =
argon; plasma gas flow rate = 1.358 slpm; aerosol gas flow rate = 0.186
slpm.
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Figure 2.6b
Spheroidized a-alum ina smaple collected from the trap. Operating
conditions: applied power = 600 watts; gas identity = argon; plasma gas
flow rate = 1.3584 slpm; aerosol gas flow rate = 0.186 slpm. Note the
difference in sphere size with those in Figure 2.6a. It is evident that
increases in applied power (from 500W to 600W) increase the ultimate
particle size.
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25
X 150
Figure 2.6c
This sample was collected from the collar region o f the apparatus.
Operating conditions: applied power = 500 watts; gas identity = argon;
plasma gas flow rate = 0.6328 slpm; aerosol gas flow rate = 0.3567 slpm.
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26
Figure 2.6d
Singular example of sphere which has not completely melted to form
smooth surface. Indeed, individual precursor platelets are discemable.
This sample was recovered from the collar region. Operating conditions:
applied power = 500 watts; gas identity = argon; plasma gas flow rate =
0.6328 slpm; aerosol gas flow rate = 0.3567 slpm.
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27
Figure 2.6e
SEM image of particles which provides evidence that particles might
become agglomerated at some point during plasma processing. Operating
conditions: applied power = 500 watts; gas identity = argon; plasma gas
flow rate = 1.1736 slpm; aerosol gas flow rate = 0.4254 slpm.
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28
First, we have been able to determine output characteristics of the particles as a
function of a number of parameters: the plasma gas and aerosol flow rates, the supplied
power and the gas identity. In particular, we have been able to map out the argon plasma
operating region at 500 watts in which the alumina becomes spherical (see Figure 2.7).
If either flow rate is too high the particles are not transformed by their passage
through the torch. Consistent with this suggestion are the nature of structures found at
flow rates which are too high. A t the edge of the region of maximum spheroidization
(see Figure 2.7), partially spheroidized particles (shown in Figure 2.8) are frequently
found. These agglomerates appear to form from the collision of softened (sticky)
precursor particles that collided and sintered together, but did not fully melt. The failure
of the particles to melt suggests insufficient time in the plasma hot zone.
Second, an empirical correlation between final particle size and aerosol mass
density can be derived from the data. As shown in Figure 2.9 the average final particle
volume falls along a smooth curve as a function of the particle density in the aerosol. In
fact, the average particle volume changes by a factor of almost ten along the 500 watt
operating curve. This indicates that ten times as many precursor particles are required to
form the particles at the high-mass density end of this curve relative to the average
number on the low-mass density end.
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29
Plasma Gas Flow Rate (slpm)
X
X
•
spherical
X
non-spherical
X
X
X
X
•
X
X
X
•
•
•
• •
•
•
0
*
X
X
•
i
0.5
•
•
X
X
X
•
•
X
X
X
X
XX
X
X
1
1
X
X
i
1.5
. . . .
2
Aerosol Gas Flow Rate (slpm)
Figure 2.7
Characteristics of treated particles as a function of operating conditions.
Notice the small region of aerosol and plasma gas flow rate combinations
which produce spherical particles.
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30
X 5000
Figure 2.8
Example of partially fused but not fully melted precursor particles.
Operating conditions: applied power = 500 watts; gas identity = argon;
plasma gas flow rate = 0.6328 slpm; aerosol gas flow rate = 1.0454 slpm.
Note that this combination of flow rate is outside of the ‘processing
window of spheroidization’ depicted in Figure 2.7.
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31
1200
350 W
500 W
Volume Average Size ((xnP)
1000 -
600 W
800-
600-
400-
200
-
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Density (mg/L)
Figure 2.9
Average spherical particle size (by volume) as a function of mass density
travelling through the torch.
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32
Some clarifications are given below. Particle density is computed for room
tem perature conditions, which apply at both the input and at the trap. Since the
temperature profile in the plasma hot zone is not measured, the actual density during
spheroidization is not known. It is assumed in this work that there is a proportionality
between room temperature density and density in the hot zone. It is also important to note
that the particle density and the mass density are related. The proportionality constant at
the input to the torch is the average mass of a precursor particle. Mass density is the
more general parameter. Indeed, particle density changes with the extent of particle
growth in the hot zone.
The impact of the power supplied to the torch was studied as well. The key
finding was that raising the power, while keeping all other parameters constant, increased
the average particle size. As shown in Figure 2.8, modulations in applied power produce
a series of nearly linear curves with a slope which increases with power. This clearly
suggests that with the present system, average sphere size can be controlled. Moreover,
optimal processing conditions can be selected through control of both power and gas flow
rates.
One of the most surprising results was the operating behavior of the particle
feeder: increasing the aerosol flow rate leads to an increase in particle density in the
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33
aerosol stream (see Table 2.1 and Figure 2.9). That is, the number o f particles per unit
volume of gas increases as the flow rate increases. No fully supported explanation for
this finding is presently available.
Preliminary studies of the impact of plasma gas identity were also carried out. In
particular, it was demonstrated that the particles formed in a dry air plasma were
significantly larger than those formed in an argon plasma (see Figure 2.10). This result is
significant for another reason as well. It appears to us that this is the first report of an
atmospheric pressure plasma generated with air (20% 0 2, 79% N2, l% Ar) at low power
(500W). Indeed, significant effort has gone into increasing the oxygen content of low
power (<1 kW), atmospheric pressure RF torches. At present, the highest reported
oxygen concentration, less than 5%, are for mixtures of 0 2 in He [36,37].
One other impact of the gas selection was the shape of the ultimate particle size
distribution (see Figure 2.11). Particles formed in the argon plasma tend to have a narrow
particle size distribution, whereas those formed in air clearly contain a ‘tail’ on the large
particle end of the distribution. As noted later this probably reflects a difference in
growth mechanism. Some of the samples were examined using x-ray diffraction (XRD)
to determine the phase. These studies clearly show that the material both before and after
plasma treatment was crystalline a —alumina.
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34
Figure 2.10
SEM o f air plasm a treated particles. Notice presence of particles
approximately 50|im in diameter. This sample was collected from the
trap. Operating conditions: applied power = 500 watts; gas identity = dry
air; plasma gas flow rate = 1.5444 slpm; aerosol gas flow rate = 0.3567
slpm.
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35
Diameter (|im)
Figure 2.1 la
Particle size distribution for spherical a-alumina particles formed in an
argon plasma. Operating conditions: applied power = 500 watts; gas
identity = argon ; plasma gas flow rate = 1.358 slpm; aerosol gas flow rate
= 0.186 slpm; mean particle size = 4.43 pm.
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36
80
Figure 2.1 lb
Particle size distribution for spherical a-alumina particles formed in an
argon plasma. Operating conditions: applied power = 500 watts; gas
identity = argon; plasma gas flow rate = 1.544 slpm; aerosol gas flow rate
= 0.3567 slpm; mean particle size = 8.56 pm.
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Number of Particles
37
0
5
10
15
20
25
30
35
40
45
50
55
60
Diameter (jam)
Figure 2.1 lc
Particle size distribution for spherical a-alumina particles formed in a dry
air plasma. The long tail evident for these particles formed in a dry air
plasma can also be seen in Figure 2.10. Operating conditions: applied
power = 500 watts; gas identity = dry air; plasma gas flow rate = 0.8109
slpm; aerosol gas flow rate = 0.7013 slpm; mean particle size = 10.76 pm.
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38
2.5
Discussion
Plasma spheroidization of ceramics at atmospheric pressure is an old art [3-7,15].
However, in previous work DC plasma systems operating at high power (generally
greater than 10 kW) were used. There are several advantages to the microwave system
described here. First, far less power is used. All results described herein were obtained
at less than 1 kW. This represents a savings in terms of both energy cost, impurity
control and system stability. For instance, there are no electrodes in a microwave system
to decompose and contaminate the product. Second, particle morphology is far easier to
control with a lower power system. It appears that often in high-power plasmas the input
ceramic is completely vaporized and the final particles form, nucleate and grow from the
‘atom’ gas in the cooling afterglow [4,11,15-17,30]. There is no apparent relationship
between the size and shape of the input particles and the output particles. In other cases,
each sphere is formed from a single input particle [1,2,18]. In contrast, we show in the
present work that spherical particles were created by the sintering of many input particles.
Moreover; control of particle size was achieved both through changes in applied power
and density o f precursor powder in the present system.
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39
Some limits to this new method of generating spherical alumina of controlled size
were tested. We showed that above a maximum flow rate particles were not modified.
One untested, but obvious lim it is precursor mass flow rate through the torch. For
exam ple, our experimental data show that only 3% of the power is adsorbed for
spheroidization for a mass flow rate of 3 gm/hr. This suggests a clear upper limit to the
rate at which ceramics can be spheroidized using the present approach. Indeed, even the
optimistic assumption that the process can be run such that 50% of the applied power is
adsorbed in the spheroidization process (and 50% to maintain the plasma), yields a
maximum spheroidization rate at 500 W of about 55 gm/hr (110 gm/kW hr). Therefore,
in order to increase particle production applied power must be increased. Yet as discussed
below, increasing the applied power carries additional ramifications on final particle size.
A simple three-component ‘agglom eration’ model can explain m ost o f the
features o f particle growth in argon plasmas. First, it is postulated that given sufficient
residence time in the plasma hot zone, the irregularly shaped precursor particles melt.
Surface tension dictates that the particles will form small liquid spheres. Second, the
melted particles agglomerate due to collisions with other melted spheres to form larger
spheres. (Alternatively, or even simultaneously, the particles form agglomerates first and
then melt.) Third, the liquid spheres are rapidly quenched once they leave the plasma hot
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40
zone and are transported through the chimney. Not all features of the observations can be
explained by the three-step model above. As discussed later there is strong evidence of
atomic addition (Ostwald Ripening) growth as well.
The first step, melting, does not occur if the particles do not spend sufficient time
in the hot zone. Thus, as shown in Figures 2.7 and 2.8, at sufficiently high flow rates/low
residence times, the precursor particles tend to agglomerate, but are otherwise little
changed by passage through the torch. At even higher flow rates no change in particle
morphology was detected at all.
It appears that the particles reach a temperature in the hottest zone of the plasma
(coupler) which is above the melting temperature of alumina (2320 °K). Moreover, it is
postulated that they reach the decomposition temperature of alumina which is a function
of oxygen concentration (3750 °K) [38]. In one percent oxygen, the decomposition
tem perature is 3570 °K, and in a pure 0 2 at one atmosphere, the decomposition
temperature of alumina is approximately 4270 °K. This is postulated to explain the
spectroscopic observation that some atomic aluminum metal is present. A detailed study
of the intensity of metallic aluminium emission lines as a function of operation conditions
is provided in Chapter 3.
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41
Tem perature measurements using em ission spectroscopic methods in our
laboratory were conducted. However, accurate temperature measurement of the plasma
coupler zone, where the temperature is highest, is restricted by the microwave apparatus
geometry. Therefore, the temperatures were measured in the afterglow region, 5 cm
above the coupler. The measured gas temperatures in the afterglow region under our
operating conditions were higher than 3000 °K. Thus, the temperature is significantly
higher than the melting temperature of alumina particles (2320°K) even in the afterglow
region. Indeed, rapid cooling outside the coupler is expected [20,22-24,27,29,39]. Thus,
the coupler should be significantly hotter than a point 5 cm downstream (detailed results
in Chapter 3).
Also, from the temperature measurements, we found that the plasma is not in the
equilibrium state. The gas, electron and excitation temperatures of the plasmas were
greatly different. Thus, particle temperature in a non-equilibrium system can be
significantly different than the temperature of the plasma. Indeed, there are mechanisms
for direct heating of alumina particles which can create particle temperatures higher than
the surrounding gas. ‘Thermal runaway’ [40,41], or the direct adsorption by valence band
electrons (promoted by high temperature) of microwave field energy, represents one
mechanism for heating particles to a temperature above that of the surrounding gas.
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42
Combing these factors, it strongly supports our assumption that the alumina
particles were "melted" in the plasma.
The degree to which particles agglomerate is a function o f the number of
collisions, which in turn is proportional to both residence time in the plasma hot zone and
the density of alumina liquid drops. The residence time is controlled both by flow rate
and by the size of the hot zone. At any given flow rate, the hot zone size is controlled by
applied power. Thus, at any given flow rate the size of the particles increases with
increasing applied power (Figure 2.9). This suggests more limits to the control of output
production rate for a given sphere size. For example, in order to increase yield, power
must be increased because of the limited ‘efficiency’ of the melting process. Yet,
increasing power for a given flow rate, increases the residence time and the mean particle
diameter. Power and mass flow rate must be concomitantly adjusted to produce a selected
particle size. Yet, present data (Figure 2.9) shows that simultaneous adjustment may
force a decrease in particle yield at higher power, thus ‘defeating’ the intent of increasing
the power input.
Another factor that potentially impacts agglomeration process is particle charging.
In the plasma, the mobility of electron is much higher than that of the positive ions,
leading to the build up of negative charge, and concomitantly negative potential on all
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43
insulating surfaces, including alum ina particles in the aerosol. This leads to the
generation o f repulsive forces between particles. Our experimental results demonstrate
that growth via agglomeration took place, but still it is clear repulsive forces do impact
the particle growth rate to some extent.
Below we develop a simple two-charged-spheres model using micro-energy
balance, potential (repulsion) and kinetic energy, to determine a ‘worst case’ computation
o f the impact of charging on growth by agglomeration. The elements of the model in
brief: It is postulated that the two spheres are of equal size and carry the same amount of
charge. The amount of charges on the particles in the plasma can be calculated by the
method provides by Matsoukas [42,43]. The kinetic energy required to overcome the
"electrostatic repulsion energy", required to allow any two charged particles to collide, is
estimated by integrating the repulsion force between them along the path from infinity to
the collision point. Since the particles are carried as an aerosol the velocity of each
particle is estimated to equal the velocity of the flow stream, and the ‘relative velocity’ of
the two particles at the collision point is also estimated to equal the gas flow velocity.
The above is a ‘worst case’ model. Indeed, the particle velocity, influenced by ion drag,
thermophoresis and other factors [44] is probably significantly higher than the gas flow
velocity. Also, the effective repulsive force is probably screened at large distances by the
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44
‘ion sheath’ which forms around any negatively charged surface. There is also an
argum ent that at close distances the repulsive force is reduced by particle/particle
‘screening effects’ [44]. Finally, the gas/particle flow rate was computed assuming the
temperature o f the gas is 3(30 °K. In fact, it is probably more than ten times larger.
In this simple two-sphere model, if the kinetic energy is greater than the repulsion
energy, the two particles will collide if the two particle centers are on the line of travel
(zero impact parameter). The ratios, E ^,,^ / Erepulsio[1, were plotted against various
experimental operating conditions, as shown in Figure 2.12 (a) and (b). It is clear that for
particles larger than 3 Jim under our experimental operating the impact of particle
charging on collisions, in which the impact parameter is zero, will be zero, even for this
‘worst case’ computation.
One question remains: Will the repulsive interaction diminish the cross section?
A calculation indicates the reduction in cross section is so small it can be safely ignored.
Computation of a ‘worst case’ scenario showed the reduction of cross section to be less
than 1%. Specifically, the repulsion force was assumed to be 100% perpendicular to the
line of travel and equal that at 2R (maximum), velocity (reduced by repulsion) was
assumed equal to that at 2R (a minimum value) for purposes to computing time of
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45
interaction, and the ratio of E ^u,. / E ^ ^ , , was 1.1. Clearly, the reduction of cross section
can be neglected for value o f E ^,.^ / ErcpuIsiongreater than 1.1.
The diameter of the precursor we used in this study is about 3 fim. Thus, under
our typical experimental conditions, the possibility for two particles to collide is not
significantly impacted by charging effects. This supports our three-step model that
postulates most growth occurs via collisions leading to agglomeration. Moreover, recent
studies [42,45] showed that particle charges are fluctuated in the plasma. Such fluctuation
could render these particles neutral or even perhaps positively charged for a brief moment
to reduce the potential barrier created by electrostatic repulsive force. Thus,
agglomeration process could still take places even if Ey^,. / ErepuIsion is less than one.
It is notable that nothing in our computations is inconsistent with many earlier
observations and calculations indicating that particle charging reduces the rate of
agglomeration growth. Indeed, our calculations show that for particles smaller than about
3 microns, the impact can be significant. Most o f the earlier treatments focused on
particles in the nanometer size range, where our model and earlier models agree charging
can reduce the collision rate.
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46
Finally, it is interesting to reflect on the implications of our work. It suggests that
only very small and very large ceramic particles can be readily grown in a plasma torch.
Small particles can form via atomic addition. G enerally, particles grown by this
mechanism will not accede tens of nanometers in diameter. Also, particles can grow by
agglomeration, as long as the agglomerating units are in the micron size range. If
particles between these two limits are desired, it appears there is no clear mechanism for
rapid growth.
The existence and the appearance of very large particles on the collar (Figure
2.6d) is also consistent with the agglomeration model. It is reasonable to believe that
some particles are caught in flow fields that cause them to ‘recycle’ through the plasma
hot zone. This would be expected to increase their residence time leading to significant
particle growth. Truly large particles formed in this fashion would be expected to loose
buoyancy and hence fail to reach the particle trap.
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47
Te=1 eV —O— Te=2 eV —± — Te=3 eV —O — Te=4 eV
10000
e
e
1000
o
«
100
o
g
•»
10
LU
u
•>
B
LU
0.1
0.01
0
2
4
6
8
Particle
Figure 2.12a
10
12
14
16
18
20
22
24
Diameter ( pm)
Ratio of kinetic energy to electrostatic repulsion energy as a
function of particles size and electron temperature of the plasma.
The aerosol flow rate was set at 0.2 slpm.
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48
-Aerosol Flow=0.2 slpm
—Q— Aerosol Flow=0.4 slpm
-Aerosol Flow=0.6 slpm
—O— Aerosol Flow=0.8 slpm
10000
e
e
•>
u
1000
100
m
e
k.
u«»
•»
LU
c€>
LU
0.1
0.01
0
2
4
6
8
P article
Figure 2.12b
10
12
14
16
18
20
22
24
D iam eter ( |im)
Ratio of kinetic energy to electrostatic repulsion energy as a
function of particles size and aerosol flow rates.
The electron temperature was set at 3 eV.
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49
Kinetics of particle formation and growth are complex. Mathematical methods for
quantification of growth by collision, which can be used to predict particle growth, and
particle size distribution, are available [42,43,45-47]. From these studies, a simple
mathematical collision model which does not allow for particle shrinkage by any
mechanism, yields the following growth equation:
V - V 0 = K (k0,t ) x N 0
(2.1)
where V is the volume of the final particles, V0 is the volume of the precursor particles,
N 0 is the initial particle concentration in the plasma and K is a function of aggregation
rate constant (&q) and residence time (f). Comparing this model with the results shown in
Figure 2.9, it is clear that this simple mathematical model can explain the linear relation,
found in this study, between the final particle size generated from plasma and the
precursor density. Noted that, the V0 values obtained for the three different power levels
are different and as the power increased the V0 also increased. This variation can be
explained as the following. As the input power increased, the plasma is hotter and
therefore the alumina tube immersed in the plasma is also hotter. Since the particles were
injected into the plasma by passing through this central alumina tube (see Figure 2.1) and
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50
then into the plasma hot zone, some agglomeration may occurred while the precursor
particles still inside the alumina tube. As the value of K increases with temperature, and
presumably with power, the size o f the agglomerates may form particles forming in the
alumina tube should increase with increasing power. This explains the increase of the
initial ‘precursor volume’ (V0) with increasing power level. In short, the growth model
described above describes behavior after the particles/agglomerates leave the alumina
tube and enter the main part of the plasma.
Another observation from this mathematical model is that the slopes are also
varied as the input microwave power changed. Since the slope is a function of the
residence time and aggregation rate constant, variation of the slope in different power
level is expected. As discussed above, the length of plasma hot zone is different resulted
in different residence tim e for particles traveling through the plasma. Also, the
aggregation rate constant is a function of the plasma temperature, which increases with
increasing power input.
This m athem atical model also supports our supposition that the growth
mechanism of particles generated in the plasma torch is collision (agglomeration)
dominated.
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51
However, the three-step model does not explain all the observations, particularly
the difference in the particle size distribution (hereafter PSD) of the argon and air
produced particles. In order to explain that difference, one possibility is growth via
atomic (aluminum) addition occurs more significantly in argon plasmas than in air
plasma. Indeed, the classic agglomeration model of particle growth yields PSD similar to
that found in air plasmas (see Figure 2.11c) whereas, PSD with maximum particle size
are generally associated with growth dominated by atomic migration. In order to test for
the possibility of atomic addition the intensity of the Al metal emission at 394.4032 nm
[48] was observed. It was found in both air and argon plasmas that metallic aluminum is
present, and that the intensity of the line increases in a near linear fashion with particle
density and applied power. Thus, there is evidence that atomic addition growth is likely
as well, but no evidence that it explains the difference in the PSD of argon and air
plasmas.
The above three-step model still requires further verification. In particular a
temperature map of the plasma hot zone, as a function of all operating parameters, is
needed. This issue is discussed in Chapter 3.
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52
2.6
Conclusion
W e have applied a low power microwave plasma source at atmospheric pressure
to the treatment of commercially available a-alum ina powders. It is demonstrated that
these precursor particles are melted as they pass through the plasma and join together to
form spheres distinctly larger in size. Also in both air and argon plasmas apparently
A120 3 partially decomposes leading to some growth by the addition of atomic aluminum.
It was shown that final particle size and size distribution could be controlled by selection
of flow rates, adsorbed power and plasma gas identity. A simple mathematical collisional
model explains most of the observed behavior, but atomic addition clearly plays a role.
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53
References
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H. Shim, J. Phillips and I.S. S ilv a., J. Mat. Res. 14, 849 (1999).
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J. R. Fincke, W. D. Swank, and D. C. Haggard, Plasma Chem. Plasma Proc. 13,
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I. Bica, Mat. Sci. Eng B68, 5 (1999).
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R. Westhoff, G. Trapaga, and J. Szekely, Metallurg. Trans B, 23B, 683 (1992).
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G. Trapaga, R. Westhoff, J. Szekely, J. Finske, and W. D. Swank, Mat. Res. Soc.
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Y. P. Wan, V. Prasad, G. X. Wang, S. Sampath, and J. R. Fincke, J. Heat Trans.,
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P. V. Ananthapadmanabhan, P. R. Taylor and W. Zhu, J. Alloys Compounds 287,
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Selwyn, Plasma Sources Sci. Technol. 7, 282 (1998).
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48.
F. M. Phelps HI, M.I.T. Wavelength Table, volumes 1 and 2 (1982).
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58
Chapter 3
PLASMA CHARACTERIZATION - SPECTROSCOPIC METHOD
3.1
Abstract
Several novel ceramic processing technologies (e.g. oxide ceramic melting and
spheroidization) using an atmospheric pressure microwave plasma torch were recently
developed in our lab. Understanding the processes which apparently includes melting of
ceramic particles and optimization requires complete characterization of the plasma as a
function of operating condition.
As a first step, a non-intrusive spectroscopic m ethod was employed to
characterize gas, electron and excitation temperatures and electron densities of the
afterglow region of a microwave generated atmospheric plasma. Two-dimensional
spatially resolved mapping of gas, excitation and electron temperatures and electron
densities as a function of operating conditions during m aterial processing were
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59
developed. The non-equilibrium nature of the microwave generated atmospheric argon
plasma was revealed, suggesting that only multi-temperature model are capable of
modeling this region of the plasma.
3.2
Introduction
A novel technique for ceramic material processing using a microwave generated
atmospheric plasma torch was developed in our lab. This unique method was successfully
employed for producing spherical alumina particles o f controlled size. Methods for
generating several unique materials including spherical boron nitride, carbon nanotubes
and unique titanium oxide photo-catalyst using this new technique are also under
development. It is necessary to understand the characteristic of the atmospheric plasma to
successfully generate the desired materials in high yield. Fundamental parameters of the
plasma, such as temperature and species concentration profiles need to be determined.
From these parameters, a better understanding of the relationship between operating
characteristics and material properties can be developed. Also a modeling strategy can be
determined. Ultimately models hold great promise. The m easurement o f plasma
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60
parameters is complex and plasma characteristics are easily changed. Models hopefully
can predict changes which occur with changes in geometry, operating parameters, etc.
It is well known now that for the low-pressure plasma, the plasma is not in an
equilibrium state. Generally, there are several subsystems in the low-pressure plasma,
such as electrons, ions and neutral molecules. Each subsystem has its own characteristic
temperature to describe the energy state of the species, such as electron temperature for
electrons, gas temperature for neutral molecules and ionization temperature for those
ionized species. Based on this concept, a novel multi-temperatures model for the lowpressure plasma was developed and successfully employed to describe a low pressure
hydrogen plasma generated with microwave energy [Chapter 4]. This modeling process
compensates for the deficiency of quality experimental work. Plasma parameters such as
electron tem perature, electron density and species concentrations were accurately
predicted by the model.
Yet, even the proper modeling approach to use to describe a microwave generated
atmospheric plasma is not clear. Actually, no data exists at this time. For example, are
such plasmas in equilibrium? If the plasma is indeed in equilibrium, a single temperature
describes the electron, neutral and ion subsystems. Then Maxwellian, Boltzmann and
Saha distribution equations can be employed to calculate the species concentrations in
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61
every energy state. One major goal of this study is to determine the appropriate approach
to apply to the modeling of microwave generated atmospheric plasma. A second goal is
to characterize the plasma during the material processing.
E m pirical correlations obtained betw een product structure and plasm a
characteristics will be useful for optimizing process conditions. It may appear that the
two goals are independent, but actually they can be integrated into a single task. That is
the m apping of the plasm a param eters, including electron, gas and excitation
temperatures, and electron density, as a function of operating conditions.
Several plasma tem peratures (electron, gas and excitation) were measured
separately by assuming the plasma is in an equilibrium state. Then, by comparing these
values of temperatures, the status of the plasma can be revealed. This determines the
modeling approach, one-temperature model or multi-temperature model in which the
charged and neutral species are treated independently.
Non-intrusive spectroscopic methods were used to characterize gas, electron and
excitation temperatures and electron densities of plasmas. In this experimental study we
used light emission spectroscopy to characterize the "afterglow" region of a microwave
generated atmospheric plasm a torch with and without the ceram ic powder passing
through. Gas (rotation), excitation and electron temperatures, and electron density were
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62
spatially m apped as a function of absorbed microwave power, flow rates and
concentration of hydrogen (probe molecule) in the experiments.
The non-equilibrium multi-temperature nature of the afterglow was revealed not
only in the dramatic difference between electron and gas temperatures, but also in the
large difference between gas and excitation temperatures. Therefore, for a microwave
generated atmospheric plasma, a multi-temperature model is better to describe its
behavior.
3.3
Experimental
3.3.1
Instrumentation
A schematic drawing of the instrumentation used in this work is depicted in
Figure 3.1 and the components are listed in Table 3.1. The whole system is best described
as three subsystems, the microwave plasma torch system, the optical arrangement and the
detection system, and the spectra analytical scheme.
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63
Mr 1
Spectrometer
Computer
Optical Fiber
Plasma Torch Flame
X-Z Translate Stage
|
Figure 3.1
Gas and Sam ple Flow Inlet
Schematic drawing of the experimental set-up. A description of the
individual components is given in Table 3.1.
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64
Table 3.1
Description and specification of the experimental instrumentation.
Component
Microwave plasma
torch system
Monochromator
Grating
CCD
Optic fiber bundle
and collimated lens
Translation stage
Description
2.45 GHz, 0-1500 W
discharge quartz tube:
inside diameter: 19 mm
length 237.5 mm
Model 1250 M
1.25 m focal length, f/11
slit width: 3 fim-3mm
Slit height: 2-20 mm and
3 Hartmann 1.2mm apertures
1800 gr/mm holographic ruled diffraction
grating covering 300-900nm
Spectrum One CCD-2000x800-9
ISA exclusive SiTe manufactured 2000x800
pixel back illuminated CCD chip with
enhanced UV sensitivity
Fiber bundle containing 19, 200 pm fibers,
range of 300-900 nm
Lens attached on the fiber,
Focal length 50mm
Fiber holding translation stage:
X(radially) -Z (axially) direction
Computer controlled stepping motor
Range of travel: 50 X 50 mm
SpectraMax for windows
Data collection and
analysis
Square quartz
48x48mm in the bottom, 30cm height and
2mm in thickness
chimney
Manufacturer
AsTex, MA
Jobin Yvon-Spex
Instrument S.A.Jnc
Jobin Yvon-Spex
Instrument S.A.,Inc
Jobin Yvon-Spex
Instrument S.A.,Inc
Jobin Yvon-Spex
Instrument S.A.,Inc
Jobin Yvon-Spex
Instrument S.A.,Inc
Galactic Industries
Laboratory-built
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65
3.3.1.1 Microwave plasma torch system
A low power, atmospheric pressure, gas-flow microwave plasma torch system
was employed to generate the spherical alumina particles (see Chapter 2).
To generate the plasma and process solid ceramics contained in an aerosol, two
feed streams are fed to a quartz torch (cylinder, 19 mm ID) which passes through a
microwave (2.45 GHz) waveguide (TEto). One o f the streams (‘plasma gas’) is passed
through the main body o f the torch, and the second stream (‘aerosol gas’-contains
particles) passes through a co-axial central alumina tube (3 mm ID) which terminates
within the torch. The three stub tuner was used to couple the microwave forward power
into the discharge cavity region and keep the reflected power as low as possible.
In all cases the primary gas for both streams was ultra high purity argon
(99.999%). In some cases a small amount o f hydrogen was added. Hydrogen acts as a
probe molecule, for the purpose o f measuring the gas temperature and the electron
density. The flow rate o f the hydrogen probe gas was controlled and fed through the
central alumina tube by a high precision mass flow meter ranged from 0~I0 seem (MKS,
NJ).
For characterizing the plasma parameters with the aerosol flowing in the plasma
region, the same aerosol feeder described in Chapter 2 was used to introduce the alumina
powders into the argon discharge region to simulate the same environment.
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66
3.3.1.2 The optical arrangement
In this study, we attem pted to spatially characterize the gas, electron and
excitation temperatures and the electron density. Determination of these parameters
requires precision measurements o f specific peaks, and hence a high resolution
monochromator is required.
In order to map the radially (x) and axially (z) resolved temperatures and
densities, a high precision translation stage with 2-D control (movement in x and z
directions) was used to hold and move the fiber bundle probe and lens.
3.3.1.2A Monochromator
A high performance 1.25-m-focal-Iength monochromator (Jobin Yvon-Spex, ISA)
equipped with a 1800 gr/mm holographically ruled diffraction grating covering 300 nm to
900 nm, with a resolution of 0.006 nm, was employed to acquire the needed high
resolution spectrum for calculating plasma temperatures. In addition, the monochromator
has a high precision bilaterally adjustable entrance slit which is continuously adjustable
from 3 |im to 3 mm to meet the require resolution. A specially designed, two-lens fiber
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67
adapter was attached right before the entrance slit to focus the entrance light through the
slit and reduce the stray light.
3.3.1.2B Optical fiber bundle and attached collimated lens
An optic fiber bundle was chosen for its flexibility allowing for more rapid
reposition than lens and mirror systems. However, the acceptance angle of the optic fiber
results in a large "probe spot", which grows as the square of the distance from the target.
Moreover, the optic fiber will be damaged if it is too close to the plasma due to the high
temperature o f the plasma. Therefore, a lens with a 50mm focal length was attached in
the front of the optic fiber to reduce the effect of the acceptance angle. The focused probe
spot is around 3mm in diameter. (See experimental procedure section for details)
3.3.1.2C x-z direction translation stage
The motorized translation stage has 50mm x 50mm travel in both the radial and
axial directions with a minimum controlled step of 10 microns.
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68
3.3.1.2D Square quartz chimney
In order to eliminate UV absorption and optical distortion from the cylindrical
glass (pyrex) chimney generally used for particle collection experiments, a specially
designed square quartz (UV transparent) chimney with flat (non-distoring) faces was
used.
3.3.1.3 The detection system and spectra analysis
3.3.1.3A CCD (Charged Coupled Device!
The liquid nitrogen cooled CCD array detector, CCD-200x800-9, includes a UV
sensitive 2000 x 800 pixel SiTe chip with a 30 mm width for a maximum coverage up to
8nm spectra range in one shot.
3.3.1,3B Spectra analysis
SpectraM ax softw are was used to control the monochrom ator, CCD and
translation stage. It also provides functions for the peak intensity and position marking
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69
and several sophisticated curve fitting routines such as Gaussian, Lorentzian and Voigt
profiles which will be applied in the electron density measurement.
3.3.2
Experimental Procedure
3.3.2.1 Position of focus and line of sight alignment
The focal plane and focus alignment procedures were conducted prior to
measurement to determine the size and position of the probed plasma region. This was
done by passing light "backward" through the optical system. A He-Ne laser light entered
from the end of fiber optic (near the entrance slit side), and passed through the lens of the
front end of optic fiber (collecting light side) and focused on a gridded surface. By this
means, the focal plane, probing size and position alignment can be determined. From this
simple exercise, the probe spot size is 3 mm in diameter. Since the shape of the plasma is
cone shaped, the depth probed varies as the length of the intersection across the plasma
varies. For example the depth probed near the edge is smaller than that of the center (full
diameter).
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70
Theoretically, the Abel inversion is needed to translate the side-on measurement
to the true radial profile. Yet, a simple test indicates this was not necessary. In this test, as
the plasma was turned on, the focal plane was moved from the center (full diameter) back
to the edge (small fraction of a diameter) to create different optical depths. The intensity
variations as a function of position were very small. Therefore, the depth effect was
insignificant and thus the Abel inversion was not employed.
For the purpose of calibration, a mercury lamp was used to determine the absolute
peak position. The mercury line at 546.0753 nm was selected to be the reference line. The
repeatability of this line is 0.001 nm, which will simplify the assignment o f peaks in the
complicated spectra while comparing to the reference.
3.3.2.2 Experimental conditions
A thoroughly systematic study of the parametric effect on the plasma parameters
was conducted. Specifically the effects of absorbed microwave power, spatial locations,
gas flow rates (plasma gas and aerosol gas), addition of alum ina powder and
concentration of probe molecules on three plasma temperatures (gas, electron and
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excitation) and electron density were explored. All parameters, temperatures and density
were determined from the average of three measurements.
Figure 3.2 (a) and (b) illustrate the spatial distribution of the probe spots related to
the plasma torch in this work. The coordinate origin is at the center of the top circle of the
quartz tube and these probing areas are all on the same focal plane (x-z plane).
In the m icrowave plasma torch processing technique for generating oxide
particles of controlled size and shape, the controllable variables are forward microwave
power and two gas flow rates (plasma gas and aerosol gas). In order to understand and
improve the particle growth process, the characteristics of the plasma as a function of
these operating variables must be fully investigated. The spatial mapping of the basic
plasma properties, temperatures and electron density as a function of operating conditions
is the first step to understand the plasma behavior. From these maps, useful and valuable
information can be derived, such as the equilibrium state of the plasma and temperature
distribution profiles.
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72
ra
/
/
red spot: probing area
/■----------4th layer
y----------- 3rd layer
r ----------2nd layer
r ---------- 1st layer
\
i
/
/
/
k -:
\
plasma flame - <
1
quartz chimney
/ ,t
/ // y/
/
✓
✓
^ - - - - quartz tube
/
(0,0)
Disdharge Coupler Region
Figure 3.2 (a)
waveguide
-
square quartz chimney
/
1—
focal plane
y^enter^piO)^.
;
I
\jrr
quartz tube
.
plasma flame
Figure 3.2 (b)
Figure 3.2 (a) & (b). Spatial distribution of the probe spots in the afterglow of the
plasma torch; (a) side view; (b) top view, x and z in mm. The
shaded area roughly represents the "flame" region as seen with the
unaided eye.
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73
All of the experiments are summarized in Table 3.2 (a)~(e). They are arranged
into five sets. Firstly, we mapped the spatial profiles of the plasma parameters as a
function of the forward microwave power in three distinct gas flow regimes: plasma gas
flow only, plasma gas plus central gas flow and plasma gas with aerosol flow containing
alumina particles. The objective of these experiments is to determine the influence of the
central flow, always used in particle processing, on the overall plasma structure.
Secondly, the effect of gas flow rate on the spatial distribution of the gas
temperature was studied. In Chapter 2, we determined those conditions under which an
aerosol of alumina precursors are melted and converted to spherical alumina particles. It
was constructed by varying the plasma and aerosol gas flow rates as for a set at 500
watts. In our hypothesis, spheroidization only occurs when the plasma melts the particles
as they pass through. Once the melted particles collide with each other to form the bigger
particles and in the afterglow are quenched to form solid spherical particles. Two possible
explanations can be offered to explain the finding that at high flow rates spheres do not
form. First, the residence time is too short for enough energy to be adsorbed for melting,
and the other is that at high flow rates the temperature of the plasma is reduced below the
melting temperature of alumina. Determining the impact of flow rates on the temperature
of the plasma will help resolve the issue.
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74
Thirdly, we studied gas temperature as a function o f the microwave power and
flow rates. This set is designed to help determine optimal conditions for alumina sphere
production.
Fourthly, alumina dissociation as a function of spatial position and particle size
was studied. The intensity of the characteristic metallic aluminum emission line at
394.4032 nm was used to indicate the degree of the dissociation of alumina. The intent is
to understand the contribution o f atomic addition to particle growth. Specifically, under
what condition is the alum inium atom concentration high enough to contribute
significantly to particle growth.
Fifthly, the effect of probe gas concentration on plasma character was studied.
Hydrogen was employed as a probe molecule and useful for aiding in the determining of
the electron density and gas temperature. Generally, the level of the probe gas
concentration needs to be kept as low as possible to reduce the impact from the
introduction of foreign gas into the plasma. Too much probe gas will alter the properties
of the plasma and lead to erroneous information. For this set o f experiments, several
concentrations of the probe molecule (H2) were introduced into the plasma torch system
to determine how the probe molecule affected the gas temperature and electron density.
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75
Table 3.2 (a) Experiment conditions for spatially resolved maps of plasma parameters
(1) Plasma Gas + Aerosol Gas + Alumina Powders
Flow Rates: Plasma gas: 1.17 L/min
Aerosol gas: 0.36 L/min with the alumina powder
Probe : Hydrogen, Flow rate: 0.5 cc/min (0.03%)
Gas Temp.
Microwave Power
(W)
350,600, 750,900,1100
Radial Position (X)
(mm)
-11,-5.5,0, 5.5, 11
Axial Position(Z)
(mm)
0, 8, 16
Excitation Temp.
350,600, 750,900,1100
-11,-5.5, 0, 5.5, 11
0, 8, 16
Electron Temp.
350, 600, 750,900,1100
-11,-5.5, 0, 5.5, 11
0 ,3 ,6
Electron Density
from Ar line at
696.54 nm
350,600, 750,900,1100
- 10, -6, -2, 2, 6, 10
0, 16, 32
Electron Density
from Hp line at
486.1 nm
350,600, 750,900,1100
-11,-5.5,0, 5.5, 11
0
Parameters
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76
(2) Plasma Gas Only______________________________________
Flow Rates: Plasma gas: 1.17 L/min
Aerosol gas: 0.0 L/min and without alumina powder
Probe : Hydrogen, Flow rate: 0.5 cc/min (0.04%)
Parameters
Electron Temp.
Electron Density
from Ar line at
696.54 nm
Microwave Power
(W)
350,600, 750,900,1100
Radial Position (X)
(mm)
-11,-5.5, 0, 5.5, 11
Axial Position (Z)
(mm)
0, 3 ,6
350, 600, 750,900,1100
- 10, -6, -2, 2, 6, 10
0, 16, 32
(3) Plasma Gas + Aerosol Gas without Alumina Powders
Flow Rates:
Plasma gas: 1.17 L/min
Aerosol gas: 0.36 L/min and without alumina powder
Probe : Hydrogen, Flow rate: 0.5 cc/min (0.03%)
Parameters
Electron Temp.
Electron Density
from Ar line at
696.54 nm
Microwave Power
(W)
350,600, 750,900,1100
Radial Position (X)
(mm)
-11,-5.5,0, 5.5, 11
Axial Position (Z)
(mm)
0 ,3 ,6
350, 600, 750,900,1100
- 10, -6, -2, 2, 6, 10
0, 16, 32
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77
Table 3.2 (b) Experiment conditions for spatially resolved maps o f gas temperature in
different flow rates.
Microwave forward power: 500 Watt
Probe : Hydrogen: 0.5 cc/min
Alumina powders are introduced into the plasma.
Plasma Gas
Flow Rate
(L/min)
1.17
Aerosol Gas
Flow Rate
(L/min)
0.36
Radial Position(X)
(mm)
Axial Position(Z)
(mm)
-11,-5.5, 0, 5.5, 11
0, 8, 16
Degree
of
Spheroidization
100%
1.17
0.72
-11,-5.5, 0, 5.5, 11
0, 8, 16
50%
1.17
1.08
-11,-5.5, 0, 5.5, 11
0, 8, 16
0%
0.81
0.36
-11,-5.5, 0, 5.5, 11
0, 8, 16
100%
2.50
0.36
-11,-5.5, 0, 5.5, 11
0, 8, 16
0%
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78
Table 3.2 (c) Experiment conditions for measuring the gas temperature in different
applied power, plasma gas and aerosol gas flow rates
The focus spot is at the (x,z)=(0,0).
Probe : Hydrogen: 0.5 cc/min
Alumina powders are introduced into the plasma.
Microwave Power
Plasma Gas Flow Rate
Aerosol Gas Flow Rate
(W)
(L/min)
(L/min)
350, 600,900, 1200,1500
0.63
0.36
350, 600,900, 1200,1500
0.63
0.53
350, 600,900, 1200,1500
0.63
0.87
350, 600,900, 1200,1500
0.63
1.05
350, 600,900, 1200,1500
0.63
1.38
350, 600,900, 1200,1500
1.17
0.36
350, 600,900, 1200,1500
1.73
0.36
350, 600,900, 1200,1500
2.50
0.36
350, 600,900, 1200,1500
3.50
0.36
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79
Table 3.2 (d) Experiment conditions for measuring the metallic aluminium emission line
intensity.
(1) Spatial distribution profile
Flow Rates: Plasma gas: 1.17 L/min
Aerosol gas: 0.36 L/min with the alumina powder
Probe : Hydrogen, Flow rate: 0.5 cc/min (0.03%)
Metallic aluminium emission line: 394.4nm
Microwave Power
(W)
350, 600, 750, 900, 1100
Radial Position(X)
(mm)
-11, -5.5, 0, 5.5, 11
Axial Position(Z)
(mm)
0, 8, 16
(2) Particle size vs. Aluminium intensity___________
Probing gas: Hydrogen, Flow rate: 0.5 cc/min (0.03%)
Metallic aluminium emission line: 394.4nm
Microwave Power
(W)
350
600
750
500
Plasma Gas Flow Rate
(L/min)
Aerosol Gas Flow Rate
(L/min)
0.63
0.63
1.36
0.63
0.63
1.38
0.63
1.36
1.36
0.63
0.63
0.63
0.81
1.36
1.17
1.17
1.17
0.53
0.36
0.19
0.36
0.53
0.36
0.36
0.36
0.19
0.36
0.53
0.70
0.70
0.19
0.43
0.36
0.70
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80
Table 3.2(e)
Experiment conditions for determining the effect of probe concentrations
on gas temperature and electron density
Plasma Gas + Aerosol Gas + Alumina Powders
Flow Rates:
Plasma gas: 1.17 L/min
Aerosol gas: 0.36 L/min with the alumina powder
Probe : Hydrogen (Hj)
Microwave Power
Probe Concentration (Ho)
(W)
(%)
Gas Temp.
350, 600, 750, 900, 1100, 1300, 1500
0.05, 0.2, 1.0
Electron Density
350, 600, 750, 900, 1100, 1300, 1500
0.05, 0.3, 0.6, 1.0
Parameters
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81
3.4
Characterization o f Plasma Parameters
3.4.1
Gas temperature
The gas temperature in a discharge is normally assumed equal to the rotational
temperature of some diatomic molecular species present in the discharge [1]. It is argued
that due to the low energy involved in the rotation process, the equilibrium between the
kinetic energy of the heavy particles and the internal rotational states of the molecular
species will be reached very rapidly. In general practice the rotational temperatures of the
molecular ion of N2 (N2+) and the OH radical are employed to determine the plasma gas
temperature as the rotational spectra (e.g. line assignment, statistical weight and transition
probability) of these two species are the best known.
As discussed below, the rotational temperature of the argon plasma could actually
only be measured in the presence of alumina aerosols and low concentrations of
hydrogen probe molecules.
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82
M ethodology:
The intensity of the emission lines (Icm) from the rotational bands measured in the
grating spectrometer can be expressed as follows [2]:
= c 'A j h j e x p
-E r hc
kTrot
(3-1)
where:
c ’ : a constant in any one band in Hund’s cases (a) and (b)
A j : transition probability of rotational level j
h : Planck’s constant
c : the speed of light
A : the wavelength of the line
k : Boltzmann constant
Trot: rotational temperature
Er
: energy level of the upper electronic state having the J ’ rotational level
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83
Using the relationship between line intensity, transition probability, wavelength
and excitation energies given in the above equation, the rotational temperature can be
calculated from the slope (slope = -0.625/Trot) of a Boltzmann plot of log
~IX
vs Ej.
A
The more lines are selected, the more accurately temperature can be determined. The
rovibronic band of N2+ is generally believed to be a better choice than the OH radical,
because it provides more lines leading to better statistics [3]. However, in an argon
plasma, nitrogen m ust be added as a probe molecule. Unfortunately, test studies
conducted with nitrogen concentrations as high as 10% did not produce lines in the
—AT2"!.* (First N egative System) band of N2+ strong enough for accurate
determination of rotational temperature. Thus, the A 2lL +—^ 1 1 ,. band system of OH
radical was chosen to be the probe for the rotational temperature.
It was found that the addition of a small amount of hydrogen (0.05%) led to the
formation of OH radicals, but only in the presence of alumina particles. Concomitant
consideration of this finding and the earlier discovery that some alumina is dissociated
into aluminium and oxygen atom inside the plasma suggested oxygen atoms from
dissociated alumina combine with hydrogen atoms, from dissociated hydrogen (H2), to
form the OH radicals. Thus, in the presence of alumina aerosols, a sufficiently clear and
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84
strong emission spectrums of the OH
—J f1n,. band in the range from 307 to 315
nm was present for determining rotational temperature.
There are five main branches (O, P, Q, R, S) and several minors can be observed
for total of 12 branches: 0 12, P,, P2, P 12, Q„ Q21, Q2, Q12, R,, R21, R2 and S2l in the
—-T'2I l / band. In this study, the rotational temperature was determined from the
Boltzmann plot by using the Q, branch of the OH (0-0) band due to its well defined line
assignment [4] and transition probabilities [4, 5]. A typical spectrum of OH (0-0) band in
our plasma torch during the growth of spherical alumina particles is shown in Figure 3.3.
Line assignments, wavelength, transition probabilities and energies are given in the Table
3.3 [4, 5].
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Counts
85
1800-
1600-
1400 -
ii
JIB
u
W a v e le n g th (nm )
Figure 3.3
A typical spectrum of the OH band, used in determ ining rotation
temperature (gas temperature).
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86
Table 3.3
Assignment, wavelengths, energies and transition probabilities for the Q,
branch o f the OH (0-0) band.
Q, Branch
Quantum Number
Wavelength
Excitation Energy
Transition Probability
K
X(nm)
(cm'1)
A (108 s'1)
2
307.844
32,543
17.0
8
309.239
33,652
67.5
9
309.534
33,952
75.8
10
309.859
34,283
84.1
13
311.022
35,462
100.6
14
311.477
32,915
108.8
15
311.967
36,397
125.2
16
312.493
36,906
133.3
17
313.057
37,444
141.5
18
313.689
38,008
149.6
19
314.301
38,598
157.7
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87
3.4.2
Excitation Temperature
In a microwave generated plasma, only electrons (free or in conduction bands of
solids) gain energy directly from the applied field. Electrons subsequently transfer energy
to the heavy particles either by elastic or inelastic collision resulting in excitation,
ionization and dissociation. These "excited" states subsequently relax by transferring
energy to rotational, vibrational and translational modes. Thus, there is no reason for the
various energy modes to be in equilibrium. Measure of the difference between rotation
and excitation temperatures can thus provide insight into the degree of non-equilibrium
existing in a plasma.
Methodology:
It is generally assumed that excitation states have a Boltzmann distribution
[6-18], In this case, the ratio of the number densities np and nq of bound electrons in two
states of energy, Eq > Ep is described by the following equation :
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88
^
ftp
=£^xp
& p
(3.2)
e x c (p -q )
where gp and gq are the statistical weights of the two levels p and q.
If consideration is given to the total number density nt of atoms in question, the above
equation can be expressed by
e
-E
ftq = ft, ^ ^ r eexp[-—
x p [ - ^9]
& T)
(3.3)
where Texc is called the excitation temperature and the Q(T) is the internal partition
function defined as:
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89
The line intensity /
deduced from the Boltzmann equilibrium is written as the following:
he
47tA.
An
(3.5)
where nq is the population of the upper state, A is the transition probability (s'1) for
spontaneous emission from state q to state p, h is the Planck’s number, c is the speed of
the light and A is the wavelength o f the emission line.
From equations (3.3) and (3.4), the line intensity of a transition from level q to level p can
be expressed in the form
he
SaA ~ —exp [—
AnX q OUT)
kT
(3.6)
From this, the excitation can be directly calculated from the absolute intensity of the line,
however, since the accuracy of the transition probability A , partition function Q(T) ,and
statistical weight gq are not high usually, the relative line intensities method is employed.
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90
Rearranging and taking the logarithm of the above equation,
J ^
_£
Iog[ ^ ] = constant + [---- - ]
g qA
(3.7)
k T ' Xc
IX
It follows that the values o f log[~— ] of several lines will be a linear function of the
g qA
excitation energies and the excitation temperature can be determined from the slope if we
IX
plot the log[] vs. excitation energies. By this relative line intensity method, the
g qA
excitation temperature can be calculated from the slope of the Boltzmann plot without the
measurement of the absolute line intensities or knowledge of the concentration of the
em itting species. Greater accuracy is obtained if the em ission lines cover a wide
excitation energy range.
A simple line pair method using only two emission lines, a special case of the
Boltzmann plot method, has also often been used to estimate the excitation temperature
[17, 19, 20]. Considering two emission lines which have m and p as two upper levels and
n and q as the two lower levels and using equations (3.3) and (3.6), we obtain
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91
k
) / ^ n m S n K m ^ n m )]
The line pair method is less accurate than the Boltzmann plot method, as slight
changes in signal intensity will dramatically alter the slope of the line and result in
erroneous temperature. Therefore, in this study, we use the more accurate Boltzmann plot
method to determine the excitation temperature.
To avoid the inevitable disturbance of the plasma from probe molecules, the
emission lines from the plasma gas itself are preferred. Thus in the present work, argon
lines were used. But, in other cases thermometric species such as Fe, Cu, Cr [6, 9, 18,
21-23] were introduced into the plasma for the same purpose.
The argon lines selected in this study were those which best fit the following criteria [24]:
(1) No spectral interference near the observation band.
(2) A wide range of the upper state energies of the selected lines to minimize errors
(3) No self-absorption in the plasma.
(4) Accurate values of the transition probabilities.
The wavelengths, transition probabilities and upper-state energies of the argon
emission lines used in this study are summarized in the Table 3.4 [25].
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92
Table 3.4
Wavelengths, energies, statistical weights and transition probabilities of
the argon emission lines used in determining the excitation temperature.
Wavelength
Excitation Energy
Statistical Weight
Transition Probability
A, (nm)
E (cm '1)
g
A (108 s'1)
415.859
117,184
5
0.0145
419.832
117,563
1
0.0276
451.073
117,563
1
0.0123
675.284
118,907
5
0.0201
696.543
107,496
3
0.067
727.293
107,496
3
0.02
738.398
107,290
5
0.087
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93
3.4.3
Electron Temperature
In microwave generated plasmas, the electrons gain energy from the field and
accelerate and then by collision with neutrals create ions, excited molecules and radicals.
The rates of these processes are a strong function of the electron temperature. Thus, any
model of microwave generated plasmas, requires electron tem perature profile for
determination of the local kinetic parameters.
The Langmuir probe method is the most commonly used technique for measuring
the electron temperature o f microwave plasmas. In fact, the floating double-metallicprobe method of Johnson and Malter [26] developed in 1950 is the standard procedure to
measure the electron temperature for plasmas. Yet, this technique is not applicable to the
atmospheric plasma torch system because the metallic probes may disturb this high
density plasma torch more significantly [27] and metal probes are not "stable" in the
conditions presented in the microwave discharge (e.g. gas temperature > 3000 °K). Also,
the Langmuir probe m ethod only measures the tem perature of the highest energy
electrons in the plasma not the average temperature [6, 26, 28]. Therefore, a non-intrusive
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94
spectroscopic method for measuring the electron temperature from the emission intensity
ratio o f an argon line and its adjacent continuum was the only option for this study.
M ethodology:
The non-intrusive spectroscopic method, line-to-continuum intensity ratio, is
employed to evaluate the electron temperature. The electron temperature is calculated
from the experimentally observable line-to-continuum intensity ratio. The following
figure, Figure 3.4, demonstrates the definition of the critical parameters; line and
continuum (continuous background) intensity.
Free electrons are effectively in non-quantisized energy levels and the free-free or
free-bound electron transitions may occur. In the spectrum region below 500 nm, the
radiative recombination process, shown below, is predominant in atmospheric pressure
argon plasmas:
Ar++ e —» A r + h v
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95
max
C ontinuum (lc)
X
Figure 3.4
Line profile with definition of line intensity Imax, continuum
intensity Ic, and full width at half maximum (FWHM).
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96
This process leads to the emission of a continuum of which the intensity is a function of
the wavelength [29, 30]:
i ca ) =
(
^ (AA)n,nt.
16tk6
3c 2 ^ [ 6 n k m * J
1 - ex p [■
] + G exp[ ^C ]
v
k k T '\
(3.8)
On the other hand, the intensity of emission line can be expressed as the following
[29,30]:
he
4 x Xl
h3
k .\S i
L 2C/<- J
(I n k n i f n
Te3n
e - .p f £ ' ~ £ M
P
kT
(3-9)
Where:
A 2, : Einstein transition probability of spontaneous emission between lelev 2 and 1;
c
: Speed o f light;
e
: charge of electron;
E2 : energy of atom level 2;
Ej : ionization potential;
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97
G : free-free Gaunt factor;
g2 : degeneracy of level 2 ;
h : Planck's constant;
Ic : observed emission intensity of continuum;
I ^ : observed emission intensity of the line;
k : Boltzmann constant;
m : mass of electron;
ne : electron density;
n, : ion density;
Te : electron temperature;
U i: partition function of ion;
Xc : wavelength of continuum;
XL : wavelength of emission line;
A X : wavelength bandwidth;
£ : free-bound continuum correction factor.
Theoretically, from the individual equation (3.8), the electron temperature can be
calculated if the electron density is known. In that case the ion density can be assumed to
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98
be equal to electron density because of the neutrality of the plasma. Unfortunately, not
only the continuum intensity is insensitive to the electron temperature, but usually the
electron density is not accurately known from other measurement. Therefore, the
accuracy of the electron temperature calculated from the continuum intensity is not high.
This is why Bastiaans [29] and Batal [30] proposed the line-to-continuum intensity ratio
method. This method unlike earlier methods does not require knowledge of the electron
density. Taking the ratio of the equations (3.8) and (3.9), we can obtain the following
formula for calculating the electron temperature:
4<j3/2„3
256n:3e6k
^2 1 # 2
exp[- - - -^ 22]
Ut AA£Tr
kT'
(3.10)
Since the adjacent continuum is chosen, the Xc is taken to be equal to A,L in the above.
The Argon 430 nm line is generally used [29, 30] because the A value (transition
probability) is well known and the % factor is independent of the temperature at this
wavelength. These parameters are summarized in Table 3.5 [29].
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99
Table 3.5
Parameters of Ar (430 nm) for the calculation of electron temperature
430nm
U,
5.5
A2j
3.1xl05 (1/sec)
Si
5
G
1.1
Ei
2.525x10 18 J
e2
2.324x10 18 J
AA,
0.0039 nm (with the slit 6 pm)
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100
The electron temperature can not be solved directly form equation (3.9), thus iterative
approach was taken.
The continuum is often wrongly identified as the "background" signal. The
background truly should be used for all the radiation that originates from the plasma and
reaches the spectrometer when no analyte is present. In this study, the continuum
intensity is determined by the following procedures:
(1)
Take the spectrum as the plasma torch off. This is the true background intensity.
(2)
Take the emission spectrum of the Argon 430 nm line with the plasma torch on.
The measured continuum from this spectrum is sum of the true continuum signal
and the steady background signal.
(3)
Subtract the background from the measured continuum to obtain true continuum.
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101
3.4.4
Electron Number Density
The electron number density is the key component in every kinetic model, energy
or power balance of a plasma [31, 32].
There are several spectroscopic methods for determining the electron number
density such as the line broadening technique (Stark effect), the Saha method, the
continuum method based on the intensity of the continuum [33] and the Thomsonscattering method [34-37].
The Stark line broadening technique is the most frequently used method, because
it does not require any assumptions about the thermodynamic states of the plasma. In
contrast the Saha method and the continuum method are both constructed on the
assumption that the plasma is in thermodynamic equilibrium. Our work shows that this is
not a valid assumption for the plasma torch. The Thomson-scattering method is simply
too complicated and expensive to use in our application. Thus, like most others, we used
the line broadening technique.
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102
Methodology:
It's well known that the broadening of spectral lines results from several natural
sources [33, 38-43], as well as by the measurement process itself. Still, the major cause
o f line broadening in a plasma is due to the high charge density present. In fact, as
discussed below, the measured line broadening can be interpreted to yield electron
density.
The first type, natural line broadening results from the Heisenberg's uncertainty
principle and generally the half-intensity width is on the order of 10 "snm. In most of the
atomic emission spectral lines, the natural line broadening is insignificant compared to
other sources, Doppler, pressure and instrument broadening.
The second type of broadening caused by the thermal motion of an emitting atom
toward or away from an observer leads to a wavelength shift of the spectral line, is called
Doppler broadening. For a purely Doppler broadened line, one obtains a Gaussian type of
intensity distribution [42]. The full width at half-maximum caused by the Doppler effect
AADcan be written as the following [42]:
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where T is gas temperature and m is the atomic mass.
From this equation, the Doppler broadening is most pronounced for lines of light
element at high temperatures.
Pressure broadening, the third natural cause of line broadening, is caused by the
interaction of emitting atoms with surrounding particles. From the physical point of view,
it can be further divided into three different types of interactions. First, resonance
broadening is caused by interactions with the atoms of the same kind. Second, the Van
der Waals broadening results from interactions between atoms or molecules o f different
kinds. Third, Stark broadening is caused by interaction with charged particles, ions and
electrons. It's the dominant mechanism of broadening in plasmas, because plasmas
contain high concentrations of ions and electrons.
Broadening also results from dispersion and scattering caused by slits, gratings,
etc, of the spectrometer. This type of broadening usually can be described by a Gaussian
profile.
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104
As noted above, broadening resulting from the interaction between the emitting
atoms and the local electric field generated by the surrounding ion and electrons is the
most significant cause o f broadening in a plasma. This phenomenon is called Stark
broadening. Mathematically, it can be described with the following equation:
AXs = C{ne,Te)na'
(3.12)
where AAr is the full width at half-maximum (FWHM) caused by the Stark broadening,
ne is the electron number density, Cfti^ TJ is a function of electron density and electron
temperature. In the case o f quadratic effect which is applied to argon lines, the constant a
is equal to 1 and in the case of linear effect applied to hydrogen line, a is 2/3. Generally,
the Stark broadening (Lorentzian) of argon and hydrogen lines is exceptionally large
compared to other broadening generated by the other mechanisms, and the C(ne, Te) for
both species is only a weak function of the electron density and electron temperature.
In this work, since argon and hydrogen (dilute probe molecule) were both present,
we had the opportunity to determine the Stark broadening effect from both the argon and
hydrogen lines. The Ar I line, 696.543 nm, was selected because it is a strong and well
isolated line of the neutral argon spectrum. Hydrogen was only added as a very dilute
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105
probe for determining rotational temperature. In fact, the impact of hydrogen atom
concentrations on line broadening was used to investigate gas interactions. Determination
of electron density from each species has advantages and disadvantages. Argon line
broadening is free from interference, but is slight in magnitude. The magnitude of line
broadening for hydrogen is greater, hence easy to measure.
The working equation for determining the electron number density from the Stark
broadening effect of the Ar line (696.54nm) is the following [44]:
ne = - ----------^ 2 ------------x lO 17
e (1+0.067) x 0.08297
(3.13)
where AAS is in nanometers and ne in cm'3.
In the measurement o f electron density from the Stark width, the Hp line
(486. lnm), which is the second line of the Balmer series of Hydrogen atom, is commonly
used for the following reasons: extensive and reliable data about the C(ne, TJ exist in the
literature, it does not overlap other lines. The line is broadening significantly relative to
the natural line width and there is no self-absorption. The most accurate equation
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106
available in the literature regarding the calculation o f electron density from the Stark
broadening of the Hp line is expressed as the following [45]:
logn, = C0 + Ct log(AAj) + C,[log(AA,)]2 + C3log(re)
(3.14)
with C0=22.578, Cy= 1.478, C2= -0 .144 and C ^O . 1265 when AA5 is expressed in
nanometers and ne in cm'3.
The natural and Van der Waals line broadening (10‘6 nm) are neglected in this
study, since they are at least two to three orders of magnitude lower than the Stark and
Doppler broadening [44].
As noted earlier, the observed spectral line broadening actually is a combination
of Doppler, Stark and instrument broadening. A deconvolution procedure is needed to
determine the true Stark broadening AAS from the observed spectral line width AAC.
Firstly, the FWHM of the instrument broadening, AA, is determined by fitting the
spectral line of the He-Ne laser at 632.8 nm through the same optical set up as a Gaussian
profile. Secondly, the equation (3.11) was used to calculate the FWHM of the Doppler
broadening, AAD. The gas temperature employed in the equation was the estimated value
from the result obtained in previous section. Since the D oppler and instrument
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107
broadening both produced the Gaussian profile, they can be lumped together as one
Gaussian part of the spectral line expressed as the following [45]:
(3.15)
Thirdly, the Voigt function which is the combination of Lorenztian and Gaussian profiles
was introduced to fit the observed spectral line [40]. During the fitting process, the
Gaussian part resulted from Doppler and instrument broadening was fixed. Then the
Lorentzian part (Stark broadening, AA5) of the line can be determined and therefore the
electron number density is known.
A comparison of various line broadening width is shown as the following, Table 3.6:
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108
Table 3.6
Comparison o f the line broadening from various sources.
Sources
Condition
Line Broadening (nm)
Natural Broadening
Doppler Broadening
10'5
T - 3000 °K
4 x 10‘3
T~ 3000 °K
2 x 10‘2
Electron density ~ 10I3cm'3
10"4
Electron density ~ 10I3cm'3
5 x 10*2
[Ar, 696.543 nm]
Doppler Broadening
[Hp, 486.1 nm]
Stark Broadening
[Ar, 696.543 nm]
Stark Broadening
[Hp, 486.1 nm]
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109
3.5
Results and Discussion
There were two motivations for this study. First, we proposed to obtain basic
information required to determine the appropriate approach to modeling. Specifically, the
focus was to test the hypothesis that the traditional LTE (one-temperature) model is
inadequate, and that a multi-temperature model is needed. Second, we hoped to produce
enough information regarding the impact of operating parameters on plasma structure to
help optimize some of the novel material modification techniques we developed using the
torch.
For example, we developed (and patented) a technique for melting and
spherodizing ceramic particles, over a narrow range of operating conditions using a
microwave atmospheric plasma system. To better understand the mechanism of ceramic
particle melting and consequent spherodization, it is clear that plasma characteristics,
including rotation and, excitation temperatures, as well as electron temperature and
density need to be mapped as a function of operating parameters.
Both goals were reached by an analysis of the plasma characteristics. For
example, it is clear from the data that there are dramatic differences in the temperatures
of the excitation, rotation and electron temperatures at virtually every point in the
afterglow. Also, the LTE model totally fails a ‘self-consistency’ test. Thus the data
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110
strongly support the need for a multi sub-system , multi-temperature approach to
modeling. There were many surprising qualitative findings regarding the structure o f the
afterglow that may prove important in designing processes. Among the most interesting
was the finding that the rotation temperature gradient is surprisingly flat, and significant
increases in adsorbed power are not matched by increases in the rotation temperature.
Also, the electron temperature under some operating conditions reaches a maximum in
the afterglow, although there is no field in this region. This suggests that there may be
charge separation in the afterglow region.
This section is arranged as the following fashion: In Part I, "Thermodynamic
Equilibrium in Plasmas", different concepts o f plasma equilibrium are reviewed. In Part
II, "Characterization of the Plasma Torch with the Aerosol Containing Alum ina
Particles", plasma parameters were determined under various applied microwave powers,
gas flow rates and probe concentrations and with and without ceramic particles added as
an aerosol. In Part III, "Non-Equilibrium Plasm as", a detailed discussion o f the
equilibrium status of microwave atmospheric plasma is offered. In Part IV, "Effect of
Two Flow Streams", the influence of the central flow on the overall plasma structure is
described. Part V is the "Summary".
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I ll
Part I. Thermodynamic Equilibrium in Plasm a
1.1
Complete Thermodynamic Equilibrium (CTE)
CTE is a state in which every energy exchange process in a system is balanced by
its own reverse process [46, 47]. The energy distribution in this state (CTE) can be fully
expressed by the Maxwellian, Boltzmann, Saha and Planck equations. From a statistical
and microscopic point of view, Maxwell's equation describes the distribution of the
kinetic energy of the particles in the system , Boltzmann's equation represents the
population distribution of the different bound states o f the particles, Saha's equation
defines the population distribution of the ionization products, and Planck' law is used for
the radiation distribution. Under this condition of complete thermodynamic equilibrium
(CTE), these distributions described above can be characterized by a single temperature
(T) because
rri
*
f ii
^ kinetic
* excitation
ion
*■
radiation
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112
where
Tkinetic : the temperature characterizing the Maxwellian distribution.
Texdtation • the temperature characterizing the Boltzmann distribution.
Tion
: the temperature characterizing the Saha distribution.
Tfadianon : the temperature characterizing black body radiation.
For a plasma system, if the pressure and composition are known and if the system
is in
complete thermodynamic equilibrium, only one temperature (T)isnecessary to
describe the energy distribution of every subsystem completely. The kinetic temperature
of all particles in the plasma is defined by Maxwell's equation. Note the population
temperatures for rotation, vibration, excitation and ionization defined by Saha's and
Boltzmann's distributions equation are all the same. Also, the macroscopic variables,
such as thermal and electrical conductivity, viscosity and enthalpy can be characterized
by the same temperature T.
However, for a plasm a system, complete thermodynamic equilibrium is a
theoretical concept never applicable to real plasmas. For a plasma in complete
thermodynamic equilibrium the energy exchange processes taking place include those
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113
collisional processes mentioned above as well as radiative processes. Based on the
concept of balance between the forward rate and reverse rate of processes, the photons
emitted from inside of the plasma must be absorbed before leaving the plasma (Planck's
law). Therefore there would be no emission from the plasma. Yet, this is simply not true
for laboratory luminous plasmas. They can not be described by this ideal complete
thermodynamic equilibrium condition due to the energy loss from the discharge in the
form of radiation that is not reabsorbed within the plasma. Also, the nature of microwave
generated plasmas preclude CTE. In a microwave system, virtually all field energy is
adsorbed by free electrons (Exception: direct adsorption by conduction band electrons of
solids in the plasma). Energy of the hot electrons is then transferred primarily by
collisional processes to other species. In short, the electrons are far hotter than all other
species.
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114
1.2
Local Thermodynamic Equilibrium (LTE)
Because of the inadequacy of the complete thermodynamic equilibrium model for
actual plasm as, an approximation, local thermodynamic equilibrium (LTE), was
introduced to model zoned plasmas [46-49].
Local thermodynamic equilibrium describes plasmas in which Planck's balance is
violated but all other balances are locally in equilibrium. All parameters have to be
specified locally. In short, the following three conditions must be met locally:
1. The absence of the balance of Planck's law is required. Readsorption o f radiation
generated in the plasma is neglected. That is, the plasma is assumed to be optically
thin.
2. Populations of all bound states are described by the Boltzmann and Saha distribution
with a common temperature (T) being appropriate to all distributions. In other words,
all the excitation, rotation, vibration and ionization temperatures are equal.
3. The kinetic energy of all particles in the plasma obeys the Maxwellian distribution
and is expressed by the same temperature (T).
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115
LTE is a concept unique to plasmas and the existence of LTE simplifies plasma
diagnostics processes, since as m entioned above, the measurement of macroscopic
parameters is sufficient to characterize the microscopic states. For example, measuring
one temperature is sufficient to characterize the entire plasma as the temperature is
known. From these distribution equations, the populations of all excited and ionization
states can be theoretically calculated. And vice-versa, if one of the species densities is
known, according to these equations, the temperature can be determined. Thus, all the
param eters of the plasm a such as tem perature and concentrations are obtained.
Consequently, it is worthwhile to devote effort to determine whether the LTE model
adequately describes our microwave atmospheric pressure plasma system. This is an
issue never previously resolved for microwave produced plasmas. Indeed, earlier studies
of atmospheric pressure plasmas focused on physically far smaller systems.
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116
1.3
Criteria for existence of Local Thermodynamic Equilibrium (LTE1
The normal method for proof of the existence o f LTE is to m easure the
temperature in the discharge region of the plasma using the equations derived from the
M axwellian, Boltzmann and Saha distributions. If all m easured temperatures are
identical, clearly LTE is an adequate model.
In practice this amounts to a self-
consistency criteria, as the equations used to derive the various sub-system temperatures
assume the existence of LTE.
Another approach for determining the appropriateness of LTE model is based on
the electron density. A necessary condition for the LTE model to apply is that the
electron-collisional rates for a given transition exceed the corresponding radiative rate by
about an order of magnitude [46]. In other words, the LTE approximation becomes useful
when time scales for local energy exchange by radiation are much longer than the mean
time between efficient collisions. In a plasma, free electrons, which have high speed and
short mean free path, are primarily responsible for collisional energy exchange. Thus to
fulfill this requirement of LTE, the plasma must be collisionally dominated and therefore
a minimum concentration of free electrons is required. Mathematically, the criterion of
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117
number density of electron necessary for complete LTE has been calculated by Griem
[46] and is given by the following:
n >9x10
17
(c m -)
(2 . 16)
where ne is the electron density in a volume of 1 cm3, E2 is the first excited level (upper
resonance level) which is 11.548 eV [50] and EH is the ionization potential for atomic
hydrogen, 13.597 eV [33].
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118
Part n. Characterization of the plasma torch with the aerosol containing alumina
particles
II. 1
Electron Temperature
It's well known that in microwave plasma, the electrons gain energy directly from
the field and then by collision transfer their energy to neutral molecules to create ions and
excited molecules and radicals. The electron temperature is the most important parameter
for characterizing the plasma and is often be used as an indicator of plasma energy. In
this study, the resolved spatial region of the electron temperature only covered the region
7 mm in height (z-axis) above the top of the coupler, because the signal from the argon
emission line (430 nm) was too weak to be detected above this level. The results are
shown in Figure 3.5 (a)~(e).
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119
(a) 350W
(b) 600W
7
7
(c) 750W
(d) 900W
7
7
10 15
100W
Te (eV)
<= 0.010
<= 0.809
<= 1.607
<= 2.406
™ <= 3.204
3SS <= 4.003
<= 4.801
<=
5.600
> 5.600
Figure 3.5
2D Spatially resolved maps of electron temperature as a function of
applied microwave pow er, (a)350W , (b)600W, (c)750W , (d)900W ,
(e)1100W, x and z in mm. Experimental condition: plasma gas: 1.17
L/min, aerosol gas with alumina : 0.36 L/min, probe (H2): 0.5sccm
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120
From the results, it is clear the electron temperatures are strongly dependent on
the microwave power. As the power increased from 350 to 1100 watts the electron
temperature of the center core (hottest area) of the plasma in the afterglow region
increased from approximately 2 eV to 6 eV (leV =11600 °K). It exhibits a nearly linear
relation between the applied microwave power and electron temperature. This is
consistent to the known fact that the electrons absorbed the power directly from the
microwave field.
Generally speaking, for the spatial profile of electron temperature, for all five power
levels, there is a hot region in the middle above the exit from the coupler region and the
electron temperature gradually decreased radially (x) and axially (z).
The shape of the vertical temperature profile is mostly as anticipated. Generally, the
coupler is designed to concentrate the energy in the center where presumably will be the
hottest in terms of electron temperature because the electron absorbed the energy directly
from the field. Therefore, it is reasonable to anticipate the electron temperature will be
highest at the exit from the coupler zone and will monotonically decrease with increasing
distance from that point. There are some conditions (specifically 600 and 750 W) where
there is some evidence of variance from this pattern. This is much more pronounced in
gas only plasmas, and thus will be discussed later.
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121
The radial profile, hottest in the center, is also similar to that anticipated. In a true
‘optically thin’ plasma in which virtually all energy is lost by radiation, a nearly flat
profile would be expected. Thus, the observed profile suggests that either the plasma is
not optically thin or, energy loss by non-radiative processes (collisions) is significant.
The latter seems more likely, particularly as electron density gradients (later) indicate
strong diffusional transfer away from the center is anticipated.
fi.2
Gas Temperature (Rotational Temperature)
The gas temperature is the representation of the kinetic behavior of the heavy
(molecules, atoms and ions) particles. In a plasma, the gas temperature is often described
by the rotational temperature of the probe molecule introduced into the plasma. In this
study, OH radicals were used as the probe molecule. The rotational temperature is
determined from a Boltzmann plot of selected line intensities in the rotational band of OH
radicals. Two typical spectra, at two temperatures, of the Q[ branch of the OH (0-0) band
observed in this study were shown in Figure 3.6. These spectrums show the clear impact
of temperature on the shape of the rotational band " envelope".
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122
4500-
3500M
3000
2000 “
l Il
1000311
W a v e le n g th (n m )
Figure 3.6 (a)
70000-
20000-
10000'
307
308
309
310
311
«
312
313
W a v e le n g th (nm )
Figure 3.6 (b)
Figure 3.6
Spectra of Q[ branch of the OH (0-0) band observed at two rotational
temperatures.
(a) Rotation temperature : 2951 °K , (b) Rotation temperature : 3346 °K
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123
A three-step model [51] postulating that the particles first melted then collided
and finally quenched in the afterglow to form solid spherical particles was shown to be
consistent with observation [Chapter 2]. The weakness of that model was the lack of
information regarding plasma temperature. In particular, it remained to be shown that the
temperature of the plasma was high enough to "melt" the alumina particles.
It was shown in the present work, Figure 3.7 - 3.9, that the gas (rotational)
temperature measured in the afterglow region was higher than 3000 °K, ( 3000 to 3500
°K) under those conditions previously shown to generate spherical alumina particles
[Chapter 2]. Thus the temperature is significantly higher than the melting temperature of
alumina particles, -2320 °K even in the afterglow. Moreover; the temperature in the
coupler region is likely to be far higher than that found in the afterglow. Thus it is clear
that the particles travel through several centimeters of space (> 6cm) in which the
temperature is above the melting temperature of alumina.
In the previous chapter it was shown that there exists a relatively narrow range
two flow rates over which spherical alumina particles form. At higher flow rates the
output particles are virtually indistinguishable from the input particles. Two possible
explanations of this experimental finding are that the residence time of particles in the hot
zone (T>2320 °K) of the plasma is too short to allow for melting and that the temperature
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124
of the plasma is too low at high flow rates (no hot zone). To determine which explanation
held greater significance, a systematic study of the operating parameters, such as applied
power, gas flow rates on spatial distribution of the rotational temperature of the plasma
was performed. It should be noted that all the rotational temperatures were determined in
the presence of alumina containing aerosol, because the probe molecule, OH radical, only
formed with alumina particles present (see Experimental section).
n.2.1 2D spatially resolved maps of the gas temperature as a function of applied power
Two-dimensional spatially resolved mappings of the gas (rotational) temperatures
as a function of applied power were determined for the microwave atmospheric plasma
torch.
The first set of temperature profiles were collected to characterize conditions that
led to the formation of spheres. Specifically, only one particular combination of plasma
gas and aerosol gas flow rates, 1.17 and 0.36 L/min respectively, were used as this
combination of flow rates is the m ost efficient, in terms of yield and stability, for
producing spheres. Also, the impact o f the applied power was fully explored. Seventy-
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125
five data points were taken; fifteen probe spots spatially for each of five applied power
levels (350 to 1100 watts) studied. The results are shown in the Figure 3.7 (a)~(e) where
the x and z are in unit o f mm.
One surprising result is that the rotational temperatures did not show a strong
dependence on the applied power. They increased monotonically over the range: 3000 to
3400 °K as the power increased from 350 to 1100 watts. This increase in temperature
clearly does not match the three fold increase in adsorbed power. It also contrasts with
the behavior of electrons, whose temperatures increased roughly proportionally to the
applied power.
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126
(a) 350W
(b) 600W
15H
15-
1On
10-
-15-10
-5
0
5
10
15
(c) 750W
(d) 900W
1 5-
1 5-
*?' •
jg s c s s s s ^
....x
10-
w
a n ^ t
r
1
15
- 10
0i
"i------- r
- 5
5
10
15
-15-10
i" -j—-5
0
|
5
i—
10
15
(e) 1100W
vs^£&
1 5-
T ro t
l <= 3 0 00.000
ft r i
*+
*^
I <= 3057.143
f- ■».
\ ^
w‘
'*2
I <= 3 114.286
I <= 3 1 71.429
1 <= 3228.571
1 <= 32 8 5 .7 1 4
<= 33 4 2 .8 5 7
! <= 3 4 00.000
I > 3400.000
Figure 3.7
2D Spatially resolved maps of gas temperature as a function o f applied
microwave power, (a) 350W, (b) 600W(c) 750W(d) 900W (e) 1100W, x
and z in mm. Experimental condition: plasma gas: 1.17 L/min, aerosol gas
with alumina : 0.36 L/min, probe (H t): 0.5sccm
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127
As the electrons provide all the gas energy, it might be anticipated that as the
electrons get hotter they would transfer proportionately more energy to the neutral
species by collisions. This w ould suggest the gas tem perature would increase
proportionally with the applied power. However, in our study the gas temperature did not
follow this pattern. This is possibly related to the nature radiation loss process. According
to Planck's black body radiation rule, energy loss by radiation is proportional to the
surface area of the emitter and to the fourth order of temperature difference. A simple
calculation showed that as the gas temperature increased from 3000 to 3500 °K, the
radiation lost is nearly doubled if the surface area is kept as the same. In fact, the surface
area of the plasma torch is not a constant as the power varies. Observation showed that,
as the applied power increased, the afterglow of the plasma increases in length, and
concomitantly the surface area increases. If we assume the afterglow is cone shaped, the
side surface area is roughly proportional to the height of the cone since its bottom surface
is fixed. Visual inspection suggests the height of the afterglow is from 2 cm to 7 cm as
the applied power increased from 350 to 1100 watts. Thus, the total radiation lost is
approximately 6 times if the applied increased from 350 watts to 1100 watts. Yet, since
the shape of the afterglow region o f plasma is not exactly a cone shape, this might
overestimate the radiation lost. Combining these factors, it is clear that an ‘energy
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128
balance’ is maintained. Still, it is interesting that the afterglow region ‘adjusts’ to the
increased energy, not by getting hotter, but rather by getting longer.
Another interesting feature of the gas temperature profile is that it is higher near
the outside region, closer to the chimney wall, than it is in the center. Normally, the heat
transfer rate at the boundary is highest because of the large temperature gradient. Thus, a
flame is always coldest toward its outside edge. It is notable that the electron temperature
profile is also hottest near the center. This would suggest more energy transfers from the
electrons to the gas near the center. Thus, the mechanism that creates this odd radial
temperature profile is not readily apparent.
One possible explanation relates to the complex flow system employed for
treating the aerosol. In our plasma system, two gas streams flow into the coupler region
(see Figure 2.1 in Chapter 2). The plasma gas flows from the bottom into the quartz tube
and the aerosol (central) flow is from the alumina tube inserted in the coaxial position of
the quartz tube. The outlet of the aerosol gas is set at the center of the coupler region. As
the diameter of the alumina tube is much smaller than that of the quartz tube, and the
volumetric flow is nearly the same the velocity is significantly higher from the central
flow. For the operating conditions employed, it ranged from 10 to 50 times higher than
that o f the plasma gas (not accounting for variable expansion due to temperature
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129
differences) at the exit of the central alumina tube. This "jet", if ‘colder’, might cause the
temperature to be slightly lower, explaining the observed hotter region at the outside of
the flow.
A second possible origin of the unusual temperature profile could be the presence
of particles at the center of the flow. The significant added heat capacity of the particles
could draw energy from the gas, thus lowering the gas temperature locally.
In terms of particle processing the observed temperature distribution is preferred,
since it prevents thermophoresis, which is the tendency of particles to be driven by
temperature gradients from hot areas to cold areas of flow. Thermophoresis would not
only lower the yield but also reduce the lifetime of the quartz tube. Clearly, optimal
operating conditions for particle modification, include higher temperatures toward the
outside of the gas flow.
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130
n.2.2
Impact o f gas flow rates on gas temperature profiles
This set of experiments was designed to contrast gas (rotation) temperature profiles
for flow regimes that led to spheroidization with flow regimes that do not lead to
spheroidization. In all cases the applied power was 500 watts. Five combinations of
plasma and aerosol flow rates were used. The extent of spheroidization for these five
flow regimes (see Chapter 2) ranged from 0 to 100%.
From the results, Figure 2.8 and 2.9, it is clear that gas flow rate has only a minor
impact on gas temperature. Indeed, there is no correlation o f temperature profile with
either single gas flow rate, or with total flow rate. It's noteworthy that the rotational
temperatures are all around 3300 °K which is significantly above the melting temperature
of the alumina particles.
Clearly, even if particles pass through a hot zone, it does not guarantee the
particles will melt. This suggests that the residence time for particles staying in the
plasma hot zone play a more important role than the gas temperature. Therefore, a high
gas temperature (> melting temperature of particles) is necessary but not sufficient for
melting particles to create a liquid form of the particles. This information is valuable for
developing an optimal process for modifying the shape of ceramic particles.
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131
(a)
(b)
— i— 1— i—
-1 0
-5
1— i— 1— i— 1— r
0
5
10
“ 1—
-1 0
1— i—
- 5
X
1—
i—
0
1—
i—
5
1—
r
10
X
(C)
15-
(K)
<= 3000.000
1orsi
<= 3050.000
<= 3100.000
<= 3150.000
<= 3200.000
<= 3250.000
<= 3300.000
< - 3350.000
<= 3400.000
> 3400.000
Figure 3.8
2D spatially resolved maps of the gas temperature as a function of flow
rates.
(a) plasma gas: 1.17 L/min; aerosol gas: 0.36 L/min;
spheroidization: 100%
(b) plasma gas: 1.17 L/min; aerosol gas: 0.72 L/min;
spheroidization: 50%
(c) plasma gas: 1.17 L/min; aerosol gas: 1.08 L/min;
spheroidization: 0%
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132
Trot (K)
™
<= 3000.000
<= 3050.000
<= 3100.000
™
<= 3150.000
™
<= 3200.000
™
<= 3250.000
S 3 < = 3300.000
~ i—
-1 0
1—
i—
- 5
1—
i—
0
X
Figure 3.9
1—
i—
5
'—
r
10
<= 3350.000
3 3
<_
3400.000
3400.000
2D spatially resolved mapping of the gas temperature as a function of flow
rates.
(a) plasma gas: 0.81 L/min; aerosol gas: 0.36 L/min;
spheroidization: 100%
(b) plasma gas: 1.17 L/min; aerosol gas: 0.36 L/min;
spheroidization: 100%
(c) plasma gas: 2.50 L/min; aerosol gas: 0.36 L/min;
spheroidization: 0%
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133
H.2.3 Gas temperatures as a function of power and two flow streams
The gas temperature profiles measured under several different flow rates and 500
watts adsorbed power, did not show a significant dependence on flow rate. To broaden
the investigation of the effect o f flow rates and applied power on T rot, the profiles under
more flow rates and microwave power level combinations were investigated. The probe
area in this group of experiments was set at the (x,z)=(0,0). The results are shown in
Figure 3.10 (a) and (b).
Again, the gas temperature did not show a strong dependence either on the
applied power or on the gas flow rates. It should be noted that given an estimated error
of 50°K and a maximum error of 150°K the variation in temperature is remarkably small.
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134
4000
3500
Gas Temperature (°K)
3000
2500
2000
1500
P la sm a gas= 0 .6 3 L /m , A ero so l gas= 0.36 L /m
P la sm a gas= 1 .1 7 L /m , A ero so l gas= 0.36 L /m
1000
P la sm a gas= 1 .7 3 L /m , A ero so l gas= 0.36 L /m
A — P la sm a g as= 2 .5 0 L /m , A ero so l gas= 0.36 L /m
500
P la sm a gas= 3 .5 0 L /m , A ero so l g a s= 0 .3 6 L /m
0
0
500
1000
1500
2000
Power (W)
Figure 3.10 (a)
Investigation of the influence of the plasma gas flow rates. Shown
are gas temperatures as a function of applied power and gas flow
rates measured at (x,z)=(0,0)
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135
4000
3500
Gas Temperature (°K)
3000
2500
2000
1500
P la sm a gas= 0.63 L / m , A ero so l g as =0.36 L /m
P la sm a gas= 0.63 L /m , A ero so l g as =0.53 L /m
1000
P la sm a gas= 0.63 L /m , A ero so l g as =0.87 L /m
P la sm a g as= 0.63 L / m , A ero so l gas=1.05 L /m
500
P la sm a g as= 0.63 L /m , A ero so l gas=1.38 L /m
0
0
500
1000
1500
2000
Power(W)
Figure 3.10 (b)
Investigation of the influence of the plasma gas flow rates. Shown
are gas temperatures as a function of applied power and gas flow
rates measured at (x,z)=(0,0)
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136
n.2.4 Probe concentration on the Gas Temperature
In order to determine the effect of different concentration of probe molecule on
the measurement of the gas temperature, temperature profiles were measured with three
different concentrations of the probe molecule (H2), 0.05%, 0.2 and 1% respectively.
One typical set of flow rates was selected for argon for this test; plasma gas is 1.17 L/min
and aerosol gas flow rate is 0.36 L/min. The applied power was varied from 350 to 1500
watts. The test, Figure 3.11, showed that at the low concentrations employed, there was
no significant impact on the measured profiles. In our work, all the probe concentrations
for measuring the gas temperature were maintained at the lowest controllable value, and
one that still delivered sufficient signal intensity, 0.05%. It is safe to state that the probe
did not significantly alter the kinetic behavior of the heavy particles, gas temperature.
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137
4000
3500 -
Gas Temperature (°K)
3000 -
2500 -
2000
-
1500 -
1000
-
H 2 : 1%
H 2: 0.2%
500 -
H 2: 0.05%
0
500
1000
1500
2000
Power (W)
Figure 3.11
Gas temperature as a function of probe concentration and applied power.
Plasma gas: 1.17 L/min, Aerosol gas :0.36 L/min, measured at (x,z)=(0,0).
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138
n.3
Excitation Temperature
As the excitation temperature is generally easier to measure than the electron
temperature, some workers, assuming the LTE model to be valid, will use measured
excitation temperatures as an indication of the lower limit of the electron temperature.
That is, if the LTE model is valid there is only one temperature, and hence the gas
temperature, electron temperature and excitation can be assumed equal. In this study we
found that assumptions of this type are inappropriate.
The results clearly show that the excitation temperature is a strong function of the
applied power. It increased as the power increased. This superficially suggests an
expected correlation with electron behavior, which also increases with applied power. A
correlation between electron and excitation temperatures is expected as electron
promotion to excited states results from interactions with hot electrons. Hotter electrons
can transfer more energy to the excitation process. However, even a cursory look at the
electron and excitation temperature profiles shows them to be significantly different. In
fact, the excitation temperature profile is disturbingly odd in one feature: The temperature
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139
increases with distance from the coupler within the m easured range. A possible
explanation for this observation is given below.
The ionization threshold energy for argon is about 15.76 eV. The threshold
excitation energy is lower than the ionization energy ranged from 10.2 eV to 14.56 eV for
different excitation states [25].
Given the relatively low average electron energies
present in the afterglow (<5 eV) it would seem unlikely that any ionization or excitation
takes place. However, the rate of these processes is com puted by integrating the
probability over the entire electron energy distribution. Thus, these processes do continue
and their relative probabilities reflect the average electron energy. For a high average
electron temperatures relatively more ionization occurs and the less excitation. Therefore,
as the height above the coupler increases, and concomitantly the electron temperature
decreases the greater is the fraction of energy transferred to excitation. In other words, the
less energetic electrons for ionization existed. Since the excitation threshold is lower than
the ionization energy, more excitation processes take place and consequently the
excitation temperature increased. Note that this does not imply that the excitation
tem perature will keep increasing as the height increases. Because the electron
temperature eventually will decrease as the height further increases, at some point the
electrons will not have enough energy to excite argon molecules any more. In our case
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140
the region we observed may be still have electrons with enough energy to undergo
excitation process but not enough energy to do the ionization. Thus, the excitation
temperature dropping as the height increased did not be observed.
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141
(a) 350W
(b) 600W
s-
15-
1
10“
1o-
5-
5-
fM
°i
I
*
-1 0
1
'
-5
I
I
0
5
*'
J
10
-15-10
-5
X
0
5
10
15
5
10
15
X
(c) 750W
(d) 900W
15
15
10
10
N
rvj
5
5
0
0
-15-10
-5
0
5
10
15
-15-10
-5
0
X
X
(e) 1000W
Texc
'< =
3 5 00.000
I <= 4 7 14.286
I <= 5928.571
I <= 71 4 2 .8 5 7
I <= 8 3 5 7 .1 4 3
1<= 9 5 7 1 .4 2 9
<= 10785.714
1 <= 12000.000
l>
Figure 3.12
12000.000
2D Spatially resolved maps of excitation temperature as a function
of applied microwave power, (a) 350W, (b) 600W(c) 750W(d)
900W, (e) 1100W, x and z in mm. Experimental condition: plasma
gas: 1.17 L/min, aerosol gas with alum ina: 0.36 L/min, probe (H2):
0.5sccm
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142
n .4
Electron Density
In this study, the electron densities were determined from the argon emission line
at 696.5 nm by the Stark broadening effect. This was decided after comparison showed
this line and the Hp line at 486.1 nm gave nearly identical values. Moreover, using the
Argon line had the advantage of higher intensity and no risk of disturbance from the
"foreign" molecules.
The comparison study was conducted by measuring the Hp line and the Argon line
at the same five power level, but only in one layer (z=0) since the line intensity decreased
rapidly as the height increased for Hp line. It was found that the results from these two
lines are roughly of the same order of magnitude, 1013 cm'3.
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143
n .4 . 1 Effect of the probe concentration fH-,1 on the electron density
The Argon line was used to measure electron density rather from the Hp line
because several major disadvantages are associated with the Hp line. First, the intensity of
the signal is very weak. In order to increase signal the concentration of H atoms can be
increased. However, this could modify the plasma. A test for determining the effect of
probe concentration on electron density measurement was conducted.
The results, Figure 3.13, showed that as the concentration increased from the 0.05% to
1%, the electron density decreased. This suggests that the addition of probe may cause
some degree of disturbance. That is the electron density apparently is a function of the
probe concentration.
n .4.2
2D spatial profile of the electron density as a function o f applied power
The spatially resolved electron density from the argon line is displayed in Figure 3.14
(a)~ (e) at five applied power levels.
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144
H2: 0.05%
H2: 0.3%
H2: 0.6%
H2:1.0%
1.0E+14
[
uE
c
o
h.
u€1
1.0E+12
0
200
400
600
800
1000
1200
1400
1600
Power(W)
Figure 3.13
Electron density measured from the Hp line as a function of probe
concentartions and applied power.
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145
(a) 350W
35'
(b) 600W
35
(b) 750W
3 02520-
N
15-
10
5
0
•5
□
• 1 0
(c) 1100W
- 5
10
353025N e (1 E l 3)
20“
■<= 0.250
n
15-
l< = 1.214
10-
•< = 2.179
l< = 3.143
5“
l< = 4.107
0- □
1 <= 5.071
- 5- 10
- 5
10
<= 6.036
1 <= 7.000
I > 7.000
Figure 3.14
2D Spatially resolved maps of electron density as a function of applied
microwave power, (a) 350W, (b) 600W(c) 750W(d) 900W(e) 1100W, x
and z in mm. Experimental condition: plasma gas: 1.17 L/min, aerosol gas
with alumina : 0.36 L/min, probe (1L): 0.5sccm.
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146
Electron densities always in the range of 5 x 1012 to 7 x 1013 cm'3 decreased as the
power increased. It is also clear there are gradients in both radial (x) and axial (z)
directions, but in the radial direction, the gradients are steeper.
The quartz chimney 30 cm in height, and square in shape was placed above the
quartz "torch". The nearest walls of the chimney are 2 cm away from the edge of the
torch. Thus, the moving of the electron will be more limited along the radial direction and
the electrons were depleted on the wall due to the recombination process. This depletion
of electron density created a concentration gradient for the electron diffused from the
center to the wall. Again, the challenge is to suggest a mechanism to explain a surprising
observation, why does the concentration decrease as the power increases? One possible
explanation: At higher power, the electrons are more energetic (higher electron
temperature), and consequently they diffuse m ore rapidly, leading to more rapid
depletion by wall recombination. The larger concentration gradient further accelerates the
diffusion of the electron toward to the wall. Therefore, as the applied power increased,
the electron density is decreased.
Another interesting finding is that the electron density profiles were asymmetric
at power levels from 350 to 750 Watts. As the power increased, the deviation from
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147
asymmetry was reduced. Possibly, static charge on the chimney impacted electron
behavior.
H.5
Metallic Aluminium Emission Line Intensity
A three-step agglomeration model was offered to explain the growth mechanism
of spherical alumina particles in the previous chapter. However, it does not explain all the
observations, particularly the difference in the particle size distribution of the argon and
air produced particles (see Figure 2.1 la, 2.1 lb and 2.1 lc). The particles size distribution
o f the air plasma produced particles is nearly a logarithmic normal distribution (with a
long tail toward large particle size, Figure 2.11c). This suggests that the growth
m echanism is dom inated by agglom eration. Indeed, all models o f growth by
agglomeration show that a logarithmic normal distribution evolves. In contrast, the
particle size distribution of particles generated by argon plasma (Figure 2.1 la and 2.1 lb)
showed a narrow distribution implying that the growth mechanism is dominated by
atomic addition. However, it was shown (Figure 2.9, 2.12a and 2.12b) that the growth
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148
m echanism of the particles generated by argon plasm a is best described by a
mathematical collisional model.
To further explore for evidence of atomic addition, the intensity of the metallic
aluminium emission line at 394.4032 nm was studied [52]. It was found that in both air
and argon plasmas that metallic aluminium is present, and that the intensity of the line
increases in a near linear fashion with particle density and applied power, shown in
Figure 3.15 and 3.16. Thus, it shows the evidence that the atomic addition growth was
happened during the growth in both plasma types.
Another interesting observation from these emission line intensity profiles is that
as applied power increased to 750 W, the slope became very steep. It seems that after
passing through the plasma hot zone, all the particles disappeared. Since the density from
the Figure 3.15, 3.16 represents the collection rate of spherical alumina particles in the
particle trap divided by the total volumetric flow rate, the decrease in particles collected
in the trap at higher power suggests the possibility that some particles were not caught in
the trap. The trap is not designed to capture particles in the nanometers size range. Such
particles do not lose buoyancy, even at very low flow rates. In sum, this suggests that at
high power nanometer particles are created. One possible mechanism is a high degree of
alumina dissociation. This creates a lot of metallic aluminium atoms in the plasma
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149
afterglow region and they will nucleate and react with other atoms such as oxygen atoms
to reform the alumina. This suggests that it is feasible to use this atmospheric plasma
torch system to generate nano-size ceramic particles. A spatial distribution of the
intensity of this metallic aluminium emission line as a function of the applied power were
shown in the following Figures, 3.17 (a)~(e):
From the distribution profiles of the aluminium emission line intensity, the
intensities increased as the applied power increased. Another important feature observed
is that the emission intensity is always the highest at the center. This strongly suggests
that the particles are concentrated near the center o f the plasma. This phenomenon
corresponds to the result from the gas temperature measurements which showed that the
temperature is higher at the edge of the plasma. In this condition, well known as the
"thermophoresis", the thermal force pushes the particles to the center and prevent the loss
of valuable product, spherical particles, to the wall of the reactor and chimney, existed in
our plasma system.
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150
A r/3 5 0 W
— ■ —
A r/S O O W
A r/6 0 0 W
— A—
A r/7 5 0 W
100000
a
10000
-
1000
-
100
-
I
10
0
0.2
0 .4
0.6
0.8
1
D e n s ity (m g /L )
Figure 3.15
Intensity in Argon plasma o f the metallic aluminium emission line
(394.4032nm) as a function of particle density and applied power.
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151
A IR /3 5 0 W
A IR /5 0 0 W
A IR /6 0 0 W
A IR /7 5 0 W
100000
10000
I
1000
100
-
0
0.2
0 .4
0.6
0.8
1
D e n s ity (m g /L )
Figure 3.16
Intensity in air plasm a of the m etallic alum inium emission line
(394.4032nm) as a function of particle density and applied power.
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152
In summary, the true growth mechanism of different size particle is far more
complicated than our three-step model and the investigation of emission line intensity did
not really reveal the true story of the particle size distribution difference from different
plasma source. Also a type of thermophoresis keeping particles near the axis was
observed during particle growth.
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153
(a) 350W
(b) 600W
15-
1o-
(c) 750W
(d) 900W
15-
15-
1o-
10-
0"1----------- 1
1
-1 5
-1 0
-5
0
1-------- 1----
5
10
15
(e) 1100W
In ten sity
1 o-
■ i< =
100.000
B i< =
3 6 5 7 .1 4 3
■ ■ <= 7 2 1 4 .2 8 6
■■<=
1 0 7 7 1 .4 2 9
■■<=
1 4 3 2 8.571
1 7 8 8 5 .7 1 4
<= 2 1 4 4 2 .8 5 7
<= 2 5 0 0 0 .0 0 0
■ ■ >
Figure 3.17
2 5 0 0 0 .0 0 0
2D Spatially resolved maps of the intensity of the metallic aluminium
emission line as a function of applied microwave power, (a) 350W, (b)
600W, (c) 750W, (d) 900W, (e) 1100W, x and z in mm. Experimental
condition: plasma gas: 1.17 L/min, aerosol gas with alumina : 0.36 L/min,
probe (H2): 0.5sccm
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154
Part III.
Non-Equilibrium Plasmas (Departure from LTE)
As noted previously in this study of a microwave generated atmospheric plasma,
two approaches for determining the validity of LTE approximation were employed.
To test the one-temperature- criteria, three temperatures, gas (rotation), excitation
and electron temperatures were measured based on the equations derived from the
assumption of local thermodynamic equilibrium. From the data collected, especially in
the case of plasma torch containing alumina aerosol, Figure 3.5, 3.7, 3.12, it is obvious
that the plasma is not approximated by the LTE. The gas temperature ranged from 30003500 °K, excitation temperature from 4000 to 15000 °K and the electron temperature
ranged from 9300 ~ 81200 °K (0.8 to 7 eV) These temperatures are distinctly different,
thus the LTE does not exist. In fact, the plasma under all operating conditions tested
always has the following behavior:
TA e ^> TL exc > Tx rot
^
For the electron temperatures measured in this work, which ranged from 0.8 eV to 7 eV,
the equation (3.16) indicates the necessary electron density to maintain the state o f LTE
in atmospheric argon plasma is of the order 1017 cm'3. A comparison of this value to the
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155
electron density measured in this study, Figures 3.14, clearly indicates the electron
number densities are three orders lower than the requirement for validity of the LTE
assumption. This also leads to the conclusion that none of the plasmas generated in this
study can be described with the LTE model. Yet, there are aspects of the measured data
which contradicted this conclusion and suggest the model is valid. Indeed, the data for
individual temperatures indicates the rotation, excitation and electron sub-systems each
independently can be described by the Maxwellian, Boltzmann and Saha distributions.
Data fit appropriate equations with r-squared values around 0.95 to 0.99. In contrast to
the differences in temperature this result suggests that the plasma is in a LTE state.
This apparent contradiction could be explained by the following hypothesis. The
relaxation times within each system, rotation, excitation and electron, are very short
relative to system-system relaxation times. If true, then each system can maintain a LTE
o f its own, while the plasma as a whole can not be described by the LTE model. The
relaxation time for the rotation process of the OH
—X 2II,. band in one atmospheric
pressure is in subnanosecond range [53]. And for the excitation process of Ar, the
relaxation time is in the range of 20 nanosecond [54, 55]. However, there are no such
data available for the relaxation time between the rotation system and excitation system.
Thus, no direct evidence to support our hypothesis that each sub-systems can maintain
"LTE state" while the different sub-systems are not in mutual equilibrium. The laser-
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156
induced fluorescence method might be applied for further investigation of determining
the relaxation time between the subsystems.
To obtain direct quantitative evidence of departure from LTE, the following
method was derived. The first step was to set up a LTE model based on one single
parameter not dependent on the existence of LTE. The electron density of the plasma,
measured from Stark broadening, is the best choice to fulfil this requirement. The line
broadening theory for calculating the electron density from the Stark effect is not derived
from the LTE model. The second step was to use the electron density measured in this
manner as well as Dalton's law of charge neutrality, to calculate an LTE temperature
using the Saha formula [56-59]. It is appropriate to call temperature computed in this
fashion the "ionization temperature", as it is derived from the Saha equation, which is the
governing distribution equation of the ionization states.
It must be noted that in the LTE condition, there is only one temperature in the
plasma, if the LTE model is valid. It is not necessary to distinguish the ionization
temperature. Therefore, the temperature calculated by this approach is generally referred
to as Tlte . A table from the literature [58] containing the relation between the electron
density and TLXE was used to calculate TLXE from our electron density data. This
temperature was used as a reference point to compare to other temperatures and to
determine how far the plasma is from a true LTE state.
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157
In this study, the electron densities were determined from the line broadening of
two different emission lines, Hp and Ar I. As the electron densities measured from these
two methods are of the same order o f magnitude, only the data sets from the Ar lines
were used to be the electron density source for calculating the Tlte . Since the electron
density did not show a strong dependence radially, only the center position (x=0) was
chosen to represent the average value of that particular layer. Because of flow pattern of
the plasma torch, the axial temperature variation is more interesting than radial variation.
Indeed, it is reasonable to surmise that at the far end of the plasma, where the electron
temperature has decreased, LTE might apply.
The difference between gas, excitation, electron tem peratures and TLXE as a
function of applied microwave power and the axial position are shown in the following,
Figure 3.18(a) and (b).
Again, the large difference between the gas, excitation, electron and Tlte
demonstrates that the plasma torch is not adequately described by the LTE model. In
particular, the electron temperature is far from Tlte . As the microwave power increased,
the deviation becomes more significant. The difference between these temperatures did
show a slight decrease as the observation point moved up from y=0 to y=8 mm above the
quartz tube. This suggests that at the tip of the plasma torch, there could be a equilibrium
state exists where every temperatures are the same.
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158
In summary, the LTE does not exist in the afterglow atmospheric argon plasma
torch. The meaning o f several temperatures measured in this study such as gas, excitation
and electron temperatures may be questionable. Therefore the better way to characterize
the plasma torch is to construct a model containing every possible reaction equations in
the plasm a and solve these equations sim ultaneously to have the energy and
concentration distribution.
From this study, it is obvious that the reason for the plasma not in equilibrium
state is the electron is much energetic than neutral particles in the plasma. Thus, an
approach similar to that used in modeling low pressure plasmas in which the plasma is
regarded as divided into charged and neutral systems [60], should be the best way to
characterize the plasma torch.
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159
Te-(Ot8)
Texc-(0,8)
Te-(O.O)
Texc-(O.O)
1COOOO
100000
10000
10000
1000
200
1000
200
400
600
800
Pow er
(W)
Figure 3.18(a)
Figure 3.18 (a) and (b)
1000
1200
400
600
800
1200
Power (W)
Figure 3.18(b)
A comparison of the calculated theoretical value of Tlte to
measured gas, excitation and electron temperatures as a
function of applied power and position, (a) Z=0, (b) Z=8.
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160
Part IV.
Two Flow Streams Effect on the Plasm a Parameters (electron
temperature and density)
Three different flow patterns were studied. In the first there is only a single gas
flow into the coupler region. In the second there are two gases, plasma gas plus the
central gas without any particles. In the third the plasma gas plus aerosol gas (central gas
with alumina particles) flow through the coupler region.
IV. 1
Effect on electron temperature
The results, Figure 3.19, 3.20 and 3.5, showed that the spatial profiles o f the
electron temperature are distinctly different around a central part above the torch. The
profiles from the two cases without alumina are alike. Both are "symmetric", hotter in the
center, and the values of the electron temperature are similar. The introduction of alumina
into the plasma changes the shape of the electron temperature. It is no longer symmetric
around a part in the afterglow, but rather cone shaped. Also, it is hottest at the bottom and
cools with distance from the coupler. Not only that, the electron temperature is much
higher (3 times) when alumina is present in the plasma.
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161
Another unusual feature is that without alumina cases, the hottest electrons are
"away" from the point o f entry in all cases. This could possibly be explained by the
charge separation effect. Due to same initiation effect heavy positive charged molecules,
such as Ar+, Ar++, form a cloud in the chimney. This creates a local electric field which
further accelerate the electron towards the upper region and thus "hotter" electrons are
created. Charge separation is a standard concept in microwave plasmas. Indeed, all
"walls" are presumed to be negatively charged due to the far higher mobility of electrons.
Negative wall charging at steady-state should create an excess of positive ions. For low
pressure plasmas this is assumed to be in the wall boundary layer. Possibly, this is not the
case in high pressure plasmas.
IV.2
Effect on electron density
The electron density distribution in the case of plasma gas flow only is symmetric
around a part above the entry to the afterglow. In contrast with a central gas flow present
the distribution is cone shaped, and the highest density is at the entry to the afterglow.
Also the electron densities with only plasma gas, are much higher with a central gas flow.
Yet, the electron density is higher in cases with an aerosol of alumina particles. This
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162
might be explained by the fact that as the electron temperature is much higher in the case
with alumina, m ore ionization process occur generating more free electrons in the
plasma.
In both cases without alumina, the electron density increased first and then
decreased as the absorbed power increased. That is, there is a maximum observed as a
function of power. But in those cases in which alumina is presented, the electron density
monotonically decreased with increased power. This can be explained by the competition
between generating free electron from ionization and losing electron by diffusion. Since
the electron temperatures with alumina inside the plasmas are much higher (> 4 eV) than
that without alum ina (<2 eV), the depletion of electrons by diffusion to the wall or
aerosol particles is more rapid than the ionization processing for generating free
electrons. In the cases without alumina, the electron temperatures ranged from 0.01 to 2
eV, a moderate range. Therefore, as the power is increased, the ionization process starts
to take place and generating more fresh free electrons. Yet, the electron temperature is
not high enough to accelerate loss by diffusion at the same rate. If this is true, the electron
density will increase. If, on the other hand, higher electron temperature leads to more
rapid diffusion to the walls, the electron density will decrease, despite higher ionization
rates. Potentially, such a "balance" of processes could lead to the observed maximum.
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163
(a) 350W
(b) 600W
(c) 750W
(d) 900W
(e) 1100W
Te (eV)
• < = 0 .0 1 0
I <= 0.294
I <= 0.579
I <= 0.863
I <= 1.147
1 <= 1.431
<= 1.716
1 <= 2.000
I > 2.000
Figure 3.19
2D Spatially resolved maps of electron temperature as a function of
applied microwave power, (a)350W, (b)600W , (c)750W , (d)900W ,
(e)1100W, x and z in mm. Experimental condition: plasma gas: 1.17
L/min, aerosol gas with alumina : 0 L/min.
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164
(a) 350W
(b) 600W
(c) 750W
(d) 900W
(e) 1100W
10
Te (eV)
^ H < = o .o io
<= 0 .2 9 4
■ ■ <= 0 .5 7 9
^ ■ < = 0 .8 6 3
■■<=
1.147
383 <= 1.431
<= 1.716
8 3 < = 2.000
2.000
Figure 3.20
2D Spatially resolved maps of electron temperature as a function of
applied microwave pow er, (a)350W , (b)600W, (c)750W , (d)900W,
(e)1100W, x and z in mm. Experimental condition: plasm a gas: 1.17
L/min, aerosol gas without alumina : 0.36 L/min.
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165
(a) 350W
(b) 600W
(c) 750W
(d) 900W
(e) 1100W
Ne (1E13)
<=
1 .0 0 0
■ ■ < = 6.357
< = 11.714
< = 17.071
< - 22.429
^
< = 2 7 .786
<= 3 3 .143
< = 3 8 .500
* * >
Figure 3.21
3 8 .500
2D Spatially resolved maps of electron density as a function of applied
microwave power, (a)350W , (b)600W, (c)750W, (d)900W, (e)1100W, x
and z in mm. Experimental condition: plasma gas: 1.17 L/min, aerosol gas
with alumina : 0 L/min.
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166
(b) 600W
(a) 350W
35
(c) 750W
(d) 900W
35
□
(e) 1100W
3 5302520-
^
151o5-
0- 5-
-
Figure 3.22
10
10
Ne (1E13)
l < = 1.000
I <= 1.429
I <= 1.857
I <= 2.286
I <= 2.714
1<= 3.143
<= 3.571
^ <= 4.000
I > 4.000
2D Spatially resolved maps of electron density as a function of applied
microwave power, (a)350W, (b)600W, (c)750W, (d)900W, (e)1100W, x
and z in mm. Experimental condition: plasma gas: 1.17 L/min, aerosol gas
without alumina : 0.36 L/min.
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167
Part V.
Data Summary and Comparison
The electron, excitation and gas temperatures measured in this work clearly
showed that the system is not in local thermodynamic equilibrium. The temperatures of
each sub-systems are dramatically different, therefore the LTE model is not a valid
description of the plasma studied here.
There are only a few data available regarding various temperatures and electron
density for the microwave generated atmospheric plasma. The following table, Table 3.7,
summarized the data available in the literature and current work. They are all microwave
generated, argon plasma at one atmosphere and characterized by the spectroscopic
method. It shows that the data we obtained is in good agreement with others. Moreover,
in none of the earlier studies was a true mapping of tem peratures and densities
performed.
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168
Table 3.7
Comparison of plasma parameters between current work and data in
literature.
Source
Abdallah & Mermet
[9]
Tanabe et al.
[10]
Bings et al.
[61]
Jonhers et al.
[62]
Timmermans et al.
[63]
Goode et al.
[64]
Current Work
Power
Tgas
Te,c
Te
ne
(W)
(°K)
(°K)
(°K)
(cm 3)
130
2570
4420
-
-
75
1150
4514
-
4 x 1014
600
2800-4300
3100-4900
-
109~ 1014
330
3000
-
1.46
3.5 x 1017
320
3000
5000
-
1015
120
-
-
2
1010
350-1100
2900-3500
3000-12000
0.7-6
1013~ 1014
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169
3.6
Conclusions
The LTE (one-tem perature) model has been tested. The gas temperature,
excitation temperature and electron temperatures are greatly different from each other. In
particular, the electron temperatures are always much higher than the gas and excitation
temperatures under the same operating conditions. This difference in temperatures of
each subsystem violates the assumption of the LTE model. Therefore, the LTE model is
not suitable for the microwave generated atmospheric plasm a under our operating
condition. This suggests that a multi-temperature model is more applicable for modeling
the atmospheric plasma.
W e developed two dimensional spatially resolved maps of electron, gas and
excitation temperatures and electron density under various operating conditions. There
are many surprising qualitative findings regarding the structure of the afterglow region.
Among the most interesting was that the gas (rotation) tem perature showed weak
dependence on applied power. The temperature gradient was also flat. The electron
temperature showed a nearly linear correlation to applied power. The spatial distribution
o f electron tem perature indicates that electrons lost their energy by collision, not
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170
radiation as the center is the hottest region and electron temperature gradually decreased
toward the edge.
Another surprise was that the electron temperatures reach maximum inside the
afterglow even though there is no field in this region. This suggested that there might be
charge separation in the afterglow region and the presence of alumina help to reduce the
charge separation.
Another surprise: the excitation temperature is higher as the observation height
increased within our observation range. A possible but not certain explanation is that the
excitation temperature distribution was mainly a function of the energy transfer process.
In the region near the coupler where the electron is hotter, the ionization process is more
likely to take place and for the region away from the coupler where the electron is not as
energetic as those near the coupler, the excitation process dominated.
Electron density was determined by the Stark line broadening from two lines, Ar
(696.54 nm ) and Hp (486.1 nm). The electron densities measured from these two lines
showed fairly good agreement. Although there is minor difference in the values, they are
all in the same order magnitude. And both presented a similar trend in spatial distribution
and power variation. Another surprising finding was that the electron density decreased
as the applied power increased. This might be explained by diffusion loss. If loss by
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171
diffusion as electron temperature is more pronounced than the creation of new electrons
by ionization, lower electron densities will be observed.
The gas temperatures, even in the afterglow region, are always higher than the
melting temperature of the alumina particles. This is consistent with the first assumption
of the three-step model that the particles melted in the plasma. The gas temperature
distributions showed that the temperature is hotter near the outside region. Thus, the
thermophoresis did not existed under current operation conditions.
In summary: I . A systematic two dimensional spatially resolved mapping of the
gas, excitation and electron temperatures and electron densities during the material
processing was developed. 2. The passage o f an aerosol dramatically changes the
structure of the afterglow. 3. The LTE model has been proven not applicable in the
microwave generated atmospheric plasma. 4. The data obtained in this work are
compatible with those under similar operating conditions in the literature.
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172
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178
Chapter 4
MODELING THE DISCHARGE REGION OF A MICROWAVE
GENERATED HYDROGEN PLASMA
The following is based on an article written by C. K. Chen, T. C. W ei, L. R.
Collins and J. Phillips. The article was published in the Journal of Physics D: Applied
Physics, 32, pp 688-698 (1999).
4.1
Abstract
A zero dimension steady-state model of low pressure (2-60 Torr) microwave
generated hydrogen plasmas was developed. Electron energy distribution function
(EEDF) was determined using the Boltzmann equation, coupled to species, energy and
power balances. The EEDF from the Boltzmann equation permitted computation of the
rate constants and average electron temperature required for simultaneous solution to the
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179
six species balances, two for neutrals (H, H2), and four for charged (H +, H£, Hj and
electron) species, and the energy balance. The average electron temperature and species
concentrations were then employed in a power balance to check for self-consistency with
the input power used to solve the Boltzmann equation. E/N values were appropriately
adjusted after each iteration until self-consistency was achieved. The model provides
information on the details of the transfer o f power from electrons via various processes
(ionization, dissociation, vibration, rotation) to the neutral species. The mechanism of
energy loss from the neutrals (radiation, convection) is also computed, thus gas
temperature can be estimated. Indeed, for low pressure (p < 15 Torr) plasmas the model
yields accurate absolute gas temperatures as a function of pressure, including the fact that
gas temperature rises steeply at pressures in excess of 15 torr. This results from the fact
that at low pressures a very large fraction of the input power is transmitted by the
electrons to the molecular vibration modes, such that Tvib » Ttrans-
4.2
Introduction
Hydrogen plasmas are widely used in the field of material treatments. For
example, pure hydrogen plasmas are used in microelectronics for surface cleaning or
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180
etching of compound semiconductors [1-3]. Commonly, low pressure (p < 10“2 Torr)
microwave ECR plasmas are used in this application. A typical high pressure (1-100
Torr) application involving microwave generated hydrogen plasmas is the deposition of
diamond or diamond-like carbon thin films [4-6]. It is postulated that at the surface the
main role of atomic hydrogen in diamond growth is the satisfaction of the dangling bonds
of the sp-3 diamond surface layer [7, 8] and preferential etching of graphitic forms of
carbon [9-12]. Also, characteristics of the plasma, such as the degree of H2 dissociation,
can be correlated to product quality [13].
Accurate models are essential for understanding and adjusting hydrogen plasmas.
Quantitative experimental probes for H-atom concentration, charged species density, and
other microwave plasma parameters are difficult. Little experimental data on microwave
generated hydrogen plasmas are available. M oreover, experimental results are not
generalizable as plasma parameters are very sensitive to reactor geometry and operating
conditions. Modeling studies are the most viable alternatives. Yet, there have been very
few modeling studies on microwave generated hydrogen plasmas, and further model
developm ents are still needed before these m odels can be em ployed as
predictive/guidance tools.
St-Onge and M oisan developed a particle balance model in which electron
temperature, as well as the concentrations of neutrals and ions, were calculated as a
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181
function of gas pressure [14]. Gas temperature was correlated to electron density on the
basis of experimental work. Koemtzopoulos and co-workers published a kinetic model in
which the Boltzmann equation, species balance, and power balance were solved to
predict the electron energy distribution function (EEDF) and species concentration [15].
Gas temperature was assumed constant and not impacted by the operating conditions.
In this work a mathematical model is developed that not only employs many of
the best aspects of the earlier models, but also includes the gas energy balance. A
sequence of equations is iteratively solved in a unique fashion to calculate the electron
temperature, gas temperature, and densities o f four charged (H +, H j, H 3 and electron)
and two neutral species (H, H2) under a wide range of operating conditions. Physical
input parameters are gas pressure, adsorbed microwave power and feed flow rate. Two
estimated, and subsequently adjusted, parameters are required as well; E/N (electric field/
neutral density) and gas temperature. The Boltzmann equation is solved first. The output
EEDF from this equation is used to generate rate constants and average electron
temperature data required to simultaneously solve the species and energy balance. This
output is used in a power balance needed to check for self-consistency in total power
adsorption. With each iteration the input E/N to the Boltzmann equation are modified.
The output includes a tabulation, as a function of operating parameters, of the fraction of
input power that transfers from the system of charged species to the neutral species
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182
system. For example, it was found that a significant fraction of the input power goes to
molecular vibration at low pressures (p < 15 Torr), and surprisingly little to ionization.
As pressure is increased less and less energy goes to dissociation and an increasing
fraction to vibration.
In order to model the gas temperature (a capability unique to the present method)
it is necessary to distinguish the translational tem perature from the vibrational
tem perature. As shown later, at low pressures the vibrational and translational
temperatures are not in equilibrium. The predicted gas temperature was compared to
experimental results and the agreement, in terms of both absolute values and trends as a
function of pressure, was found to be very good. This is postulated to be a meaningful
test of the model as gas temperature is one of the few non-intrusive measurements of a
hydrogen plasm a which yields reliable quantitative results. M oreover, the model
predicted gas temperature behavior at low pressure (p < 15 Torr) is far different than that
anticipated by a equilibrium energy balance (i.e., where thermal equilibrium is assumed
among vibrational and translational modes). In fact, two different energy balance
equations were employed, one for low pressure (p < 15 Torr) and the other for high
pressure (p > 15 Torr).
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183
4.3
Experimental Apparatus
The plasma was generated in a quartz tube using a 2.45 GHz, 250 W att
commercial microwave system (AsTex, MA). As shown in Figure 3.1, the microwave
system consists of a power supply with magnetron, coaxial cable, three stub tuner and a
coupler. The quartz tube, approximately 17 mm I.D., passes through a 25mm diameter
slot in a 40 mm high coupler [16]. Hydrogen (Matheson, 99.999%) was supplied to the
quartz reactor via a Pyrex gas handling manifold. The flow rates o f the gas were
monitored using calibrated rotameters. Gas pressure was measured with a MKS Baratron
pressure gauge about 50 cm upstream from the plasma. The pressure was regulated with a
one-inch steel throttle valve just upstream from a one-stage, 75 Liter/min rotary vane
pump (Alcatel, MA) supplied with Fomblin oil.
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184
Triple Stub Tuner
1 Pressure
Gauge
/
Thermal Couple
Microwave Power
Supply (250 W)
Vacuum Pump
Figure 4.1
Hydrogen
Cold Trap
Schematic diagram of experimental apparatus.
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185
4.4
M odel
The “model” plasma in this study is a pure cylindrical hydrogen discharge of
radius R (0.85 cm) and length L (4 cm) in a constant-intensity 2.45 GHz field. These are
the same values found in the experimental system employed. Microwave power, pressure,
and flow rate, (parameters which can all be duplicated in the experimental system), are
input parameters to the model. On the basis of these inputs the model yields electron
temperature, gas temperature, species density, and the distribution of energy transfer
mechanisms between electrons and neutrals. Experimental determination of gas
temperature was made using a thermocouple placed at the center of a 2.45 GHz
microwave system with the same physical dimensions as those used in the model.
The structure of the mathematical model developed here is similar to the model of
high-density argon plasma discharges proposed by Meyyappan and Govindan [17]. Both
species and energy balance are established under the following basic assumptions :
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186
(1)
The values of all plasma parameters are constant throughout the discharge
volume. Spatial variations are not considered and steady state is assumed.
These are the standard “continuous-stirred tank reactor (CSTR)”
assumptions [18]. This approach allows the inclusion of multiple species
without extensive computational resources. Thus, all concentrations nj are
volume averaged, i.e.,
j jnj(r,z)27Crdrdz
(2)
(4.1)
The reactor is isotherm al. Gas and electron tem perature, as well as
microwave power, are uniform throughout the discharge.
(3)
The electron energy distribution function is accurately determined from the
Boltzmann equation.
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187
(4)
There are two neutral species (H2, H), and three positive ionic species (H +,
H j, H3), which along with electrons constitutes a pure hydrogen discharge.
The presence o f negative ions are neglected because their production
presupposes the presence of supratherm al electrons (electrons with
temperatures near 40 eV) [19].
4.4.1
Boltzmann Equation
The normalized electron energy distribution function (EEDF) was determined
using the Boltzmann equation. For this work it was assumed that E/N was sufficiently
small (10 Td < E/N < 80 Td, where 1 Td = 10"l7Vcm2) that the drift velocity is less than
the thermal velocity. This permits the use of the two term expansion in spherical
harmonics to calculate the approximate EEDF [15]. Since the electron energy relaxation
frequency is much lower than the microwave frequency (typically the case in the
microwave frequency range) and the momentum exchange frequency is much higher than
the microwave frequency, the time-independent EEDF is only a function of E/N and the
gas identity. The code used in the present work was a slightly modified version of the
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188
code developed by Morgan and Penetrante [20]. Simple modifications were required to
allow the code to compute rate constants from EEDF, and to permit rapid iteration based
on the output from the power balance.
4.4.2
Species balances
The only input species to the reactor is molecular hydrogen, whereas H2, H, H+,
H2, H2 and electrons exit the reactor. A complete description o f the reactor therefore
requires six species balance equations, and the assumption of charge neutrality. It is most
convenient to formulate the species balances in terms of the molecular concentrations,
rij, where the subscript “j ” designates the species (e.g., nHi is the number of hydrogen
molecules per unit volume). The steady state species balance for the “jth ” species in a
‘CSTR’ is of the form [18]
n‘,
n,
X-
X-
0
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c4-2>
189
where T is the reactor “space time” (i.e., T = V/Q), SGj is the rate of generation of “j ”
atoms per unit volume, S Lj is the rate o f loss of “j ” atoms per unit volume, and Swj is
the rate of loss of “j ” atoms at the wall per unit volume. The superscript “i” designates
input conditions.
Table 4.1 summarizes the reactions introduced in the model. The reactions are
grouped into five categories: (i) electron-neutral collisions, (ii) electron-ion collisions,
(iii) ion-neutral collisions, (iv) neutral-neutral collisions, and (v) wall recombination
(Tables 4.1 and 4.2). From these reactions and Equation (4.2), the species balance for
atomic hydrogen is written as
° = - ^ r + 2 k , n en H^ + k 3nenH2 + ku n
n„z
—k4 ne n H —2 k n n H —2 k l3 n H n H2 —kl4 n H
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(4.3)
190
Table 4.1
Rate Processes in a Hydrogen Plasma
R eaction
Electron-Neutral:
2H + e
e + H2
—» H 3 + 2e
e + H2
—> H+ + H + 2e
e + H2
e+H
—> H++ 2e
Electron-Ion:
—» H
e + H+
Source
[49]
[50, 51]
[51,52]
[53, 54]
[Rl]
[R2]
[R3]
[R4]
[33]
[55]
[55]
[55]
[55]
[R5]
[R6]
Ion-N eutral:
H+ + 2H2 —» h 3+ + h 2
h* + h 2
—» H3 + H
[56]
[57]
[RIO]
Neutral-Neutral:
h 2+ h
H+H+H
H + H + H2 -> 2H2
[15]
[58]
[R12]
e + H3
e + H3+
e + Hj
e + H3
H+H
—> h 2 + h
H+ + H + e
—> H+ + 2H + e
Wall Recombination :
H + Wall
-» 1/2 H2
H + + Wall
H
+ Wall
+ Wall
H2
-> H2 + H
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[R7]
[R8]
[R9]
[R li]
[R13]
[R14]
[R15]
[R16]
[R17]
191
Table 4.2
Dissociation
e + H2
Ionization :
e + H2
e + H2
e+H
Electron-Neutral Collisions in a Hydrogen Plasma
R eaction
Source
-+ 2H + e
[49]
[R l]
[50,51]
[R2]
[R3]
H+ + 2e
[51,52]
[53, 54]
-» H2* (B il£) + e
[59, 60]
[R18]
[61,62]
[R19]
[63, 64]
[R20]
-+ H*(2p) + e
[65, 66]
[R21]
-> H2(v=l) + e
—> H2(v=2) + e
-» H2(J=0->2) + e
[65, 67]
[R22]
[68]
[R23]
[R24]
.
—> H 2 + 2e
-+ H+ + H + 2e
-+
[R4]
Excitation :
e + H2
-+ H ^C C ^u) + e
-> H2*(E,F1Xg) + e
e + H2
-> H + H*(n=2) + e
-> H + H*(n=3) + e
e+H
e + H2
e + H2
-+ H*(2s) + e
Elastic Collision :
e + H2
—> e + H2
e+H
-> e + H
[68]
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192
Similarly, the species balances for H+,
and H3 are
+ + k 3ne n Hz + k 4 ne n H + k 8nen m
—
0 = ----n H
+ k9 ne nH. - k 5 ne n H. - k XQn \ z n ^ - k x5 n ^
0=
n fr
-f- + k2ne n Hz- k8 ne n
nH+
0 = -------- + k xo n Hz nH. + kx, n Hz n
- k x, n Hz n
- k 7 ne n
- k9 ne n
- k X6 n
- k x7 n
(4.4)
(4.5)
(4.6)
An equivalent balance can be written for the hydrogen molecule density; however, a
more accurate equation is obtained from an overall hydrogen atom balance, as shown
below
nK
= n ~ n H
-> V ~ V
"
h ht
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(4 -7 >
193
where for an ideal gas,
n = ----kT.
(4.8)
Furthermore, as the plasma is charge-neutral, the electron density is equal to the sum of
all three positive ion densities, i.e.,
ne = n H. + n H. + n
(4.9)
The input parameters to the species balance equations are the inlet flow rate, Q ‘,
the inlet gas temperature, Tg, and the inlet pressure, p ‘. The flow rate exiting the reactor,
Q , is then determined from an overall mass balance to be
Q = ~ T — 1 ----------- —---------- 7 a
v p (2
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(4.10)
194
In general, the pressure drop across the reactor is small, suggesting that p ‘/ p ~ 1. On the
other hand, the gas temperature change is significant and m ust be solved for with an
energy balance (see Section 4.4.3).
4.4.2.1
Rate constants
The rate constants of the gas phase reactions in the proposed mechanism were
obtained in two ways. For reactions other than electron-neutral collisions, the rate
constants were taken directly from the literature. For electron-neutral reactions (R1-R4,
R18-R24), the rate constants were obtained from the integration o f the electron collision
cross sections over the EEDF calculated from the Boltzmann equation,
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195
where
—e
is the electron charge
m is mass of electron
kj is the rate constant of reaction j
u
is the electron energy in eV
<Jj(u) is the cross section of reaction j
f { u ) is the EEDF
The collision cross sections data for electron-hydrogen excitations has been reviewed in
detail by Tawara [21] and Janev [22]. The sum o f the cross sections of the most
im portant reactions in each type of the excitation were used to calculate the rate
constants. The excitation processes studied are listed in Table 4.2.
4.4.2.2
Wall recombination
Earlier studies [23, 24] have shown that the tube wall plays a very important role
in plasma chemistry, especially for low-pressure plasmas. Positive hydrogen ions are
neutralized by wall collisions, and atomic hydrogen recombines to form molecular
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196
hydrogen on the wall. From equation (13) in [25] we found that the radial density profile
o f atomic hydrogen was nearly uniform across the tube. The difference between the
radial average density and the wall density is less than 4% in the present study, thus
allowing us to substitute the average density, ny, for the wall density in the wall
recombination expression. Furthermore, for mathematical consistency, the rate constant
of the wall recombination of atomic hydrogen is converted to a volumetric reaction rate.
This is done by multiplying by the surface to volume ratio ^/ r . The corresponding rate
coefficient is given by
(4.12)
y = 0.151exp(-1090/Tg)
(4.13)
where y is the wall recombination coefficient which depends critically on the conditions
o f the surface. The experimental measurements of y on quartz reported by Wood and
Wise [24] have been fitted as a function of gas temperature [26].
As extensively discussed elsewhere [27-30] the most important depletion reaction
for charged species is the surface neutralization, which in this case is limited by the rate
o f ambipolar diffusion of positive ions to the sheath. The radial density profile of the
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197
charged species j can be approximated by a Bessel profile [27]
n , (r) = n f
7
7
X JA X r/R )
2 /,(A )
(4.14)
where hj (r) is the radial profile of species j , normalized so that it is consistent with
Equation (4.1), and X = 2 .4 0 5 . W e can then approximate the radial flux of electrons
(and hence the depletion rate) by the diffusional flux at the wall. If we integrate the
diffusional flux over the boundaries of the system and divide by the volume we obtain the
following expression for the wall depletion rate [27, 31]
D.
dn;
2 _ D a j n j = D aj
^
T T
dr r = R R ~ ( R / * ) 22 ~~ ~ A:
nj
(4 - 1 5 >
where
D; = V JQ
(4.16)
1 stp
and
A = R!X
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(4.17)
198
Daj and ujg are the ambipolar diffusivity and the reduced mobility o f ionic species j. A
is the characteristic diffusion length. The subscript “stp” refers to standard conditions.
Values of reduced mobility for H+, H 2 and H2 in H2 in used in the present study were
taken from the literature [32, 33].
4.4.3
Energy and power balance
A unique feature o f low pressure plasmas is that the translational energy
(temperature) of the electrons is substantially higher than that of the ionic and atomic
species. Thus, there are distinct “temperatures”, one for the electrons ( T e) and one for
gas species ( Tg). Two forms of the energy balance, one high pressure and one low
pressure, which accounts for energy losses from the neutral species, were employed and
solved simultaneously with species balances to compute gas temperature and species
concentrations. The second energy balance, often referred to as the power balance in the
literature [15], was then performed to test for self-consistency. That is, the assumed input
power used to solve the Boltzmann equation must match the power computed with this
power balance equation. Each subsystem balance is discussed separately below.
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199
4.4.3.1.
Power balance
The power balance, which describes transfer o f energy from the electrons to the
neutral species, is expressed as follows
0 = - Qne CP" Tc + Pmw - Pev- P iw- Pcw- Pei
(4.18)
where Pmw is the applied microwave power, Pn is the rate of electron energy loss due to
all electron-neutral collision processes in the volume, Piv/ is the rate of ion energy loss to
the wall, Pew is the rate of electron energy loss to the wall, and Pei is the rate of energy
loss due to homogeneous electron-ion neutralizations.
An order of magnitude estimate of the terms in Equation (4.18) shows that the
flow term (first term on the right hand side) and the homogeneous neutralizations (final
term on the right hand side) are much smaller in magnitude than the other terms and
therefore can be safely neglected. The remaining terms must be explicitly expressed in
terms of physical parameters.
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200
The rate of kinetic energy loss of charged particles to the wall can be described as
[34-36]
(4.19)
Pew —TTensugA.i
(4-20)
where m and Te are electron mass and electron temperature, M is the average mass of ion
mixture, ns is the plasma density at the sheath edge, ug is the Bohm velocity, and A; is
the surface area of the inner wall.
The volumetric electron-neutral collisions include elastic and inelastic collisions
o f electrons with the gas particles in the discharge. Elastic collisions occur with both H
and H2 species. The inelastic collisions include ionization, dissociation, electronic
excitation, vibrational excitation, and rotational excitation. Thus, the volumetric power
loss can be written as :
(4.21)
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201
where
P io n
=nev (EiHk4rnH+EiHl (k2+k3)nH2)
(4.22)
P d is
= VEd k in enHl
(4.23)
P e le
= neV (EeIf k2onn + EeH2(k/s +k]g)nH2)
(4.24)
P v ib
= VEv k 2inenH2
(4.25)
P rot
= VEr k22nenH2
(4.26)
Mj is the mass of species j; Eij and Eej are the threshold energies for ionization and
electronic excitation of species j
with electrons, and Ed, E v, and Er are the threshold
energies for dissociation, vibrational, and rotational excitations of molecular hydrogen
with electrons. The electron-neutral reactions considered in the power balance are
summarized in Table 4.2.
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202
4.4.3.2.
Energy balance on neutral species
The low pressure energy balance for the neutral species is written as
° = P ' Q! Cp T'g —p Q C p T g + Pela + Piw +
- AH n k l2 n l
- A H l3k l3n zH n H2 - Atf14 k l4 n H +hA{T„ - Tg ) + £<TA(Tl - T 4g )
where Cp is the specific heat of the gas mixture,
AHj
(4.27a)
is the heat of reaction j, h is the
convective heat transfer coefficient, A is the outer surface area of the quartz tube in
microwave coupler, T„ is the ambient temperature, and £ is the emissivity. The above
energy balance accounts for the sensible heat associated with the gas flow, heat gain due
to elastic collisions and wall neutralizations, heat of chemical reactions, as well as the
heat loss to the ambient by natural convection and radiation.
For low -pressure processes the energy transfer between vibrational and
translational modes (via V -T and anharmonic V -V collisions) is assumed to be small at
low pressures (p < 15 Torr) and not included in the energy balance. The V -T processes
are discounted because lifetime calculations indicated that the V -T relaxation time is
longer than the residence time at low pressures. Moreover, this standard computation
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203
assumes all atoms except one are in the ground state. In fact, it is likely that most (>
80%) o f the H2 species are vibrationally excited. For example, at 1 torr, there are not
enough H2 species to store all of the required energy in the first vibrationally excited
state. A significant fraction (> 50%) of the energy must be stored in higher vibrationally
excited states. At higher pressures, even more energy must be stored in higher vibrational
states. For example at 5 torr, 90% of the vibrational energy must be stored in higher
excited states. If it assumed that 80% of the H2 species are vibrationally excited, the
V -T relaxation time only becomes less than the residence time at pressures of 15 torr or
more. Thus, it is postulated that a small fraction of H2 molecules exist in the ground
state and consequently V -T relaxation can be ignored at pressures lower than 10 torr.
One question remains: How is vibrational energy transferred to higher level
states? This transfer occurs via relatively rapid V -V processes. The V -V relaxation time
is much shorter than the V -T relaxation time [37, 38] therefore, the fast V -V exchanges
will rapidly populate the higher vibrational levels of H2 molecules. However, the rate of
exchange o f energy to translational modes remains very small due to the small
anharmonicity of molecular hydrogen.
In the final analysis, discounting V-T processes in the model for low pressure
plasmas (p < 15 Torr) can be justified by experimental measurements of gas temperature.
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204
As noted later, measured gas temperatures and the pressure dependence of temperature
agree well with the model only if V -T transfer is considered insignificant.
The high pressure (p > 15 Torr) form o f the energy balance is as follows:
® = P Q CpTg —pQCpTg + Pe[a + Piw +
+ Pvib + Pro[ —A H l2kl2nH
- A H l3kl3n 2„ n Hi - AH l4k l4n H + h A (T „ - T g) + e < r A ( T l - T g4 )
(4.27b)
Clearly, at high pressures it is assumed that the translational, rotational and vibrational
temperatures are in equilibrium.
It is also assumed that Tg is the same as Tw, the temperature of the outer quartz
wall, because the resistance of the convective heat transfer from wall to ambient is much
greater than that from gas to wall and the conduction through the wall.
An empirical expression for the convective heat transfer coefficient of air can be
found in several heat transfer textbooks [39, 40], The emissivity employed in this
equation is only the value of quartz emissivity, since the aluminum wave guide is
surrounded by cooling water [39].
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205
4.4.4
Method of solution
The first equation which is solved is the Boltzmann equation. Next, the energy
balance and the species balances are solved simultaneously in order to obtain the gas
temperature and the species concentrations. Note, this is done in two different pressure
ranges. For pressures less than 15 torr the energy balance does not have a term which
couples the vibrational energy to the translational gas temperature. The temperatures of
each of these sub-systems are considered distinct. In contrast, the high pressure form (p
> 15 Torr) assumes equilibrium exists between all energy modes of the neutrals.
Sim ultaneous solution of the energy and species balances yields all species
concentrations and the temperature. Finally, the power terms are directly computed from
the temperatures and species concentrations determined. These power values are used in
the power balance to test for self-consistency. The total power in this balance must equal
the total power initial added to the system. To make a match requires iterations of the gas
temperatures and E/N values employed in the Boltzmann equation.
Finally, it is
important to note that the input electron density to the Boltzmann equation is also
changed, on the basis of the solution to the species balances and the charge neutrality
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206
requirement, with each iteration. The above algorithm is best understood as a flow chart
in Figure 4.2.
The model was used to calculate the electron temperature, gas temperature, and
species density as a function o f operating parameters. The parameters examined in this
study are pressure, power, feed flow rate, and wall recombination coefficient.
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207
NewE/N
Te, Tfcas, Electron D » s ^ , E/N
1
EEDF
NewTe
G
NewTe
Calculation o f the Rate Constants Ocj>
G
r^ rr-
iSzrfil^:
B srrej:
■v—
■
y^—
'
if.'.+ T r v<.—
.*
Calculation o f
FowerBalance Equations
C oniarison
^5»S55n>*
If FowerfModel) - Power(Exp)=0
r -T e
New -Tfeas
- Electron Density
Figure 4.2
Yes
I
Done
I
No
Change E/N Value
Algorithm of the modeling in a fashion of flow chart.
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208
4.5
R esults and discussion
The following discussion is designed to explore the impact of changes in
operating parameters on plasma characteristics. The model developed here is found to
yield improved insight regarding the means of energy transfer from the electrons to the
neutral species. For example, it is shown that a large fraction of the electron energy
transfers to the vibrational modes of the hydrogen molecules. The model also yields
information on the relative concentrations of the ionic species. Finally, agreement with
experimental measures of gas temperature as a function of pressure are found to be very
good.
Previous models did not predict gas temperatures and in fact required input
temperature values. The model values of electron density are within an order of
magnitude of measured values found in the literature.
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209
4.5.1
Pressure
4.5.1.1 Gas Temperature: p < 15 Torr
Virtually every plasma characteristic is strongly impacted by changing pressure
while holding all other operating parameters constant.
One o f the few testable
predictions is that gas temperature decreases as pressure increases for low pressures (p <
15Torr). As shown in Figure 4.3 the measured temperatures follow the predicted values
with very good agreement.
The principle reason for the decrease in temperature with increasing pressure is
found in Figure 4.4. As the pressure is raised an increasing fraction of the input power is
transferred to molecular vibration. Thus, the vibrational “temperature” rises with
increasing pressure, whereas the translational temperature falls.
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210
1400
Gas Temperature (K)
1200 1000-
800600400200
Tgas (Model)
-
Tgas (EXP)
1
10
100
P ressure (torr)
Figure 4.3
Gas temperature as a function of pressure.
Power: 200 W; Flow rate: 100 seem.
In this, and subsequent figures, the vertical line at p=15 torr represent the
pressure at which the energy balance employed was changed from the low
pressure to the high pressure form. See text for detail.
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211
240
Pover Loss Distribution (W)
200
160
□
□
■
ED
E3
B
120
80
Elastic Collision
Dissociation
Ionization
Electron Excitation
Vibrational Excitation
Rotational Excitation
40
10
100
P re ssu re (to rr)
Figure 4.4.
Power transfer. As pressure increases, the major channel for power
transfer from electron to neutrals shifts from dissociation to vibrational
excitation. Power: 200 W; Flow rate: 100 seem.
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212
The increase in Tvib with increasing pressure can be correlated to the effect of
pressure on electron temperature.
As shown in Figure 4.5, electron temperature
decreases with pressure. As pressure increases, more neutral particles are available to
collide with the electrons and hence the mean free path for the electrons is shorter. More
frequent elastic and inelastic collisions result in a decrease in electron temperature. In
turn, lower Te leads to increased power input to vibration. That is, a lower Te shifts the
major electron-neutral reaction pathway toward processes with low threshold energy.
This is essential a result of the fact that the vibrational threshold energy (E > 0.5 eV) is
significantly lower than that for dissociation (E > 8.8 eV), electronic excitation (E > 10.5
eV), and electron-impact ionization (E > 13.5 eV).
4.5.1.2 Gas Temperature: p > 15Torr
The high pressure region (p > 15 Torr) model also agrees well with the data
(Figure 4.3). The energy balance for this pressure range is based on a “thermal
equilibrium” assumption. That is the translational, vibrational and rotational temperatures
are all assumed to be equilibrated via rapid collisions in this high pressure regime.
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-6
g
«
o.
E
«
5 -
-5
4-
-4
-3
2
2-
-2
ui
0
10
20
30
40
50
Electron Density (1011 cm-3)
213
60
P re ssu re (torr)
Figure 4.5
Electron temperature and density as a function of pressure. Power:
200 W; Flow rate: 100 seem.
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214
Re-call (see Energy Balance section above) that the energy balance is modified in
this pressure range because calculations based on pressure (i.e. collision frequency)
dependent relaxation times shows that V -T relaxation times only becomes less than the
residence time at pressures of 15 torr or more. Thus, only at high pressures is true
internal equilibrium for all molecular modes expected.
The model is broken down into two pressure ranges because of the difficulty of
finding a model for the intermediate pressure range. It is only possible to write a simple
expression when the impact of relaxation is minimal or maximal. It appears that
experimental agreement with the model in the two limits justifies the approach taken.
4.5.1.3 Species density
One parameter which is found to have a maximum as a function of pressure is
electron density. The generation of electrons is determined mainly by two factors; the
ionization rate constants, and the density of neutral species available for ionization. The
ionization rate constant, which is a function of electron temperature, decreases with
pressure. However, the neutral species density increases with increasing pressure. The
net result is that electron density has a maximum at a certain pressure (3.0 Torr).
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215
In Figure 4.6 the densities o f all three positive ions in a hydrogen plasma are
shown. It was found that H3 is the dominant ionic species at all pressures examined.
This result is implicit in the m echanism (Table 4.1). Specifically, the ion-neutral
reactions determine the dominant ionic species in a hydrogen plasma. Both H+ and H t
react with molecular hydrogen to form H3 (see reaction RIO and R l l ) . The rates of
these reactions increase with the density of molecular hydrogen, which increases with gas
pressure. Therefore, at sufficiently high pressure the dominant ionic species should be
H 3 ions. Note that this result is consistent with the experimental evidence that H 3 is
negligible in low pressure (p < 1 mtorr) ECR plasma reactors [41-43].
Finally, it is important to ascertain the influence of pressure on H-atoms (Figure
4.7). As with the electron density, the H-atom density has a maximum at 3 torr whereas
the fractional dissociation, defined as x = 2 n H
+ 2 n „ j , decreases monotonically
with pressure. The explanation for the maximum in the H-atom density is qualitatively
similar to the one for the electron density described above; that is, the maximum results
from a competition between the decreasing (with pressure) dissociation rate constant and
the increasing (with pressure) overall species density. The net result is a maximum in the
H-atom density at a pressure of approximately 3 torr. The fractional dissociation, in
contrast, is completely controlled by the hydrogen dissociation rate, which decreases
monotonically with pressure.
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216
The influence of pressure on H-atom dissociation may have operational
consequences. Generally, dissociated hydrogen has the greatest chemical value. Thus,
operation at low pressure is the most energy-efficient (Figure 4.4). As pressure increases,
input power is lost primarily to vibrational excitation, and the fraction o f input power
which leads to dissociation is significantly reduced. Again, the physical basis of the lower
efficiency is related to electron tem perature. As noted, the electron temperature is
lowered as pressure is increased. Thus, high threshold processes such as dissociation are
less likely at lower Te (higher pressure) values.
4.5.1.4 E/N
Prior modeling work suggests there is a reasonable range of E/N values. As one
test of the present model, comparisons were made to prior predicted E/N values for
microwave generated hydrogen plasmas. As shown in Figure 4.8(a), the values of E/N,
clearly a function of density (pressure and temperature), are in the same range as those
previously reported.
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Ion Density (crri)
217
10 ®
H+
H2+
10 ®
0
10
20
30
40
50
60
P r e s s u r e (to rr)
Figure 4.6
Ion density as a function of pressure. Hj ion is the dominant ionic species
over the entire pressure range. Power: 200 W; Flow rate: 100 seem.
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218
0.2
20
0 .1 6
16
<7
uE
•«
u
©
e
0.12
o
«5
c
o
0 .0 8
-12
o
E
e
<
O
e
0 .0 4
0
10
20
30
40
50
60
P re s s u re (to rr)
Figure 4.7
Fractional hydrogen dissociation. Fractional hydrogen dissociation
decreases with pressure. However, H-atom density has a maximum at 3.0
torr. Power: 200 W; Flow rate: 100 seem.
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8.0 1016
EB
7.0 1016
03
(eUlOA) N/3
6.0 1016
-
Model
EB
5.0 1016
EB
EB
ffl
Eariler Model
4.0 1016
EB
EB
t
0
1
■---- 1---2
1---- ----- 1— ---- 1---------- r
-
3.0 1016
3
4
5
6
7
N (1017 c m ^
Figure 4.8a
E/N as a function of gas density.
Note: The data is plotted in terms of gas density, in order to permit
comparison with earlier model (ref. 15), in which neither pressure nor
temperature was specified.
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220
52
51-
CN
E
u
>
50-
r-
49111
48-
47
50
100
150
200
250
Pow er (W)
Figure 4.8b
E/N as a function of microwave power. Pressure: 10 torr; Flow rate: 100
seem.
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221
4.5.2
Microwave power
The impact o f microwave power on hydrogen plasmas is shown in Figures 4.9
and 4.10. When the applied microwave power is increased, more electrons are generated
(Figure 4.9) through electron-impact ionization (R2-R4), which in turn, produces more
hydrogen atoms (see Figure 4.10). The degree of hydrogen dissociation was found to be
proportional to microwave power (Figure 4.10). However, electron temperature is only
slightly increased from 1.87 to 2.05 eV when microwave power increases from 70 to 200
Watts. Figures 4.5 and 4.9 show that electron temperature is a function of both input
power and pressure. Apparently, the dependence on power is much weaker than the
pressure dependence. Similar results have been found in low pressure oxygen plasmas
[34].
Figure 4.11 shows the effect the microwave power has on the gas temperature.
As the applied power is increased, the rate of exchange of energy between the hotter
electrons and the gas also increases causing the gas temperature to rise. Notice the higher
sensitivity of the gas temperature to the applied microwave power as compared to the
electron temperature. This may suggest a control strategy for both the electron and gas
temperatures in “cold” plasmas. Perhaps gas temperature can be controlled by adjusting
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222
the microwave power while the electron temperature is controlled by the operating
pressure. Figure 4.11 also shows experimental measurements for comparison. The model
agrees well with the experiments (within 15% for all cases) over the entire range of
power inputs. The impact of power on E/N values is found in Figure 4.8(b).
4.5.3. Wall recombination coefficient
The wall recombination coefficient, y , has long been found to have a profound
influence on diatomic plasmas. However, there is a large range of experimental values of
y for a quartz wall reported in the literature. For instance, the value o f y published by
Wood and W ise [25] is about an order of magnitude higher than the value reported by
Green [44] which is about another order of magnitude higher than that reported by Kim
and Boudart [45]. Such a discrepancy is due to the difficulty of characterizing precisely
the quartz surface, as y is a strong function of surface roughness, purity of feed gas, and
temperature o f the inner wall. Furthermore, all values of y were measured in a flowing
afterglow where ionic and electronic processes do not occur. As ionic bombardment is
likely to increase tube surface temperature, it is reasonable to surmise that y in the
discharge is higher than in the afterglow. Therefore, in the present, the values of W ood
and Wise [25] which are the highest, were employed.
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223
In order to assess the impact o f the assumed y value, a parametric study was
conducted and results are shown in Table 4.3. No convergence was found using Green's
coefficient at the pressure lower than 5 torr. It was found that 7 affects H-atom behavior
more strongly than it does the charged species. The maximum H atom density obtained
using W ood and W ise’s values of 7 is more than an order of magnitude higher than that
found using the value reported by Kim and Boudart. In contrast, the electron density is
nearly the same at all pressures. Both electron and gas temperature are only slightly
changed by the wall recombination coefficient. The dominant ions is H 3 for all three wall
recombination coefficients.
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Electron Temperature (eV)
3. 5 -
-
3. 5
-
2. 5
-
1. 5
3-
2. 5 21. 5 -
0. 5
50
100
150
200
0. 5
250
P ow er (W)
Figure 4.9.
Electron temperature and electron density as a function of
microwave power. Pressure: 10 torr; flow rate: 100 seem.
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Electron Density (1011 cm43)
224
225
0.06
16
12
-
-0.04
S'
M
-0.03
50
100
150
200
-
0.02
-
0.01
Fractional Dissociation
-0.05
250
Power (W)
Figure 4.10
H-atom density and fractional dissociation as a function of microwave
power. Pressure: 10 torr; flow rate: 100 seem.
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1200
Gas Temperature (K)
1 000 -
800-
600-
400-
200-
50
100
150
200
250
P o w er (W)
Figure 4.11
Gas temperature as a function of microwave power. Model
Experiment: ■ ; Pressure: 10 torr; flow rate: 100 seem.
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227
Table 4.3
The Impact o f Wall Recombination Coefficient on Model Results
P ressure
W & W 's y a
2 to n
1 .4 x l0 15
10 to n
50 to n
1 .3 x l0 15
5 .2 x l0 14
3 .8 x l0 15
4.2X1013
1.2x l 0 15
1.2x l 013
2torr
10 torr
50 torr
4.8X1011
3.4xlO n
1.5xlOu
*******
3.5X1011
1.6x l 0 n
5 .2 x lO u
3.3X1011
1.5X1011
2 ton-
3.07
*******
Electron Temperature
(eV)
10 torr
50 to n
2.05
1.48
2.04
1.47
1013
941
1069
*******
Gas Temperatue (K)
2 ton10 ton50 to n
2 to n
HT
nr
nr
P roperty
H-atom Density (cm-3)
Electron Density (cm*3)
Dominant Ions
10 to n
50 to n
G reen's y b
K & B ’s y c
4.4X1013
937
1070
:£
a. 7 = 0.151 exp{-1090/Tg)
Wood and Wise [25]
b. 7 = 0.207exp(-2423/Tg)
Green [44]
c. 7 = 1.5 x l0 '5(Tg/300)4
Kim and Boundart [45]
^ sfes(:
nr
nr
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3.06
2.06
1.48
1002
944
1069
nr
nr
H3+
228
4.5.4
Feed flow rate
Compared to pressure and power, flow rate has very little effect on the species
densities in a hydrogen plasma. Although the transport of neutral species is mainly driven
by convection, convection is still several orders of magnitude smaller than the rate of
production o f H atoms and their destruction by recombination at the reactor wall.
Furthermore, the convective losses o f the charged species is also negligible because the
transport o f charged species is totally dominated by ambipolar diffusion. One
consequence of the relatively minor role that convection plays in the species balance
equations is that the flux of H atoms leaving the plasma will increase approximately
linearly with flow rate, at least over the range considered in this study (100—500 seem).
On the other hand, the flux of charged ions will remain nearly unchanged with increasing
flow rate because it is dominated by ambipolar diffusion. This suggests that the flow rate
can be used to adjust the ion-neutral flux ratio exiting the glow discharge. This has
important implications for many plasma processes where ions can assist or be detrimental
to surface processes [46,47].
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229
4.5.5
Comparison with prior experimental studies
An effort was made to demonstrate the broad applicability of the model and to test
it against experimental results. Specifically, the operating parameters of two prior studies
were input to the model, and model plasm a parameters were compared to values
measured in those studies (see Table 4.4).
The model was also used to predict Te and ne values for the plasma operated by
Tahara et al [48]. The agreement was good in both cases. Indeed, over the range of
operating conditions of interest, model values for Te showed the same trend and same
range of values as the measured Te values. Agreement was excellent. The predicted
values for ne was not as good as for Te- Over the span of operating conditions studied,
the model values were consistently a factor of four greater than the measured values.
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230
Table 4.4
Comparison Between Model Results and Experimental Measurements.
Property
Operating
Condition
Model
Result
Exp.
Result
3 torr
2.3
2.1
[48]
0.8x l 0 11
0 .9 x l0 n
[48]
Electron Temperature
(eV)
5 torr
2.7
2.4
Electron Density (cm-3)
3 torr
5 torr
5 - l x l O11
4.4X1011
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Reference
231
4.6
Summary
A model describing the discharge region of a microwave hydrogen plasma has
been developed. The model predicts the densities of neutral ( H , H 2) and charged ( H +,
H 2 , H 2 ) species, as well as electrons.
Furthermore, two energy balances were
employed to predict the temperatures of the neutral species ( T ) and electrons {Te).
Parametric studies were performed to determine the effect that pressure, microwave
power, and flow rate had on neutral and charged species density and the gas and electron
temperatures.
A number of experimental tests were conducted to test predictions of the model.
The dependence of the gas temperature with operating pressure and microwave power
was computed and compared to experimental measurements.
In both cases, the
agreement between model and experiment was very good.
The basis of the successful prediction of gas temperatures, which decrease with
increasing pressure is the model prediction that at low pressures (p < 15 Torr) much of
the input microwave power enters the H j molecular vibration channel. At low pressures
T y _ T is large, hence vibrational and translational temperatures can be significantly
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232
different. And at higher pressure (p > 15 Torr), the 'E y_ T is relatively small, so it is in
the "thermal equilibrium" which result in gas temperature rising as pressure is increased.
Thus, the successful prediction of magnitude and pattern of gas temperature indicates the
model captures much of the complexity of the plasma behavior.
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233
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238
Chapter 5
CONCLUSIONS AND RECOMMENDED FUTURE W ORK
In this thesis, a new technique, microwave generated atmospheric plasma, has
been successfully employed to produce spherical oxide ceramic particles of controlled
size. We developed a means of continuous modification of ceramic by passing an aerosol
containing precursor materials rapidly (residence time - 0.1 seconds) through a low
power microwave generated plasma. A patent was awarded for the use of this technique
to make spherical oxide ceramics of controlled size. Next, a systematic characterization
o f the afterglow region o f plasma using spectroscopic methods was conducted for the
purpose of developing an optimal process and determination of the equilibrium state of
the plasma. One result was the finding that the electron, gas and excitation temperatures
are totally different which indicates the LTE model is not applicable approach to
modeling atmospheric plasmas. Finally, a novel model for the coupler region of the lowpressure hydrogen plasma was developed. The speciality of this model is that it separates
the plasma into charged and neutral species with different temperatures but coupled with
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
239
the power balance equations. This multi-temperature model approach proved is a better
method for the modeling work.
In future work, a priority should be placed on creation other high value ceramic
materials using the plasma/aerosol technique. For example, initial work shows boron
nitride, which is an electrical insulator, but with high thermal conductivity, can be
produced in spherical form using this approach. This may greatly impact the integrated
circuit package industry. Currently, spherical silica is used in integrated circuit packages
because of its low co-efficient o f thermal expansion. But the thermal conductivity is
much lower than that of boron nitride. Therefore, boron nitride certainly is a better choice
for the purpose. The challenge is to develop a low cost approach to the generation of
spherical boron nitride. Another priority should be the development of sophisticated
models. Our plasma characterization studies show a m ulti-tem perature model is
necessary for modeling. The experimental data of the temperatures and densities can be
used to test the validity of future model. Our own modeling work represents only the first
stage in a tough process to develop high fidelity models of this system. Future models
will need to account for many factors not included in our model such as complex flows,
presence of solid particles and high pressures.
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VITA
Personal Information :
Chun-Ku Chen
Date of Birth : May 4, 1970
Marital S tatus: Single
Place of Birth : Ping-Tung, Taiwan
Education :
Pennsylvania State University, University park, PA
- Entered in January, 1997
National Taiwan University, Taipei, Taiwan
- B.S. in Chemical Engineering, June 1993
Selected Publications:
1.
2.
3.
4.
5.
6.
C. K. Chen. S. Gleiman and J. Phillips, Journal o f M aterial Research, 16,
pp 1256 (2001).
C. K. Chen. T. C. Wei, L. R. Collins and J. Phillips, Journal o f Physics D:
Applied Physics, 32, pp 688 (1999).
L. C. Chen, C. K. Chen. S. L. Wei, D. M. Bhusari and Applied Physics
Letters, 72, pp 2463 (1998).
D. M. Bhusari, C. K. Chen. K. H. Chen, T. J. Chuang, L. C. Chen and M.
C. Lin, Journal o f Material Research, 12, pp 322 (1997).
D. Y. Lin, L. C. Chen, C. K. Chen. K. H. Chen and D. M. Bhusari,
Physical Review B, 56, pp 6498 (1997).
L. C. Chen, D. M. Bhusari, K. H. Chen and C. K. Chen, et. al., Thin Solid
Film, 303, pp 66 (1997).
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