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Heating effects during microwave plasma sintering of ceramics

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O rder N um ber 9129004
H eating effects during microwave plasma sintering o f ceramics
Hsu, Matthew, Ph.D.
Northwestern University, 1991
C o p yrig h t © 1 9 9 1 by H su , M a tth e w . A ll rights reserved.
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
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NORTHWESTERN
UNIVERSITY
HEATING EFFECTS DURING MICROWAVE PLASMA
SINTERING OF CERAMICS
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
DOCTOR OF PHILOSOPHY
field of Materials Science and Engineering
By
MATTHEW
HSU
1
EVANSTON, ILLINOIS
June 1991
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
© Copyright by Matthew Hsu 1991
A ll Rights Reserved
ii
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ABSTRACT
Heating Effects during Microwave Plasma Sintering of Ceramics
Matthew Hsu
A variety of ceramic materials, including oxides and nonoxides, have
been fired in various microwave excited plasmas at reduced pressures.
Specimen heating was accomplished prim arily by direct contact with the
plasma and, to a smaller extent, by direct coupling w ith the microwave
energy which was not fully screened by the plasma. Temperature of thimble­
shaped ceramic samples immersed in the plasma was measured by optical
fiber thermometry.
The effects of gas composition on plasma sintering behavior were
quantified.
Higher specimen temperatures were achieved in polyatomic
gases with greater reactional enthalpy. In general, for any given material,
increasing temperatures are obtained for plasmas in the order of He, H 2 , O 2 ,
and N 2 .
Specimen temperature was also found to be highly dependent upon the
material composition. Thus, for any given plasma gas, materials with lower
conductivity, e.g. A I2 O 3 and MgO, generally achieve higher temperatures
than semiconducting or covalently bonded materials, such as N iO and SiC.
Two surface catalyzed atom recombination mechanisms, one electronic and
iii
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the other ionic, were proposed to account for the observed difference in
heating behavior.
A first order approximation of specimen heating by a plasma was carried
out based on the thermal fluxes of individual species present in the plasma.
Fair agreement was obtained for estimation of surface temperatures of the
insulating oxides. The predicted trend of heating in the gaseous discharges
was consistent with that observed. Calculations indicated that the transfer of
kinetic energy and chemical energy of recombination of atomic species
dominate the heat transfer process.
Chemical etching by radical species generated in the plasma occurred for
several solid/gas systems. Nitrogen plasma was observed to attack A 1 2 0 3 ,
T i 0 2 , ZnO, and ZrC>2 and appeared to be the most reactive atmosphere.
Moreover, plasma enhanced reduction of the thermodynamically less stable
oxides, such as Fe2C>3 , N iO , Ti0 2 , and ZnO, was also observed in He, H 2 , and
N 2 plasmas.
Direct heating by coupling of microwave energy was significant only for
firing of SiC in a He plasma. Measurements of relative field strength using
an E-field probe showed that helium plasma was indeed the most
transparent to the microwaves.
iv
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ACKNOWLEDGEMENTS
There are many who contributed in large ways to the material presented
in this thesis.
To begin, I would like to thank the Lord, my God, who
faithfully sustains me from the beginning to the end of this project by His
infinite mercy and abounding grace.
I am grateful to my advisor, Professor D. Lynn Johnson, for his guidance,
with much patience and wisdom, throughout the course of this research
project.
The other faculty members who also had notable impact on my
work include, Professor M . E. Brodwin, Y. W. Chung, W. E. Olmstead, and
A. Taflove. They have provided generous assistance, valuable insight, and
many helpful suggestions. And to a very supportive group, Jim D. Hansen,
Mary P. Sweeny, and the rest of my contemporaries in our lab group, I thank
them for their many stimulating discussions and helping me through many
of the trials of graduate school, and perhaps more importantly, of life.
Wilma Hackl, the best secretary one could ask for, has been especially
helpful. I thank her for putting up with me all these years at Northwestern.
Very special thanks go to my parents, family, and Rev. Grace Chen for
having faith in me and for being supportive during times when I have been
down.
Finally, my deepest gratitude goes to my wife, Esther, for her
invaluable assistance, sacrifice, constant spiritual support, and for her
patience to endure w ith me this long process. She deserves as much credit
for this degree as I do.
v
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Funding of this work under NSF grant No. DM R 8216710 was greatly
appreciated.
vi
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TABLE OF CONTENTS
iii
ABSTRACT...........................................................................................................
ACKNOW LEDGEMENTS.................................................................................
v
LIST OF FIGURES...............................................................................................
xi
LIST OF TABLES................................................................................................... xix
CHAPTER
I.
IN TR O D U C TIO N .................................. ............................................
A.
B.
II.
1
Motivations ..........................................................................
Objectives..............................................................................
1
2
BACKGROUND..................................................................................
4
A. Introduction....................................................... :..................
B. Literature Review................................................................
1. Early investigators
2. RF Induction coupled plasma
3. DC discharge
4. Microwave excited plasma
5. Other workers
C. Sintering Theory................................................................
1. Two sphere model
2 . Universal sintering model
D. Plasma State...........................................................................
1 . Constituency
2. Temperature
3. Density
4. Debye sheath
E. Theory of Langmuir Probe..................................................
1. Single probe
2 . Double probe
F. Plasma Chemistry................................................................
G. Interaction of Plasma with Surfaces...................................
1. Adsorption
2. Ion induced chemical reactions
3. Electron induced chemical reactions
4. Electron-ion recombination on surfaces
5. Interaction of neutral species with surfaces
4
5
vi i
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27
37
43
53
60
H.
I.
m.
6 . Recombination of atoms on surfaces
Mechanism of Microwave Power Absorption...................
Heating Mechanisms..............................................................
1. Plasma heating
a. Thermal fluxes of particles
b. Electron density estimation
c. Electron temperature estimation
2. Microwave heating
88
90
EXPERIMENTAL APPROACH......................................................... 106
A.
B.
C.
D.
E.
F.
G.
H.
I.
Experimental Apparatus........................................................
1. Microwave excited plasma
2. Induction coupled plasma
3. Hollow cathode discharge
Plasma Characterization.......................................................
1. Langmuir probe
2. Plasma length
3. Plasma power absorption
4. Power density determination
Specimen Preparation...........................................................
1. Powder materials
2. Binder addition
3. Pressing of rods
4. Pressing of thimbles
5. Binder burnout
Temperature Measurement..................................................
1. Optical pyrometer
2. Optical fiber thermometer
Density Measurement..........................................................
Sintering of Ceramic Rods...................................................
1. Plasma generation
2. Sintering procedure
Sintering of Ceramic Thimbles...........................................
1. Plasma generation
2. Cleaning of adsorbed species
3. Stationary heating of sample
Conventional FurnaceHeating...........................................
E-field Measurement............................................................
1. Microwave probe
2. Empty cavity
a. Probe characterization
3. E-field with plasma
v iii
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106
110
117
122
125
126
127
128
129
J. Microstructural Examination.............................................. 134
1. Scanning electron microscopy
a. Surface morphology
b. Fractography
IV .
RESUTLS A N D DISCUSSION......................................................... 136
A.
B.
C.
D.
E.
F.
Preliminary Sintering Trials.................................................
1. Sintering of SiC
2. Sintering of Si3N 4
3. Sintering of TiB2
Langmuir Probe Results......................................................
Power Density Determination..............................................
1. Plasma length
2. Power density
3. Power distribution profiles
Plasma Density and Temperature Estimation..................
1. Electron density
2. Electron temperature
3. Neutral gas temperature
Sintering of Ceramic Thimbles...........................................
1. OFT temperature measurement
a. Plasma luminosity effect
b. OFT calibration
c OFT time-temperature profiles
2. Sintered densities
3. Surface modification
a. Plasma etching
b. Reduction
4. Sample temperature estimation
a. Assumptions
b. Recombination coefficient
c Atom concentration near the surface
d. Theoretical estimation
Mechanisms of Surface Heating.........................................
1. Electronic factors
a. Semiconductivity
b. Fermi level
c d -electron configuration
2. Chemical factors
a. Surface oxygen bond energy
b. Correlation of qs with recombination
ix
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136
145
151
160
177
209
efficiency
c Correlation of qs with electronegativity
difference
3. Rate equation for a recombination process
4. Bronsted-Temkin relation
5; Effect of charging on recombination activity
a. Retardation of reaction rate
b. Destabilization of adsorbate-adsorbent bond
6 . Discussion on dopant effect in AI2 O 3
7. Ionic factors
G. E-field Probe Measurement................................................... 236
1. Probe characterization
2. H elium
3. Hydrogen
4. Oxygen
5. Nitrogen
V.
V I.
260
CONCLUSIONS
FUTURE STUDIES
263
REFERENCES
269
APPENDICES
A.
B.
C.
D.
E.
F.
Material data sheets..........................................
Derivation of boundary layer equations........
OFT time-temperature profiles.....................
Length of plasma for various gas discharges
Power density curves......................................
Ne/Pd*A and E /p as function of pA..............
X
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288
290
313
343
346
350
LIST OF FIGURES
1.
Schematic of sintering geometry for (a) two sintering bodies
during in itial stage of sintering and (b) intermediate-stage
sintering.
29
Paths of mass transport with (A) as volume diffusion from the
grain boundary, (B) grain boundary diffusion, (C) volume
diffusion from the particle surface, (D) surface diffusion, and (E)
vapor transport.
31
Variation of F(p) w ith relative density computed from
simulations of initial stage sintering of spherical compacts.
36
4.
Temperatures in arcs as a function of pressure.
38
5.
Ranges of temperatures and densities of species present in a
typical plasma process operated at reduced pressure conditions.
41
6.
The electron and ion densities in the sheath region of plasma.
44
7.
The current-voltage characteristics of a probe introduced into a
plasma
46
8.
Schematic of a double probe immersed in a plasma.
50
9.
Schematic of the I-V characteristics for an unequal area
Langmuir double probe.
51
Pictorial representation of the surface of (a) a covalent solid and
(b) an ionic solid.
62
11.
Ion-assisted gas surface chemistry using Ar+ and XeF2 on Si0 2 -
67
12.
Electron-assisted gas surface chemistry using 1500 eV electrons
and XeF2 simultaneously incident on SiC>2 .
72
The relative excitation cross section versus electron energy for
nitrogen molecules.
77
2.
3.
10.
13.
14
Schematic of the interaction of microwaves with materials.
x i
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98
15.
Variation of relative dielectric constant
temperature.
16.
Loss tangent
17.
Variation of skin depth as a function of electrical conductivity.
18.
Schematic of the reduced height microwave plasma sintering
system.
19.
Schematic of a Langmuir double probe circuit.
20.
Microwave output power as a function of the magnetron anode
current of the Reeve microwave generator.
21.
Sketch of the thimble making assembly.
22.
Schematic close-up of the plasma tube and thimble specimen
during sintering.
23.
E-field probe for sampling microwave field within the plasma.
24.
Scanning electron micrograph of the fracture surface of (a) a-SiC
and (b) 0-SiC rod specimens sintered in a plasma gas mixture of
Ar, H 2, He, and N 2 in an ICP system at 7 kV.
25.
X-ray diffraction pattern of a Si3N 4 sample fired in an induction
coupled nitrogen plasma.
26.
Plot of Langmuir probe data for an argon plasma operated at 1
torr and a constant applied power of 30 watts.
27.
Plot of Langmuir probe data for an argon plasma operated at 14
torr and a constant applied power of 60 watts.
28.
Plot of Langmuir probe data for a nitrogen plasma operated at 10
torr and a constant applied power of 1 0 0 watts.
29.
Plot of Langmuir probe data for a nitrogen plasma operated at 1
torr and a constant applied power of 30 watts.
30.
Plasma length as a function of applied power for an oxygen
plasma at various pressures.
(8
(8
to 10 GHz) on
to 10 GHz) as a function of temperature.
xii
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31.
Average power density as a function of applied power for
various gases at a pressure of 25 torr.
32.
The dependence of the neutral gas temperature on the average
power density.
33.
Schematic profiles of (a) linear, (b) parabolic, and (c) exponential
power distribution along the length of discharge tube.
34.
Plots of E /p and n^/Pd A vs pA for an oxygen plasma.
35.
Electron number density as a function of applied power for a
microwave excited oxygen plasma at various pressures.
36.
Electron number density as a function of pressure for a
microwave excited oxygen plasma operated at power levels of
230 W and 530 W.
37.
Electron number density as a function of pressure for a
microwave excited nitrogen plasma operated at 530 W.
38.
Plots of electron temperature and average electron energy as
function of E /p for an oxygen plasma.
39.
Electron temperature as a function of applied power for an
oxygen plasma at 25 torr.
40.
Electron temperature as a function of pressure for an oxygen
plasma at 530 W.
41.
Gas temperature as a function of discharge current in nitrogen
at a pressure of 1.35 torr, frequency of 80 M H z, and a discharge
tube diameter of 1 0 cm.
42.
Temperature-time profile during a quench study w ith the
maximum sampling rate at 38/sec.
43.
Calibration curve of the OFT.
44.
Temperature profile for alumina fired in 25 torr N 2 plasma at a
power density of 35 W /cm 3 with the first 300 second devoted to
cleaning of adsorbed gases from the specimen at low applied
power levels.
xiii
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45.
Scanning electron micrographs of the external surface of an
A I2 O 3 thimble specimen fired in a plasma (a) and conventional
(b) furnace in nitrogen.
188
Scanning electron micrographs of the external surface of a ZnO
thimble specimen fired in a plasma (a) and conventional (b)
furnace in oxygen.
189
Scanning electron micrographs of the external surface of a Zr 0 2
thimble specimen fired in a plasma (a) and conventional (b)
furnace in nitrogen.
190
Scanning electron micrographs of (a) the external surface and (b)
inside surface of an Fe2 0 3 thimble specimen fired in an oxygen
plasma.
191
49. Scanning electron micrographs of (a) the center and (b) fracture
edge region of the fracture surface of an Fe2 0 3 thimble specimen
fired in a helium plasma.
192
50. Scanning electron micrographs of (a) the external surface and (b)
inside surface of a TiC>2 thimble specimen fired in a nitrogen
plasma.
194
51. Temperature dependence of the rate of hydrogen and oxygen
atom recombination on fused quartz and alumina surfaces.
200
52. Variation of the surface oxygen bond strength with the heats of
formation of the metal oxides.
215
53. The dependence of catalytic activity of various oxides in the
recombination of O atoms upon the bond energy of the surface
oxygen.
216
54. Correlation between the logarithm of catalytic activity for
oxygen recombination and the difference in electronegativity.
218
46.
47.
48.
55.
56.
The dependence of the activation energy of the atom
recombination process on the bond energy of the surface
oxygen.
224
E-field probe output as a function of absorbed microwave power
in the absence of a plasma.
238
xi v
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57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
Variation of the microwave power absorbed by the empty cavity
as a function of applied power without a plasma.
239
Power absorption as a function of applied power in a
microwave excited helium plasma at a pressure of 25 torr.
240
E-field probe output as a function of absorbed power in a
microwave excited helium plasma at a pressure of 25 torr.
241
The dependence of electrical conductivity of hydrogen,
nitrogen, argon and helium plasma upon the electron
temperature at one atm.
243
Electron density as a function of applied power for a microwave
excited helium plasma at several pressures.
244
Microwave power absorbed as a function of applied power in a
hydrogen plasma at a pressure of 25 torr.
246
E-field probe output as a function of absorbed power in a
microwave excited hydrogen plasma at a pressure of 25 torr.
247
Electron density as a function of applied power for a microwave
excited hydrogen plasma at various pressures.
248
E-field probe voltage and power absorbed as a function of
pressure for a microwave excited hydrogen plasma at a constant
input power of 360 W.
249
Average electron number density as a function of pressure for a
hydrogen plasma at a constant applied power of 360 W.
250
Power absorption as a function of applied power
microwave excited oxygen plasma at a pressure of 25 torr.
in a
252
E-field probe output as a function of applied power
microwave excited oxygen plasma at a pressure of 25 torr.
in a
253
Power absorption as a function of applied power in a
microwave excited nitrogen plasma at a pressure of 25 torr.
254
E-field probe output as a function of applied power in a
microwave excited nitrogen plasma at a pressure of 25 torr.
255
xv
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71.
Average electron number density as a function of power for a
microwave excited nitrogen plasma at various pressures.
72.
E-field probe voltage and power absorbed as a function of
pressure for a microwave excited nitrogen plasma at a constant
applied power of 740 W.
C l.
Temperature profile for A I2 O 3 fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3.
C2.
Temperature profile for A I2 O 3 fired in 25 torr H 2 plasma at a
power density of 33 W /cm 3.
C3.
Temperature profile for A I2 O 3 fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C4.
Temperature profile for A I2 O 3 fired in 25 torr Ne plasma at a
power density of 36 W /cm 3.
C5.
Temperature profile for MgO fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C6 .
Temperature profile for MgO fired in 25 torr Ne plasma at a
power density of 36 W /cm 3.
C7.
Temperature profile for Ti0 2 fired in N 2 plasma at a power
density of 35 W /cm 3.
C8 .
Temperature profile for T i 0 2 fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3.
C9.
Temperature profile for T i0 2 fired in 25 torr H 2 plasma at a
power density of 33 W /cm 3.
CIO.
Temperature profile for Ti0 2 fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C ll.
Temperature profile for Ti0 2 fired in 25 torr Ne plasma at a
power density of 36 W /cm 3.
C1 2 .
Temperature profile for ZrC >2 fired in 25 torr N 2 plasma at a
power density of 35 W /cm 3.
xvi
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C13.
Temperature profile for Z r 0 2 fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3.
C14.
Temperature profile for ZrC>2 fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C15.
Temperature profile for SiC fired in 25 torr N 2 plasma at a
power density of 35 W /cm 3.
C16.
Temperature profile for SiC fired in 25 torr H 2 plasma at a
power density of 33 W /cm 3.
C17.
Temperature profile for SiC fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C18.
Temperature profile for N iO fired in 25 torr N 2 plasma at a
power density of 35 W /cm 3.
C19.
Temperature profile for N iO fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3.
C20.
Temperature profile for N iO fired in 25 torr H 2 plasma at a
power density of 33 W /cm 3.
C2 1 .
Temperature profile for Fe2 0 3 fired in 25 torr N 2 plasma at a
power density of 35 W /cm 3.
C22.
Temperature profile for Fe2 0 3 fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3.
C23.
Temperature profile for Fe2 0 3 fired in 25 torr H 2 plasma at a
power density of 33 W /cm 3.
C24.
Temperature profile for Fe2 0 3 fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C25.
Temperature profile for ZnO fired in 25 torr N 2 plasma at a
power density of 35 W /cm 3.
C26.
Temperature profile for ZnO fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3.
xvi i
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C27.
Temperature profile for ZnO fired in 25 torr H 2 plasma at a
power density of 33 W /cm 3.
C28.
Temperature profile for ZnO fired in 25 torr He plasma at a
power density of 36 W /cm 3.
C29. Temperature profile during a cleaning cycle for the optical fiber
thermometer (OFT) fired in 25 torr N 2 plasma at a power
density of 35 W /cm 3.
C30. Temperature profile for during a cleaning cycle for an OFT
lightpipe fired in 25 torr O 2 plasma at a power density of 31
W /cm 3.
D l.
Plasma length as a function of applied power for a microwave
excited helium plasma at various pressures.
D2.
Plasma length as a function of applied power for a microwave
excited hydrogen plasma at various pressures.
D3.
Plasma length as a function of applied power for a microwave
excited nitrogen plasma at various pressures.
E l.
Average power density as a function of applied power for a
microwave excited helium plasma at various pressures.
E2.
Average power density as a function of applied power for a
microwave excited hydrogen plasma at various pressures.
E3.
Average power density as a function of applied power for a
microwave excited oxygen plasma at various pressures.
E4.
Average power density as a function of applied power for a
microwave excited nitrogen plasma at various pressures.
F I.
Plots of ne/P d A and E /p as a function of pA for a microwave
excited helium plasma.
F2.
Plots of ne/P d A and E /p as a function of pA for a microwave
excited hydrogen plasma.
F3.
Plots of ne/P d A and E /p as a function of pA for a microwave
excited nitrogen plasma.
xviii
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LIST OF TABLES
1.
Classification of catalytic efficiency of metals based on
adsorption properties.
63
2. Classification of semiconducting and insulating metal oxides.
65
3. The standard free energy of formation of
reduction induced by Ar+ ion bombardment.
70
4.
oxides andtheir
Summary of numerical values for the recombination coefficient
of oxygen atoms for various surfaces at room temperature.
82
Comparison of catalytic efficiency on some surfaces for oxygen,
nitrogen, and hydrogen atoms.
86
Calculation of power density using different pow er/length
distributions for various plasmas.
159
Average electron number density for various plasmas
calculated at an average peak power density of 34 W / cm3.
169
Computed electron temperature for various plasmas and an
average peak power density of 34 W /cm 3.
173
Summary of temperature measurements for various gas
plasmas at 25 torr and an average peak power density of 34
W /cm 3.
183
10.
Comparison of heating by inert gas plasmas on some solids.
184
11.
Summary of density measurements for various gas plasmas at
25 torr and an average peak power density of 34 W /cm 3.
185
Variation of plasma fired temperature and density as a function
of pressure for A I2 O 3 at an average peak power density of 34
W /cm 3.
186
5.
6.
7.
8.
9.
12.
13.
Comparison of calculated and experim ental specimen
temperatures for alumina and magnesia in various plasma
xix
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gases at 25 torr and an average peak power density of 34
W /c m 3.
205
14. Comparison of calculated and experim ental specimen
temperatures for helium plasma at 25 torr and an average peak
power density of 34 W /cm 3.
206
15. Values of the strength of bonding of surface oxygen and the
electronegativity difference of dopant oxides.
231
16. Summ ary of estimated values of atom recombination
coefficient, y x 1 0 3, on various oxide surfaces in different
gaseous discharges.
234
17. E-field probe output voltages measured for various gaseous
discharges operated at an average peak power density of 34
W /c m 3.
258
18. The net gain in microwave power absorbed relative to that in
an empty plasma for various samples placed in a helium
plasma operating at a power density of 36 W /cm 3.
259
xx
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CHAPTER I
INTRO DUCTIO N
I. A. Motivation
Since its inception, plasma sintering of ceramics has shown to be a
promising processing technique*1-28!.
Besides the ability to attain high
temperatures rapidly, at rates from approximately 30 to 100 °C/sec, there are
several other unique characteristics that distinguish plasma sintering from
conventional sintering methods.
Plasma sintering produces an extremely fast rate of sintering in ceramic
materials. Sintering duration is very short, i.e., several minutes as opposed
to several hours for current commercial processes. Plasma-sintered ceramic
materials achieved very high densities. For instance, relative densities of 9899.5% of the theoretical value were commonly obtained.
Because of the
short time spent at high temperatures, small fired grain sizes on the order of
a few microns were attained without exaggerated grain growth. In addition,
higher room temperature mechanical strength has been observed for
plasma-sintered ceramic materials. Since cool down time was minimal, the
system could be cycled more rapidly than current methods.
No
conventional firing technique has yet matched all of these qualities.
During the course of earlier plasma sintering studies, a number of
heating effects were observed.
First, specimen heating was found to be
strongly dependent on material composition.
For instance, doped AI2 O 3
1
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2
samples did not reach nearly as high a specimen temperature as the pure
samples.!14! Moreover, materials with higher electrical conductivity did not
heat as well as those with lower electrical conductivity. A 1 2 0 3 , for example,
was readily melted in a nitrogen plasma, whereas SiC only attained a
temperature of 1300 °C. Gas composition also has a large influence on the
specimen temperature. A pure argon plasma, for instance, was unable to
heat an alumina sample to any appreciable temperature, while a polyatomic
gas nearly melted the specimen under identical conditions.!18'19! A similar
observation had been observed in a plasma flame study, where monatomic
gases were found to produce less heat when compared to a flame produced
by polyatomic gases.!29!
I. B. Objectives
Thus, this work was undertaken w ith the following objectives: to study
the heat transfer mechanisms involved when a given solid is immersed in a
plasma; to further explore the effects of gas composition on microwave
plasma heating in He, H 2 , N 2 , and O 2 and to determine the relative
efficiencies of these species; to investigate a variety of surfaces, oxides as
well as non-oxides, to see whether there was any relation between the
effectiveness of specimen heating and material properties such as, for
example, bond type, acidity, electrical conductivity, dielectric characteristics,
etc;
therefore, to establish the mechanism of the surface activities
responsible for heating from such relationships; to compute electron and
ion densities and their temperatures characterizing the plasmas used; to
examine the extent of morphological modifications as a result of chemical or
physical interactions for various gas-solid systems; and finally, to determine
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the extent of the contribution of microwave heating during the plasma
sintering process.
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CHAPTER II
BACKGROUND
II. A. Introduction
Plasma provides a unique environment for extremely fast rate of reaction
and innovative processing because the gas molecules and atoms are present
in highly excited states. A combination of the high internal energy and high
activation energy of the plasma enables this technique to gain greater
importance in materials processing as seen in the following examples of a
rapidly expanding variety of applications in the industry. Plasma-assisted
etching, perhaps the most familiar one, is use of a plasma in the fabrication
of semiconductor devices where a glow discharge is maintained in an
atmosphere of halo-carbon gases (e.g., CF4 , CCI4 , CCI2 , CF3 CI, CF3 Br, BCI3 ,
etc.).*30"321 Another wide use of a plasma process is plasma-assisted chemical
vapor deposition (CVD).
This technique is commonly used for the
deposition of amorphous silicon, which shows promise for the manufacture
of solar cells.133'351 Other materials deposited by plasma-assisted CVD include
aluminum nitride , 1361 amorphous phosphorus/
carbide /
391
boron nitride /
401
371
silicon nitride /
381
titanium
gallium nitride .!411 and a number of other
im portant inorganic compounds for integrated circuitry, optics, and
tribological applications/ 421
Plasma polymerization is another use of plasma to deposit organic
materials on a variety of substrate materials/
43,441
Plasma de-smearing
describes the process of using a plasma containing CF4 and O 2 reactants to
4
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5
condition or remove contaminations from the drilled holes in m ultilayer
printed wiring boards. 1451
Plasma de-smearing is also used to improve
w ettab ility
or
of adhesives
inks
for polym er
surfaces and
for
injection-molded parts. Other techniques using plasma processing include
the modification of surface properties (e.g., hardness) by exposure of
materials to plasma containing nitrogen, 1461 growth of thin films by glowdischarge sputtering , 1471 growth of rather thick oxide layers by plasma
a n o d iza tio n , 1481 removal of organic materials by plasma ashing, 1491
spectrochemical elemental analysis by plasma excitation, 1501 and densification
of ceramics by plasma sintering.I1"281
This list is not intended as a
comprehensive review of the utilization of plasmas in practical situations
but merely as an indication of the large number of applications.
II. B. Review of Plasma Sintering Literature
The type of plasma used in the sintering of ceramic materials ranges from
low-temperature to thermal plasmas. Such plasmas are typically operated
under pressures of 0 .0 1 torr to
1
atmosphere and are characterized by a small
degree of ionization, where neutral particles usually outnumber the charged
ones by more than 104 to 1. In the case of a low-temperature plasma, these
species are not in equilibrium w ith each other, and as a result electrons can
achieve temperatures on the order of 104 to 105 °K w hile the temperatures of
the ions and neutrals are roughly at ambient levels. Thermal plasmas, on
the other hand, are characterized by a single temperature, typically several
thousands of degrees, at which the ions, electrons, and neutral species are in
thermal equilibrium.
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The plasma is sustained by three different types of equipment, differing by
their operating frequencies:
(1 ) dc plasmas:
hollow cathode discharge (HCD)
(2 ) rf frequency plasmas:
induction-coupled plasma (ICP)
(3) microwave plasmas:
microwave excited plasma (MEP)
In principle, any frequency in the range of dc to GHz can be used to excite
a gas at low pressures. The latter two methods have the advantage of being
electrodeless to avoid contamination. However, a dc discharge is preferred
when measurements on plasmas have to be made using sensitive electronic
instruments due to strong interference from rf and microwave frequencies.
The HCD system rarely operates above 10-2 torr, therefore it may be
classified as a low-temperature plasma.
The radio frequency ICP system
usually operates between 50 torr to atmospheric pressure, hence it is
considered to be a high temperature or therm al plasma.
Since the
microwave plasma employed in this study was maintained under reduced
pressures ranging from 1 to 50 torr, it falls somewhere in between the two
types and is considered as a non-equilibrium system with average electron
energies in the range of 0.5 - 3 eV.
microwave system could also go to
1
In tuned cavities, however, the
atnrJ24!
II. B. 1. Earlier Investigators
The possibility of using a plasma as an intense heat source for the
processing of ceramic material was first suggested by Dugdale.f51^ He
developed a spherical hollow cathode glow discharge apparatus, which
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7
produced a hot zone at the geometric center of the cathode sphere by a
focused beam of electrons. Various glass and refractory materials placed at
the center of the HCD could be readily melted by the kinetic energy of the fast
electrons. Typical operating conditions for a hydrogen discharge were a
pressure range of 0.1 to 1 torr at a current of 0.4 A and a cathode voltage of 1.5
kV. The best efficiency obtained for this device was over 40% of the input
power as measured by a constant flow calorimeter. The major disadvantage
is the sputtering of the cathode due to ion bombardment of the electrodes,
thus leading to a potential contamination problem.
Bennett and coworkers11'21 were the first to report the sintering of ceramic
oxides in a plasma.
The authors used a MEP generated at 2450 M H z at
reduced pressures (between
1
to 50 torr) to sinter A I2 O 3 and other metal oxide
compacts for various times and temperatures. The plasma was excited and
confined in a short zone within a quartz or alumina tube which passed
through a tunable rectangular waveguide.
They found that the plasma
sintered materials had higher densities and greatly reduced grain sizes than
the conventionally sintered materials under the same sintering conditions,
such as temperature, tim e, and gas compositions.
For example, plasma
sintered Linde A alumina reached well in excess of 94% of the theoretical
density at 1600 °C for 20 minutes in air at reduced pressure, while identical
specimens conventionally sintered attained a relative density of ~85%. Other
alum ina powder compacts investigated also experienced accelerated
densification in the discharge, with greater enhancement for very fine highly
sinter able powders.
They also found insignificant differences in the
mechanical strength (4-point bent test) between the conventionally sintered
and plasma sintered specimens when the densities were less than 87% of the
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theoretical value, but for relative densities greater than 90% the plasma
sintered specimen showed a substantially higher modulus of rupture.
Bennett et al.111 hypothesized that the enhanced sintering phenomena
may have been caused by either the creation of point defects or other
mechanical effects by ion bombardment of the powder surfaces or by
localized internal heating as a result of ionic recombination.
may be the most plausible explanation.
The former
It is still doubtful whether the
plasma is sustained in the pore regions to allow for localized heating.
Bennett and M cKinnon^ determined that the presence of the plasma was
a critical factor in activating the sintering process. An alumina specimen was
initially placed in the plasma and fired for 20 minutes at 1300 °C.
specimen was subsequently sintered conventionally for
100
The
minutes, also at
1300 °C. The measured density after this second stage of firing was 74.7% of
the theoretical density, which was only a slight increase from 74.4% obtained
after the first firing. In the final stage of the experiment, the specimen was
returned to the plasma and resumed sintering for 100 minutes at 1300 °C. A
final density of 83.1% of the theoretical value was obtained. From this, they
concluded that simple surface cleaning may not be a factor, otherwise the
specimen would have sintered more rapidly conventionally after the initial
plasma treatment.
The next to report enhanced sintering behavior was Gordon and
Martinsen[3] for sintering alumina rods in a dc glow discharge. They used a
cylindrical hollow cathode device similar to that of Dugdale. Rapid sintering
of extruded Reynolds RD-172 AI2 O 3 rods produced densities greater than 96%
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of the theoretical value within 5 minutes, after attaining a temperature of
1370 °C.
Thomas et al.14-55 also used a dc glow discharge similar to that employed by
Gordone and Martinsen in order to sinter pellets of U 0 2 - They reported
sintered densities exceeding 90% of the theoretical value after sintering in
argon for 5 minutes, again at 1370 °C. Though the uranium dioxide powders
were not well characterized, the authors noted several advantages of the
plasma sintering process compared to conventional techniques:
sintering
times were dramatically reduced from hours to minutes, high densities can
be obtained, and minimal cool down time that resulted in shorter times
between system cycles was achieved.
Research activity in this field became dormant for a number of years until
Johnson and his students undertook a series of investigations on the
sintering of alumina and other materials, first with a radio frequency ICP16'9'
then with a dc glow discharge,116,17' and a microwave plasma.'13,15,20'
II. B. 2. RF Induction Coupled Plasma
In itia lly Jonhson and Rizzo'6' developed a radio frequency (5 M H z)
induction coupled argon plasma to study the sintering of P"-alumina tubes.
They rapidly zone sintered 14 mm diameter thin w all tubes, which were
isostatically pressed, in an elliptical shaped, argon plasma operated at
atmospheric pressure and power levels of 2 kW. The discharge was confined
w ithin a water-cooled fused quartz tube wound around w ith
3
turns of
induction coil. Translated at up to 2 cm /m in, sintered tubes achieved greater
than 98% of the theoretical density in less than 90 seconds, from the onset to
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10
completion for any given point on the tube. The microstructure consisted of
a nearly complete transformation to the equilibrium f}"-alumina form ,
which was comparable to that of samples obtained by conventional sintering.
The sintered grains were about 5 microns. Soda losses were minimized as
evidenced by a fa irly
uniform distribution of N a 2 0 in the grain
microstructure and axial electrical resistivity measurements.
Johnson and Kim 17,81 used the same ICP apparatus at reduced pressure, in
the range of 25 to 100 torr, to sinter both pure and MgO-doped, submicron
alpha A I2 O 3 in argon. 14 mm diameter thin wall tubes and 5 mm diameter
rods were translated through the argon plasma at rates up to
6
cm /m in.
W ithout optimizing conditions, the fired densities of 0.25 wt% MgO-doped
rods approached 99% of the theoretical density. MgO-doped tubes, on the
other hand, achieved densities in excess of 99.5% of the theoretical value
when translated at
100°C /s.
6
m m /s, which represents heating rates in excess of
Undoped tubes, on the other hand, attained lower relative
densities of about 96% and showed significantly larger grain sizes than that of
the doped tubes at equivalent power levels.
The maximum specimen
temperature measured was approximately 1980 °C.
It was observed that
MgO-doped specimens did not reach the same temperature as the undoped
ones.
A few anomalous heating effects involving the measured specimen
temperatures were also observed in the study by Johnson and Kim.
Temperature of the specimen was determined by quenching the plasma
during sintering and monitoring the temperature decay with a two-color
optical pyrometer. When the translation rate was increased the specimen
temperature increased such that at the highest rates surface melting would
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11
result. If translation was suddenly halted during the sintering process, the
temperature of the immersed specimen spontaneously fell as much as
800 °C.
Moreover, reheating of this sintered specimen could produce
temperatures no higher than 1200 °C under identical plasma conditions.
Two explanations were proposed for the observed heating effects. The first
attributed the phenomenon to the presence of porosity, which w ould
contribute to heating by plasma sustained w ithin the pores. The second
suggested that the liberation of transient volatiles associated w ith the
adsorbed species on the surface of the starting powder during sintering
would alter the temperature of the plasma in the vicinity of the specimen.
The latter has now been confirmed.
K ram b 191, who worked on the same ICP system, also found these
temperature anomalies.
Rods and tubes employed in this study were
isostatically pressed from Baikowski CR30 (30 m 2 /g ) alumina powders.
Samples of pure and MgO-doped alumina exhibited cyclic heating and
cooling in the argon plasma at low translation rates (<
1
cm /m in ).
Maximum temperature of the reheated specimen was about 1200 °C.
To test the hypothesis of the enhanced plasma heating due to the
presence of porosity, Kramb introduced
a large concentration of
interconnected porosity into the powder compact by adding 40 wt% of
organic binder or adding 0.5 mm diameter organic particulates to the starting
powder. These porosity rich specimens did not experience the same heating
anomalies as the denser green compacts. Spontaneous cool down did not
occur when translation of the specimen was arrested; moreover, fired
specimens could be reheated in the plasma back to the sintering temperature.
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12
Thus, the transient heating effects were attributed to the differences in
porosity w ithin the green compact.
Besides observing similar anomalous heating effects in the same argon
ICP, K now lton 1141 also discovered a strong
dependence of the sample
temperature on the dopants added to alumina rods pressed from Baikowski
CR30 powders. It was observed that different dopant species depressed the
temperature to different extents under identical experimental conditions.
Specimen temperatures were found to decrease in the order of Y 2 O 3 , MgO,
TiC>2 , N iO . The dopant level used was 0.25 wt% for all except Y2 O 3 , which
was at 0.125%. For the N iO temperature dropped as much as 650 °C, while
the other dopants caused a reduction in the temperature of more than 100 °C.
This effect was found to correlate w ith the formation energy of the dopant
oxides, where the most easily reduced oxide has the greatest influence in
temperature reduction.
Chenl19! studied the effect of additive gases on plasma sintering of pure
and MgO-doped alumina rods in the same ICP device. Specimens were first
passed through a "low power " plasma, which was operated at a pressure of
50 torr and a plate voltage of 3 kV, at a rate of 1 cm /m in in order to
minimize the effect of the adsorbed gases. Little if any densification occurred
during this plasma cleaning stage.
After cleaning, the specimens were
immediately fired in a pure argon plasma at a pressure of
voltage of 3.8 kV, and a translation rate of 4 cm /m in.
100
torr, plate
The final density
obtained for pure alumina was merely 67% and for the MgO-doped alumina
was 53% of the theoretical value, both of which were significantly lower than
those w ithout cleaning.
However, the "cleaned" specimens experienced
dramatic increases in the final density as a result of introducing minute
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13
quantities (up to
2%
by volume) of polyatomic gaseous species, including
hydrogen, oxygen, nitrogen and water vapor, to the argon plasma. For
instance, less than
1%
of the additive diatomic gases was required to obtain
densities equivalent to that of the pure, uncleaned specimen, whereas
2%
was necessary for the doped rods. Water vapor had the most pronounced
effect of all the dopant gases on the final density. For MgO-doped rods,
additions of as little as 0.03% water vapor raised the final sintered density
from 53% to over 95% of the theoretical density. Nitrogen and hydrogen
additions were found to have comparable effects on density, with oxygen
having the least effect among the diatomic gases tested.
By using emission spectroscopy, Chen confirmed the presence of water
vapor liberated during plasma sintering of fresh samples of pure and MgOdoped alumina and was able to explain the cause of the aforementioned
temperature anomalies. Chemically bonded water molecules are not easily
removed, even by presintering to 650 °C and subsequent storage at 100 °C.
Thus water would be released into the plasma during translation.
With
higher translation rates, the water vapor concentration would be greater,
resulting in increased temperatures.
Halting translation caused a sudden
drop in the specimen temperature for the water vapor was rapidly diluted by
the flowing argon. Therefore the presence of polyatomic gases, such as water
vapor, was found to be crucial in the heating of AI2O 3 to high temperatures.
Kotecki1211 was also successful in densifying pure, chromium doped and
tantalum doped TiC>2 in the argon ICP, but only by the incorporation of up to
10% oxygen in the plasma. In the absence of oxygen gas flow, the argon ICP
could barely heat up titania to incandescence.
The addition of oxygen
increased the specimen temperature and somewhat helped in preventing
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14
reduction during sintering. The oxygen content of the plasma was found to
be the most significant factor in determining the final density. W ith a total
system pressure of 45 torr and a translation rate of 2 cm /m in, pure TiC>2 rods
achieved 94.6% of the theoretical density. Chromium proved to be a better
sintering aid than tantalum at the 0.5 mole% dopant level. The maximum
relative densities attained for Cr- and Ta-doped samples were 96.8% and
93.6%, respectively.
These densities were relatively lower than the results obtained for
alumina. Several possible explanations were offered to account for the lower
sinterability of T i0
2
.t21^ However, the most reasonable may be that at
elevated temperatures in the plasma, titania becomes a semiconductor,
which may be heated up differently because of semiconductivity. Statements
made by Kotecki about energy expended in vacancy formation and phase
transformation can be discounted because of the minuscule amount relative
to the energy flux used to heat specimens.
The surface of the TiC>2 rods showed a thin black layer of reduced oxide,
when fired in the argon plasma. Even with up to 10% oxygen added to the
argon gas stream, partial reduction was manifested by the blue-gray color in
the interior, while the surface of the specimens turned white during cooling
due to reoxidation after leaving the plasma zone. However, the specimen
was black at temperature or when cooled in the absence of oxygen. The
observed reduction was attributed to the loss of oxygen caused by
bombardment of energetic plasma particles
The dielectric properties of the chromium doped specimens improved
significantly as the electrical conductivity was reduced by as much as four
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15
orders of magnitude. Tantalum doping, on the other hand, had little effect
on the electrical properties. Etching was observed on the surface of the TiC>2
specimens sintered in the partial oxygen atmosphere.
Demet1221 used the same induction coupled plasma system to investigate
the sintering behavior of lanthana and alumina doped V2 O 3 and compared
the results w ith that of alumina.
5 mm diameter rods were isostatically
pressed from Alfa, Molycorp and Nyacol Y2 O 3 powders. The latter powder
was obtained by freeze drying a 14 wt% liquid solution. In contrast to the
increase in density with increased translation rate found in the alumina
work, densities of undoped rods of Alfa and Molycorp Y 2 O 3 showed a linear
decrease as a function of translation rate, in pure argon and at a system
pressure of 90 torr. A spontaneous cool down was also observed for a Ladoped Nyacol sample, translated through the plasma at 3 cm /m in, upon
cessation of translation in the argon plasma, but only 100 °C and not the
800 °C drop exhibited by plasma sintering of alumina. Perhaps only a small
amount of water is adsorbed on the surface of the yittria specimens to make
any significant contribution to heating during sintering.
The addition of up to 7% oxygen to the argon plasma did not result in any
significant increase in the final density of sintered La-doped Nyacol
specimens. Unlike Ti0 2 , which required oxygen for effective heating, Y2 O 3 ,
as well as A I2 O 3 , can apparently be heated to sufficiently high temperatures
in pure argon in the ICP device to obtain high densities.
Demet also studied the effect of surface area on the sintering of Y2 O 3
derived from three different sources. Specimens of Nycol (120 m 2 /g ) and
Molycorp (20-40 m 2 /g ) attained comparable densities, approximately 95% of
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16
the theoretical value. Alfa specimens, which have a lower specific surface
area (0.6 m 2 /g ), achieved only 85% of the theoretical density. Thus specimen
heating was found to be critically dependent on the powder surface area,
where best result appeared to be obtained for powders having a specific
surface area of 20 m2/g m or higher. The higher surface area increases the
overall driving force for sintering and allows for greater plasma-surface
interaction that result in heating.
Addition of dopants as a sintering aid in Y2 O 3 was noted to lower the
specimen temperature.
A t a pressure of 100 torr and input power
maintained at 3kW , the observed temperature for undoped Molycorp
specimens fired in pure argon was 2100 °C and was lowered slightly to
2085 °C by alumina doping.
The greatest temperature drop, almost 200
degrees, occurred for the addition of lanthana.
Sim ilar temperature
depression as a result of doping had also been seen in the plasma sintering of
alumina and titania.
The densities obtained did not follow the same
temperature trend. The densities of the liquid phase sintered alumina doped
(0.25 wt%) and the pure yttria were approximately 90% of theoretical,
whereas the 10 mole% La-doped specimens achieved densities exceeding 97%
of the theoretical value.
Similar cleaning procedures employed by Knowlton and Chen were
adopted for the sintering of yttria to determine the effect of adsorbed gaseous
species. No significant differences in the final densities were noticed for the
plasma cleaned and the uncleaned Molycorp samples fired in identical
conditions.
The cleaned specimen exhibited a 100 degree lower sample
temperature as well as smaller fired grain sizes than that of the uncleaned
specimen. In addition to the lower maximum temperature, sodium, which
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17
was confirmed by spectroscopic analysis during sintering, were thought to
cause the large grain sizes in the uncleaned specimens.
During the course of his work, Demet also found that the system
performance was strongly influenced by both the induction setting and the
number of turns of the induction coil used. The one turn coil yielded the
highest efficiency at about 40%.
The system efficiency was measured by
taking the ratio of power dissipated in the plasma, or the plasma power, as
determined by calorimetry, to the input power delivered by the induction
unit.
It was observed also that either the 3- or 4-turn coils, which the
previous investigators used for the same ICP system, could not achieve the
optimum efficiency under his experimental conditions.
H rd in a [231 followed up on Chen's observation of enhanced heating by
dopant gaseous species to study the thermal and chemical effects of additive
gases on fully sintered alumina tubes.
He first characterized the effect of
dopant gases on the normalized efficiency of the system, plasma power and
power density w ith respect to those measured in pure argon. The power
density was determined from the plasma power averaged over the entire
luminous volume of the plasma. For the 4-turn induction coil at 3 kV plate
voltage and a pressure of 50 torr, the efficiency was found to have more than
doubled when
2%
additions of hydrogen, nitrogen and oxygen were added.
However, with 0.03% water vapor, system efficiency remained unchanged.
Recall that in Chen's work, the same amount of water vapor produced a
dramatic increase in the final density of MgO-doped alumina from 53% to
over 95% of the theoretical density.
Since the system efficiency is
approximately proportional to the power dissipated in the plasma, the same
trends with the dopant gases were found. In general, over the range of up to
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18
2%
additions of the dopant gases, water vapor has a larger effect on these
three system characteristics than the diatomic gases. Similar trends were
observed for the 1 -tum coil, though the relative magnitudes of diatomic gas
effects on system characteristics were not the same.
W ith the aid of an optical fiber thermometer (O FT), specimen
temperatures were measured to determine the amount of temperature
increase achieved by a specimen fired in a plasma w ith additive gas over that
fired in pure argon plasma.
The OFT monitored the temperature of the
closed end of the tube, which was immersed in the plasma, by transmitting
the thermal radiation from the end of the tube through a sapphire single­
crystal lightpipe to a remote detector. W ith the 1-turn induction coil, it was
shown that the greatest temperature increase occurred for water vapor,
followed by hydrogen, oxygen, and the least with nitrogen. The effect of
dopant gases on the system efficiency and plasma power also showed a
similar pattern. This trend may be largely due to the effect gas dopants on
the system characteristics.
However, for a given power density, while both
the system efficiency and plasma power were held constant, the amount of
increase in the specimen temperature follows the order: N 2 > O 2 > H 2 . This
trend correlates well with results of the effect of diatomic gases on specimen
temperature at a constant power density found in the present study.
Surprisingly, the addition of 0.06% water vapor produced a temperature
increase of only 78 °C compared to a 172 °C increase for the addition of 1%
hydrogen.
Chen had indicated that these same additions caused equal
increases in specimen density; yet, the same indicated quantities yielded
unequal temperature increases. It was speculated, therefore, that the thermal
effects were not the only factor causing the density increase.
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19
To test the hypothesis of whether chemical effects play a role, in addition
to the thermal effects, in densifying powder compacts, 4 mm diameter MgOdoped Baikowski CR30 alum ina rods were subjected to controlled
temperature increases as those experienced previously by tubes that were
fired in plasmas doped with various polyatomic gaseous species. Thus under
identical condition as in heating tubes, Hrdina found that for similar
temperature increases relatively the same final densities were obtained
regardless of the dopant gases used. This observation implies that chemical
effects do not play a major role in enhancing densification. Chen's results,
however, suggests the opposite. For similar temperature increases, magnesia
doped alumina sintered in water vapor plasma achieved higher density than
that sintered in hydrogen plasma. Direct comparisons of these two studies
may not be totally valid since experimental conditions were not identical.
Striking morphological modifications of fully sintered alumina rod
surfaces were observed for various plasma compositions. Pure argon does
not appear to affect the surface morphology, whereas the polyatomic gaseous
species produced varying degrees of physical or chemical etching of the
specimen surface.
For MgO-doped specimens soaked in each of the
individual plasmas at a higher plate voltage, 4 kV instead of 3 kV, all the
dopant gases including argon caused distinct morphological effects on the
specimen surface, whose morphologies changed drastically at different points
down the rod.
Dopant gases were also found to have affected the modulus of rupture (3point bend test). Both nitrogen and oxygen doped plasmas were observed to
increase the average modulus of rupture of an alumina rod by nearly
2 0 %.
Additions of hydrogen to the argon plasma, on the other hand, caused a 40%
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20
drop in the strength. Water vapor apparently has an insignificant affect on
the strength. Several explanations were advanced to interpret the affected
specimen strength. First, surface grain growth would weaken the structure.
Second, formation of a liquid phase would also reduced the structural
integrity.
Third, deposition of material onto the surface or chemical
modification of the surface composition could either strengthen or weaken
the structure. Fourth, changing the flaw population of the surface by etching
could also alter the surface structure. These experiments demonstrated that
both thermal and chemical effects were actively involved during plasma
sintering.
II. B. 3. D C Discharge
Using an aluminum truncated spherical H C D device similar to that
developed by Dugdale, Sanderson116'171 sintered specimens of pure and doped
Baikowski CR30 and CR6 alumina rods. Unlike radio frequency and the
microwave plasma devices, heating of specimens in the hollow cathode
discharge was accomplished by a beam of fast electrons focused on the surface
of the sample positioned at the center of the cathode sphere. Several support
gases, including air, O2 , N 2 , CO2 , H 2 and Ar, were used. A ll but the argon gas
could successfully heat specimens to temperatures in excess of 1500 °C.
Following Dugdale, hydrogen was employed for the majority of the
sintering study in order to minimize sputtering of the cathode. The use of
aluminum eliminated potential contamination from the cathode material
during sintering of alumina. The cathode surface morphology was noted to
affect specimen heating. Since heating was by a focused fast electron beam,
blistering of the aluminum surface resulted in defocusing of the beam and
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21
thus reduced specimen heating. Typical operating conditions were pressure
in the range from 100 to 550 mtorr, current at few tenths of an ampere, and a
cathode voltage of several hundred volts.
Specimen temperature was found to vary linearly with power for pure
A I2 O 3 specimens translated at a rate of 1.4 cm /m in over a wide range of
pressures.
Thomas and Freiml4! had made similar observations in their
cylindrical hollow cathode. This linear dependence of temperature on power
was thought to be a result of the increased electron density with power at the
the central axis of the hollow cathode. The on-axis electron density, on the
other hand, decreased w ith increasing pressure due to a corresponding
increase in the number of scattering events w ith electrons.
Therefore,
raising the pressure resulted in less efficient heating.
Doped specimens achieved a higher maximum density than the pure
specimens did.
For instance, densities about 96% of the theoretical value
were obtained for pure specimen, whereas relative densities greater than 98%
was achieved for the doped alumina in a hydrogen plasma with a translation
rate of 3 cm /m in. Although doped samples were more dense than undoped
samples for a given temperature, they exhibited lower temperatures than
those of the pure specimens under identical power conditions. This may be
related to the significant loss of magnesia from the surface region of the
doped specimens. These results were similar to those reported on the ICP
sintering of alumina.
Powder compacts of CR30 were found to heat more efficiently than CR6
rods.
A densified CR30 rod could only be heated up to 1600 °C,
approximately 400 degree less than the 1990 °C achieved by a green rod.
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22
These experiments demonstrated the importance of the available free surface
area of the rods for effective heat transfer from a plasma to a given immersed
solid. Sanderson also performed an experiment in which a plasma cleaned
specimen was fired under identical sintering conditions as a standard
specimen. Both the cleaned and uncleaned specimens achieved virtually the
same temperature, in contrast to the dramatic im purity effects observed by
Chen.
Ow ing to the intense heating by the focused electron beam,
contributions from heating by recombination of im purity gaseous species in
the discharge may only be a secondary effect in HCD sintering.
The sintered density at a given sintering temperature was observed to be
independent of gas pressure. This further confirmed the above conclusion
that the discharge itself may not have a strong influence in the sintering of
alumina.
However, Sanderson also observed that he could not heat
specimens in argon, though for different reasons as in ICP sintering studies.
The lack of heating in an argon discharge was attributed to the increase in
collision frequency at high energies exhibited by argon, causing a significant
reduction in the electron mean free path lengths.
Thus the observed
densification in the hollow cathode discharge was solely dependent on the
specimen temperature produced by electron beam heating.
II. B. 4. Microwave Excited Plasma
Lynch *201 studied the sintering of both AI2 O 3 and MgO in argon and
nitrogen plasmas excited by microwaves. A magnetron operating at 2.45 GHz
generated the MEP within a tapered rectangular microwave applicator that is
terminated by a short. Tuning of the cavity was accomplished using a sliding
short adjacent to the applicator to allow for maximum coupling of
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23
microwave energy. The sintering chamber consists of a quartz tube inserted
transversely through an open slot in the applicator.
translated through the plasmas at rates up to
11
Sample rods were
cm /m in with power levels
ranging from 220 to 750 watts.
Sintered densities of pure and MgO-doped alumina attained 98.4% and
99.8% of the theoretical value, respectively.
Both density and grain size
apparently increased with higher powers and faster translation rates in the
argon plasma, while only the grain size was affected in the case of a nitrogen
plasma.
This result obtained for pure and doped A I2 O 3 sintered in the
microwave plasmas were very similar to those obtained in the rf plasma
work. Nitrogen was found to provide better heating than argon.
The MgO-doped alumina was noted to exhibit large grains near the
surface of the specimens, and it did not reach the same temperature as the
pure sample under identical experimental conditions.
The grain growth
may be indicative of a loss of magnesia from the sample surface. Haroun
and BudworthI52J had indeed observed MgO loss at the exposed surface of
MgO doped alumina. Drawing from the work of Avni and Winefordnert53!
who have shown that additives such as 5 pg of cesium or thallium lower the
electron temperature of an argon MEP, Lynch suggested that the loss of MgO
into the plasma may be the cause for lower plasma temperature.
Sanderson!17! also made a similar speculation concerning the sintering of
MgO doped alumina in his HCD work.
Sintering of MgO resulted in non-uniform grain structures. Rods of MgO
derived from magnesium carbonate sintered in both argon and nitrogen
plasmas produced large grains in the center and very fine grains near the
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24
surface, whereas MgO obtained from magnesium hydroxide yielded larger
grains near the surface and smaller grains at the center, which was also
porous. The cause for this was not determined.
Kemer[13'151 used a modified version of the MEP apparatus employed by
Lynch to investigate the rates of shrinkage and grain growth for the sintering
of MgO-doped alumina powder compacts. It was observed that densification
occurred mostly during the nonisothermal heat up portion of the sintering
cycle. Without the use of a microwave tuning device to optimize conditions,
Kemer maximized the plasma power density by controlling the pressure, and
thus the plasma volume and the microwave power absorbed.
through a nitrogen plasma at a rate of
1
Translated
cm /m in, specimens attained
densities greater than 99% of the theoretical value w ithin 2 minutes time
from the onset to completion, and a maximum relative density of 99.9% was
achieved within
10
minutes by holding the sample statically in the plasma at
a pressure of 37 torr and an applied power of 475 W.
The maximum linear shrinkage rate measured was about 2.5%/sec
during the heat up segment of the plasma sintering process. Moreover, the
plot of shrinkage rate as a function of time exhibits a double maximum in
the curve. This behavior was ascribed to the bimodal distribution of pore
sizes existing in the initial powder compact.
The Baikowski alumina
powders used consists of a mixture of gamma and alpha phase alumina,
where the finer gamma phase is known to exist in agglomerated form. At
high heating rates, the two peaks began to coalesce as the densification of the
two pore groups occurred closer in time. The average grain growth rates
during the nonisothermal heat up period were found to be on the order of
1.5 pm /m in .
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25
Microstructural examination of the nitrogen plasma fired surfaces
showed dramatic modifications in the surface morphology. In a span of 2
minutes, the surface microstructure changed from smoothing of the grains
to intense pitting and channelling on the surface of the sample. Nitrogen
plasma corrosion of the sample surface was also observed in Hrdina's ICP
work. This further suggests strong plasma-surface interaction taking place
between nitrogen and alumina.
It has been observed that active nitrogen
reacts with alumina to form AIN J54'55!
II. B. 5. Other Workers
W ith extensive experience in working with plasma devices, Pfender1261
began modelling the heat transfer effects during sintering of alumina based
on the aforementioned ICP results. His model predicted that an electrically
insulating surface should be hotter than one which is electrically conductive
due to the acceleration of the positive ions toward the surface by the negative
sheath potential developed at the insulating surface.
The anomalous
temperature effects mentioned previously were explained by the reduction
in the heat fluxes to the specimen surface during sintering rather than gas
composition effects.
Pfender et al.[271 also reported sintering of undoped MgO in an argon ICP
to final densities of about 97% of the theoretical value. Small additions of
oxygen and water vapor, in general, improved the final densities.
The
sintered density versus pressure curve exhibited high values at very low
pressures, less than 5 torr, and at pressures near atmospheric, with a
m inim um in between.
This was attributed to increased ion-electron
recombination effects due to higher degree of ionization at low pressures and
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26
enthalpy effects at high pressures. The minimum was less pronounced for
oxygen and H 2 O dopants because of added enthalpy from recombination of
atomic species.
Employing the same design of ICP system as that of Johnson and
coworkers, Kijima^28' reported successful sintering of silicon carbide in argon.
Large power input in tens of kilowatts, however, were required to achieve
near theoretical density. Minimal grain growth was observed.
Thus, we have seen from the above survey of the plasma sintering
literature that plasma processing is a viable means of sintering ceramic
materials. A variety of oxides as well as nonoxides have been successfully
sintered to high densities, notably, alumina oxide, in the dc, radio frequency,
and the microwave plasma devices. Extremely rapid sintering rates, very
fine grain sizes, and high sintered de.nsities are common characteristics
achieved by the plasma sintering process.
In summary, insulating oxides appeared to be more amenable to the
plasma sintering technique than the more electrically conducting oxides.
Adsorbed gaseous species, such as water molecules, were found to affect
specimen temperature during the sintering process. Specimen heating was
dependent on the gas composition in the plasma.
Higher specimen
temperatures were obtained in polyatomic gases than in monatomic gases.
Specimen composition also strongly influenced heating of the sample. Pure
rods permitted higher temperature than doped rods. Dopant oxides affect
specimen temperature to different extents.
Reduction and morphological
changes in the immersed solids were also observed, indicating thermal as
well as chemical interactions were taking place at the plasma/solid interface.
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27
The main objectives for carrying out this study were, therefore, (a) to look
further into the heating effects during the plasma sintering process and find
how thermal energy is imparted to solids immersed in a plasma; (b) to vary
the plasma gas composition to determine the effect of plasma enthalpy and
the relative activities of the various gases; (c) to examine several materials,
including dopant materials used in the previous studies, to see whether the
heating effects could be related to material properties, such as the type of
bonding, electrical conductivity, and dielectric characteristics of the ceramics;
(d) to establish the cause and mechanism of the surface activities from such
relationships; (e) to compute the basic plasma characteristic parameters, such
as electron and ion densities and their temperatures, and related them to the
heating process; (f) to predict steady-state sintering temperatures from plasma
parameters and the physical properties of the specimens; (g) To observe
physical and chemical interactions that may occur on these surfaces with
various gas plasmas; (h) to determine the extent of microwave heating in the
plasma sintering process.
II. C. Sintering Theory
Jo h nso nt56i has developed a model that combines the in itial,
intermediate and final stages of the sintering process, with a particular
application to describing shrinkage rates during plasma sintering. A more
lax derivation of this general sintering equation is given in this section. The
main purpose is to introduce some important basic understandings of
sintering in light of the plasma process.
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28
II. C l . Two Sphere Model
Sintering, simply stated, is the process associated with the morphological
changes of a powder compact. While there is a tendency for the particles to
reduce their surface energies by densifying to form a solid, thermal activation
is normally required to facilitate the diffusion process.
This is typically
accomplished by heating to some temperature greater than half of the
absolute melting temperature.
Figure la illustrates a geometric representation as two
particles
approaching each other during the initial stage of sintering. Sharply concave
necks are formed at points of contact between neighboring particles of a
compact as sintering begins. The circular neck in Fig. la can be related to the
neck-like region where the grain boundary intersects the pore surfaces in the
intermediate and final stages of sintering (see Fig. lb). The curvature of the
neck surface gives rise to capillary pressures in the solid which result in a
pressure difference at the boundary region between the sintering bodies.
This is described by the Gibbs-Thomson equation:
A p = yK
= y ( 1 - J -)
fp
(1 )
where 7 is the surface tension, x is the neck radius, rp is the minimum
radius of curvature of the neck surface, and K is the curvature defined in
this equation in terms of the principal radii of curvature of the surface, x and
rp . Compressive pressures w ill be positive and the radii of curvature w ill be
positive if the center of curvature is on the solid side of the surface. Thus,
hydrostatic pressure less than ambient w ill exist immediately beneath
concave surfaces at the neck (i.e., regions of negative curvature associated
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29
(a )
rx
(b )
Figure
1.
Schematic of sintering geometry for (a) two sintering bodies
during initial stage of sintering (based on ref. [57]) and
(b) intermediate-stage sintering.
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30
with the pores). If the two particle system is considered as a free body with
no external forces acting on it, the summation of forces requires that these
tensile stresses be balanced by compressive stress in the central portion of the
grain boundary.
The chemical potential of atoms and vacancies under these hydrostatic
pressures can then be related b y :
O
where
Ha = n°a + p Q a + kT In aa
(2 )
fiv =
(3 )
+ p Qv + kT In av
O
and
are the chemical potentials at zero pressure and unit
activity, Qa and Q, are the volumes, and aa and av are the activities of
atoms and vacancies, respectively, and kT has its usual meaning. Thus we
see that the chemical potential gradients arising from the pressure gradient
due to the curvature of the neck surface w ill cause migration of atoms from
the grain boundary between the two sintering particles to the adjacent neck
surface.
Due to the curvature at the solid-vapor interface, the chemical
potential of the atoms on convex surfaces is greater than those on concave
surfaces.
Therefore, atoms move down their chemical potential gradient
from regions of the convex tothe concave portion of the particlesurface.
Figure 2 shows various pathsof mass transport in response
to the
chemical potential gradients: within the vapor phase, along the surface,
through the bulk or along the grain boundaries of the particles. Of these
mechanisms, vapor transport, surface diffusion, and volume diffusion of
matter from the particle surface to the neck surface cause losses in surface
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E
Figure
2.
Paths of mass transport with (A) as volume diffusion from
the grain boundary, (B) grain boundary diffusion, (C) vol­
ume diffusion from the particle surface, (D) surface diffu­
sion, and (E) vapor transport.
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32
area, neck growth, and particle coarsening, resulting in a reduction of driving
force for sintering and an increase in diffusion distance. Transport of atoms
from the grain boundary to the neck surface via grain boundary and volume
diffusion, on the other hand, allows the particles or grains to approach each
other, resulting in densification.
Herring!58! showed that the flux of atoms by volume diffusion in the neck
region between two sintering particles is given by
I-- - f ir
where D is the volume diffusion coefficient.
<4 >
The flow of atoms is thus
driven by the gradient in the chemical potential of atoms and vacancies. We
assume that rapid annihilation of vacancies at sinks occurs to ensure local
equilibrium vacancy concentration everywhere. But the chemical potential
of vacancies at equilibrium is zero, by definition. Consequently, there is no
gradient in the chemical potential of the vacancies, and the vacancy
concentration gradient alone cannot produce a net vacancy flux, as some
believed. Equation (4) then becomes
i‘
m
(5)
We assume that this equation is also applicable for grain boundary diffusion
and that grain boundary and volume diffusion can operate concurrently,
since the change in geometry w ill be the same for both grain boundary and
volume diffusion.!571 If we further assume that the chemical potential
gradients for grain boundary and volume diffusion paths are identical,
because both atom fluxes have the grain boundary as their source for atoms
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to fill in the neck and sink for the annihilation of vacancies, then the sum of
these atomic fluxes to the neck surface from the grain boundary by
simultaneous volume and grain boundary diffusion can be then written as
Ja
=
jv
Av
+ jbAb
(6)
where A v is the effective neck surface area across which atoms are
transported by volume diffusion, Ab is the effective area prescribed by the
region of enhanced diffusion via grain boundary diffusion. This flux can be
related to the rate at which the two sintering particles interpenetrate by
-u
= *L2a
^ 4
at?-
( 7)
where h is the distance between reference points across a grain boundary and
Jtx 2 is the area of the grain boundary in the two sphere model.
In the
intermediate and final stages, however, the actual area of the grain boundary
would be used.Thus dh /d t describes the rate of approach
in terms of the
instantaneous geometry. Equation (7) implies then that theflux at any given
instant is proportional to the rate of interpenetration.
For an idealized
powder compact of uniform spherical particles, the rate of the distance of
approach normalized to the grain size G can be related to the instantaneous
change in length of the specimen L by
_
l.d A
oc
G dt
- 1
dL
( g )
L dt
Similar scaling can be performed for expressions in Eqs. (5) and (6 ), giving the
following approximate proportionalities
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34
x, rp ~
G
(9 )
Av
oc
G2
( 10)
Ab
oe
SG
( 11)
( 12)
G2
where S is the width of the region of enhanced diffusion at the grain
boundary.
II. C. 2. Universal Sintering Model
By combining Eq. (5) and (6 ) and collecting the proportionality factors, one
obtains a universal sintering equation of the initial, intermediate, and final
stages w ith simultaneous grain boundary and volume diffusion from the
grain boundary to the neck or pore surface in the form of l56l
1 dL _
L dt ~
y&a
kT
\DvFv (p)
SDbFb(p)
G 3
g 4
where D v and D b are volume and grain boundary diffusion coefficients,
respectively, p is the relative density, and Fv (p) and Fb (p) are collections of
proportionality factors and are functions of density. These factors, though
not known precisely, depend on various aspects of the microstructure and
can be thought of as measures of the tendency for densification.
This rather general sintering equation allows us to gain some insight into
the effect of rapid heating of a powder compact.
Slow heating permits
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35
significant sintering by surface diffusion which predominates at low
temperatures because the surface diffusion coefficient generally tends to have
lower activation energies and thus higher diffusivities than grain boundary
and volume diffusion, in that order. Surface diffusion alone cannot produce
any densification but does result in particle coarsening. As discussed above,
the gradients in curvature on the surfaces of sintering bodies induce a
driving force for diffusion and that the diffusion flux is directly proportional
to the curvature gradient. Therefore, it may be easily seen that as coarsening
occurs, the driving force for atom transport to the neck decreases significantly
due to the reduction of the neck curvature.
Rapid heating, on the other
hand, rapidly brings sintering to a higher temperature so that only a short
time is spent in the low temperature regime, thus permitting densifying
grain boundary and volume diffusion to be activated before nondensifying
surface diffusion can substantially coarsen the microstructure.
The importance for the suppression of surface diffusion during sintering
is exemplified in Fig. 3 where F (p) is plotted as a function of relative density.
The curves were computed based on simulations of initial stage sintering of
uniform spherical powder compact.
The curve labeled "isothermal"
represents a simulation of the ideal compact that was sintered w ith
significant contribution from surface diffusion. The same compact sintered
in the absence of surface diffusion, only grain boundary diffusion being
operative, resulted in higher values of F (p), as shown by the upper righthand curve labeled "no surface diffusion." Sintering of silver spheres 1 pm
in diameter was also simulated at at a constant heating rate of 100 °K /s for
comparison and is labeled "Ag, CRH." The general decrease in F (p) with
density is the result of a combination of microstructural changes, such as
decrease in curvature, increase in diffusion distance, and increase in the area
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36
10 *d
no surface diffusion
Ac. CRH
10
0.50
0.54
0.5B
0.62
Relative density
Figure 3.
Variation of F(p) w ith relative density computed from
simulations of intial stage sintering of spherical com­
pacts (after Johnson [59]).
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37
for diffusion, since F (p) depends upon the microstructure and changes as
sintering proceeds.
Though the model is still in its early stages of
development, qualitative predictions of shrinkage behavior can be obtained
for alumina based on typical particle dimensions and heating schedules
encountered in plasma sintering.
II. D. Plasma State
The material covered in this section is to briefly and simply introduce the
terminology of the field, fundamental definitions, and concepts of plasma
physics. The state of the plasma described here are those we are familiar with
in the operation of plasma processing found in the electronic industry.
These plasmas are usually maintained at low pressures, 1 torr or less, and are
nonequilibrium in nature. The plasmas employed in the plasma sintering
studies, however, are frequently operated at reduced pressures, from 30 to 100
torr, and can go to 1 atm. They are therefore characterized more by thermal
or equilibrium plasmas, as shown in Fig. 4.
The microwave plasma, in
particular, occupies an intermediate position between a low temperature and
a thermal plasma.
II. D. 1. Constituency
Plasmas are a state of matter which consists of nearly equal numbers of
free positive and negative charges. The free charges are mainly produced by
passing an electric field through the discharge. If ionization is not very high,
as is most often found in laboratory gas discharges, the plasma is mainly
composed of neutral particles. Typically there is only one charged particle
per 105 to 106 neutral atoms and molecules.!61!
The positively charged
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.-3
.- 2
-1
P (torr)
Figure 4.
Temperatures in arcs as a function of pressure (after von
Engel [60]).
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39
species is predominantly in the form of singly ionized species from which an
electron has been removed from the attraction of its parent nucleus. While
the bulk of the negative charges is prim arily free electrons, many plasmas
may also contain stable negative ions formed by electron impact with
electronegative gases, such as molecular oxygenJ62!
Transitions involving ionization, fragmentation and excitation processes
of reactive species that arise from collisions with electrons make the plasma
systems an abundant source of electromagnetic radiation, particularly in the
ultraviolet and vacuum ultraviolet regions. t63^ They are, therefore, often
used as sources for these radiations. The characteristic colors observed for
plasmas, however, are the result of the relatively small output in the visible
region, hence the term "glow discharge."
II. D. 2. Plasma Temperature
The species composing a nonequilibrium plasma may vary widely in
temperature.
An externally applied electric field can only influence the
charged species in the plasma.
Because of their small size, electrons are
much faster and more readily accelerated than the more massive ions, thus
absorbing most of the energy input to the system. This energy is distributed
to neutrals by collisions. Since electrons are much lighter than the positive
ions and neutral species by a factor of ~5 x 10- 4 to 5 x 10-6, energy transfer
from electrons to the heavier particles is thus comparatively poor, as
predicted by the following expression for the exchange of kinetic energy in
elastic collisions, 1641
ecoii = — 2m M „ Ae = &n-Ae
( tn + M ) 2
M
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(14)
40
where Ae is the initial energy difference. Therefore, electrons can attain a
greater velocity and thus a higher temperature than ions and neutrals, often
several electron volts (equivalents to several tens of thousands of degrees).
The ions, on the other hand, exhibit average energies and temperatures only
slightly higher than the corresponding neutral species because of the rapid
thermal equilibration between them.
The ions are thousands of degrees
cooler than the electrons but significantly hot enough to require cooling of
the surrounding walls. Figure 5 shows the range of temperature for the free
electrons, gas molecules, and ions at low pressures. The elevated electron
temperature permits electron-molecule collisions to excite high temperature
type reactions in a low temperature neutral gas.
It is precisely this
nonequilibrium character that distinguishes the plasma based processing
from conventional thermal processing. Thermal plasmas, as seen from Fig.
4, are characterized by equal temperature between the electrons and heavy
particles as a result of thermal equilibration at higher pressures.
II. D. 3. Plasma Density
Another important parameter characterizing a plasma is its density.
In
the region of the plasma glow, the plasma density is normally in the range of
108 ~ 1012 cm-3 as shown in Fig. 5. This range is set by fundamental limits.
When the number density of electrons is below ~108 cm-3, the rapid loss of
charged particles to form neutral atoms and molecules causes the plasma
state to be destroyed. Hence, to sustain a plasma, its temperature must be
kept above some minimum, about 1 eV or 10,000 °K, which again depends
on the density.
A t too high a density, high temperature leads to plasma
instability and nonuniformity.
Since the Boltzmann temperature of the
ions and the neutrals is relatively low while that of the electrons is one or
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
10
£
V
I0 2
C/D
Ixl
§
h<
cn
10
Lxl
I
Q.
electrons
1
2
Ll!
h— ~ I
ions
10
neutrals
-2
10
jo
a
10
10
10
10
’
10
14
12
10
10
10
J5
10
D E N S IT IE S ( c n f 3 )
Figure 5.
Ranges of temperatures and densities of spedes present in a typical plasma
process operated at reduced pressure conditions (adapted from ref. [65]).
42
two orders of magnitude greater, a plasma, in general, may be characterized
in terms of the average electron temperature and the charge density within
the system.
II. D. 4. Debye Sheath
At its boundaries plasma possesses a skin, called the plasma or Debye
sheath. In the bulk of the plasma, there are equal numbers of positive and
negative charge particles. Because the electrons are lighter and have higher
kinetic energy than the ions, they diffuse much more rapidly to the walls of
the neighboring containment vessel, establishing a region of local charge
imbalance in the vicinity of the confining walls, known as the sheath. The
electron flow progressively charges the walls to a negative potential. When
the sheath potential exceeds a few times the electron temperature, most
electrons are repelled by the field.
Thus, the flow of electrons is greatly
reduced until it is balanced by the flow of ions, at which a steady state is
reached. The wall is then said to be at floating potential,t65l
( 15)
where me and nti are the masses of electrons and ion respectively, Te and
Ti are the respective temperatures, k is the Boltzmann constant, and q is the
electronic charge.
This sheath-field propels positive ions into boundary
surfaces at normal incidence. The voltage across the sheath ranges from a
few volts to thousands of volts, depending on other parameters. The excess
random thermal flux of the electrons makes the w all potential negative
relative to the bulk of the plasma (glow) which is at nearly equipotential.
The potential in the glow region is often called the plasma potential.
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43
As shown in Fig.
6,
the plasma is severely perturbed in the immediate
vicinity of the walls. The electron and ion densities do not balance because
of the electric sheath field developed by the difference in the mobility of
positive and negative charge. For a sheath potential of a few electron volts
the distance of the perturbation is several times the Debye length,
a, =
(i6 )
\ Ak ne q 2 I
where ne is the number density of the electrons. Low pressure plasmas used
in material processing that typically operate between
.0 1
to
1
torr have a
Debye length of less than 1 mm, across which the electric field developed by
the sheath is reduced to 1 /e of its Coulomb value.!65!
II. E. Theory of Langmuir Probe
One of the earliest diagnostic techniques for obtaining localized
measurements of plasma properties was a probe developed by Langmuir
about 1924.166'67! A Langmuir probe consists basically of a small electrode, be
it planar, cylindrical, or spherical, frequently just a partially exposed
insulated w ire, which is inserted into a plasma.
A dc power supply is
attached to the probe and is usually arranged so that the potential of the
probe with respect to the plasma can be varied continuously over a range of
both negative and positive values.
The current collected by the probe is
determined as a function of the biasing voltage, yielding a voltage-current
characteristic curve.
It is from the shape of this characteristic that one
attempts to derive information concerning plasma properties such as
electron temperature, electron and positive ion densities, and plasma
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44
>i—
co
2
UJ
Q
0
2
4
6
8
X/X,
Figure
6.
The electron and ion densities in the sheath region of plasma
(from Cohen [65]).
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45
potential.
Useful reviews concerning the theory and use of electrostatic
probes have been written by Chenl68!, de Leeuwl69^ and Schottf70!.
In this section we shall discuss several aspects of the probe theory
applicable to plasma conditions similar to those prevailing in low-pressure
gas discharge, as studied by Langmuir. As far as the probe theory is concern,
the im portant features of such discharges must have the follow ing
properties: the probe radius is much larger than the Debye length and the
probe is nonemitting. Where the probe dimension is of comparable size or
smaller to the Debye length, numerical computations are needed to interpret
the data. Laframbois^71! has performed extensive calculations of this nature
and given a useful summary for the interpretation of probe characteristics.
The plane probe approximation, as first derived by Langmuir, is the most
simple to describe. Therefore the discussion begins with the method of plane
single probe and extends to cover the double Langmuir probe method that
was actually used in the experiments.
II. E. 1. Plane Single Probe
In the plane Langmuir single probe method, a plane electrode immersed
in the plasma is connected to a potential source which in turn is usually
connected to some nominal ground plane such as a metal vacuum vessel
wall and the current is measured as a function of the probe potential. From
the volt-ampere characteristics of the probe, called the "probe curve," three
fairly distinct regions are observed. The general appearance of a probe curve
is shown in Fig. 7.
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46
ELECTRON CURRENT SATURATED
ALL ELECTRONS COLLECTED
IONS REPELLED
PLASMA POTENTIAL
(RANDOM CURRENT)
ENERGY
OF FASTEST
ELECTRONS
MOST ENERGETIC ELECTRONS
START TO BE COLLECTED
ION CURRENT SATURATED
ALL IONS COLLECTED
ELECTRONS REPELLED
Figure 7.
The current-voltage characteristics of a probe introduced
into a plasma (after Flamm and Herb [61]).
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47
Region C: V « 0:
When the probe in the plasma has its potential made sufficiently
negative, all the electrons in the plasma are repelled and the ions are
attracted and thus the probe current consists only of positive ions.
The
resulting current from the ions is found to be nearly constant in magnitude
as the potential on the probe is made more negative. This current is called
the positive ion saturation and the ion current density is given byi72l
The general expression for the net current density to the probe is expressed as
j = )+ +
= e ne
where V = V p - V s is the difference between the potential of the plasma and
the probe.
Thus, in the ion saturation region the current decreases and
saturates at a small negative value and is only weakly dependent on voltage.
Region B: V f ~ V < V p :
As the voltage increases, the probe starts collecting electrons, only the
fastest electrons in the plasma being able to strike the probe. W ith further
voltage increase, a larger fraction of slow electrons of the distribution can
reach the probe. The floating potential, V f , is obtained when the net current
collected by the probe is zero. Most of the electrons leaving the plasma are
repelled by the probe at this condition in order that the separate electron and
ion currents reaching the probe just balance. This is the potential that the
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48
probe w ill assume if it is left w ith an open circuit.
When the voltage
somewhat exceeds the floating potential, more electrons w ill be collected
than ions, resulting in a positive value of I. Continuing increase in V causes
a steep rise in the electron current, which is given by the second term on the
right hand side of Eq. (18). It is from this region that the value for electron
temperature, Te , may be obtained from the slope of the semi-log plot In (/ jsat) = f ( V ). As the voltage increases even further, the electron current w ill
continue to increase until the probe is at the plasma or space potential, Vp .
The exponential term approaches one, and the electrons are attracted from
further regions of the plasma until finally the entire electron distribution is
admitted. A t this condition both the random electron and ion currents from
the plasma reach the probe unimpeded.
Region A : V > V P :
For all V s < Vp , the probe is surrounded by a positive sheath.
Thus,
when the voltage is increased beyond Vp , some of the ions are prevented
from reaching the probe, and the net electron current to the probe is again
increased, but the probe is now surrounded by a negative sheath.
At
sufficient large positive voltage, all the ions w ill be repelled and the probe
w ill collect the electron saturation current. This is the "electron saturation"
regime. In practice, the probe current at either large negative or positive
voltages does not saturate at a constant value, but continues to increase
slowly in magnitude.
This behavior is often attributed to an increasing
sheath thickness, which results in an increasing effective current collection
area for the probe.
After Te is calculated and with Vp known, plasma
density and ion temperature can then be computed from the above
equations.
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49
II. E. 2 . Double Langmuir Probe
There are situations where the use of a single probe may be difficult. For
example, as in the case of an electrodeless plasma in a dielectric container,
there are no well-defined counter electrode (ground). In such an instance,
one may employ a double Langmuir probe. The double probe consists of two
equal electrodes, usually wires, which are a few cm apart and immersed in
the plasma. The probe power supply system floats at V f and the current
flowing in the probe circuit is measured as a function of the voltage applied
between the probes, varied between ± V (Fig. 8 ).
The current-voltage characteristics may be obtained by treating both
electrodes as single probes.
unequal area, so that A 2 > A \.
Let us suppose that the electrodes were of
Since the measuring circuit is floating, the
total net current of positive ions and electrons flowing to the system from
the plasma must be zero. As in a single probe, current increases with applied
voltage, V = (Vi - V2). However, as V is increased a point must eventually
be reached where the second probe becomes so negative with respect to the
plasma that no electrons can reach it.
flowing into electrode
1
At this point, the electron current
w ill be limited by the maximum ion current that
electrode 2 w ill accept. This part of the double probe characteristic is known
as the saturation region. The current-voltage characteristic for an unequal
area Langmuir double probe is shown schematically in Fig. 9. Thus, for (V i V2) - » the curve shows that I - » f2 . Moreover, this saturation is the result
of ion saturation because the ion current at the second probe is the limiting
factor, i.e., total current to the probe can never exceed the positive ion
current to them.
This may be contrasted w ith the result of electron
saturation for a single probe. Further increase in V w ill not significantly
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V,
Probe 1
i,
V,
111
Probe 2
V
V
Figure
8.
Schematic of a double probe immersed in a plasma.
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51
v=o
Figure 9.
Schematic of the I-V characteristics for an unequal area
Langmuir double probe (from Manos and Dylla [72]).
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52
change the situation.
For (V i - V 2 ) -» - 00, ion collection at probe 1 is
limiting and we obtain the similar result as for a single probe, that I - » - i* .
However, ideal saturation does not occur, for cylindrical probes, unless
the probe radius satisfies Laframboise's condition, i.e., the ratio probe
size/Debye length is less than about 3.t73l The general equation describing
the double probe characteristic is given byt72l
12
+ I
= 4 1 exp [ i£ f - )
A2
\k T e }
where I = the current in the external circuit,
(*1
(19)
or - i i ) ,
11 = the ion saturation current for probe 1 , i.e., the current observed
when V \ « V i ,
12
= ion saturation for probe 2 ,
A \, A2 - the collection area of probe 1 and 2 , respectively.
The electron temperature can be computed from the slop of I vs.V at V = 0.
Assuming equal probe areas and differentiating I (V ) we find
kTe _ h+ d (V 1 - V
dl
2
)
/
(20 )
=0
As in the case of the single probe, ne can be determined from the ion
saturation value, the calculated Te, and the assumed, or independently
measured, T,-.
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53
II. F. Plasma Chemistry
%
The type of elementary reactions involving species constituting a plasma
(electrons, ions, atoms, and molecules) is both numerous and relatively
complex.
The reactions are, without exception, initiated by collisional
processes that transfer energy from electrons to neutral gas molecules to
form various reactive species. Since electrons are more mobile and easily
accelerated than ions they are the agents through which external energy is
supplied.
This energy is then channelled into the system via elastic and
inelastic electron-neutral collisions to maintain a steady supply of ions and
radicals which are continuously lost by conversion and recombination.
Thus, the energy transfer by the electrons can be written implicitly as
£e =
eelastic
+
erot +
e vibr +
Selectr +
£diss +
Sion
(21 )
where energy gained by the electrons from the applied electric field is
balanced by the energy loss due to elastic and inelastic processes (rotational,
vibrational, electronic, dissociation, and ionization processes). The exchange
of energy for a particular process w ill depend on the collisional probability
and cross-section which are treated much more extensively elsewhere in the
literature.t64'74"77! Naturally, detailing each specific elementary process is
impossible. Therefore, examples of the most typical reactions are illustrated.
In the plasma, each formation step balances various processes that destroy
plasma particles. The equilibrium between formation and loss determines
the steady concentration of species in a discharge. The production and loss
processes for the various gaseous species may be grouped into three
categories as follows.1781
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54
1. Electron-neutral collisions:
Ionization:
e + A2 -> A? + 2e
(22)
Dissociative ionization:
e
+ A2 - * A + + A
+ 2e
(23)
e
(24)
Dissociation:
e +
A2 -» 2A +
Dissociative attachment:
e
+ A2 -» A + + A~ + e
(25)
Excitation
(rotational, vibrational, electronic):
e + A2
He
Az +
e
( 2 6a )
e + A
A* + e
( 26b)
or
De-excitation
(generation of heat and light):
A2
—> A2 + hv
( 27a )
or
A * -» A
+ hv
( 27b)
Here A 2 represents a molecule and A2 , A * are the respective excited
states of A 2 and A. Reactions (22) and (23) are the main source of ions and
electrons that sustain the plasma. Ionization resulting from electron impact
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55
creates ions not only in their ground state, but also in excited states. While
rotational excitation relaxes after a few collisions, vibrational excitation and
electronic excitation of molecular ions can be very persistent, surviving up to
104 collisions.!62! The degree of ionization in a typical laboratory plasma, as
pointed out earlier, is normally in the range of 10‘ 9 to 10'5. For the four gas
plasmas, nam ely, He, H 2 , 0 2 / and N 2 , employed under the present
experimental conditions, calculations show that the fraction ionized is on
the order of 10"5. For a fixed value of electron temperature, the degree of
ionization decreases w ith increased pressure as electrons are unable to gain
sufficient energy due to frequent encounter w ith the heavy particles.
Lowering the pressure therefore would lead to greater ionization.
Reaction (24) is primarily responsible for the production of atomic species.
The radical fragments can be highly reactive under situations which appear
inert to the parent molecule.
Therefore they constitute one of the most
important species in this reactive plasma environment.
The dissociation
process is believed to involved the direct electron excitation to an
electronically excited state of the molecule which then dissociates.t74l The
extent of the plasmochemical dissociation generally depends on the electron
energies and the dissociation cross-section. The work of Brake and Kerberl79!
indicated that the degree of oxygen dissociation was
discharge.
100%
in a microwave
Using the nitrogen dioxide titration technique to determine
oxygen atom concentration at fixed points downstream from the exit of the
discharge, they found that the titration data extrapolated to the cavity exit as
well as theoretical calculations showed complete dissociation at the exit.
Since their experimental conditions were similar to the present study, it is
believed that the majority of the species in the four working gases are
dissociated.
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56
Reaction (25) produces a stable negative ion when the negative charged
electron is said to be attached upon impact w ith neutral molecules.
The
active metastable species and electronic excitation are generated mainly by
Reaction (26a) and (26b). Under most operating conditions, the electron of
the latter-most species w ill remain in the higher quantum level for some
8
10"
seconds before falling back to a lower state in one or several jumps or with
die emission of radiation. The metastable species, on the other hand, can last
for about
10"2
seconds, although they may be destroyed within this time by
another collision.
The characteristic plasma induced optical emission is
formed by Reaction (27a) and (27b).
Though the reactions were written
explicitly for diatomic molecules, noble gases, such as A r and He, undergo
similar ionization and electronic excitation reactions listed for diatomic
species.
2.
Inelastic collisions between heavy particles:
(M , M
= metastable species in their respective ground and excited states)
Penning ionization:
M.
+ A2 —^ ^ 2
^
(28)
Penning dissociation:
M * + A2 -> 2A + M
(29)
Charge transfer:
(30)
Collisional detachment:
M
+ A2
A2 + M
+ e
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( 31)
57
Associative detachment:
A~ + A
(32)
Az + e
Ion-ion recombination:
A4
+ A2
(33)
—^ Az + A4
Electron-ion recombination:
6 + Az
e + A2
+ M
( 3 4a )
—^ 2A
->■ A2 +
M
( 34b)
Atom recombination:
2A
+ M. —> Az + A4
(35)
A
+ BC —^ AB + C
(36)
Atom abstraction:
Atom addition:
A
+ BC + M
-» ABC + M
(37)
In Penning ionization, the excited metastable species, M *, formed by
electron impact has sufficient energy to ionize another species (reaction 28)
or yield neutral fragments (reaction 29). Penning ionization has been found
to be an important process where M is a noble gas w ith a metastable state
excitation energy level just above the ionization energy for A z ^ ] Reaction
(30) involves transfer of charge for collisions of ions and neutrals, whereas
heavy reactants are transferred when neutrals collide in Reaction (36). These
tw o reactions together w ith
the associative Reaction (37) proceed
exothermically at high rates with conversions occurring practically on every
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58
collision. I-62J The detachment processes (31) and (32) yield a free electron,
since the negatively charged ion was formed in the first place.
The
recombination of electron w ith positive ions, Reaction (34a) and (34b),
represents some of the most important charge loss mechanisms, resulting in
neutral species which are usually free radicals. Ionic recombination reactions
such as Reaction (33) are important at significant concentrations of negative
ions in more highly ionized plasmas. Reaction (35) for homogeneous gasphase atom recombination occurs at a negligibly small rate, on the order of
1 0 -32
cm-3 molecule-1 s 'U 62!
3. Heterogeneous reactions:
Besides participating in various homogeneous reactions, plasma species
can also undergo a variety of interactions with the boundary surfaces. It is
these heterogeneous reactions that are particularly important in a large
number of material processing applications.
In the following table of
reactions, S is a designation for the solid surface in contact with the plasma
Electron-ion recombination:
S —6 + A>2
—^ S + A.2
(38)
Atom recombination:
S —A
+ A —> S + A 2
(39)
Metastable de-excitation:
S + M *
-> S + M
(40)
Atom abstraction:
S —B + A —> S + AB
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( 41)
59
Sputtering:
S -B
(42)
+ M + —* S + + B + M
Reaction (38) describes the predominating process for the destruction of
the charged species by the diffusion of ions and electrons to the walls
followed by recombination on the wall surfaces.
Consequently, this
neutralization process can cause significant heating of the solid surface.
W hile
atom recombination in the gas phase is negligibly small,
heterogeneous recombination (reaction 39) can be significant and contribute
to heating of a substrate surface by releasing the chemical energy of
association. The possibility of the deactivation at the wall of various excited
species is considered in Reaction (40). Plasma etching caused by reaction with
the w all may be represented by Reaction (41). Substrate material is ejected
from the surface when an ion, accelerated by the sheath potential, transfers
energy to the substrate at the point of contact, resulting in sputtering
(reaction 42).
The kinetics of the plasma production and loss processes are determined
by the externally applied electric field and by the rate constants of elastic and
inelastic collisions between electrons and neutral or other charged species.
The rates of surface processes can vary considerably and depend on the
temperature of the reacting surface, adsorption coefficient, accommodation
coefficient, recombination coefficient for the particular process, the transport
coefficients of species to the walls, and other such reactions.
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60
II. G. Interaction of Plasma w ith Surfaces
The interaction of plasma w ith a solid is much more complicated than in
the case of an ordinary gas and is, in fact, much more involved than that
presented earlier under the heading of "heterogeneous reactions."
The
existence of free electrons, positive ions, and radicals in a plasma give rise to
a number of effects which are still poorly understood.
A detailed
understanding of the interaction of a plasma w ith a surface requires the
knowledge of how each individual species in the plasma reacts with the
given surface.
This section summarizes in more detail the reactions
occurring on surfaces that are induced by ions, electrons, and neutrals and
present the results of heterogeneous recombination processes of atomic
oxygen, hydrogen, and nitrogen on various surfaces which are relevant to
the present sintering study.
II. G. 1. Adsorption
Before we proceed it may be appropriate to discuss the concept of the
adsorption of molecules at solid surfaces since this is usually the first of a
sequence of steps occurring in a heterogeneous reaction. It is well known
that the interaction we call adsorption comprises two entirely different
processes involving quite different forces.
The first type of adsorption,
termed chemical adsorption or chemisorption, is the result of the interaction
between a molecule and free valence electrons; this type may be regarded as a
chemical reaction because there is a rearrangement of the electrons within
the molecule. The free valences arise as a result of the situation where a
surface atom has fewer neighboring atoms than those w ithin the bulk of the
solid. Therefore, each surface atom may possess one or more free valencies.
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61
Moreover, there is also an imbalance of forces as shown in Figure 10;
consequently, a surface atom suffers a net force acting inward. A similar
situation exists at the surface of ionic solids as depicted above.
Chemisorption on these surfaces attempts to rectify the situation and lower
the total energy of the systems, resulting in the liberation of heat.
The other type of adsorption which occurs at the surfaces of the solids is
due to van der Waals forces. These include electrostatic attraction in the case
of molecules w ith permanent dipole moments, and induced dipolar
attraction w ith readily polarizable molecules; dispersion forces caused by
slight fluctuations in electron density are the only forces of attraction
between non-polar atoms or molecules. When these forces are in effect there
is a physical attraction without chemical alteration of the molecule.
situation is called physical adsorption.
This
There is, however, one important
point concerning physical adsorption: it does not depend much on the
chemical nature of the solid, but the strength of physical adsorption may be
related to the physical properties of the adsorbing species.
II. G. 1. a. Adsorption and Catalysis by Metals
The chemisorption of a few simple gases has been investigated on many
metals and is summarized in Table I, as compiled by Bond.f80! The + symbols
in the table means that strong chemisorption occurs; ± means that is weak;
and - means unobservable.
According to this table, their strength of
adsorption on the vast majority of metals fall in the following sequence:
C>2 > C2H 2 > C2 H 4 > CO > H 2 > CO 2 > N 2
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Figure 10.
Pictorial representation of the surface of (a) a covalent
solid and (b) an ionic solid (after Bond [80]).
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63
Apparently, oxygen is the easiest molecule to activate, whereas nitrogen
seems to be the most difficult.
Study of Table 1 below shows that strong
chemisorption is firmly associated with transition metals.
Table 1
Classification of metals based on adsorption properties. Data
from [80].
Group
A
Metals
2
2
02
C 2H 2
C2H4
CO
+
+
+
+
+
+
+
h
C02
n
Ti, Zr, Hf, V,
Mb,
Ta, Cr, Mo, W,
Fe, Ru, Os
Bi
N i, Co
+
+
+
+
+
+
+
b2
Rh, Pd, Pt, Ir
+
+
+
+
+
+
+
b3
Mn, Cu
+
+
+
+
±
—
—
C
A l, Au
+
+
+
+
—
—
—
D
Li, Na, K
+
+
-
—
—
—
—
E
Mg, Ag, Zn, Cd,
In, Si, Ge, Sn,
+
Pb, As, Sb, Bi
To truly understand this classification of adsorption properties, we really
need an accurate description of the electronic structure description of the
electronic structure of surface metal atoms. We know, however, that the
transition metals are characterized by having one or more unpaired d electrons in the outermost shell, and the w eakly chemisorbing non-
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64
transition metals have only s or p valence electrons. It has been suggested
that unpaired d -electrons are involved in bonding the adsorbed molecule to
the surface in a weakly-held precursor state, from which it then passes to the
final strongly-bonded state. Those metals not having unpaired d -electrons,
on the other hand, may have a prohibitively higher activation energy for
adsorption without the availability of this intermediate state. Not only do
the transitional metals, themselves, possess high catalytic activity, but also
their alloys and compounds with nonmetals: oxides, sulfides, etc.
II. G. 1. b. Adsorption and Catalysis by Oxides
The chemisorption of gases is more complicated on oxides than on metals
because the adsorbed molecule may be attached either to a cation or to an
oxide anion. There are three possibilities for the type of bonding between a
chemisorbed molecule or atom and an oxide surface^81! i) weak bond,
ii) strong acceptor bond, and iii) strong donor bond. In the first case, an
electron of the chemisorbed particle is drawn close to a cation of the lattice, or
an electron of the anion of the lattice is drawn close to the chemisorbed
particle. In the second case, an electron of the particle adsorbed on the cation
interacts with a free electron of the semiconductor oxide, thus bringing about
a chemical bond w ith the lattice.
The acceptor reaction is therefore
accompanied by the transfer of an electron from the catalyst to the adsorbed
particles. In donor reactions, an atom or molecule is adsorbed on an anion of
the lattice and interacts with a free hole of the semiconducting oxide (i.e., the
transfer of an electron proceeds in the opposite direction).
It is convenient to subdivide these oxides into p - or n- type semi­
conducting and insulating oxide in Table 2 below.
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65
Table 2
Classification of semiconducting and insulating
metal oxides. Data from [81].
Classification
Example
negative (n-type)
ZnO, TiC>2 , ZrC>2
positive (p-type)
NiO, Cu20 , PbO, Cr20 3
insulator
AI2 O 3 , MgO, SiC>2 , B2O 3
The catalytic properties, especially for reactions involving hydrogen and
hydrocarbons and oxidation-reduction reactions, of the three classes of oxides
are substantially different. For example, the high activity of p -type oxide in
oxygen chemisorption indicates their facile adsorption of oxygen, whereas
insulator and n -type oxides are much less active because of their inability to
chemisorb oxygen. However, the correlation between the change of catalytic
activity with the change of conductivity type is at best only a rough guide to
catalytic activity, since we are usually concerned just with the oxide surface,
and at temperatures and in atmospheres quite different from those usually
used in measurement of semiconductivity.
II. G. 2. Ion Induced Chemical Reactions
This section discusses the chemical reactions of adsorbed species with a
given surface that are induced by ion bombardment. The phenomenon is
universally found in the field of plasma etching. Consider for example, the
XeF 2 -S i-A r+ system, i.e., etching of silicon.
A t room temperature the
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66
reaction of XeF 2 gas w ith silicon is significant, but simultaneous
bombardment w ith argon ions greatly enhances the probability the the
incident fluorine from the XeF2 w ill react to form the volatile SiF4 .
The etch rate of silicon as determined from microbalance measurements
is plotted against time in Fig. 11 as an Si sample is rotated into a jet of XeF2
gas w ith and without ion bombardment.!82!
The cooperative interaction
between the A r+ beam and neutral XeF2 is shown clearly in this figure. The
simultaneous incidence of both neutral XeF2 and A r+ ion upon the surface
resulted in a greatly enhanced etch rate. When used by itself, the argon ion
beam produced physical sputtering. Similar ion enhanced chemical reaction
has been observed by these authors for F2 and CI2 on Silicon substrate and F2
and O 2 on C.
The chemical mechanisms involved in the heterogeneous reaction of
solid material exposed to gas phase particles with or without plasma is
customarily analyzed in terms of the following sequences of steps: (1 ) nondissociative adsorption of gas phase species at the surface of the solid;
(2 ) dissociation of the adsorbed gaseous species (i.e., dissociative
chemisorption); (3) reaction between adsorbed radicals and the solid surface
to form adsorbed product molecule, e.g., SiF4 (ads); (4) desorption of the
product molecule into the gas phase; (5) the removal of nonreactive residue
from the surface.
The first two steps could be combined and labeled "adsorption" as
presented above.
Since there usually exist attractive forces between
undissociated molecule and the surface, the first step always occurs. This
step may involve adsorption into a so-called "precursor state" where the
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67
|«— XeF 2Gas-»j*—A r+ Ion Beam + X e F jG a s — ►{*— A r+ Ion Beam —>|
Only
Only
70
c
E
60
<<
50
0>
ro
CC
40
JC.
u
w
UJ
c
o
u
30
20
M
10
0
J ------------- 1_______ 1________L
100
200
300
400
500
600
700
800
900
Time (sec)
Figure
11.
Ion-assisted gas surface chemistry using Ar+ and XeF2 on
SiC>2 (from ref. [82]).
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68
molecule is mobile and diffuses across the surface until it dissociates, possibly
at a step, kink, vacancy, or other defects.
Ion bombardment may affect the process of dissociative chemisorption in
at least three ways. First, dissociative chemisorption may occur exclusively
or preferentially at defect sites produced by the impinging ions. Secondly,
ion bombardment may cause an adsorbed molecule to dissociate in situations
where this would not normally happen. Thirdly, dissociative chemisorption
often occurs on a clean surface, whereas it may not occur on the same surface
when it is covered by a monolayer of adsorbed gas.
Etching by ions that react w ith and remove substrate material is rare. It is
now accepted that plasma etching is brought about by the action of neutral
gas-solid reactions, which are stimulated or directed by ion bombardment.
The ions themselves are rarely the etchant, neutrals are responsible for
almost all reactive etching at pressures above about 0.001-0.005 torr, except at
extremely low pressures where ions can have very high kinetic energies to
cause etching by physical material ejection.t61l
A t higher pressure, ion
energies are often low; therefore, the role of ions, when they participate in
plasma etching, is more physical than chemical - they enhance the etch rate
and lend directionality.
Ions "damage" the solid surface, making it more
reactive toward incident neutral radicals. The disruption of the surface being
etched can include diverse mechanisms such as the formation of highly
reactive dangling bonds, disruption of lattice structure and formation of
dislocations, forcible injection of adsorbed reactant into a lattice by the
collisional cascade, or even bond-breaking in intermediate tightly-adsorbed
surface compounds.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
The volatility of the product species is essential in a chemical etching
process.
If the species are volatile they w ill desorb causing etching or
gasification of the surface. If the species are involatile, a layer of reaction
product would coat the surface and prevent gaseous species from reaching it,
and cut off the etching reaction.
It may be possible that for involatile
products (e.g. oxides) the ion bombardment may enhance diffusion which
allows the oxygen to diffuse into the lattice, thus causing an increase in the
reaction rate at the surface.
Ion bombardment can, in some cases, result in metal oxidation state
changes for metal oxides. By using x-ray photoelectron spectroscopy (XPS),
oxide surfaces bombarded w ith A r+ and C>2 + ions show a reduction in the
oxidation states to the corresponding metal or lower oxide.!83!
As shown in Table 3 for a variety of oxide systems, thermodynamic
arguments were put forth to rationalize this phenomena. Bombardment of
the metal oxides with A r+ ions produces a deficiency of oxygen and reduces
the metals for systems that are thermodynamically less stable.
II. G. 3. Electron Induced Chemical Reactions
The phenomena of electrons interacting with a surface is also important
in a plasma environment. Their reaction with a surface may be classified as
follows: ( 1 ) chemical reactions between gas phase species and a surface where
electron bombardment is required to activate the process, (2 ) electroninduced dissociation of adsorbed molecules, and (3) lattice damage produced
by energetic electrons.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3 The standard free energy of formation of oxides and
their reduction induced by A r+ ion bombardment.
Data from [83].
Sample
-AGf (Kcal/mole)
Reduction
observed?
AU2 O 3
-39
Yes
Ag2 0
2 .6
Yes
Ag2C>2
PdO
6.4
Yes
20
Yes
CuO
30
CU2O
35
Yes
Yes
Ir 0 2
PbO
40
Yes
45
Yes
Pb0 2
N iO
52
Yes
52
Yes
CdO
54
Yes
FeO
58
Yes
RuG 2
60
ZnO
76
Yes
No
N i (OH ) 2
108
No
W 02
118
Yes
M 0 O2
No
Sn0 2
M 0 O3
119
124
No
162
Yes
Fe2 0 3
177
Yes
W O3
S i0 2
182
Yes
192
No
Cr2C>3
250
No
Ti2 0 3
346
No
A I2 O 3
377
No
Ta2 0 5
471
No
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71
Again an example is used to illustrate electron-induced chemical
reactions which are believed to be w idely occurring in a plasma
environment. When SiC>2 , Si3N 4 , or SiC are exposed to XeF2 gas an adsorbed
layer of fluorine is produced on the substrate material. Xenon desorbs into
the gas phase, therefore does not remain on the surface. This is all that
happens in the absence of electron bombardment. However, in the presence
of electron bombardment, SiF4 and other volatile products evolved.!82]
Figure 12 illustrates the results, for which the reaction proceeds until all the
material is volatilized. Similar data were also obtained by these authors for
silicon nitride and silicon carbide.
Many of the mechanisms previously discussed w ith regard to ions may
also apply to chemical reactions enhanced by electron bombardment. It is
known, for instance, that electron bombardment of SiC>2 causes oxygen to be
desorbed into the gas phase.!84'85! Silicon which remains on the surface can
now be attacked by the XeF2 gas to produce volatile SiF4 gas. In this manner
the material is etched by the removal of both oxygen and silicon from the
SiC>2 lattice.
Electron bombardment of surfaces also causes the dissociation of adsorbed
molecules on the surfaces.
For example, adsorbed layers of halogens, the
alkali metals, hydrogen, oxygen, and carbon monoxide often have large cross
sections.
Madey and Yates!86! have summarized the major experimental
observations related to electron induced desorption. They concluded that the
bombardment of solid surfaces w ith electrons can cause desorption of
ground-state neutrals (both atoms and molecules), ions, and metastables
species. In addition, dissociation of adsorbed molecules w ith the resulting
fragments remaining attached to the surface can be induced by electron
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72
9000
8000
S iO
P = 6 x 10
7000
_
vt
Torr.
45 |ia , 5 0 m n /c m ^ , 1 5 0 0 eV
Rate 'Vi 200 ^/m in
6000
uj
5000
UJ
o ’ 4000
u.
K
3000
< 2000
1000
X e F 2 in system
0
500
electron beam on
1000
1500
2000
25000
3000
TIM E (S E C O N D S )
Figure
12.
Electron-assisted gas surface chemistry using 1500 eV
electrons and XeF2 simultaneously incident on Si(>2
(from ref. [82]).
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73
bombardment. The cross sections for electron-stimulated-desorption (ESD)
processes on most surfaces are usually much smaller than cross sections for
comparable gas phase processes involving electron-induced dissociation and
dissociative ionization.
Moreover, typical cross sections for desorption of
ions are smaller (by a factor of ten or more) than cross sections for neutral
desorption.
Cross sections for desorption of adsorbed species are very
sensitive to the mode of bonding.
Observation indicates that desorption
proceeds via a direct electronic excitation mechanism rather than a direct
momentum transfer.
It is conceivable that highly energetic electrons could supply sufficient
kinetic energy to disrupt the surface as described for damage-induced-ion
assisted etching. Since the mean energy of a large segment of the electron
population in a plasma sintering process is only around 1-5 eV and not more
than
8
eV for a typical plasma etching situation, this damage mechanism is
usually not an im portant consideration, though the small number of
electrons in the tail of the distribution that are responsible for ionization
may be more likely to produce any significant lattice damage.
II. G. 4. Electxon-Ion Recombination on Surfaces
When the wall acquires a negative charge caused by electron charging, the
positive ions follow and the two tend to form a two-dimensional plasma on
the wall surface. The surface molecules or atoms are always present as third
bodies to take up the liberated energy of neutralization.
When ion and
electron encounter each other within the attractive-force region, the chance
of capture and recombination is very high. Gubin and Reznichenkol87! had
shown that the efficiency of recombination and neutralization of electrons
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
and ions of molecular nitrogen and several noble gases is nearly unity.
Thus, in addition to carrying their respective thermal energies to the surface,
electron and ion can recombine at the surface, releasing the energy of
ionization for each pair.
II. G. 5. Interaction of Neutral Species with Surfaces
T h e
is
in t e r a c t io n
m o s t
im
p o r ta n t
c o n c e n tr a tio n
s u rfa c e
h a v e
c a n
is
b e
a llu d e d
p r o b a b ility
fo r
to
in
fo r
in
a to m s
c h e m is o r b e d
a re
m o le c u le
is
n o t
s u rfa c e s
c o n c e n tr a tio n
T h e
w h e re
v o la t ile
p la s m a
m o le c u le s
c h e m is o r b e d
w h ic h
c a n
r e a c t iv ity
n e u tra l
d o
o fte n
o f
g a s
b e
o f
s u rfa c e
a n y
o f
a n d
c h e m is o r b
in v o lv e d
in t e r a c t
w it h
in te r s !91! h a s
p la s m a
to
r e la tiv e ly
to
s ilic o n
a n d
g e n e r a tio n
its
c o m p o u n d s
o f r e a c t iv e
n a tu re
im p lie s
r a d ic a ls
b y
o f
th e s e
th a t
th e
d is s o c ia tin g
r e a c t io n
1.
th e
e x a m p le ,
w h e re
th e
o f
T h e re
p a re n t
n it r o g e n
n it r o g e n
M o re o v e r,
e v e n
th e
s u rfa c e
a n o th e r
e x a m p le
a to m s .
is
m a te r ia l
o f
th e
g a s e s
g lo w
h a lo c a r b o n
to
p ro d u c e
g a se s
n o t c h e m is o r b
h a lo c a r b o n
r o le
w e
s u m m a ry
T a b le
th a t s e v e ra l o f th e
4.
in e r t
a
g iv e n
A s
h ig h
n it r o g e n ,
s o lid
( C F 4 , C F 3H , C F 3C I , C F 2C I 2 C C I 4) d o
T h e
,
a
in e r t to
F o r
e tc h in g
g iv e n
s h o w n
in
a p p e a r
m o le c u la r
a
a n d
s u r f a c e s .1 8 8 - 9 0 ]
e tc h in g
S i3N
h a v e
it
th e ir
a
p h e n o m e n a .
ill
r h o d iu m
s in c e
re a c t w it h
p re s e n te d
e x p o s u re
in
w
r a d ic a ls .
th e s e
b y
p a r t ic le s
m a y
a ll s p e c ie s , b u t
m o le c u le s
d is c h a r g e
w a s
c o p p e r,
fo r
e ffic ie n t ly ,
c h e m is o r b
in c r e a s e d
s p e c ie s
W
o n
n o t
r a d ic a ls
c o m p o u n d s .
o r
th e
s ta te
n ic k e l,
a n d
m a t e r ia l
c h e m is o r b
g iv e n
p o rta n t
th e s e
g iv e n
th a t
a
im
a to m s
W h e th e r
e ffe c tiv e ly
o n
is
in te r p r e ta tio n
in s ta n c e s , h o w e v e r , w h e r e
w h ic h
s ta te
s e c tio n s , a
g ro u n d
b u t
fo r
th e
p a r t ic le s
m o le c u le s
s u rfa c e s
la r g e .
e a r lie r
fo r
w it h
g r o u n d
g e n e r a lly
c r u c ia l
c h e m is o r p tio n
a re
o f p la s m a
o n
w it h
u s e d
S i, S i0 2 ,
re s p e c t
d is c h a r g e
m o le c u le s .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in
is
T h e
75
radicals subsequently react with the surface to form volatile compounds. F2
also reacts slowly w ith a silicon surface!92!, whereas evidence from plasma
etching experiments suggest that F atoms rapidly attack silicon.!93!
The importance of radicals in initiating and sustaining chemical reactions
has long been recognized. The investigation by Balooch and Olander!94! for
the hydrogen-carbon system serves as a good example. They found that
molecular H 2 was very unreactive toward graphite because of the lack of
dissociative chemisorption. Hydrogen atoms, on the other hand, show an
elevated activity. For instance, atomic hydrogen generated in a hot tungsten
oven reacted quite rapidly to produce either methane or acetylene depending
upon the surface temperature. Thus, atoms generated in a discharge may
have similar increased reactivity with a surface.
The interaction of electronically excited molecules with surfaces may also
be significant in discharges. Particles which are excited to optically allowed
states are probably not important because they generally remain in the
excited state for a period less than ~10' 7 sec. Metastable molecules and ions,
on the other hand, have longer lifetimes and therefore may be de-excited at
surfaces.
Metallic or semiconducting surfaces are very efficient for de-excitation via
an Auger or resonant transition. For slow particles, the de-excitation appears
to occur before the particle begins to interact strongly with the surface.
Therefore, from a chemical point of view, the particle is in its electronic
ground state, although it may well be vibrationally excited. The work by
Winters and Horne!95! tends to support the view that the energy contained
in electronic excitation is not by itself effective in causing a chemical reaction.
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76
The authors showed that an N 2 + ion, which has more than 15 eV of
electronic excitation energy, does not react chemically w ith tungsten,
molybdenum, or nickel surfaces unless it also has greater than 9 eV of kinetic
energy. Nitrogen atoms, however, with small kinetic energy w ill react with
these same surfaces.
Another piece of experimental evidence from which we can draw similar
conclusions is the interaction of metastable nitrogen molecules (the A 3 ZU+
state) w ith these same surfaces!96'97) The relative excitation cross section for
this state is shown in Fig. 13. Direct excitation by electron impact has a
threshold at approximate
6
eV and has a maximum at a higher energies. The
metastable excitation cross section is large where the adsorption cross section
is small, e.g. at 10 eV.
Furthermore, there is no indication from the
adsorption curve the presence of a contribution from metastable molecules.
Although they may be efficiently de-exdted at a metallic surface, metastables
have only a small probability of causing a chemical reaction.
The situation may be different for materials such as ionic solids or
insulators.
There are some evidence which suggest a two-electron, inter­
atomic Auger process that can produce a positive ion at a position in the
lattice where a negative ion originally resides!") The positive ion now finds
itself in a strongly repulsive Madelung potential and can be desorbed into the
gas phase.
Thus, the de-excitation of ions or metastable neutrals at the
surface of some ionic solids may produce chemical reactions and also
desorption.
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77
METASTABLE
EXCITATION
'ADSORPTION
IONIZATION
CROSS
SECTION
(ARBITRARY
UNITS)
7r
ELECTRON
Figure 13.
ENERGY
(ev)
The relative excitation cross section versus electron energy
for nitrogen molecules (adopted from ref. [98]).
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78
II. G. 6 . Recombination of Atoms on Surfaces
As has been mentioned, a plasma is an efficient source for supplying free
radicals by the dissociation of polyatomic molecules. Therefore, it is not
surprising that the radical species can carry with them the potential energy of
recombination toward a cooler surrounding surface which can then catalyze
the atom recombination, resulting in the release of chemical energy at the
surface. Gas-surface recombination reactions can be very rapid where a solid
surface acts as the third body to provide a way for removal of the excess
product energy. For example, if two species, say A and B , recombined,
A + B -> A B *
(4 3 )
an energetic activated state, AB *, is formed. However, unless some of the
energy from combining A + B is removed, "AB *" w ill contain enough
energy to decompose via the reverse reaction
A B * -> A + B
(4 4 )
This energy can either be transferred by interacting w ith a third body or
removed by the emission of a photon, thereby stabilizing the product "AB."
However, the mean lifetime of an unstabilized AB * is only ~10*12 - 10-13 sec,
while the average time for a (fast) radiative transition to occur is about
1 0 '9
-
108 sec and thus is improbable J10°l On the other hand, when the reaction
occurs on or near a surface, where the surface acts as the third body, the heat
of reaction between two species, A and B, can be efficiently transferred to the
surface.
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79
The specific influence of surfaces in heterogeneous recombination of
atoms and radicals has been a longstanding problem of chemical reactivity at
solid surfaces. Numerous works were carried out to elucidate the role of the
surface and of the dependence of the reaction variables upon the properties
of the solid.
The majority of studies on heterogeneous recombination
reactions on various solid surfaces were performed using the side-arm
method originated by Smithl101l
Linnett and Marsdent102! used Smith's method extensively to study the
kinetics of the recombination of oxygen atoms on Pyrex glass, potassium
chloride, lithium chloride, molybdenum trioxide, and lead monoxide. The
inner surface of one of the two closed-end side arms of the discharge tube
was coated with the substance under investigation, the other side arm was
used as a reference to check whether a constant concentration of oxygen
atoms was being produced under a given set of discharge condition. Oxygen
atoms were produced by a radio frequency discharge operated in the range of
2 to
6
M H z in a stream of oxygen. The concentration along the two side arm
tubes was studied with thermocouple probes whose tips were coated with
silver which catalyzed the recombination of oxygen atoms.
The movable thermocouple recorded the resulting temperature rise
which measures the relative residual oxygen atom concentration.
Thus a
high probe temperature indicates that few atoms are lost to the walls of the
side arm, whereas a low probe temperature shows that many atoms are lost
to the walls. A t equilibrium, the balance between recombination of atoms on
the side-arm walls and diffusion of atoms from the source maintained an
atom concentration gradient which depended in a known way on the
recombination coefficient of the side-arm walls, the temperature, and the
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80
overall pressure. The evaluation of the catalytic efficiency of the tube wall
was therefore based on a mathematical analysis of a model in which the
recombination (loss) of atoms at the walls is balanced by the diffusion of
oxygen atoms down the side arm from an atom source of constant intensity.
The efficiency or the coefficient of recombination, y, is a measure of the
fraction of the collisions of oxygen atoms at the surface which led to their
recombination.
Like most gas-surface reaction of this type, the recombi­
nation of oxygen atoms was found to be a first-order process.
Employing a similar apparatus as that of Linnett and Marsden, Greaves
and Linnett!103-105! examined the efficiencies of recombination at room
temperature for numerous surfaces, including metal, non-metal, oxides, and
salt surfaces. Dry electrolytic oxygen was used to produce atoms by a rf
generator controlled at 14 M H z and with power output at 50-100 W. Most of
the surfaces were prepared by vacuum evaporation, the material to be
evaporated being coated on a tungsten wire located coaxially in the glass tube,
either as soluble salts, hydrides, metal wires or ribbons. A ll of the oxides,
except those of aluminium, silicon and boron, were produced by heating the
corresponding metal surfaces to 550 °C in pure dry oxygen. Boron oxide was
prepared by coating the tube w ith boric add and dehydrating it by heating to
450 °C in dry oxygen. Alum inum and silicon oxides were obtained in the
form of tubing.
The results of their determination for y using the
geometrical area of the tube wall are tabulated in Table 4 below.
Dickens and Sutcliffe 11061 also used the side-arm technique to study the
rate of recombination as w ell as the temperature coefficient of the
heterogeneous recombination of oxygen atoms on a variety of oxide surfaces.
The measurements were performed over the temperature range 300-650 °K.
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81
The surface areas of the films used in the investigation were measured by
krypton adsorption at liquid-nitrogen temperature in a B.E.T. apparatus. The
sample surface appeared to be non-porous and the surface areas were
approximately geometric. The recombination reaction was again found to be
first-order w ith respect to gaseous oxygen atoms on all the surfaces in the
temperature ranges used. Their room temperature results are listed in Table
4 for comparison. Catalytic recombination were found to occur rapidly and
required small activation energies (usually less than 10 Kcal/mole).
By utilizing the paramagnetic properties of oxygen, Krongeleb and
Strandbergt107! monitored the recombination reactions taking place in the
cavity of a paramagnetic resonance spectrometer. Following the course of
the reaction by observing the intensity of the absorption, they were able to
measure the oxygen concentration in recombination studies more accurately
than by means of introducing a metal probe into the system and measuring
the temperature rise that resulted from the heating by oxygen atoms
recombining on the probe. The result of surface recombination coefficient of
oxygen atoms on a quartz surface, y = 3.2 x 10-4, was consistent with the
works mentioned above. The gas phase recombination of oxygen atoms was
also shown to be negligible for the experimental pressures used in these
studies.
The recombination reaction is obviously highly sensitive to surface
composition.
The efficiencies w ith which these surfaces catalyze the
recombination of oxygen atoms range from 10"4 to 1(H.
The activity,
however, cannot be related to any single parameter associated w ith the
surface material though some trends can be observed.
A ll of the metals
examined were more active than the non-metals that have been studied.
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82
Table 4
Summary of numerical values for the recombination coefficient
of oxygen atoms for various surfaces at room temperature. Data
from [103-105,106].
Classification
Metal
M aterial
silver
copper
iron
Non-metals
Halides
Recombination coefficient, y
ref. [103-105]
ref. [106]
2.4 x 10- 1
1.7 x 10-1
3.6 x 1 0 -2
—
x
—
—
nickel
gold
5.2 x 10-3
magnesium
2.6 x 10-3
bismuth
2 .2 .x 1 0 - 2
—
antim ony
2.7 - 8.2 x 10- 4
—
arsenic
0.81 - 4.6 x lO- 4
—
selenium
1.7 x 10-4
—
phosphoric acid
1.2
x 10-4
—
lithium chloride
1.9 x 10-3
—
potassium bromide
1.3 x 10-3
—
potassium iodide
0 .7 4 -3 .5 x 10-3
—
barium chloride
0.57 - 1.9 x 10-3
—
sodium chloride
potassium fluoride
9.4 x 10-4
9.2 x 1(H
potassium chloride
7.8 x 10-4
—
rubidium chloride
4.5 - 24 x lO" 4
3.4 - 16 x 10-4
—
—
2 .8
cesium chloride
1 0 -2
—
—
—
—
(Continued on next page)
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83
(Table 4 continued)
Oxides
alum inium
1.8 - 3.4 x 10-3
—
gallium
1.3 x 10- 4
6.3 - 28 x lO" 5
—
1.0 x 10-3
—
—
germanium
6.3 - 58 x lO" 4
1.3 x lO" 4
silica
1 .6 -7 .1 x lO" 4
3.5 x lO" 4
-
molybdenum
1.7 x 10- 2
1.0 x 10-3
chrom ium
2.5 x lO" 4
2.0 x lO" 4
magnesium
3.5 x 10-3
1.1 X 10-2
calcium
1.6 x 10-3
—
copper
2.0 - 4.3 x lO- 2
4.5 x lO" 2
boron
tin
lead
tungsten
manganese
nickel
1.3 x lO" 2
—
—
-
2 .0
x 10-3
1.5 x lO” 3
7.7 - 8.9 x lO" 3
5.2 - 8.2 x lO- 3
8.5 x lO" 3
cobalt
4.9 x 10-3
-
vanadium
4.8 x lO" 4
-
zinc
4.4 x lO- 4
5.9 x lO" 4
iron
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84
Moreover, the most active surface appears to be associated w ith the
transition metals, next come their compounds (e.g. oxides), and then,
dielectrics and salts.
A s
re g a rd s
s ilic a ,
a n d
m o re
a c tiv e .
T h e s e
s tu d y
e x p lo r e d
fo r
m a y
s u g g e s te d
fr o m
T h e
le s s
in
o f
th e
tr a n s it io n
s h e ll
c o n f ig u r a tio n
e it h e r
T h e
e m p ty
d o e s
e le c t r o n
p e r io d ic
w e ig h t
th e re
G a 2 C>3 ,
d3
o f
i.e .,
a s
s o m e
w a s
to
th e
C u
z in c
p la s m a
a n d
r e s u lt
in
T a b le
g la s s
th e
b y
e x p e c te d
b e
w a s
a ttr ib u te d
d - s h e ll,
(C u O ).
w a s
d0
i.e .,
tr a n s it io n
c o r r e la tio n
e le m e n t
a
th a n
th e
( V 2O 5)
to
a s
b e
a n d
b e
T h e y
b o u n d
a to m .
T h e
fo r
o n e
to
in c r e a s e
th e
d-
r e s u lt
d 10
(Z n O ).
th e
o th e r
w it h
g ro u p
a s
th e
a c t iv it ie s
a c tiv it y
te n d s
th e
o f
th e
th e
a to m ic
e le c t r o p o s it iv e .
A I 2O 3 w a s
M g O
o f
ill
a c tiv e .
lo w e r
a n y
a n d
th e
in c o m p le t e
in
PbC>2,
o f
o x y g e n
s u c h
th a t
in s ta n c e ,
th e
la c k
lo o s e ly
m o re
th o u g h t
m o re
to
o x id e s . ^ 1 0 3 !
T h e
c a t a ly t ic
b e c o m e s
F o r
th e
m e t a l o x id e s , o n
o f th e
in d ic a te s
e ffic ie n c y
a c tiv e
d9
to
th o s e
a re
c o n s is te n t w it h
a n o th e r
to
s t a b le
s u b je c t w
w a s
th e
o x id e ,
tre n d
fo r
re m o v e d
r e p la c e d
b e
4
a n d
a to m
le s s
a n d
o f th e
fo r
( b o r ic
o p p o s ite
re a s o n
o n w a rd s
e x c e p t io n s .
m o re
e x a c t
a re
K n o w lto n I14!
(M n C > 2) a n d
a ls o
r e c o m b in a t io n
w h ic h
T h e
s o o n
S to n e t108! o n
4
b y
e n e rg y
o f t r a n s it io n a l m e t a l o x id e s
fille d
s im p le
a n
o x y g e n
th e n
M n
fro m
T a b le
w e re
S n 0 2
a c tiv it y
c o m p le te ly
n u m b e r.
th e
w o u ld
a n d
w o r k
in c r e a s e s ,
H o w e v e r,
th a n
o r
a n
b e in g
fr o m
n o t s u p p o rt a
t a b le
s u rfa c e s
c a tio n s
v a n a d iu m
T h e
M a rs d e n
lo s s
th o s e
m a te r ia ls .
p re s e n c e
a n d
th e
e le m e n ts
e x p e r im e n ta l
h a n d ,
d
in
o x id e
o x id e s
o f
s h o w e d
c h a p te rs .
th e s e
fo r m a tio n
le a s t a c tiv e , w h ile
th e
c a ta ly t ic
la t e r
o b s e rv e d
to
L in n e tt
e x o th e r m ic
h ig h e r
m e a s u re m e n ts
la t e r
s u rfa c e ,
h ig h
w it h
o b s e r v a tio n s
d u e
th a t w it h
p a r t ic u la r ly
o f
th e
o n e s
v a r io u s
b e
fu rth e r
c o n c lu s io n
o n e
a re
th e
te m p e ra tu re
p a r a lle lis m
th e
o x id e s ,
a lu m in a )
s p e c im e n
p re s e n t
to
w a s
m o re
a c tiv e
m o re
a c tiv e
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85
than CaO. Catalytic activity also declined in the series LiCl, NaCI, KC1, RbCl,
and CsCl.
Chemical effects of atomic oxygen were also observed for some of these
surfaces. The surfaces definitely affected by atomic oxygen were silver, which
was converted to black peroxide, selenium, which became selenium dioxide,
and potassium iodide, which converted to potassium oxide and iodine. The
order of activity for the metals copper, iron, nickel, and magnesium is the
same as the order of the oxides. The order of nickel and iron oxides are
reversed, but since both have comparable activity this difference is not very
serious. This suggests that the metal surfaces become covered with an oxide
film though this may be different from the bulk oxide. The unusually high
activity of MgO measured by Dicken and Sutcliffe was questionable because
the sample had a lower purity than die other oxides.!106!
Data for the recombination of atomic nitrogen was scarce.
Prok!109!
reported measurements of the catalytic efficiency of several surfaces for
atomic nitrogen by a technique which utilizes a coated glass-bead thermistor
placed in the stream of nitrogen atoms.
Energy released by the
recombination process at the probe thus characterizes the efficiencies with
which platinum, lithium chloride, and lead monoxide surfaces catalyze the
recombination of nitrogen atoms.
vacuum evaporation.
The test surfaces were prepared by
Nitrogen atoms were produced by a microwave
discharge with a 125 W microwave generator operating at a frequency of 2450
M H z. Table 5 contains a summary of the catalytic efficiencies obtained by
Prok. Also included in this table, for comparison, are the works of Smith!101!
and Greaves and Linnett!105! for the room temperature recombination
coefficients of hydrogen and oxygen on some of the same surfaces,
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86
respectively, and a few other measurements, from the literature, of the
catalytic efficiency for the much studied glass surface.
Table 5
Comparison of catalytic efficiency on some surfaces for oxygen,
nitrogen, and hydrogen atoms.
Material
Oxygena
Platinum
Lithium chloride
Lead monoxide
Potassium chloride
Hydrogenb
—
1.9 x 10-3
0 .6 x 1 0 - 2
Nitrogen 0
x
1
2 .2 2
—
7.21 x 10-2
4.52 x 10-2
—
1 0 -2
7.8 x lO"4
0 .2
x lO" 4
—
Silica
7.1 x lO"4
7.0 x lO" 4
—
Pyrex
1.2 x lO" 4
4.6 x lO" 4
7.5 x 10-5 e
1.7 x 10-5 g
3.0 x 10-5 h
x 10-5 f
900x10-4
1.5 x 10-5 i
2.5 x 10-3 k
2 .0
x
10- 5
d
1.8
Aluminum oxide
Teflon
1.8-3.4 x 10-3
2 .1 x 10-3 j
-
1.8
x 10-4 f
—
2.9 x 10-5 g
a J. C. Greaves and J. W. Linnett [ref. 104]
b W. V. Smith [ref. 101]
c G. M. Prok [ref. 109]
d F. Kaufman [ref. 110]
e B. Wood and H. Wise [ref. I l l ]
f M . Green, K. R. Jennings, J. W. Linnett, and D. Schofield [ref. 112]
s R. Young [ref. 113]
hT. Wentink, Jr., J. O. Sullivan, and K. L. Wray [ref. 114]
1 T. J. Herron, J. L. Franklin, P. Bradt, and V. H. Dibeler [ref. 115]
JJ. C. Greaves and J. W. Linnett [ref. 105]
k R. Goulard[116]
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87
O f the surfaces tested, lead monoxide and lithium chloride appear to be
slightly better catalysts for nitrogen atom recombination than oxygen. The
poisoning of the platinum surface upon standing may be the reason for its
poor catalytic activity for nitrogen recombination. There is, in addition to
the effect just mentioned, another poisoning effect many authors use to
intentionally retard or m inim ize the effectiveness of a surface to
recombining atoms. Metaphosphoric acid (HPO 3 ) has been shown to have
very low recombination coefficient for various atoms, y =
1 0 '5
-
1 0 '7,
and
therefore was used as the ideal coating to reduce atom recombination to a
minimum.!54'101'113!
The similarity between y for atomic oxygen, on the one hand, and y for
atomic nitrogen and hydrogen, which are not a normal surface constituent,
on the other hand, for the results on glass surfaces is perhaps surprising.
One would not expect the number of sufficiently displaced lattice oxygen
atoms to correspond simply to the number of hydroxyl radicals replaceable by
atomic hydrogen or nitrogen. Therefore, the similarity in activity may imply
that the surface reaction mechanism is similar.
There is fair amount of
disagreement in the result obtained for the hydrogen recombination on
alumina. Warren!117! studied first limits of hydrogen + oxygen mixtures in a
vessel with various coatings. He was able to assess the relative efficiencies of
the different surfaces both for destroying H atoms and for destroying O atoms
and O H radicals. Warren noted that, in the case of alumina, the surface was
unselective as regards their relative activity to H or O. The scatter in the
values of y indicates that the absolute accuracy of y is doubtful, but they may
be satisfactory as to order of magnitude and as regards to the relative values
for different surfaces.
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88
II. H . Mechanism of Microwave Power Absorption
The mechanism of microwave plasma formation and stabilization is
treated in more detail elsewhere!118"122! and w ill only be discussed briefly
here. The most common method of operating a MEP is to sustain a working
gas in a quartz tube located w ithin a microwave resonant cavity.
The
microwave frequency is ordinarily 2.45 GHz, which has unlimited use for
commercial purposes and also many components such as magnetrons are
available at this frequency. The resonant cavity is simply a hollow metal
container w ith a rectangular or circular cross-section in which a standing
electromagnetic wave is established.
A plasma forms when "breakdown" of a neutral gas occurs at some
critical value of an imposed electric field resulting in the rapid
multiplication of free electrons caused by ionization processes. The rate of
gain of electrons, at this point then, exceeds their rate of loss. Controlling
most of the high-frequency breakdown is the loss by diffusion. Consider an
electron present in an alternating field, represented by E = E0 sin (cot + 8 ),
which experiences a force, F, given by
F = eE = eE0 sin{ cot + 9 )
(45)
where e is the charge, E0 is the maximum field amplitude, co is the angular
frequency, 8 is the phase angle, and t is the time. Since the acceleration of
the electron is the force on the electron divided by the electron mass,
therefore the velocity of the electron can be found by integration and is
expressed as
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89
V
=
V0
+
^y^-[ cos 6
- cos (cot + ©)]
( 46)
where v0 is the electron's initial velocity and m is its mass.
From Eq. (45) and (46) we see that a free electron in a vacuum under the
action of an alternating field oscillates with its velocity 90° out of phase with
the field; consequently, it takes no power, on the average, from the applied
field. The electron can gain energy from the field only by making collisions
with the gas atoms. These collisions changed its ordered oscillatory motion
to random motion, thereby promoting efficient energy exchange between the
electrons and the imposed electric field. This process continues with the
electron gaining random kinetic energy on each collision from the field until
it reaches the ionization energy and is able to make an inelastic collision
with a gas atom. Despite the fact that the electron may move either with or
against the field, it can still continue to gain energy in the field because the
energy absorbed is proportional to the square of the electric field and, thus,
independent of its sign. The rate of energy gained by a single electron from
the imposed field, E (rms), is given byl118l
P = e E vd
(47)
where Vd isthe average electron drift velocity. Thispower gain can also be
expressed in terms of the collision frequency,vc, as^22l
p2 f 2
p = e
- ^
r
(48)
where Ee is the effective field that would produce the same energy transfer as
a steady field.
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90
Thus, for a certain value of the electric field, the gas contained in a vessel
placed in an alternating electric field w ill break down into an electrical
discharge when the production of electrons caused by ionization becomes
equal to the loss of electrons by diffusion to the surrounding walls.
A t extremely low pressures a plasma can not be produced because the
electron makes little collisions with the gas atoms to have its ordered
oscillatory motion changed to random kinetic energy. On the other hand, at
sufficiently high pressures, the mean free path of the electrons diminishes
considerably, the collision frequency becomes so great that an electron is
unable to gain sufficient energy to ionize an atom upon collision. Therefore,
an optimum pressure exists for the efficient energy absorption of the electron
from the field that would result in the formation and stabilization of a
microwave excited plasma.
II. I. Heating Mechanisms
Heating of a solid in contact with a plasma mainly occurs by the direct
heat transfer between the ions, electrons, and neutral species and the
submerged specimen.
In addition to the transport of kinetic energy, the
specimen may also be heated by electron-ion recombination on the surface.
When polyatomic gases are involved, additional heating by the chemical
energy of association between atomic species at the sample surface is
available. Moreover, in a microwave excited plasma, materials characterized
by high dielectric losses are able to couple the microwave energy directly into
the solid, thereby produce internal heating of the material, though the
microwave field w ill be partially screened by the presence of the plasma that
envelops the solid.
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91
II.1 .1. Plasma Heating
The degree of rarefaction plays a major role in determining the heat
transfer mechanism governing the thermal transport processes in plasma
heating. For instance, thermal plasmas, which are characterized by a single
species temperature, typically operate at gas pressures greater than
100
torr.
Thus the heat transfer of a solid immersed in a thermal plasma may be
described by the usual continuum approach used in fluid mechanics and
heat transfer, i.e., the Fourier's conduction law with continuous boundary
conditions may be applied.!123!
In rarefied gas situations, such as those encountered in the hollow
cathode glow discharge, where the pressure is much lower,
~1
torr or less, a
different thermal transport process is seen. The pressure is such that the fast
electrons can traverse through the plasma without colliding with any other
molecule. Heating is predominated by accelerating the electrons through the
low pressure discharge and focusing this beam of fast electrons on the surface
of the specimen.
The heavier plasma species are relatively immobile,
therefore do not contribute to the heat transfer process.
Microwave plasma sintering is normally performed at reduced pressures
between 30 to 50 torr.
For this pressure range, the common continuum
equations or Fourier's laws are no longer applicable.!26'123-124! This heat
transfer regime is also known as "free molecular flow" where plasma species
fall freely through the boundary layer without encountering collisions before
striking the solid surface, i.e., the mean free path lengths are on the order of
the boundary layer thickness. In this situation, another approach which is
based on the kinetic theory may be used.
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92
II. 1.1. a. Thermal fluxes
From the kinetic theory of gases, the one-dimensional number flux, F,
striking a surface is given by the integral:!125!
■I
vx f ( v ) dv
(49)
where vx is the x directed velocity component of a plasma species. The xaxis is perpendicular to the surface. The amount of energy contributed per
unit time by the plasma particles, carrying an average energy e, colliding with
unit area of the surface of a body can be expressed similarly by:
Q = | e vx f ( v ) dv
(50)
=/
where / ( „ )
,
2^
( » £ ) ^
^
^
Contribution to the overall energy transfer process from each of the
plasma species incident on the solid surface can thus be evaluated according
to Eq. (50). Therefore, the energy fluxes transported from the plasma ions,
electrons, and neutrals to the neighboring solid is given by:
Qatom - ”a (
Qion - ”i
)W |[ 2k (Ta - Ts) + yEd]
- T») + Ei +
a * * "
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(51)
<52>
(53)
93
where na, tii, ne = concentration of atoms, ions, and electrons, respectively,
T a, T i, T e = respective species temperatures,
Ty = temperature of the solid in contact with the plasma,
y = recombination coefficient of atoms,
Ed = average energy of atomic recombination,
Ei = ionization energy,
<ps = sheath potential.
The amount of energy transported by the neutrals to the surface of the solid
is described by Eq. (51). Each neutral species carries with it 2kTa of thermal
energy towards the surface. The net kinetic energy transfer is found by the
difference of the incident energy and that carried away by the same neutrals
as represented by (Ta - Ts), in the case of complete thermal accommodation.
The im plicit assumption is that, with complete accommodation, the neutrals
particles reflected from the solid wall reaches thermal equilibrium with it. In
actual cases, complete accommodation is not usually achieved, and the
accommodation coefficient is less than unity.!126! The atom energy flux
equation also includes a term, yEd, to account for the contribution by
chemical energy released during the recombination of atoms at the solid
surface. Since the population of excited neutral species are quickly destroyed
at pressures above 16 torr!127/128!, heating due to the de-excitation of excited
neutrals can be neglected.
Equation (52) represents the energy flux due to contribution by the ions.
Again, the first term inside the closed bracket describes the kinetic energy
difference between the energies of the ion arriving and leaving the solid.
Since the efficiency of recombination and neutralization of ions and
electrons is very high!87!, this additional energy is accounted for by E /. These
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94
ions are also accelerated from deep within the plasma into the sheath by the
negative sheath potential.
The energy contribution due to this presheath
acceleration is relatively small, ~0.5 kTe .I65! Equation (53) represents the
energy flux of the electrons impinging on the solid w all in the presence of a
retarding field established by the sheath.
II. 1.1. b. Electron Density Estimation
As part
ofthe evaluation of the incident energy fluxes of plasma species
transported to a neighboring solid surface it was necessary to determine the
average electron and ion concentration.
Since electron densities for the
present experimental conditions were not measured, therefore their values
were estimated from principles of discharge physics. This method was first
used by Belli129' 133! to model the dissociation process in various gas
discharges.
From the power absorbed by a single electron, P, we obtain the total power
absorbed by a plasma
E P = ne V P
(54)
where V is the volume of the plasma. By combining Eq. (47) and (54) the
average power density can therefore be expressed as
Pd = ^
= ne e Vd Ee
(55)
One very useful set of proper variables commonly used as correlating
parameters in electric discharge physics isf6°!
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95
where p is the gas pressure and A is the characteristic dimension describing
the discharge vessel.
Thus, by introducing the characteristic dimension A into Eq. (55) and
rewriting we obtain
ne _
PdA
'Hur
e v d {p A )\^ )\
(56)
Since the electron drift velocity is usually correlated to the ratio of the
effective electric field to the gas pressure
But, the ratio E / p is commonly expressed in terms of the product of pA and
ne A 2 1120], e#g.
^
However, when neA »
= / {pA ,ne A 2 )
(58)
109 , E /p becomes
(59)
Therefore, the right hand side of Eq. (56) is a function of pA alone,
(60)
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96
Hence, the electron density can be determined by knowing only the average
power density, gas pressure and temperature, and radius of the discharge
tube.
II. 1.1. c. Electron Temperature Estimation
It is also necessary to evaluate the average electron energy in order to.
determine the amount of thermal energy transported to the solid in contact
w ith the plasma.
The electrons are assumed to have a M axwellian
distribution. It is thus legitimate to talk about the electron temperature. The
mean energy of electrons is found by making a simple energy balance on the
electron.!60!
If an electron loses in one collision on the average a fraction k of its
energy, the energy lost in elastic collision is the product of k, the mean
‘electron energy, e, and collision frequency, vc,
energy loss =
k
e vc
( 61 )
Therefore, by balancing the energy of electron gain from the field and the
energy loss by collisions, we obtain
e Ee Vd =
k
e vc
( 62 )
But, the collision frequency is related to pressure by
vc = p Pc c
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( 63)
97
where Pc is the probability of collision and c~ is the random velocity of the
electron. Also from the relation va / c" ®
an(^ ^y rearrangement, Eq.
(62) becomes
(64)
Thus,
( 65)
Once the value of E I p is known for a given value of pA it is possible to
estimate the average electron energy, e .
II. 1.2. Microwave Heating
Depending on the dielectric characteristics of the sample material being
heated, microwaves can also contribute to the overall heating of specimens
during the plasma sintering process.
Basically microwaves are electromagnetic energy waves that consists of
electric and magnetic field components. They have a frequency range of 300
Mhz to 300 G H z with corresponding wavelengths ranging from 1 m to 10' 3
m. Microwaves are coherent and polarized and obey the laws of optics, so
that, depending on the material properties, they can be transmitted, absorbed,
or reflected.
The heating of materials is made possible by exploitation of these wave
characteristics and material properties, as shown in Fig. 14. Many electrically
insulating ceramics such as A I 2 O 3 , MgO, and SiC>2 are transparent to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AA/WWV
/V \/W v w _
M aterial typ e
P en etratio n
TRANSPARENT
T o ta l
(Low loss
insulator)
OPAQUE
None
(Conductor)
(R e fle c te d )
ABSORBER
Partial
to T o tal
(Lossy insulator)
ABSORBER
/W
Figure 14.
®
:*
(M ixed)
(a) M atrix = low loss insulator
(b) F ib e r/p a rtic le s /a d d itiv e s =
(absorbing m a te ria ls )
Partial
to T o tal
Schematic of the interaction of microwaves with materials (after Sutton [134]).
co
00
99
microwaves at room temperatures. However, when they are heated above a
critical temperature these materials w ill absorb and couple more efficiently
with microwave energy. Other materials such as metals are poor absorbers
and reflect most of the incident radiation. Some ceramic dielectric materials
(e.g. C 0 2 O 3 , M n 0 2 , N iO , and CuO) are good absorbers at ambient
temperatures.
Conductive and magnetic phases can also be added to
transparent ceramics to enhance or selectively absorb microwave energy into
the material.
Heating by microwaves is due to loss mechanisms induced by
microwaves penetrating and propagating through a material. The primary
loss mechanism and perhaps the most familiar is the dielectric loss.
The
applied electric field generated w ith the material is able to polarize or rotate
charge complexes such as dipoles. The resistance to these induced motions
due to inertial, elastic, and frictional forces cause losses and attenuates the
electric field, resulting in internal heating of the m aterial.
Other less
important loss mechanisms include conductive and magnetic losses.
The most im portant parameters that influence microwave power
absorption in a given material can be seen from the following approximate
expression of the average absorbed power per u n it volume for a non­
magnetic material,
P = cr \ E \ 2 = 2n fe 0 e'r tan 8 \ E \ 2
where | E | = magnitude of the electric field in the material,
cr = total effective conductivity,
= a (ionic) + <r (dipole),
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(66)
100
/
= frequency,
Eo = permittivity of free space,
e,. = relative dielectric constant,
tan 8
= loss tangent.
Equation (6 6 ) shows the general relationship between pertinent variables
where the absorbed power varies linearly with the frequency, the relative
dielectric constant, the loss tangent, and the square of the electric field in the
material.
Moreover, these four factors are all interrelated in a complex
manner during the ongoing dynamic heating process.
During heating
e,,
and
ta n 8
change with temperature. The value of £,.
can be taken is a measure of the polarizability of a material in an electric
field, whereas the
ta n 8
describes the losses w ithin the material as the
microwaves penetrate through the absorbing medium. Figure 15 shows the
slow increase in the dielectric constant with increasing temperature for a
variety of ceramics. Hoi136! attributes this increase with temperature to the
increase in the polarizability due to an increased volume by thermal
expansion In contrast to Ej, the loss tangent exhibits a greater dependence on
temperature as evident in Fig. 16. In addition to intrinsic losses within the
grains, the rapid increase in
ta n 8
for polycrystalline ceramics is interpreted
by the associated softening of intergranular phases, resulting in a rise in local
conductivity.^136! This would explain why a pure material is less affected by
temperature.
The variation of the dielectric losses with temperature has an important
bearing on the the present work. Most of the insulating materials do not
absorb any appreciable microwave energy when they are cold. Since plasma
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101
Temperature (°C)
200
600
1000
1400
12
11 — 99%
pure
c
CO
10 I - Al20 3
w
c
o
o
o
o
0)
0)
(>1)
9
7 _
5
a:
4
0)
Pyrolytic Si3N4 r 3-15 g/cm3
6
JO
*3
97% pure Al20 3
8
3
9606 (Glass-ceramic)
^ r o ly tic b n ° 2,45 9/cm3 Reaction-bonded Si3N4
"
-* 2 .1 4 g/cm3
7 *2 .0 6 g/cm3
'^Hoi-pressed' blN
.94 g/cm3 ‘
2%Fused silica^
20%|(porosity) slip cast
I
I
I
1000
2000
3 00 0
Temperature (°F)
Figure 15.
Variation of relative dielectric constant (8 to 10 GHz) on
temperature (from Walton [135]).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Temperature (°C)
Loss tangent (tan 6)
200
1000
600
1400
0.0 1 0
Hot-pressed BN:
Pyrolytic Si3N4
0 .0 0 8
S iO ;
0 .0 0 6
9606 (G lass-ceram ic)
99 + % pure
0 .0 0 4
^ AI2O3
0 .0 0 2
Pyrolytic BN
0
0
500
1000
1500
2000
2500
Temperature (°F)
Figure 16.
Loss tangent (8 to 10 GHz) as a function of temperature (from Walton [135]).
103
sintering is a high temperature process, significant heating can occur at high
sintering temperatures, and in some cases result in catastrophic thermal
runaway, in which tan 6 increases w ith temperature, thus absorbing more
power and converting it to heat, thus increasing tan S, and so on, until the
sample melts.
The process of energy absorption also depends on the material's "skin
depth" or the depth where the field is attenuated by
1 /e
of its value at the
surface. This depth, 6, is given byl137l
-l
S =
for -2 - »
coe
1,
5 =
where
(67)
I
....
i nf/ I a
(0
= frequency in radians/sec,
H
= permeability,
( 68 )
e = dielectric constant.
Thus, the degree of transparency to electromagnetic radiation w ill be
determined by the frequency, specimen size, and material property. Figure 17
shows the variation of skin depth as a function of conductivity at a frequency
of 2.45 GHz. For high values of conductivity, the skin depth is dominated by
ohmic losses and is approximated by Eq. (6 8 ). For materials that have low
conductance, i.e., lossy mediums, other forms of dielectric losses set in and
the dependence of skin depth on the conductivity is described by Eq. (67).
Since plasma is also a conductor, this effect was manifested during
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104
5
4
2
1
Log
8
(cm)
3
0
-1
-2
-3
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
Log a (Q-cm ) ' 1
Figure 17.
Variation of skin depth as a function of electrical conductivity.
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105
microwave penetration measurements using an E-field probe immersed in
gas plasmas of varying conductivities.
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CHAPTER i n
EXPERIMENTAL APPROACH
III. A. Experimental Apparatus
The m ain components o f the microwave excited plasma system are
shown in the schematic diagram in Fig. 18. Tw o systems were used during
the course of the microwave plasma sintering experiments. The first was a
m odification of that used by Lynch!20! and Kem erl15!.
The earliest
experiments with sintering of ceramic rod samples used a Raytheon power
generat or* having a m axim um available power of 800 W.
In latter
experiments, the microwave generator used was a Reeve power source**
capable o f delivering up to 2.5 kW. Both of these generators operated at an
nominal output frequency o f 2.45 GHz in the pulsed mode where the
amplitude of the microwave output is varying at 120 Hz, corresponding to
the full-w ave rectified 60 H z supply voltage.
Microwave energy fed by the generator passes through a circulator and a
series o f rectangular waveguides to a tapered rectangular m icrowave
applicator***, which is term inated by a short. Neither a coupling aperture
nor a tuning device was used in the system.
A 16 mm i.d. fused quartz
discharge tube situated in the reduced height portion of the applicator at a
M odel No. PGM-100, Raytheon Manufacturing Co, Waltham, M A
Reeve Electronics, Chicago IL
*** M odel No. FC 7097-1001001, Raytheon Manufacturing Co, Waltham, M A
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Manometer
U
Calorimeter
A
Discharge
Tube
Oil
Trap
Pump
Generator
*1— T Waveguides
Circulator
Needle Valve
Bellows
Valve
T
Flow
Meter
Oil
Reservoir
Figure 18. Schematic of the reduced height microwave plasma sintering system.
A
Gas
108
position 1 /4 wavelength from the terminal short, such that the localization
of the electric field was well suited to the production and maintenance of a
plasma.
To safeguard the operator, two cylindrical brass tubes, often referred to as
beyond cutoff or choke tubes, enclosed the discharge tube on either side of
the applicator to contain the microwave radiation effectively.
Small pin
holes along the beyond cutoff housing permitted the observation of light
from the discharge region.
The circulator diverts the power reflected from the applicator to the
calorimeter, thus avoiding possible interaction between the applicator and
the generator.
The calorimeter measures the amount of reflected power
from the applicator.
Since the microwave plasma is a moderately high temperature discharge,
cooling of the quartz chamber was necessary. Two cooling systems were
employed. The first one directed compressed air at the discharge tube in the
narrow portion of the applicator, since the plasma is generally confined to
this region.
With the Reeve generator installed, better cooling had to be
provided. Because of inadequate cooling of the discharge tube at high power
levels, several quartz tubes, which melt at ~1400 °C , developed m elting spots
in the gap region of the applicator. In all subsequent experiments, the quartz
plasma tube was cooled by a vacuum pump oil*, which is transparent to
microwave energy. Thus, oil cooling was implemented by way o f a cooling
Fisher brand mechanical pump fluid #19, Fisher Scientific, Pittsburgh, PA
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109
jacket, w ith the low loss oil flow ing through the annulus between the
discharge tube and the jacket tube.
An outer quartz tube 22 mm i.d. was inserted over the discharge tube to
contain the mechanical pump o il.
The fluid was driven by a 1 h.p.
centrifugal pump* which circulates the coolant through stainless steel pipes
from a 5 gallon capacity oil reservoir. With five coils of 0.5 in diameter
copper tubing immersed in the pum p oil, the reservoir also serves as a near
ambient temperature heat exchanger.
The working gases employed in the microwave sintering experiments
were of ultra high purity grade and was used straight from the cylinder
regulated at 10 psi gauge pressure. The volume flow rate was controlled at
approximately
1
ml/sec by a needle valve placed before the entrance to the
plasma chamber.
The system pressure was m aintained by adjusting the
outflow to the pump and m onitored by a manometer positioned
immediately to the downstream side of the discharge tube.
In addition to the microwave system, both the induction coupled plasma
and hollow glow discharge units were employed in the sintering of SiC and
TiB2 . The ICP apparatus offered a greater power capability than the MEP for
firing silicon carbide; for instance, it can provide voltages up to ~10 kV and
current up to about 4 amps. Being electrodeless, it also provided a clean
plasma environment, avoiding contamination from electrode material. The
rf plasma is produced by using an induction coil wrapped around the plasma
chamber.
Radio frequency current passing through the coil creates an
Eastern Industries model J-34D, Hammden, CN
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110
alternating magnetic field which in turn initiates and maintains the plasma.
A more detailed description of the theory and the operation of the induction
coupled plasma can be found in several of the previous ICP sintering studies,
for example, that of Hrdinal23!.
As we have mentioned in the literature survey, specimen heating in the
hollow cathode discharge was accomplished by a focused electron beam. The
geometry of the H C D is such that the trajectories of highly energetic electrons
are directed toward the geometric center of the sintering chamber. Since the
heat transfer mechanism was different from the other two plasma units, the
H C D system was attempted for the sintering of SiC. Pure graphite electrodes
were used in these experiments to eliminate contamination.
Again, for a
better understanding of the workings of the hollow cathode discharge device,
the reader is referred to previous studies by Sanderson!*7!.
III. B. Plasma Characterization
III. B. 1. Langmuir Probe
The determination of electron concentration and temperature is crucial
in evaluating the level of heat transfer between a plasma and an immersed
solid. The electrostatic or Langmuir probe was employed in an attempt to
obtain these bulk plasma parameters.
This technique consists of inserting a small metallic probe of known area
and simple geometry into the plasma. The current is then measured as a
function of applied voltage. Ideally this voltage-current relationship is solely
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111
a function of the properties o f the plasma in the immediate vicinity of the
probe.
Many variations of the technique exist including probes of cylindrical,
spherical, or planar geometry w ith one, two, or three electrode tipsJ138!
Extensive research effort has gone into developing theories to explain the
voltage-current characteristics for the various probe configurations and
plasma conditions.t139l
The present study used a double tip probe in
conjunction w ith an automated Langmuir probe analysis system developed
earlier by Feuersteinl140!.
The system used a microcomputer and associated hardware to obtain the
voltage-current characteristic fo r cylindrical duel tip Langmuir probe. The
current flow ing into each electrode was measured simultaneously as the
probe voltage was varied in steps o f 5 volts through the attached dc power
supply to a maximum value of ±100 volts. The voltage-current characteristic
obtained was then analyzed using the theory of Laframboise, who has
developed an iterative technique for cylindrical probes operating in the
orbital m otion limited regime.
The plasma density, electron temperature,
and sheath voltage were subsequently computed and tabulated. An output
in the form of a plot of the voltage-current characteristic curve was also
generated.
The duel tip Langmuir probe systems were constructed with 0.322 cm
diameter, double alumina housing.
Pt wires, 0.025 cm in diameter, were
used as the electrode material in the double probe. The length of the exposed
probe w ire which was immersed in the plasma measured 2.2 cm. Fig. 19
shows a schematic wiring diagram for the probe. The dimension of the wire
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112
Probe 1
Probe 2
Alumina Housing
Variable Voltage
Source
Figure 19.
Volt Meter
Schematic of a Langmuir double probe circuit.
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113
used was such that the probe radius is comparable to the Debye distance so
that Laframboise's analysis of the orbital motion lim ited regime is applicable.
III. B. 2. Plasma Length
The gas plasma is distinguished by the characteristic optical emission as a
result of electronic transitions involving ionization and excitation processes.
The glowing region was found to be strongly affected by operating conditions.
The determination of the discharge volume was undertaken because this
information was needed for the interpretation of the sintering data.
Since the visible glow is actually not very well defined, a simplification
was made by assuming that the plasma may be represented by the volume
occupied by a cylinder with diameter equivalent to the inside diameter of the
discharge tube and length of that of the visible glow. The lengths for various
gases were measured by using the luminous portion of the plasma.
Thus, plasma lengths were evaluated for He, H 2 , N 2 , and O 2 for a large
range of power levels, 100 to 1700 W, at three pressures, namely, 5,25, and 40
torr.
III. B. 3. Plasma Power Absorption
The amount o f microwave power available from the generator was
obtained by varying the anode current of the magnetron. The actual value of
the incident power, P; , entering the applicator as a function of the anode
current was measured by connecting the calorimeter to the port of the
circulator normally feeding the applicator (see Fig. 18). The other port was
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114
then shorted. Transmission losses in the circulator were taken into account
by having it remain in the circuit between the applicator and the calorimeter.
Thus, the measured P/ was actually the output power after the circulator.
The calibration curve is shown in Fig. 20.
Since the present microwave plasma system does not utilize any sort of
coupling device, power absorption is determined strongly by the properties of
the plasma.
The amount of power reflected from the whole applicator
structure was determined by measuring the inlet and the outlet temperatures
of water flowing through the calorimeter at a fixed flow rate. The reflected
power Pr was then calculated from,
Pr = ih Cp (t 0
T j)
(63)
where m and Cp are the mass flow rate and the heat capacity of water,
respectively, and T0 and Tj are the respective outlet and inlettemperatures.
W ith negligiblelossesin the circulator and a knowledge of
the amount of
the reflected power, the power absorbed by the applicator can be
approximated by
Pa = Pi - Pr
(64)
Since the discharge is the major sink for the absorption of microwave energy
in the applicator, the power absorbed in the plasma may be assumed to be
\
equivalent to that absorbed by the whole applicator structure.
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115
Incident Power (watts)
2000
1500“
1000
-
500-
0
200
400
600
800
Anode Current (mA)
Figure 20.
Microwave power output as a function of the magnetron
anode current of the Reeve generator.
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116
In addition to the plasma, power absorption characteristics was expected
to vary with the placement of a load such as a ceramic solid into the
applicator.
Moreover, w ith the insertion of various ceramic materials,
power absorption should also change as dielectric properties change with
composition.
Thus, power absorbed by the plasm a/solid system was
determined by measuring the amount of microwave power absorbed by the
calorimeter, which was on the usual arm of the circulator, as in the case of an
empty cavity.
III. B. 4. Plasma Power Density
The determination of power density was not only important for making
comparison among the four gases but also allows us to calculate the electron
density and temperature from the principles of discharge physics. These
were otherwise unattainable in the present study.
By assuming uniform power distribution over the length of the visible
glow region, the average power density was determined by dividing the
measured absorbed power by the plasma volume. In reality, however, the
power distribution had a higher electric field strength in the narrow portion
of the applicator.
An average power density of 25 W / c m 3 was used in subsequent sintering
studies. This power density was chosen because it could be attained in all
four gases at a pressure of 25 torr.
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117
III. C. Specimen Preparation
III. C. 1. Powder Materials
In itial experiments were performed with rod samples of AI2 O 3 *, SiC**,
and Si3 N 4 *“ . The AI2 O 3 powders used were CR30 which is a mixture of a
(~ 6
m2 /g m ) and y (~125 m2 /g m ) aluminas with an average B.E.T. specific
surface area of 30 m2/gm and a spherical equivalent diameter of 0.05 pm.
The success of the plasma sintering of ceramic oxides as seen in prior
sintering studies!6'23! as w ell as initial experiments w ith alumina in this
work prompted examination of carbides, nitrides, and borides. High purity
submicron a (~0.6 pm) and P (~0.7 pm) silicon carbide powder compacts were
tested in the MEP and ICP systems. As densification aids, amorphous boron
and polyphenolene resin were added to these SiC powders.
concentration was approximately
0 .6
The boron
wt% and the free carbon content was
about 2 wt%. A feasibility study was also conducted on submicron silicon
nitride and titanium diboride powders.
In the sintering studies of the effect of sample composition on specimen
temperature w ith thimble shaped ceramics, a variety of submicron powder
particles of oxide and non-oxide ceramics were examined.
measures
8
mm in diameter and
11
The thimble
mm in height and provides a hollow
Baikowski Int'l Corp., Charlotte, NC
Superior Graphite Co., Chicago, IL
Herman C. Stark Inc., New York, NY
*** Ibid.
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118
cavity for temperature determination by optical means. Except for Z 1O 2 , pure
specimens of A I2 O 3 , Fe2C>3, M gO , NiO , Ti0 2 , ZnO, and SiC were used without
dopants to eliminate any additional heating effects due to dopants. Partiallystabilized zirconia with 3 mole% of yttria was used. These materials were
selected because they represent a wide range of electrical, magnetic, and
physical properties and because of their technological importance.
Moreover, various undoped samples of alumina, magnesia, and titania have
been fired successfully in the plasma, but their heat transfer characteristic
have not been evaluated quantitatively. Since Y 2 O 3 , MgO, TiC>2 , and NiO
were used to investigate the effect of dopants on the sintering of alumina,
their individual heating characteristics relative to alumina were also of
interest.
During prelim inary experiments, y ttria was found to heat
excessively such that melting would occur under conditions that produced
only moderate heating fo r the other materials.
Therefore, Y 2 O 3 w as
discontinued from this study. These powder materials were acquired from
various manufactures. Powder specifications are listed in Appendix A.
III. C. 2. Binder and Dopant Addition
To increase the strength and sinterability of the green compact, binder was
added to both doped and undoped powders.
A solution of 3 wt% of
polyvinylbutyral (PVB)* dissolved in acetone was added to the powder. The
resulting powder slurry was thoroughly mixed by kneading in a plastic bag to
maintain good dispersion of the PVB and then allowed to dry in open air at
room temperature.
Monsanto B-76, St. Louis, M O
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119
Doping of powder w ith MgO was accomplished by adding appropriate
amounts of an aqueous solution of Mg(NC>3 ) 2 *6 H 2 0 to the as-received
powders.
Since the identical mixing procedure was employed to ensure
good dispersions in both the binder and dopant addition, the concentrated
nitrate solution was typically added in the same step as the binder. The
magnesium nitrate was calcinated to MgO during the binder burnout stage.
III. C. 3. Pressing of Rods
Powders prepared in the manner described above were ground in a
mortar and pestle and sieved through a 60 mesh screen (250 jxm opening)
prior to pressing into rods.
Sample rods were made using a wet bag
technique. Clean latex rubber tubing approximately a foot in length, coated
w ith PEG 400* on the interior, was knotted at one end and secured with a
piece of wire while the other end was stretched through a perforated brass
tubing and folded over the sleeve. The pin holes allowed the latex tubing to
be drawn against the inside of the restraining brass tubing when the sealed
chamber, in which the brass tube sits, was evacuated. Mounted in a modified
vibrator, the whole assembly was vibrated at 120 H z during packing of the
powder. After filling, the tubes were carefully capped with brass plugs and
isostatically pressed to 40,000 psi. The resulting rod diameter depended on
the amount of powder. Typically the rod specimens varied from 4 to 5 mm
O.D. and were 20 cm long.
P-167 Polyethylene Glycol 400, Fisher Scientific, Pittsburgh, PA
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120
III. G 4 . Pressing of Thimbles
Ceramic thimbles were prepared using two sets of stainless steel die
assemblies. One set was used to produce a thimble shaped polyurethane
mold.
The mold was formed by pouring a thermal set polymer into a
stainless steel die assembly consisting of a highly polished mandrel and a
hollowed mold having contours proportioned to yield the shape of a
thimble. The second set of the stainless die assemblies, which is sketched in
Fig. 21, was used to make the actual thimble specimens. The polyurethane
m old then served as the actual mold into which powders were filled.
A
m iddle mandrel, the powder feed mandrel, w ith six holes drilled equally
apart around its periphery at the bottom was made to seat on the shoulders
of the urethane mold and become flush w ith the side walls of the mold.
This assembly was then mounted in a vibrator, which was a modified
micromill, to facilitate fillin g of the powder into the thimble shaped pocket.
After filling, the top mandrel affixed with six rods, was slipped on top of the
powder feed mandrel to plug up the holes. Extra wide rubber bands were
wrapped around the metal-rubber junction to prevent slippage and screwed
tightly to ensure good O -ring seal. Thimble shaped specimens were also
pressed isostatically to 40,000 psi. The resulting thimbles had dimensions of
8
mm I.D., 11 mm O.D. and 11 mm in height.
III. C. 5. Binder Burnout
Pressed ceramic specimens were pre-sintered at 650 °C in air for
1/2
hr to
burn out the binder and permit conversion of the magnesium nitrate to
M gO for doped samples. Thimble specimens, in particular, were polished
after firing to remove thin metallic coatings and irregularities found on the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ag-ga*
Powder Feed
Mandrel
o o
Polyurethane
M old
Figure
21.
Sketch of the thimble making assembly.
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122
bottom and allow them to seat better on the sintering stage. Pre-sintered
specimens were kept in a drying oven until they were to be used.
III. D . Temperature Measurement
Two temperature sensing devices were used to measure the surface
temperature of the specimens. An optical pyrometer* was used to measure
the apparent temperature of the rod specimens.
Sintering temperature of
thimble-shaped specimens, on the other hand, were determined by an optical
fiber thermometer (OFT)**.
I II. D . 1. Optical Pyrometer Measurement
The pyrometer measures the steady-state surface temperature by using a
hot filam ent, calibrated against a black body. During the experiment, the
pyrometer was focused on a single spot on the sample rod through one of the
peep-hole tubes located on each side of the applicator. The temperature of
the specimen was indicated when the brightness of the filament was the
same as that of the rod surface. The Leeds and Northrup pyrometer was only
useful for steady-state measurements because the filament brightness had to
be manually adjusted. W ith interference from the luminous plasma and the
variation of emissivity w ith temperature, the measured temperature was
expected to be lower than the true surface temperature.
Leeds and Northrup Model 8626-C, Philadelphia, PA
Accufiber, Inc., Beaverton, Oregon
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123
III. D. 2. Optical Fiber Thermometer
The high-temperature optical fiber thermometry system used to measure
temperature of thimble specimens was especially attractive because of its
rapid response and its immunity to RF interference. The automated OFT
sensor was a closed-end lightpipe design composed of a bare single crystal
sapphire enclosed in a protective sheath.
The sapphire fiber is 1.25 mm
diameter and 300 mm long. It was coupled through an air gap to a fusedsilica optical glass fiber approximately one meter long.
Temperature
measurement was conducted by inserting the OFT into the thimble such that
the lightpipe sensor scanned the inside closed end of the thimble, as shown
schematically in Fig. 22. The sapphire fiber serves as a waveguide to transmit
the radiation from the high temperature sample to the fused-silica fiber.
After the radiation passed through the glass fiber, it was coupled across an air
gap to a lens that focuses it on one or more photodiode sensors.
The
instantaneous surface temperature was determined from the sensor output
voltage and Planck's law .
The system was capable o f measuring
temperatures in the range of 500 to 2000 °C and the manufacture claimed a
resolution of .00002 °C per minute, a precision of 0.2 °C, and an absolute
accuracy of 1 °C at 1000 °C and 3.25 °C at 1500 °C. Data sampling rate was set
at one reading per second.
The length-to-diameter ratio of the thimble was such that the emissivity
o f the cavity approaches a constant value near unity over the entire
temperature r a n g e . T h e r e f o r e , the effect of emissivity w ith specimen
composition in the temperature measurement was minimized.
However,
after the completion of this study, Hansen!25! discovered that for some
specimens, particularly alumina, the apparent temperatures are biased by the
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124
Gas Flow
Ceramic
Thimble
Plasma
Quartz Tubing
Alumina Stage
Cooling
Oil
Optical
Fiber Thermometer
Figure
22.
Schematic close-up of the plasma tube and thimble specimen
during sintering.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
transparency of these specimens to the wavelength sampled by the OFT.
Thus, the luminosity of the plasma and the background temperature w ill be
factors. The plasmas employed in this study were relatively cool plasmas,
therefore, if any, the OFT reading w ill tend to underestimate the true
specimen temperature. Hence, for solids such as AI2 O 3 , we should consider
its temperature to be only approximate. This however w ill not affect the
conclusions drawn from relative comparisons.
III. E. Density Measurement
Specimen density was measured by immersion in w ater using
Archimedes's principal taking into account the effect of the buoyancy of air.
A small section of a rod specimen or a thimble specimen was first cleaned in
acetone, then rinsed in methanol to remove residue from the acetone. After
complete drying, the specimen was weighed on a precision balance to
determine the dry weight of the specimen.
Then, the specimen was
submerged in distilled water and the open porosity of the specimen
impregnated by boiling the specimen in water for about 2 hrs. The specimen
was subsequently re-weighed with and without a basket suspended in water.
Few grains of a surfactant, usually Alconox detergent was used, were added
to the distilled water to reduced the surface tension between the thread
suspending the basket and the water surface. After various quantities were
obtained, the density of the specimen was calculated following Prokict142!.
The density value is typically expressed as % of the theoretical density, which
generally is the x-ray density.
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126
III. F. Sintering of Ceramic Rods
III. F. 1. Plasma Generation
Prior to the generation of the plasma, the system was first evacuated to
~100 mtorr. The desired carrier gas was then introduced into the discharge
tube and evacuated to flush out any im purity gases that might still be in the
sintering chamber.
When the pressure reached approximately 5 torr, the
flow was stopped and the system was re-evacuated. This procedure was
repeated several times to ensure atmospheric integrity.
When forced air
cooling was used, it was turned on at this point and directed at the sintering
tube. Otherwise, the flow of oil through the cooling jacket would be initiated
at this point.
W ith the pressure at approximately 1 torr, the magnetron
current of the microwave generator was adjusted to yield an output power of
approximately 150 W . A stable plasma was then initiated w ith a Tesla coil.
Pressure and translational and rotational speeds were then adjusted
according to the specific test.
III. F. 2. Sintering Procedure
With a stable plasma established, the pressure and power were set to the
desired values. Sintering proceeded as the sample rod, which was held by a
chuck, was translated into the plasma at a rate between 1 and 4 cm /m in. The
specimen was also rotated at a speed of 60 RPM for even heating to avoid
warpage. Sintering was terminated by slowly cutting the magnetron current.
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127
III. G. Sintering of Ceramic Thimbles
III. G. 1. Plasma Generation
In the sintering study of thimble specimens, the length of the discharge
tube was shorten to accommodate the OFT lightpipe. W ith the discharge
tube completely enclosed in the beyond-cutoff tubes, plasma was initiated
without the aid of a Tesla coil as was in sintering of rods.
Before igniting the plasma, the system was again evacuated and flushed
w ith the working gas at least 2 times.
W ith the system pressure at a
m inim um , a small amount of Ar was introduced and the pressure was
allowed to build up to 1 torr. The output of the magnetron was then slowly
increased to about 200 W when a stable Ar plasma was produced.
Since the thimble specimen was already sitting on the stage within the
sintering chamber, a gas was to be chosen that would permit easy initiation
and would not excessively heat the specimen before the desired value of
power density and pressure could be established. Pure argon was found to be
relatively cool compared to the four gases used in the present study, He, H 2 ,
N 2 , and O 2 . Even under lowest pressures, plasmas of these gases were very
difficult to initiate.
III. G. 2 . Cleaning of Adsorbed Species
Since adsorbed water vapor and volatiles have a significant effect on
plasma sintering!14/18], the presintered thimble specimens were cleaned in
the A r plasma to drive out adsorbed species. After initiation of the argon
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128
plasma, the pressure was raised to about 3 or 4 torr while maintaining the
power at 200 W. W ith the specimen already on the sintering stage, cleaning
took place immediately following plasma generation and lasted until the
water vapor glow disappeared (~5 min). The cleaning temperature in the
low power A r plasma was typically in the range of 800 to 1000 °C.
H I. G. 3. Stationary Heating of Sample
After cleaning the specimen of adsorbed species, power was raised to the
desired value to achieve a power density of 25 W /cm 3. The working gas was
bled into the system to obtain a pressure of 25 torr; at the same time, A r flow
was switched off. Thimble specimens were allowed to sinter statically for a
duration of
10
minutes, so that sufficient time was permitted to attain steady-
state heating temperatures and to record pertinent power absorption
measurements from the calorimeter.
III. H . Conventional Furnace Heating
Since the gas plasmas were observed to etch the samples surfaces and
induce chemical reduction, a comparative study was carried out in a
conventional furnace.
A m uffle tube was constructed from a closed end
A I 2 O 3 tube. Thimble specimens were placed in an alumina boat situated in
the center of the furnace.
Identical gas flow , system pressure, and gas
composition were maintained.
The furnace was programmed to ramp at
80 °C /m in , which was much lower than the heating rate experienced in the
plasma, at ~30°C/s. Nevertheless, the final steady-state temperatures were
matched.
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12 9
III. I. E-field Measurement
III. 1.1. Microwave Probe
From the results of previous sintering experiments, penetration of
microwaves through the plasma gas was thought to play a significant role in
contributing to the heating of ceramic samples. Since the charge density in a
plasma is usually greater than
good conductor.
1 0 9 - 1 0 10
cm-3, it is therefore a comparatively
As a conductive matter, plasma possesses a skin depth,
through which the electric field is attenuated to
1 /e
of its original value.
Thus the thickness of this skin or the effectiveness of the screening depends
on the conductivity of each gas plasma. For a weakly ionized plasma, typical
electrical conductivities ranges from ltH -lO 1 S/m t53'143!, which translates to
skin depths of 0.1-1 cm at a frequency of 2.45 GHz. W ith the envelop of
plasma only 3 mm thick, the greater the degree of ionization the more
probable that the specimen w ill be heated by the plasma rather than
microwaves.
An electric field sensing device with microwave frequency
response was used to confirm this hypothesis and to determine the extent of
the contribution from microwaves to heating.
The present MEP setup made this kind of characterization most difficult
for two reasons. First, the presence of the plasma would m elt if not destroy
any device placed within its high temperature environment. Furthermore,
most crystal detectors designed for microwave frequencies are rated at room
temperatures. Second, the conductive leads of any device that are inserted
into the microwave applicator through the beyond cutoff tubes automatically
form a coaxial configuration which would act as a transmission line for the
microwave field to the rest of the laboratory, thus presenting a hazardous
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130
condition to the operator and those in the laboratory. The success of the
experiment, therefore, hinges on finding extremely high-resistance leads or
low-conductive wires to minimize microwave transmission and providing
adequate cooling to enable field measurement.
Carbon-impregnated Teflon wires (14-20 K Q /ft) generously provided by
the National Bureau of Standards and Technology made the construction of
the present electromagnetic (EM) field probe possible. Since light molecular
weight oil was found to be an excellent cooling medium for the sintering
chamber, the same oil was drawn from the main cooling line and fed into
the inner tube of the probe. Figure 23 illustrate the schematics of such an EM
field probe. The probe features a diode w ith a frequency response range
which included 2.45 GHz and a pair of high-resistance transmission cables for
connecting the probe's outputs to a high impedance voltmeter. Cooling oil
was forced through a 5 mm o.d. quartz tube, w ith a notch at the end to allow
the diode to be securely seated, and exited through the area between inner
tube and the envelop of the containing closed end alumina tube.
Tiny
ferrules allow crimp connections between the diode and the Teflon wires.
III. 1.2. E-field Measurement in an Empty Cavity
Ideally the probe should be calibrated w ith respect to the following
parameters:
1)
frequency response, 2 ) dynamic range, and 3 ) probe isotropy.
In other words, immersing the probe in a calculable or known field
generated through open-ended waveguide or horn antenna. Since we lacked
the means to carry out the above calibration, the probe response was
characterized with the microwave applicator itself with the plasma absent in
the cavity.
This means that exact quantification of how much power is
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131
Plasma
Quartz
Tubes
Carbon Imprignated
Teflon Wire
Alumina
Tubes
Hot Carrier
Diode
DDDD
VA <
Oil Flow
Connecting
Ferrule
N/">
<ys
S/*
Figure 23.
E-field probe for sampling microwave field within the plasma.
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132
delivered to the probe was not possible, though relative differences between
various gas plasmas can be determined.
III. 1.2. a. Probe Characterization
Several probe configurations were tested in order to obtain a good signal
to noise ratio in the empty chamber.
The first configuration was with a
simple low power rating Schottky diode which was placed w ithin the tip of
the probe. To ensure good contact and at the same time to avoid melting
either the diode or the Teflon wire, crimp connections were made between
the diode and the soft Teflon cable. The induced voltage was monitored as
the power from the generator was increased.
However, above about 530
watts of input power, the diode failed due to over heating.
The second configuration was conducted with the diode placed outside of
the probe, because the sole purpose of the diode was simply to rectify the
high frequency a.c. signal to d.c. signal. The pair of high-resistance cables
were simply connected by a single ferrule near the top of the probe. The
diode was preserved in this case. Because of their low conductivity, the highresistance wires did not suffer any damage. Without tuning, the applicator
was inherently poorly matched to the input impedance; in other words,
more than 90 % of the input power was reflected.
In order to improve the induced probe signal, a 3 mm o.d. coaxial line
was used as the third configuration.
The major concern was the
transmission of the microwave energy out of the applicator towards the
surrounding environment.
To m inimize M W energy leakage, aluminum
foils were used to shield the bottom of the lower attachment and the outer
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133
conductor of the coaxial line was carefully grounded in a simple pigtail
fashion. Significant microwave leakage was detected at low power settings.
Consequently, this experiment was discontinued.
W ith the aim of improving induced voltage signal to the probe, a high
power rating point contact diode having frequency response up to 9 G Hz was
employed. This diode has a thick ceramic as its enclosure, as compared to the
glass bead packaging of the Shottcky diode. It too was positioned at the probe
tip, where the field is maximum. Because of its larger dimension, oil flow
was diminished near the tip of the probe, resulting in a impaired detector.
The fourth configuration was attempted using a bare copper wire loop
similar to that of an inductor coil. Thus a thin metal wire bent into a loop as
figure "8 " w ith the lower portion connected to each of the two highresistance wires. The heavier rated diode was connected at the outside of the
probe.
As the input power was increased, the inductive loop became
progressively hotter until the circuit was disconnected at approximately 500
watts. Again, gas bubbles in the oil were observed, indicating extremely
localized hot spots.
Though the signal was less than desired, nevertheless the simple
inverted U loop made up of the high-resistance transmission lines and the
placement of the diode exterior to the probe, the second configuration
mentioned above, provided a workable solution for determining relative
differences in the field penetration.
The result of probe response as a
function of input power in an empty cavity is discussed in the next chapter.
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134
III. 1.3. E-field Measurement with Plasma
W ith the probe in the aforementioned configuration, relative electric
field strengths were measured for various plasmas, namely, He, H 2 , N 2 , and
O 2 plasma. Probe response was monitored with respect to the input power
and gas pressures. Power absorption of the plasma-probe system was also
determined by measuring the power reflected to the calorimeter.
For each plasma, background noise was established first by measuring the
output signal w ith the microwave source power off. After approximately
five to ten minutes, microwave power was raised to some level where
plasma could easily be initiated. At this'point the pressure was ~10-3 torr.
The plasma was established as soon as the designated gas entered the
sintering chamber. W ith the plasma excited, EM field characterization was
conducted for each gas plasma to cover a wide range of power and pressure
settings including operating conditions at which plasma sintering took place.
III. J. Microstructural Examination
III. J. 1. Scanning Electron Microscopy
The effect of plasma processing on the ceramic thimbles was also
investigated by SEM*. Specimens prepared for analysis were obtained by
cutting small notches into the sides of the thimble with a low speed diamond
saw. The notched thimble was then sandwiched between thick layers of
paper acting as a cushion and fractured using a hammer. Small pieces of
Hitachi S-570, Japan
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135
samples, exposing their outer surface morphology, fracture surface, edge of
fracture/outer free surface, and interior surface, were taken from the domed
portion of the thimble.
These specimens were mounted with cement on
standard aluminum stubs, sputtered w ith a thin coating of gold, and
examined.
Samples of thimbles that were fired in the conventional furnace were
prepared in a similar manner and examined in the SEM for comparison.
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CHAPTER IV
RESULTS AND DISCUSSION
IV. A. Preliminary Sintering Trials
The success achieved w ith alumina and magnesia in prior plasma
sintering experiments prompted the idea to undertake sintering of silicon
carbide, silicon nitride, and titanium diboride in a plasma. High strength
and excellent oxidation resistance at high temperatures make dense
polycrystalline silicon carbide a very attractive high performance ceramic
material. Therefore, a major effort was made to sinter SiC in the microwave,
ICP, and H C D systems. The other non-oxide materials were only studied in
either the rf or the dc plasma devices.
IV. A. 1. Sintering of Silicon Carbide
High p u rity submicron a - and p-SiC pow der compacts w ith small
additions of boron and carbon were fired in the MEP.
Prochazka and
others!144-146! showed that simultaneous additions of boron and carbon were
necessary to achieve significant densification of silicon carbide. The role of
boron in aiding densification, though still uncertain, is believed to decrease
the grain boundary tension due to selective segregation, thus favoring the
driving force for densification during firing. Prevalent on the silicon carbide
surface is a thin oxide film incorporated during powder processing. The role
of excess carbon, therefore, is suggested to be prim arily the de-oxidation of
the surface oxide films originally developed on SiC particles.
136
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137
The earliest results indicated the necessity for a carbon rich or a strong
reducing atmosphere that would ensure a low oxygen partial pressure of less
than 10' 8 atm for densifying silicon carbide. Doped sample rods fired under
reduced pressures (35 torr) in nitrogen and argon yielded a gray-colored
coating on the the surface. This was thought to be caused by oxidation of the
SiC surface layers. Two sources of oxygen infiltration into the system were
confirmed when a helium leak detector was employed. A minute leakage
through the copper tubing constitute the majority of the oxygen entering the
vacuum system, whereas the other source of leakage was introduced into the
system during translation of the rod specimens. From the leakage rate the
oxygen partial pressure within the system was estimated to be ~ 1 0 '5 atm,
which is about three orders of magnitude higher than that maintained in a
typical graphite furnace for sintering SiC.C146! Though these two sources of
leakage were subsequently corrected, the integrity of the vacuum system
maintained by a mechanical pump was still inadequate to prevent oxidation
of SiC.
Since creating a carbon rich environment would easily result in
blackening the quartz chamber, ultra- high purity grade gases containing 5 %
hydrogen were used to ensure sufficient reducing atmosphere.
Straight microwave sintering of doped compacts in air, which resulted in
the same exterior appearance, gave further evidence for the occurrence of
oxidation.
W ith increasing sintering tim e the coating grew from a thin
surface layer to a cylindrical annular ring.
Apparently oxidation had
occurred w ith oxygen depleting the free carbon near the surface, leaving a
coat which resembled that of an undoped compact.
Sample rods fired in microwave plasma generated w ith the Raytheon
microwave generator at full power showed no evidence of densification.
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138
The maximum temperature attainable, as measured by an optical pyrometer,
during sintering of SiC was approximately 1300 °C which is about 300 degrees
below that necessary to initiate densification and 700 degrees less than that
required to obtain high densities.
In comparison, an alumina rod fired
under identical sintering conditions in the MEP achieved about 1700 °C .
Though the plasma temperature might be higher than the specimen
tem perature, being tenuous or optically thin, the microwave plasma
becomes transparent to the emitted thermal radiation. In other words, the
em itted radiation was not reabsorbed by the plasma particles but rather
escaped through the volume of the plasma to the surrounding walls. Thus,
having a higher emissivity and being four times more conductive, silicon
carbide was able to dissipate thermal energy away from the hot plasma zone,
resulting in a lower sample temperature.
A simplified calculation reveals that the low er SiC sample temperature
obtained may be reasonable if we account for radiation losses. Assume that
the loss of thermal energy is dominated by thermal radiation and the
alumina and silicon carbide specimens were of the same dimensions. If both
specimens received the same amount of energy input, Q , then the steadystate surface temperature o f the specimen follows from the StefanBoltzmann law
Q = os emT 4
( 7 1)
where <7S is the Stefan-Boltzmann constant, em the emissivity of the solid
surface, and T the surface temperature of the sample. And if alumina was
heated to 1700 °C, then the temperature of silicon carbide heated under
identical conditions can be obtained by the simple relation
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139
T’ 4 -
f e
(72)
) T >4
Thus for emissivities of 0.42 and 0.95 for alumina and silicon carbide!147),
respectively, the predicted surface temperature is about 1300 °C. Therefore,
the observed temperature drop can be accounted for by the thermal radiation
from the specimen.
The 2.5 kilowatt source was subsequently used to boost the power density.
Various gases were used, including A r, He, N 2 , CH 4 , and N 2 / 5 % H 2 . Helium
was thought to provide good thermal conductivity and both methane and
nitrogen balanced w ith 5% hydrogen were used to ensure a non-oxidizing
environment. A variety of gas combination and pressures ranging from 30
torr to one atmosphere were tested. The sintering results of both alpha and
beta SiC in the m odified system under fu ll power showed only a slight
improvement.
The highest density obtained did not exceed
66%
of the
theoretical value compared to the starting green density of about 60%. A
small increase in the flexural strength of the fired rod was noticed when
broken by hand.
Evolution of carbonaceous material from residual polyphenolene resin
used as a source of carbon dopant during the sintering process coated the
discharge chamber, thus hindering any possible optical measurement of
sample temperature. However, judging from the fired densities, specimen
temperature would still be several hundred degrees below that required to
achieve high densities (~ 2000 °C).
Since the ICP!6-9' 14/ 18/2l-23] system also provides high sintering
temperature and a potentially higher power source than the MEP system, the
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140
ICP was used to sinter silicon carbide. Again various gas combinations and
pressures were attempted. In addition, one, three, and four turn coil ICP
configurations were used to find the most efficient firing condition in an
attempt to achieve a high sintered density for SiC.
The best result was accomplished by using a four turn coil and a
combination of gases composed o f A r, N 2 / 5 % H 2 m ixture, and He
pressurized to atmospheric pressure at an anode voltage of 7 kV, plate
current of 2.5 A, and grid current of 25 mA. A maximum relative density of
88.5% was obtained for a sample rod of a-SiC when held in the rf plasma for
a period of 15 minutes.
Typical boron and carbon doped a - and p-SiC rods sintered in the rf
plasma achieved relative densities in the range of 80 to
88%
of theoretical
density. Moreover, sintered rod surfaces usually had a lubricious graphite
film and flakes, which resembled carbon deposits that peeled off easily.
Presumably surface decomposition had taken place where silicon, being
more volatile, was carried into the gas phase leaving the carbon residue.
Temperature measurement, again, was not possible because of the
carbonaceous deposits on the inner w all regions of the quartz tube in contact
with the plasma. Since silicon carbide begins to densify at about 1600 °C, we
would expect the temperature to be somewhat higher but not exceeding
1900 °C. Typical microstructures are shown in Fig. 24 for a and P silicon
carbide.
The dc glow discharge offers another possibility to sinter silicon carbide.
Since the heating mechanism is different, i.e. by way of electron beam
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142
heating, it was thought that sufficient heat can be generated to produce high
fired densities in SiC. The experimental instrumentation and methodology
were described previously by Sandersonl17!. Firing of SiC under a variety of
power conditions in hydrogen at reduced pressures did not produce any
significant densification over the green compact.
Silicon carbide has traditionally been one of the most difficult covalent
solids to process as attested to by this sintering study. The highest attainable
sintered SiC sample rod was less than 90% of theoretical density in the ICP.
Apparently, higher power is needed to fully densify a SiC powder compact by
the plasma processing technique.
A simplified analysis of the radiation
losses leads to a similar conclusion that at least 4 times the present power
generated is required to achieve high sintered densities. As mentioned in
section n , Kijima^28! had used a similar rf plasma system to obtain 96 to 99%
dense SiC compacts. However this was not without paying a price, for more
than 30 kilowatts of input power were used during the process.
IV. A. 2. Sintering of Silicon Nitride
Both the MEP and ICP systems were also used to sinter silicon nitride.
Because the sintering temperature required to achieve a dense Si3N 4 compact
is relatively low, about 1600 °C, and that N 2 gas would be a perfectly suitable
atmosphere, nitrogen plasma was considered as an advantageous means of
sintering silicon nitride.
Sample rods of silicon nitride with additions of 5 wt% MgO as a sintering
aid were fired in both rf and microwave plasma devices. The results showed
that Si3 N 4 has a strong tendency to decompose when heated under reduced
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14 3
pressures. Even when the discharge chamber was pressurized to about 10 to
15 psig, the extent of decomposition did not improve. The fired surfaces of
the sample rods showed evidence of erosion as pits uniformly distributed in
the fired region. Since silicon nitride is generally hot pressed or sintered at
tens of atmospheres of pressure it is not surprising to find decomposition of
Si3N 4 under the present firing conditions. Figure 25 exhibits evidence of this
surface decomposition. The x-ray sampling of a fired silicon nitride surface
shows strong Si peaks dominating the surface features.
IV . A. 3. Sintering of Titanium Diboride
The HCD apparatus was also used to test the sinterability of TiB 2 - Upon
translation of the titanium diboride sample into the dc discharge, a ball of
plasma becomes attached to the tip of the sample rod. W ith about 3 cm
length of the rod inserted into the hollow cathode electrode, the tip of the
sample was heated to incandescence under otherwise identical conditions
which would have melted an AI2 O 3 rod. When translation was ceased the
discharge soon became extinguished. W ithout manipulating any controls, in
about 30 seconds the discharge would be reinstated and begin to heat up the
sample rod again. The o n /off cycle of the discharge continued until further
translation of the titanium diboride caused the plasma to become completely
extinguished. Since TiB2 is a fairly good conductor, electrons necessary to
maintain the discharge were removed, and the dc plasma extinguished itself
because the loss is greater than the production. Insertion of a graphite rod
also resulted in plasma extinction.
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o
VO
co
o
in
C/5
<U
CL)
&b
O)
3
C/5
®
CM
o
o
CD
O
CM
(S 4iim -q iB ) A }is u 0 }iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 25.
C/5
X-ray diffraction pattern of a S 13 N 4 sample fired in an induction coupled nitrogen plasma.
144
145
IV . B. Langmuir Probe Results
The basic parameters which are important in determining the flux and
energy of ions and electrons impinging upon a given surface are usually
undefined.
The aim of using the electrostatic or Langmuir probe was to
measure bulk plasma parameters, such as electron and ion concentrations
and their temperatures, and for calculating heat transfer effects to a
neighboring solid surface, thus, permitting one to interpret the strong surface
interactions observed in plasma sintering. The use of electrostatic probe in a
MEP to measure electron densities has been shown to work w ell for low
power levels, approximately 10 wattsJ148! However, some difficulties have
been encountered at high powers and high temperatures in the present
study.
Some typical results o f the probe measurements are presented in Figs. 26
to 29. In general, the plots exhibit voltage-current characteristic typical of
Langmuir double probes shown earlier in the background section in Fig. 9.
The plateau in the curves represents saturation in the ion current of the two
electrodes as the applied voltage varied from ± 1 0 0 volts. Displayed in the
plots also were the experimental parameters, which include the type of gas,
probe radius Rp, probe length Lp, applied power, and pressure. In addition,
the electron temperature, electron number density, and the plasma potential
were computed and the results tabulated in the plots.
The asymmetry
exhibited in the voltage-current characteristic curve indicate that the current
collection by the electrodes was at variance. Since the duel tip probe was
constructed from the same platinum wire, it is possible that the wire was not
of uniform thickness or the electrodes were not of the the same lengths or
both. If we follow the same designation for labeling the probe electrodes as
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146
RUN GAS Rp
Lp “
POWER
P - 1
1
ARGON
0 .0 2 5 cm
2 .2 0 0 cm
30 W atts
TORR
(MICROAMPS)
m
PROBE
CURRENT
/
j
.
/
C a lc u la t e d R e s u lts
To 21251 K
N - 7 . 5E+009 / c . c .
Ve - - 1 1 . 08 v o lt s
I
L i
_i— i— i.
-100
Figure 26.
i— i— i
i— i— i— — i— i— i__ i— i— i— i— i— i— i__
-SO
0
50
PROBEVOLTAGE(VOLTS)
100
Plot of Langmuir probe data for an argon plasma operated at
1 torr and a constant applied power of 30 watts.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RUN 6
GAS - ARGON
Rp ■ 0 .0 2 5 cm
Lp “ 2. 2 0 0 cm
POWER 6 0 W a tts
P - 14 TORR
-
f
PROBE
CURRENT
(MICROAMPS)
147
}
C a lc u la te d R e s u lts
Te 31875 K
N - 3. BE+009 / c . c.
Vs " - I B . 61 v o l t s
_
u
----1---- 1--- 1----1--- 1--- 1----U—l----1_ __
-1 0 0
-5 0
0
• 50
PROBE VOLTAGE (VOLTS)
Figure 27.
100
Plot of Langmuir probe data for an argon plasma operated at
14 torr and a constant applied power of 60 watts.
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148
1500
RUN 15
GAS - NITROGEN
Rp “
0 . 0 2 5 cm
Lp "
2 . 2 0 0 cm
POWER *
100 W ctto
P - 10 TORR
500
PR03E
CURRENT
CMICRSAMPS)
1000
-SOO
C a lc u la t e d R e s u lts
Te 97852 K
N - 3. 2E+009 / c . c.
V e ■ - 4 3 . 6 9 v o lt e
lODt -
-100
-1 SOtS— 1
1— 1
1
-50
1
1
1
1
i
0
i— J
i
PROBE VOLTAGE
i
i
i
50
i
i
i
i
100
i— i—
(VOLTS)
Figure 28. Plot of Langmuir probe data for a nitrogen plasma operated
at 1 0 torr and a constant applied power of 100 watts.
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149
300
RUN GAS Rp "
Lp =
POWER
P - 1
200
A
(/)
n_
z<
§
5
NITROGEN
0. 025 cm
2. 000 cm
30 W a tts
TORR
100
b-
Z
ui
n
n:
u
u
i
CD
ar.
g -100
ft
C a lc u la t e d R e s u lts
Ta
19303 K
2. 5E+009 / c . c.
Vs “ - 8 . 6 2 v o lts
••200
-3 0 0
-1 0 0
-5 0
Figure 29.
50
0
PROBE VOLTAGE
100
(VOLTS)
Plot of Langmuir probe data for a nitrogen plasma operated
at 1 torr and a constant applied power of 30 watts.
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150
those used in Figs.
8
and 9, then we would have A\, the effective collection
area of probe 1, greater than A%. This condition, however, does not preclude
the probe from obtaining plasma properties in low-power, low-pressure
discharges.
The lack of symmetry in the probe curve was evident in all the plots as a
result of unequal probe areas. Moreover, for argon, as the pressure was
raised to about 15 torr, irregularities were noticed in the curves.
This
worsened as the power was increased from 30 to 60 watts. This irregularity
was due to the formation of vertical arcs or running streaks which wiggled
continuously throughout the discharge volume.
Eventually, probe
measurements broke down at a power level greater than
pressures.
100
watts for all
Figure 28 illustrates a typical breakdown of a voltage-current
characteristic at 100 watts. Apparently probe 1, which has a larger collection
area than probe 2, drew an unusually large current. This behavior may be
attributed to an increase in the sheath thickness, as Eq. (16) would predict for
an increase in the electron temperature as a result of an increase in the
applied power. Therefore the effective current collection area for the probes
were also increased.
At a sufficiently large power level the difference
between the probe areas become greatly magnified. In the lim it that A \ »
A 2, the voltage-current characteristic for a double probe becomes identical
with that for a single probe and the current collected by electrode
1
will be
negligible in comparison with that collected by electrode 2. Figure 28, thus,
resembles that of an inverted voltage-current characteristic of a single probe
shown in Fig. 7.
Even at low powers in a nitrogen plasma, similar breakdown of the
double probe behavior was observed when the probe was inserted close to
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151
the center of the cavity, where the field strength is the greatest. However,
when the probe was placed an inch below the field maximum, a reasonable
probe measurement was obtained as shown in Fig. 29.
Thus, the simple Langmuir probe appeared to work favorably under low
power and low pressure conditions.
This correspond well w ith other
studies.t129l Under these circumstances the probe data predicted the correct
downward trend for the electron temperature w ith increasing pressure. But
prediction of the electron number density was less accurate. The utility of
the double probe as a diagnostic device for other plasma conditions, such as
high power and high pressure, seems dubious.
In a similar microwave-
excited plasma system, Dorman and M cTaggartl118! concluded that the
determination of the electron concentration by the probe method was not
sufficiently reliable for pressures greater than
1
torr.
IV . C. Power Density Determination
Since characterizing the plasma by measuring the average electron energy
and the electron density experimentally using the Langmuir probe was
unsuccessful, these values had to estimated by applying the principles of
electric discharge physics. As pointed out earlier in the background section,
an evaluation of the flux and energy of plasma species impinging upon an
immersed surface requires a knowledge of the species concentrations and
temperatures.
The macroscopic parameter, average power density, was
essential in such an approximation.
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152
IV. C. 1. Plasma Length
During the plasma sintering experiments, the plasma volum e was
observed to be a strong function of power and pressure. The glowing region
was found to expand as the power was increased or as the pressure was
decreased and contract when the pressure was raised or the power was
lowered. Figure 30 describes how the discharge length varied as a function of
power and pressure for an oxygen plasma. The plasma was assumed to be
represented by a cylinder w ith a diameter equivalent to the inside diameter
of the discharge tube. The length of the discharge was taken as the distance
equivalent of the luminous region. In general, under the same power and
pressure conditions the length of the discharge would vary depending on the
gas. The tendency for a gas to become more diffuse was observed in the
following order: oxygen < hydrogen < nitrogen < helium.
IV . C. 2 . Power Density
Once the discharge volume was determined, the average power density
was obtained by dividing the total power dissipated by the cylindrical
volume, defined by the discharge tube diameter and the glow length. By
doing so, it was assumed that the power dissipated is uniform throughout
the discharge. But the central region of the cylindrical discharge was, in fact,
brighter than the rest of the regions along the upper and lower portions of
the tube. The increased brightness is due to the enhanced electron and ion
recombination rate and therefore indicates greater power dissipation in the
center.
The possible error incurred in making such an assumption of
uniform distribution of power is discussed further below.
The average
power dissipated in the discharge per unit volume for several gas plasmas
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153
5 ton
15-
10 -
25 ton-
40 torr
0
200
400
600
800
1000
1200
Incident Power (watts)
Figure 30.
Plasma length as a function of applied power for an oxygen
plasma at various pressures.
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154
measured at 25 torr is plotted as a function of the applied power in Fig. 31.
The power density data show a monotonic increase with increasing incident
power.
The average power density has also been related to the neutral gas
temperature. Brown and Beltf132! established a correlation between the gas
temperature and the power density, the results of which was used for
subsequent interpretation of the observed kinetic data.
Temperature
measurements were made by insertion of a glass-sheathed thermocouple
probe into the glow of the discharge. The temperature data, denoted by
discrete open circles in Fig. 32, show a monotonic increase with increasing
power density.
Besides being used as a means of obtaining electron density and
temperature estimates, the power density was also used as a parameter by
which temperature of specimens sintered in various gas plasmas can be
compared. It was found that only at a discharge pressure of 25 torr do the
power density curves show regions of overlapping value as shown in Fig. 31.
Choosing a high value of power density would mean operating the helium
plasma at maximum power levels, which could shorten the life of the
generator considerably, and would also nullify the whole experimental effort
due to partial melting of the optical fiber thermometer. At a lower value,
not all of the gases, particularly oxygen, would be included in the comparison
because the discharge is unstable at such power conditions. Thus, the value
of the power density to be used in comparing results from the four plasmas
was established at 25 W /cm 3.
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Average Power Density (W/cm3)
155
40
30
He
20
10
0
0
500
1000
1500
2000
Incident Power (watts)
Figure 31.
Average power density as a function of applied power for
various gases at a pressure of 25 torr.
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156
1000-
800-
<W
600-
400-
200
0
3
6
9
12
15
Pd (W/cm3)
Figure 32. Dependence of the neutral gas temperature on the average
power density (adapted from ref. [131]).
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157
IV . C. 3. Power Distribution Profiles
For the sake of simplicity and convenience, the majority of theoretical
and experimental work involving radio frequency and microwave discharge
systems have im plicitly assumed that the power dissipation was uniformly
distributed throughout the volume of the discharge. But in reality this is not
true. Therefore, the possibility of other forms of power density profiles was
considered. Figure 33 sketches three different forms of power distribution
along the length of the discharge tube. The x-axis represents the longitudinal
direction in thedischarge
and xm measures the halflength
of the visible
glow. Theelectric field maximum was assumed to be constantwithin the
tapered section, whose height measures 28, of the applicator through which
the discharge tube was inserted. If we assume a uniform power distribution,
then P0 is the power level that would yield an average power density of
25 W /c m 3 by integrating the area bound by the dashed lines. However, the
power dissipated in the central region, Pm, was found to be greater than P0 at
the same power density of 25 W /c m 3 by assuming the other forms of power
distribution expressed by the following:
(a)
Linear Power Distribution
P =
(b)
Pm - b £
(7 3)
Parabolic Power Distribution
P =
Pm - H
2
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( 74)
158
(a)
P
(b)
( c)
Figure 33.
Schematic profiles of (a) linear, (b) parabolic, and (c)
exponential power distribution along the length of
discharge tube.
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159
(c) Exponential Power Distribution
P = Pme-«
(75)
where & is a constant and £ = x - 5.
Since the height of the ceramic thimble, about 1 cm, is well within 25,
which measures about 1.25 cm, the volume in the central region bounded by
the narrow section of the applicator would be more critical than anywhere
along the tube in terms of sample heating. Therefore, the power densities
computed from the new Pm for the volume within 25 are tabulated in Table
6
for the three distributions.
Table
6
Calculation of power density using different power/length
distributions for various plasmas.
Plasma gas
Dischg.
Power Density (W /cm 3)
length
xm (cm)
Lin.
Parabolic
Exp.
02
1.9
36
31
28
h2
2.9
40
33
45
n
6 .0
45
35
87
10.5
47
36
153
2
He
Thus, the assumption of constant power density throughout the
discharge seems to have underestimated the power density in the region
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
160
where the sample is located for all three distribution functions. Though the
electric field is known to attenuate exponentially along the longitudinal
direction of an empty tube of the dimensions used here, the presence of the
plasma causes the field to be altered in such a way that power dissipation will
no longer follow an exponential decay. W hile we lack data to either support
or refute the possibility of a linear power dissipation, we have, however,
observed parabolic temperature profiles for the various gases along the
discharge tube using the optical fiber thermometer enveloped in a dense
closed end alumina tube as the sensor. Since the extent of heating is a good
measure of the amount of power received by the dense A I2 O 3 tube, the
resulting temperature profiles may indicate the likelihood of a parabolic
power distribution in the discharge. If that is the case, then the error caused
by assuming a uniform power distribution in estimating the power density
in the most intense region of the discharge would be about 30%. Therefore,
the corrected peak values of the power density were used instead of the
average value of 25 W /cm 3 for subsequent calculations.
IV. D. Plasma Density and Temperature Estimation
IV. D. 1. Electron Density
From the determined average power density and knowledge of the gas
pressure and radius of the discharge tube, the electron density was estimated.
First, the average electron density must be represented as a function of the
conditions used to sustain the plasma as discussed in the background section.
This requires data concerning E /p as a function of pA.
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161
E I p curves were generated using microwave breakdown data for
nitrogen, oxygen, hydrogen, and helium as tabulated by Brown and
others.!60/120/149*151! The microwave breakdown data are usually plotted in
terms of the effective electric field strength E as a function of pressure p.
Therefore the value of E was obtained for various gas pressures. But the
steady-state field is always lower than the breakdown field.
Since the
breakdown field is a measure of the initial breakdown condition when the
ionization rate equals the diffusion rate, the build up of a sheath potential at
the container walls under steady-state operation w ill thus reduce diffusion
losses. Consequently, it takes a lower field to maintain the balance between
the loss and gain of charges. Therefore, by taking into account the lower
diffusivity in a steady-state field we obtain the corrected operating voltage for
m aintaining a steady-state discharge.!152! The ratio of E / p was then
correlated with the product of the pressure and the characteristic dimension
A, which is the radius of the discharge tube employed in the present study.
From plots of electron drift velocity as a function of E I p for various gases
we obtained the electron d rift velocity associated the ratio of the effective
electric field to the gas pressure.!60/120/149' 151! As outlined in section II,
Eq. (56) then allows us to evaluate the expression ne /Pd pA. With the aid of
plots such the one illustrated for an oxygen discharge in Fig. 34, electron
concentrations under various discharge conditions can be obtained once the
average power density, gas pressure, and radius o f the discharge tube are
known. The maximum in the curve is due to the fact that for small values
of pA, E I p increases very rapidly, thereby causing a decrease in the value of
average electron density, ne, needed to maintain a fixed value of Pd (see
Eq. 56). Data from high-frequency discharges and dc discharges have been
plotted to show that the dc values of E I p were equal to the effective values
of E I p in a high-frequency discharge.!130!, since the effective field E would
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162
5
4
-1 6
fc
sI
03
£
3
au
©
'©
tM
X
-
2
C
M
o
w
A3
Si
U
a
12
1
0
0
5
10
15
20
pA (torr-cm)
Figure 34.
Plots of E /p and ne/Pd A vs pA for an oxygen plasma.
Curves were generated from microwave breakdown
data and electron drift velocity data (see text).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
163
p ro d u c e
a re
th e
s a m e
a p p lic a b le
T h e
to
e n e rg y
h ig h - fr e q u e n c y
c r e d ib ility
q u a n tita tiv e
tra n s fe r
o f
th is
a g re e m e n t
m e th o d
p r e d ic te d
v a lu e s
a b s o rb e d
p o w e r s . 1 1 2 9 -1 3 3 }
a
w a s
B e ll
a g re e m e n t
d is s o c ia t io n
o f o x y g e n
a
r a d iu s ,
m o d e l
a n d
th e
s h o w n
fr o m
a
p lu g
fo r
a n d
c a lc u la te d
p r e d ic te d
B ro w n
o f
d e c o m p o s it io n
b e tw e e n
q u ite
W
h ile
o f
E k in c il129!
L a n g m
u ir
a g re e m e n t
v a lu e s
a re
fo r
n o t
a s
g o o d .
g o o d .
a n d
w h e n
T h e
m
a x im
th e
o c c u rre d
d e n s ity
w e re
a t
H z
r f
p r e d ic te d
d e n s itie s ,
th o s e
e s tim a te d
e x p e r im e n ta l
e le c t r o n
d e v ia tio n ,
a n d
to
o f
to
o b t a in e d
flo w
ra te
d a ta
In
to
p o w e r
a n d
o n
b e tw e e n
th e y
re a c h
w it h
th e
th e
a n d
th e
g e n e r a l,
5-10%
b y
33%,
t h e ir
d e te r m in e
d is c h a r g e ,
d e n s itie s
in
c o m p o s itio n
to
m e a s u re d
tu b e
e x p e r im e n t
m o n o x id e
h y d r o g e n
u p
a n d
w h e re
d is c h a r g e .
fr o m
d e n s ity
y ie ld
k in e tic s
a m o u n te d
a s
th e
d e v ia tio n s
v a lu e
m ic r o w a v e
fo r
a n d
a n d
o r d e r
fr o m
o b t a in e d
c o m b in e d
2 to r r
th e
d is c h a r g e
th e o ry
c a rb o n
m o le c u la r
a
m a x im u m
in
o f
d is c r e p a n c y
o f
th e
u m
w it h
d a ta
e le c tr o n
c o n v e r s io n
g o o d
c a lc u la t e d
e ffe c t o f p re s s u re
13.6 M
a
in
e le c tr o n
w it h
in
k in e tic s
e x p e r im e n ta l
d is c h a r g e ,
th e
r e a s o n a b ly
e x a m p le ,
p re s s u re ,
o x id a tio n
a n d
a b s o r p tio n
T h e
th e
fo r
B e l l i 1 3 2 ' 1 3 3 ! , a ls o , c o m b i n e d
c o n v e r s io n
th e
th e
c o n v e r s io n s
th e
b e tw e e n
o n
f it
s ig n ific a n t
p ro b e s ,
o f
T h e
d io x id e
th e
th e
d is c h a r g e
th e
p o w e r
o n ly
c o m p a re d
d o u b le
w it h in
s im u lta n e o u s
p o w e r
le s s
o f
e x p e r im e n ta l
T h e
b a s is
te m p e ra tu re
th e
s tu d y in g
fu n c tio n
a n d
o f c a rb o n
th e
g o o d .
w a s
w it h
b y
d e n s itie s
p e rfe c t a g re e m e n t b e tw e e n
m e a s u re d
e le c tr o n
c o m p o s itio n
f it
re a c to r.
a n d
le v e l o f 2 2 % .
d e n s ity
e ffe c t
y ie ld
th e
a n d
r e s u lts
d is c h a r g e s .
d is s o c ia t io n
K w o n g l131 !,
m ic r o w a v e
o n
N e a r ly
th e
flo w
c o n v e r s io n
a
p o w e r
c a lc u la tio n .
w e re
th e
c o m p u te d
d c
d e m o n s tra te d
a n d
q u a n tita tiv e
T h e r e fo r e , th e s e
a s w e ll a s
e n e r g ie s
r e a s o n a b le
te m p e ra tu re ,
f ie ld .
e x p e r im e n ta l
e le c tr o n
in
s te a d y
d is c h a r g e s
b e tw e e n
u s in g
a s
w a s
d if fe r e n c e .
a to m s
M e a rn s
p la n e ,
a s
a
a n d
p a r a lle l
d e n s itie s .
th e
th e
T h e
c a lc u la t e d
o c c u rre d
a t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80 W
.
16 4
The likely reason for this divergence was attributed to uncertainty in the
assessment of discharge volume and gas temperature.
' The effect of applied power on the electron density is illustrated in Fig. 35.
Electron concentration increases with power as a result of the dependence on
Pd which increases with absorbed power, as seen in Fig. 31. There is a second
effect also, in that as the power density increases, the gas temperature
increases, causing a reduction in the gas density which can be expressed by an
equivalent pressure, p0 ,
p0 = 298 p / T g
(76)
Consequently, p0 falls which results in an increase of ne / P d pA. The net
effect of the increase in the electron density is to enhance the rate of the
electron impact reactions.
Calculation of electron number density as a function of pressure for an
oxygen plasma maintained at constant applied power levels of 230 W and
530 W is presented in Fig. 36. The first effect of increasing the pressure is to
cause a decrease in the discharge volume. As a result, the power density also
increases, which in turn produces an increase in the gas temperature. The
gas density is thus reduced and the corresponding effective E / p 0 increased.
The net effect is to bring about a rise in ne /Pd PA.
A point is reached,
however, when the rate of increase in Pd is insufficient to compensate for
the drop in ne / Pd pA as the pressure increases further. In their study of
absorption of microwave power as a function of pressure by various plasmas,
Dorman and McTaggartf118! used a theoretical model to relate the computed
electron density to the experimental power absorption data. They found that
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Electron Density
(cm*3)
165
□
5 torr
0
25 torr
A 40 torr
0
300
600
900
1200
Applied Power (watts)
Figure 35.
Electron number density as a function of applied power for a
microwave excited oxygen plasma at various pressures. Data
from microwave breakdown for oxygen (refs. [60,120,
149-151].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
166
m
i
§
co
S
530 W
230 W
Q
a
s
8
w
Pressure (torr)
Figure 36.
Electron number density as a function of pressure for a micro­
wave excited oxygen plasma operated at power levels of 230
W and 530 W.
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167
the electron density passed through a maximum at a pressure characteristic
of each gas as was in the observed power absorption curves.
Thus the
electron density curve mimicked the absorbed power curves very closely.
The authors concluded, therefore, that the shape of the power absorbed
curves could be determined by the electron concentration curve. In addition,
they showed that by increasing the applied power the pressure as well as the
absorbed power at which the maximum occurs also increases.
Thus the
shifting of the maximum to the right at the higher power seen in Fig. 36 is in
agreement w ith the findings of these authors. During our work, as well as in
the previous microwave sintering work by Kem erl13!, of the sintering of
alumina in a nitrogen plasma, we also observed an increase in the absorbed
power which passed through a broad maximum at a pressure range between
30 and 40 torr at an applied power of 500 W. Theoretical calculation of the
electron density as a function of pressure for a microwave excited nitrogen
plasma at 530 W is shown in Fig. 37. The result indicates good agreement
with the experimental observations.
Table 7 below tabulates the theoretical electron concentrations for the four
gas plasmas at a pressure of 25 torr and similar peak power density values
(see Table 6 ) rather than 25 W /cm 3. Helium is shown to have the highest
number concentration followed by hydrogen, nitrogen, and oxygen.
IV . D. 2 . Electron Temperature
Determination of the average electron temperature requires data
concerning the electron energy e as function of E / p .
Again, from
Brown's!150'151! collection of experimental measurements of discharge
properties, a typical average electron energy curve for oxygen plotted against
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Electron Density
(10‘n cm'3)
168
4
3
0
10
20
30
40
50
Pressure (torr)
Figure 37.
Electron number density as a function of pressure for a micro­
wave excited nitrogen plasma operated at 530 W.
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169
Table 7
Average electron number density for various
plasmas calculated at an average peak power
density of 34 W / c m 3 and a pressure of 25 torr.
Plasma Gas
ne (
10-1 1
He
67.0
h2
13.9
n2
8.45
Qz
4.17
cm-3)
E / p was obtained as shown in Fig. 38. Since the relationship between E /p
and pA was established from the previous procedure for estimating the
electron concentration, it is possible to estimate the average electron energy
for various discharge conditions. The dependence of electron temperature
on the applied power is shown in Fig. 39.
In principle, the electron
temperature is a function of E /p, which is a function only of pA, according to
the theory presented in the background section (see Eqs. 60 and 65).
Therefore, Te should only be a function of pA and independent of power.
The slight increase in Te with increasing power is due to an increase in the
gas temperature as power increases.
This relationship was demonstrated
experimentally in the works of Mearns and Ekinci!129! and Busch and
Vickers!127! using double probes to measure the electron temperature.
Figure 40 shows the effect of pressure on the electron temperature. As
predicted by the theory, Te decreases as pressure increases, in agreement with
observation by the probe measurements as well.!127'129! The drop in the
electron temperature with increasing pressure reflects the loss of energy as
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170
3.0
6
5
-2.5
4
o
-
X
<o
2.0
D
C
O
3
E-h
2
1.0
1
5
10
15
20
E / p (volt/cm-torr)
Figure 38.
Plot of electron temperature and average electron energy
as a function of E /p for an oxygen plasma. Curve gene­
rated from electron drift velocity data (Brown [150-151]).
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171
6.0
u
5.0
0
200
400
600
800
1000
Applied Power (watts)
Figure 39. Electron Temperature as a function of applied power for an
oxygen plasma at 25 torr.
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172
Te xlO
{ K)
8
7
6
5
0
10
20
30
40
Pressure (torr)
Figure 40.
Electron temperature as a function of pressure for an oxygen
plasma at 530 W.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
173
the frequency of encounters with heavy particles is raised. For comparison,
the electron temperatures were calculated for the four gas plasmas used in
the present experiment, at similar values of power density and a constant
pressure of 25 torr. The result of this computation is presented in Table
8.
The electron temperature values in various gases appear to follow in the
descending order: O2, He, N 2, and H 2 .
Table
8
Computed electron temperature for various
plasmas and an average peak power density
of 34 W /cm 3 and a pressure of 25 torr.
Plasma Gas
Te ( 10- 4 °K )
O2
5.6
He
5.0
n
2
1.8
h2
1.4
IV . D. 3. Neutral Gas Temperature
In addition to electron concentration and temperature, the gas
temperature also needed to be evaluated in order to compute the sample
temperature resulting from heating in a plasma.
In general, the gaseous
species in a discharge is at much higher temperatures than 300 °K and the
temperature increases as the gas absorbs electromagnetic energy through
elastic and inelastic collisions w ith electrons.
Since the neutrals
outnumbered charged species by about a m illion to one, they can be a
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174
predominating factor in the heat transfer process during plasma firing.
Therefore, accurate determination of the neutral species temperature is
crucial.
Generally the neutral gas temperature is not known for certain. Various
methods have been adopted to measure their temperature.
Besides
spectroscopic methods, perhaps the most suitable instrument for measuring
the neutral gas temperature appears to be a small gas thermometer employed
by VeprekJ54/153!
This thermometer is made of quartz and filled w ith
nitrogen at approximately 250 torr.
A "U" manometer that uses a
gallium /indium alloy (being a liquid at room temperature and has negligible
vapor pressure up to 1000 °C ) measures pressure differences which are
proportional to the temperature.
The top of the thermometer which in
actual contact with the discharge was poisoned w ith HPO 3 to reduce
deposition of the recombination energy of atoms at the surface.
Since
metaphosphoric acid (H P03) exhibits very low recombination efficiency for
various atoms, as indicated in Section II, it is often employed as the ideal
coating to minimize atom recombination deliberately.
An estimate of the
neutral gas temperature can thus be obtained. Gas temperature was found to
be a monotonic increasing function of the applied power for high frequency
discharge, as shown in Fig. 41. W ith the high frequency (80 M Hz) generator
operating at 5 A and a pressure of 1.35 torr in a 10 cm dia. discharge tube, the
gas temperature was roughly 800 °K . The temperature rises more slowly at
high current levels.
As mentioned earlier, Brown and Beltf132! used a Pyrex sheathed
thermocouple to determine the gas temperature w ithin a C O / O 2 radio
frequency discharge.
The authors found that the gas temperature was
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175
1000
600
Tg
(°K)
800
400
200
0
2
4
6
8
1(A)
Figure 41.
Gas temperature as a function of discharge current in nitrogen
at a pressure of 1.35 torr, frequency of 80 M Hz, and a discharge
tube diameter of 10 cm (adapted from Veprek [54]).
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176
prim arily affected by the power and pressure.
Temperature and power
density were found to correlate best, in which the neutral gas temperature
showed a monotonic increase w ith increasing power density as shown in
Fig. 32. A t an average power density of 8 W /cm 3 the temperature was found
to be about 800 °K. The authors expected the temperature to rise more slowly
at higher power densities. Veprek's gas temperature measurements using
the small gas thermometer confirmed the prediction of Brown and Bell
concerning the dependence of the temperature w ith power.
Studying the dissociation of oxygen in a microwave discharge, Brake and
coworkersl79'154! were able to predict the oxygen atom concentration using a
one dimensional temperature-dependent model in a system of neutral
species. The gas temperature was estimated by fitting the model at different
temperatures to the experimental data. The model was found to accurately
predict the oxygen atom concentration profile as measured by nitrogen
dioxide titration.
The model also indicated that the temperature of the
neutral gas to be approximately 1000 °K at an absorbed power of 576 W,
pressure of
8
torr, discharge tube diameter of 1.79 cm, and a flow rate of
1.39 cc/sec. Since the flow rate and the tube diameter diameter were similar,
~
1
cc/sec and
1 .6
cm tube diameter in the present study, and assuming
similar oxygen discharge behavior in the microwave, the power density was
estimated to be about 18 W /cm 3. If we could extrapolate the curve of gas
temperature as a function of power density, Fig. 32, to this power density
value, we w ould see that there may be a possibility of a satisfactory
agreement in the values of gas temperature at the indicated power density.
If we assume that the power dissipation can be adequately represented by
a parabolic profile, then as Table
6
suggests, at the indicated peak power
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177
density values the gas temperature was estimated to be approximately
1200 °K. Hence, in all subsequent sample temperature calculations the value
of 1200 °K was used for the neutral gas temperature.
IV . E. Sintering of Ceramic Thimbles
The difficulties we encountered in achieving high fired densities in
silicon carbide and the gas composition effect noted by Chent18! and
Hrdinat23] together w ith the dopant effect observed by Knowltonl14! initiated
this series of sintering study. Different gaseous discharges were used to see
whether plasma heating can be distinguished into purely thermal and
chemical effects. A variety of ceramic materials were sintered in the plasma
to determine whether the effect of specimen heating can be related to
m aterial properties and to establish surface mechanisms responsible for
heating from these relationships. Thimble-shaped specimens were used in
combination with the Accufiber optical fiber thermometer to measure the
fired specimen temperature in situ.
IV . E. 1. OFT Temperature Measurement
IV . E. 1. a. Plasma Luminosity Effect
The fiber optic thermometry system has proven to be advantageous when
used in a high-frequency field to measure sample temperature in situ.
In
principle, the OFT is immune to electromagnetic and radio frequency
interference.
How ever, during the course o f temperature quench
experiments, it was discovered that the OFT temperature oscillates w ith
time. Figure 42 shows the temperature-time profile as recorded about one
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178
500
490
L_
Q .1 4 S 0
6.0
6.5
Time
Figure 42.
7 .0
7 .5
(sec)
Temperature-time profile during a quench study with a maxi­
mum sampling rate of 38/sec.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
179
second before the power generator was shut off. W ith the sampling rate set
to a maximum value of 38/sec, it still could not follow the rapid motion of
the rectified ac field cycling at 120/sec. Thus, an average of three repeating
units in the temperature measurements per second is seen. Also, a couple of
ripples appeared even when the source may have been turned off (though
we cannot tell precisely when) and with the plasma completely extinguished
the temperature dropped off rather smoothly. Due to thermal inertia the
sample temperature could not have alternated at such a rapid rate; therefore,
the OFT must be responding to a radiative effect caused by the plasma. If the
base line is an indication of the period of time when the plasma was off, then
that temperature would appear to be the true sample temperature
The
temperature fluctuation caused by the ongoing oscillating plasma seems to be
about 5 to
6
°C. This effect can eliminate by synchronizing the sampling rate
with the ac field at 120 Hz. We would then see only the temperature of the
sample as it is being heated by the plasma.
IV . E. 1. b. OFT Calibration
Satisfactory reproducibility of the OFT measurements was demonstrated
in A I2 O3 specimens. Temperature measurements taken a month apart agree
to within 5 degrees under the same sets of experimental conditions. During
this period, the same OFT was being used to measure temperature of various
other ceramic samples. Careful polishing of the sapphire sheath was done
using 5 J im diamond paste in between groups of materials. Calibration of the
OFT was carried out in a conventional furnace in which the temperature was
increased in steps from 250 to 1550 °C .
The tips of the OFT and a
thermocouple were placed 5 mm apart in a 1.5 cm dia. hollow cavity created
from a 9 cm alumina fiber block. The whole assembly was then placed in the
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180
center of the furnace. Results of the OFT calibration are shown in Fig. 43.
The temperature measurements indicated that the OFT readings did not
deviate from that of the thermocouple by more than
10
degrees in the range
from 800 to 1550 °C. Both temperature readings, however, were consistently
higher than the furnace temperature, perhaps because the thermocouple for
the furnace was located further back towards the insulating wall.
IV. E. 1. c. OFT Time-Temperature Profiles
Several ceramic materials were fired in various gas plasma systems. A
typical specimen temperature-time profile is illustrated in Fig. 44. In this
case, an AI2 O 3 thimble provided the cavity as the blackbody radiation source
for the OFT. Argon was found to be relatively cool compared to the other
four gases used in this study.
A pinkish water vapor glow often
accompanied the in itia l cleaning process, indicating argon initiated
desorption of the water molecules from the oxide surface.
When the discharge glow returned to its usual bluish-white color, the
second stage of heating began.
We see the rapid rise in the specimen
temperature as soon as the working gas, nitrogen in this case, was switched
on. Within 2 minutes, the sample attained a final steady-state temperature
of about 1450 °C at a heating rate of approximately 30 °C/sec. The observed
hump may be due to the loss of surface associated with shrinkage, reducing
the total surface area available for heating.
As mentioned in the
experimental section, another possible explanation for the droop in the
temperature is an increase in transparency of the specimen with sintering
and therefore a greater disparity between indicated and true temperature.
Cool down by radiative loss is seen to be extremely rapid.
Various
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181
1600
1 400
1200
1000
>-
800
<U
600
Q.
400
«
A
200
3000
6000
OFT
Thermocouple
9000
12000
1500
Time, t (sec)
Figure 43.
Calibration curve of the optical fiber thermometer.
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182
1600
1400
H 1000
<u
^
600
nJ
v
B
V
600
04
400
200
200
400
600
800
1000
1200
Time, t (sec)
Figure 44.
Temperature profile for alumina fired in 25 torr N 2 plasma
at a power density of 25 W /cm 3 with the first 300 seconds
devoted to cleaning of adsorbed gases from the specimen at
low applied power levels.
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183
representative OFT temperature measurements for the other solids are
located in Appendix C.
Table 9 below presents a summary table of the OFT temperature
measurements obtained for samples fired in several gas plasmas operated at
a pressure of 25 torr and a power density range of 31 to 36 W /cm 3 for each gas
as indicated in Table
6.
Examination of Table 9 shows that polyatomic gas
plasmas are more effective in heating these samples than a monatomic gas
plasma. In general, higher temperatures are achieved in the following order
of gases: He < H 2 < O 2 < N 2 .
Another pattern that can be noted is the
dependence of sample temperature with material composition. In general,
for a given plasma, solids w ith lower conductivity usually obtain higher
temperatures than semiconducting or covalently bonded solids.
Table 9
Summary of temperature measurements for various gas
plasmas at 25 torr and an average peak power density of
34 W /cm 3.
Gas
MgO
A12C>3
T i0 2
He
844
809
840
h2
1120
1190
835
O2
1290
1180
n
1460
1470
2
Z r0 2
N iO
ZnO
SiC
808
—
751
870
930
1020
940
553
860
1220
1 210
1047
950
942
—
1300
1350
1280
1368
1180
1050
—
Fe20 3
In addition to helium, neon gas was also employed to ascertain if heating
trend follows that in helium in a few solids. That is, the noble gases were
considered to have only thermal heating as opposed to polyatomic gases
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184
which can contribute to heating by additional chemical mechanisms. Results
of this comparison are shown in Table 10.
From Table 10 we see that
materials do not heat up very efficiently under inert gas plasmas. In general,
heating by inert gas plasmas are very similar and the extent of heating
usually do not exceed more than 900 °C.
Table 10 Comparison of heating by inert gas plasmas on
some solids.
Material
He
Ne
MgO
844
809
A I 2O 3
809
815
T i0 2
840
787
IV . E. 2. Sintered Densities
The sintered densities of undoped ceramic thimbles fired in various
plasmas are tabulated in Table 11. As indicated in Fig. 44, sintering duration
at temperature typically lasts about 7 to
8
minutes. The density data were in
general not very high as expected from the corresponding temperature data
shown in Table 9. The highest sintered densities, which ranges from ~84 to
99% of the theoretical density, were obtained in nitrogen plasma. Because
Fe2 0 3 , ZnO, NiO , and TiC>2 were reduced to some extent in He and N 2 and
more severely in H 2, the corresponding density measurements do not truly
reflect the density of the indicated oxide phase. However, the final density
obtained among the gases followed the general pattern: N 2 > O 2 > H 2 > He.
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185
Silicon carbide experienced very little or no densification in all four
discharges. The effect of powder particle size was less important since all of
the powder materials were submicron particle sizes.
Table 11 Summary of density measurements (% TD) for various gas
plasmas at 25 torr and an average peak power density of
34 W /cm 3.
Gas
MgO
a i 2o 3
T i0 2
He
47.6
51.1
58.2
h2
49.7
59.9
58.3
65.5
02
50.8
72.5
70.3
95.8
n
84.4
97.1
76.8
97.9
2
Z r0 2
—
Fe20 3
N iO
ZnO
SiC
—
-
—
61.6
71.0
50.1
61.2
80.2
71.3
99.9
90.7
91.7
99.9
—
—
61.6
The sintered density as well as steady-state temperature of alumina
specimens fired in a nitrogen plasma were measured at various pressures at
a constant power density of 35 W /cm 3. The results are presented in Table 12.
As we expected, the final density and temperature data were similar at the
three pressures. The measured temperature ranges from 1420 to 1490 °C and
the density from about 95 to 97% of the theoretical density. The tendency for
a higher density and temperature at increasing pressures may be due to the
uncertainty in determining the plasma volume as plasma shrinks at higher
pressures.
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186
Table 12
Variation of nitrogen plasma fired temperature
and density as a function of pressure for AI2O 3
at power density of 35 W /cm 3.
Pressure (torr)
T (°C )
p (% TD)
5
1420
94.8
25
1470
97.1
40
1490
97.3
IV . E. 3. Surface Modification
Plasma is a very unique medium.
Besides providing as useful heat
source in sintering, plasmas also present an extremely reactive chemical
environment. Most surfaces that are brought in contact with a plasma, more
or less, undergo some topographical changes.
For example, etching by
reactive radical species w ith a giyen surface to form volatile products is
believed to occur for some solid/gas systems during the microwave plasma
sintering process. Sputter etching (physical ejection of substrate material by
ion impact) is thought to be less likely at the pressures employed in this
study. The positive ion energy tends to be low, between ~1 to 10 eV. These
ions, however, may participate by stimulating or accelerating the reactions
between the solid surface and the neutral species by ion bombardment.
Studies have shown enhanced etching by combining controllable fluxes of
reactive neutrals w ith ion beams.[ 100 ]
Some solids also experienced
reduction in plasmas, whereas under identical conditions in a non-plasma
environment they would not have reduced as much.
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187
IV . E. 3. a. Plasma Etching
Chemical etching was observed for A I 2 O 3 in the presence of nitrogen as
illustrated in Fig. 45a.
Identical specimens fired conventionally under
similar experimental conditions did not exhibit such deep pits as shown in
Fig. 45b. Kemerl13! found similar surface pitting of AI2 O 3 in a nitrogen gas
plasma. Alumina is believed to react w ith the active nitrogen radical species
from the gas phase to form A lN l54'55!.
None of the other three gases
produced any noticeable chemical corrosion of the A I2O 3 specimens.
ZnO was also found to be attacked by nitrogen as well as oxygen. Figure
46 shows the more open microstructure of a ZnO surface exposed to an
oxygen plasma. Corrosion effects of either He or H 2 was not clearly evident
based on the surface microstructure because of large existing porosity as a
result of low sintering temperature attained in these plasmas.
Z r 0 2
re a c te d
s tr o n g ly
C o m p a re d
w it h
th e
s in t e r e d
p la s m a
le a v in g
a
to
n it r id e
fo rm
th e
s u rfa c e
n ic e
w it h
g r a in
s p e c im e n
th a t
a t h ig h
th e
n it r o g e n
s tru c tu re s
s h o w e d
r e s e m b le d
a
o f
p la s m a
s p e c im e n
r e a c t iv e
e tc h in g
s k e le ta l n e t w o r k .
as
s h o w n
fir e d
o f
in
F ig .
47.
c o n v e n tio n a lly ,
th e
Z r C >2 h a s
g r a in
b e e n
m a t e r ia l,
re p o rte d
te m p e r a tu r e s .i1 5 5 l
The disruption of the surface features of a Fe2 C>3 specimen is seen in Fig.
48. The exterior surface of the Fe2 C>3 thimble fired in the oxygen plasma
showed corrosion of the grain boundaries, whereas the corresponding inside
surface does not.
The extent of this structural disruption can be several
microns deep as shown in Fig. 49.
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(a )
Figure 45.
(b )
Scanning electron micrographs of the external surface of an A120 3 thimble
specimens fired in a plasma (a) and conventional (b) furnace in nitrogen.
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(a )
Scanning electron micrographs of the external surface of a ZnO thimble
specimen fired in a plasma (a) and conventional (b) furnace in oxygen.
189
Figure 46.
(b )
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Figure 48.
Scanning electron micrographs of (a) the external surface and (b) inside surface
of an Fe20 3 thimble specimen fired in an oxygen plasma.
191
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of an Fe20 3 thimble specimen fired in a helium plasma.
192
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193
TiC >2 also showed chemical corrosion of the surface material when
exposed to active species in a nitrogen plasma as observed in Fig. 50.
K oteckil21! had observed similar etching of Ti0 2 in A r/C >2 rf induction
coupled plasma.
IV . E.3. b. Reduction
As we have indicated in the background section the strongly reducing
environment of the gas plasmas can also induce reduction of some ceramic
oxides to lower oxide phases by ion bombardment or electron abstraction
which would not have otherwise occurred. Several materials that showed a
strong tendency to be reduced in the plasma, were fired in a conventional
furnace as well in the same gas at similar temperatures.
Reduction of Fe2 C>3 thimbles were observed. The exterior surfaces were
reduced in Ar and He as indicated by a black coating, characteristic of a lower
oxide phase, Fe3 0 4 , whereas the cross-section and inside surface of the
thimble remained reddish brown. Conventional firing in He under identical
conditions did not show reduction at all. A nitrogen plasma fired specimen
was completely reduced throughout to Fe3C>4 by its black appearance and
strong magnetic character. Samples fired conventionally at the same reduced
pressure conditions showed a smaller degree of reduction as indicated by a
less intense discoloration and lack of magnetism. Hydrogen plasma reduced
the Fe2 C>3 thimble to its elemental Fe. Therefore, the strength of reduction of
Fe2C>3 may be indicated in the following order of plasma gases: H 2 > N 2 > He.
Whereas under identical conditions in a conventional furnace, we find the
extent of reduction in H 2 » N 2 and none in He.
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195
ZnO specimens were also reduced. The reduction occurred throughout
the thimbles for He, N 2 , and H 2 plasmas with the indicated extent of
reduction increased in the same order. Firing in an Ar plasma also yielded
similar reduction as in He. Conventional firing of zinc oxide in N 2 and He
under same temperature and pressure conditions produced only a very slight
off-white coloration on the sample surface.
N iO is known to reduce easily!155! as observed in N 2 and H 2 plasmas.
Reduction of N iO to metallic nickel occurred on surfaces where nitrogen
plasma was most intense.
Complete reduction to N i was observed in
hydrogen plasma. Zr 0 2 was only slightly reduced in N 2 plasma as exhibited
by a grayish coloration. Strongest reduction occurred in H 2 plasma in which
the sample turned gray throughout.
Firing of zirconia under reduced
pressures of nitrogen in a conventional furnace did not indicate evidence of
reduction.
As observed previously by Kotecki!21!, TiC>2 tends to be reduced in a gas
plasma. The cross-sections of the thimbles were bluish gray, indicative of
loss of oxygen!156'157!. The exterior surfaces turned black in He and H 2
plasmas and gray in N 2 . Reduction of TiC>2 to lower oxide phase by the loss
of oxygen were noted when heated in atmospheres of low oxygen
activity.t158l The extent of reduction of plasma fired samples was, again,
greater than those conventionally fired as indicated by the discoloration of
the samples.
Thermodynamically less stable oxides appears to be more susceptible to
reduction in a plasma. In addition, most reduction occurred for transitional
metal oxides having multivalent oxidation states, namely, Fe2 C>3 , NiO, and
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196
TiC>2 . Thus, reduction may be effected by the loss of oxygen as a result of ion
bombardment or oxygen reacting with active gaseous species in the plasma to
form volatiles. Conversion of metal ions to a lower valent oxidation state by
absorbing excess free electrons may also lead to the observed reduced state.
The actual mechanism of reduction is not yet known, but plasma enhanced
reduction of oxides over that fired in a non-plasma environment under
similar conditions had clearly been observed in this study.
IV . E. 4. Sample Temperature Estimation
One of the goals in this study was to predict the surface temperature of
specimens fired in a plasma using formulations developed earlier in section
II. To do so, some assumptions were made to simplify these calculations.
Since various quantities needed could not be determined experimentally at
this stage, we either computed from basic principles or tried to make the best
educated guess we can from the available literature for these parameters in
order to complete this exercise. For instance, the value of neutral species
temperature, which we have speculated earlier, and recombination
coefficients were estimates, whereas characteristic plasma parameters were
determined from published gaseous breakdown data together with the basic
principles of discharge physics. Thus we first made a reasonable guess of the
neutral temperature, calculated the ion and electron number density and
temperatures, determined recombination coefficients, and then performed
an overall energy balance according to Eq. (77) to yield estimated specimen
temperatures as outlined in Appendix B.
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197
IV . E. 4. a. Assumptions
Having determined electron densities and average energies together with
recombination coefficients and estimated heavy particle temperature
obtained from published data!101-107'109'113'159-161! , it is possible to attempt a
first order approximation of the steady-state temperature of a specimen fired
in a plasma.
There are several underlying assumptions im plicit to the
theoretical calculation of the heat transfer process:
a) The plasma is optically thin and transparent to thermal
radiation,
b )
T h e
19»1261
n e u t r a l s p e c ie s
a re
c o n s id e r e d
to
b e
fu lly
d is s o c ia t e d
a n d
a re
u n e x c i t e d . I 2 9 , 1 2 7 -1 2 8 ,1 5 4 ]
c) Radiative dissipation is the major loss mechanism of thermal energy.
d) Complete energy accommodation occurs at each collision w ith the
solid surface for both atoms and positive ions.I126'162!
e) The gas temperature (i.e., heavy species) is uniform throughout the
discharge and recombination zone.t132'133!
These assumptions were made to sim plify the analysis. To do otherwise
would open up an extremely difficult problem which is beyond the scope of
the present effort.
These assumptions were also commonly made in
theoretical calculations of heat transfer in gas-solid systems and those
involving discharges. In typical laboratory discharges, plasma species are
considered to be "optically thin" so that they do not reabsorbed the emitted
radiation. I119J It is generally believed that in a plasma system such as MEP or
ICP which is used for plasma sintering the majority of species are dissociated
and not ionized as Brake and coworkersf79'154! demonstrated for a
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198
microwave-initiated oxygen plasma.
Since de-excitation is an efficient
process, excited neutral species are quickly destroyed by two- and three-body
collisions at pressures up to 16 torr.!127'128!. Conduction and convection
losses of thermal energy from the small ceramic thimble are expected to be
small compared to radiative dissipation. The gas molecules are assumed to
be very efficient in transferring their thermal energies to a given solid
surface upon impingement, i.e., accommodation coefficient of unity.!126'162!
And finally, effective energy exchange between colliding heavy particles
ensures uniform neutral gas temperature throughout.!132'133!
A t reduced pressures, 25 torr, the mean free path lengths of the plasma
species are on the order of the boundary layer thickness (~ 0.1 to
1
mm),
therefore, they w ill fall freely through the collisionless boundary layer
region. I26! The heating of a solid immersed in plasma can thus be described
w ith the aid of gas kinetic methods.
Taking into account the above assumptions and the fact that the heat
fluxes to the solid surface are transported by the individual plasma species,
we can determine the specimen temperature by an overall energy balance
giving rise to the following equation,
Qatom +
where
Q ion +
Qelectron = & £m
( T j 4 - T04 )
a - Stefan-Boltzmann constant,
em = emissivity of the solid surface,
T0 = temperature of the surrounding wall.
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(77)
199
The left-hand side of Eq. (77) represents the respective energy fluxes of atoms,
ions, and electrons delivered to the solid as described previously in Section
II, while the right-hand side of the equation represents the heat lost by
radiation from the surface of the sample to its surroundings.
IV . E. 4. b. Recombination Coefficient
The other parameter necessary in the determination of energy flux is the
atom recombination coefficient, y, which is a measure of the fraction of
atoms arriving at the surface that recombine, since the recombining atoms
constitute an energy source. The homogeneous gas phase reactions have
been under intensive investigation and are, therefore, better understood.
However, for heterogeneous chemical reactions the corresponding data base
and level of understanding is comparatively poor.
Lim ited studies of
surface-catalyzed atom association on certain metals and oxides have actually
been done for O, H , and
N
a t o m s ^ O l- 1 0 7 ,109,113,159-161] an £ j
were mostly
restricted to measurements near room temperature as discussed in the
background section. The evaluation of the temperature dependence of the
recombination efficiency for hydrogen and oxygen atoms on some oxide
surfaces has also been determined for temperatures up to 600 °C .f105‘
106,111,163]
xhe catalytic activity of silica surface for H and O atoms appears to
coincide when plotted against temperature, as shown in Fig. 51. The high
temperature result is consistent with the similar behavior shown in room
temperature. The variation of log y with temperature for the recombination
of hydrogen atom on alumina was also included in the plot as shown in Fig.
51. Since the surface catalyzed recombination is an activated process, the
catalytic efficiency increases with temperature. From the similarity of results
for atomic oxygen and atomic hydrogen on fused silica seen in Fig. 51 and the
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200
Recombination Coefficient,
10-1
200
400
A
S11tca-H2
O
51l1ca-02
□
A lu m ln a -H 2
600
800
1000
Temperature (°K)
Figure 51.
Temperature dependence of the rate of hydrogen and oxygen
atom recombination on fused quartz and alumina surfaces
(adapted from refs. [105,112]).
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201
comparable activities o f H , O, and N atoms on glass surfaces as shown in
Table 5, the surface reaction mechanism on insulating surfaces is believed to
be similar. As pointed out earlier in section II, W arrenl117! had noted closely
paralleled catalytic activity of O atoms and H atoms on alumina surface for
room temperature results. However, Fig. 51 suggests that there may be an
increase in the activity above 700 °K for hydrogen atoms on alumina. Thus,
the temperature dependence as y for hydrogen served as the basi$ for
estimating the y values of atomic oxygen on alumina surfaces to be used in
subsequent temperature calculations. Estimations based on the lim ited data
points for alumina above 800 °K must, however, be regarded as approximate.
IV . E. 4. c. Atom Concentration Near the Surface
The fraction of chemical energy released on a given surface w ill also
depend on the atom concentration one mean-free-path length from the
specimen surface. The mean free path lengths were evaluated according to
the following expression
(78)
where Pk_j =
mk - 0.2 rtij
,n j is the species concentration, and Sk.j is the
mk + rtij
effective cross section in impacts between particles of the k th and of the j th
type. Thus, from the respective values of the collisional cross sections, we
obtained the mean free path lengths of the atoms, ions, and electrons in an
oxygen plasma at 25 torr:
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202
Sm
=
Sa-i =
2 .0
x
10~24
10~24
cm2
/,• = 1.03 mm
an 2
Sa-e = 2.83 x
1 0 " 24
cm2
Sj-e = 3.87 x
1 0 - 22
cm2
Se-e
~
la = 0.78 mm
le = 1.25 mm
0
The mean free path lengths are, therefore, about the same order of
magnitude as the width of the hydrodynamic boundary layer.
In principle, one may determine the distribution of species concentration
from simultaneous solution of the particle density and energy equations as
outlined in the Appendix.
However, such an approach involves coupled
nonlinear differential equations which are very difficult to solve.
In the
present experimental arrangement, the gas flow moved through a gap about
3 mm between the sample and the discharge tube w all. Since the distance
from the bulk stream to the particle surface was only about
10
mean free path
lengths, the atom concentration at the edge of the boundary layer may not be
very different from the gas stream composition.
Therefore, in this
calculation we assumed, as a first approximation, that the near-surface atom
concentration may be represented essentially by the bulk concentration.
IV . E. 4. d. Theoretical Estimation
In this exercise we first estimated the neutral species temperature based
on temperature found in a similar plasma system and on correlations w ith
the power density. We also assumed that their number density one mean
free path from the surface was nearly the same as that in the bulk stream.
The principles of discharge physics also enabled us to compute the electron
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203
and ion concentrations and their temperatures in various discharges.
Because of the lack of recombination data on alumina, the oxygen
recombination efficiency was estimated by extrapolating the data measured
for H atoms on alum ina
The catalytic dependence on temperature for
magnesia was obtained from the work of Dickens and Sutcliffe.^106! Though
one would not expect equivalent behavior among the various gases, but
based on the reported close paralleled activity of H atom, O atom, and N
atom on the insulating oxides as discussed in the background section, e.g., for
alumina and silical 1 1 2 -1 1 3 ,1 1 6 -1 1 7 ] we assumed, therefore, that in this first
approximation calculation the data for hydrogen were applicable to oxygen
and nitrogen as well, in the case of alumina. Similarly, the activity of oxygen
atom recombination on magnesia was assumed to be equivalent to that of
nitrogen and hydrogen.
By making these estimates, incorporating them into energy flux
determinations, and solving for the steady-state specimen temperature
according to Eq. (77) using Newton's method, we obtained some temperature
estimates of AI2 O 3 and M gO specimens fired in various plasmas. A sample
calculation is included in the Appendix to show how we computed the
sample temperatures. Due to the availability of pertinent data, alumina and
magnesia were the only two materials able to be compared among the three
diatomic gas discharges employed in this study.
The values of catalytic
efficiency in combining O, H , and N atoms on alumina and magnesia
surfaces used in the calculation were 2.63 x 10‘ 2 and 3.15 x 10'2, respectively.
The numerical value of the catalytic efficiency expresses the fraction of atoms
impinging the surface that result in recombination.
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204
After going through this little exercise in estimating surface temperatures,
we now present the preliminary results of this first order approximation
calculation. Table 13 shows the results of the temperature estimation as they
are compared to the experimentally measured temperature.
W ith the
limited availability of literature values, the results of the approximation
indicate fair agreement was obtained.
In general, the temperature
approximation appears to be over estimated, possibly indicating diminished
activities for the atoms.
Though the agreement between the actual
temperature values may be less than desired, the general trend of relative
heating is correctly predicted, i.e., the effectiveness of heating achieved by the
plasma gases decrease in the following sequence: N 2 > O 2 > H 2 > He. The
discrepancy between the calculated and the experim entally measured
specimen temperature may arise from errors in estimating gas temperature
and the temperature dependence of recombination coefficient.
The atom
recombination coefficients, y(H+H), y (0 + 0 ), and y(N+N), were assumed to
be equal, but in reality the actual values may differ slightly though their
activities appeared similar at lower temperatures.
A third reason for the
disagreement in the calculated and the measured temperature may be due to
the transparency of the specimens to the wavelength (0 .9 pm) sampled by the
OFT. As a result, the apparent temperature may be lower than the actual
temperature. Another source of error may be due to the uncertainty in the
energy accommodation coefficient.
Published thermal energy accom­
modation coefficients are lacking for the gaseous species w ith the materials
employed in these experiments, but it is most certainly less than the assumed
value of unity. Thus, heating by chemical energy released at the surface as a
result of atom recombination may be a plausible mechanism during plasma
sintering.
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205
Table 13
Comparison of calculated and experimental specimen
temperatures for alumina and magnesia in various
plasma gases at 25 torr and an average peak power
density of 34 W /cm 3.
__________ A I 2O 3__________________
MgO_______
Plasma Gas
Texpt(°C)
Tcaic(0 C)
TexPt(°C )
Tcaic (0 C)
He
809
911
844
919
2
1190
1260
1120
1390
O2
1180
1280
1290
1370
2
1470
1600
1460
1760
h
n
In accordance w ith the above postulate that atom recombination reaction
was prim arily responsible for heating, the reduced surface temperatures of
specimens fired in a helium plasma may be understood. Since helium is a
monoatomic gas, the reactional enthalpy of the plasma is diminished
considerably without the contribution from atom recombination.!164! As
shown in the sample calculation in Appendix B, heating by electronic
recombination, i.e., recombination of ion and electron, was negligible
because the number flux of electrons and ions were small compared to that
of the neutral species. Therefore, heating is perhaps dominated by atoms
alone.
Shown in Table 14 are the results of the computed temperatures
compared to the measured values in helium gas plasma.
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206
Table 14
Comparison of calculated and experimental specimen
temperatures for helium plasma at 25 torr and an av­
erage peak power density of 34 W /cm 3.
M
Texpt (°C)
TCalc(°C)
Z n O
751
899
0.97
F e 2 0 3
808
901
0.86
A I 2O 3
809
911
0.49
T i0 2
840
918
0.28
M g O
844
919
0.26
S iC
870
898
0.95
a te r ia l
Evidently, rankings among the solids and temperature predictions are
only in rough agreement w ith the experimental results.
We have not
observed any obvious relation between electronic and structural properties
and specimen temperatures except for a rough correlation w ith surface
emissivity values. The discrepancy between the measured and computed
temperatures may arise from the uncertainty in the gas temperature in
helium.
Since the helium discharge was very diffuse (see Table
6 ),
one
source of error may be due to the visual method used in measuring the
discharge volum e and the assumption that the active volume of the
discharge corresponds exactly to that of the visible volume.
Thus the
determination of the power density may also be affected. Because Pd was
used to estimate various other properties, the experimental error in the
measurement of the power density may lead to the differences between
experimental and calculated temperatures. Another source of error may be
due to a lack of knowledge of the true thermal accommodation efficiencies
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207
on these surfaces.
The accommodation coefficients of the surfaces were
assumed to be unity.
However, the lighter helium are not as efficient in
exchanging kinetic energy w ith surfaces as the heavier diatomic gases.
Hof126! concluded that thermal accommodation coefficient not only varies
with mass of the gaseous species but also with material. Since experimental
data for energy accommodation of helium on ceramic surfaces are
nonexistent, we are therefore unable to verify the results of the present
calculation.
These observations are consistent w ith those of Cobine and W ilbur!29!
who studied the physical characteristic of various gaseous discharges
produced by a high frequency electronic torch. The authors noted that both
argon and helium flames were quite cool. For example, the flame of a 1 kW
unit would not ignite paper when impinging norm al to the surface.
Conversely, the flame produced by polyatomic gases readily melted a quartz
rod placed in its path. As we noted earlier in the section II, similar results
have also been observed in the previous rf and microwave plasma sintering
studies.!13'15'18! Pure argon plasma was unable to provide sufficient heat for
sintering. However, small additions of dopant gases, including O 2 , N 2, H 2 ,
and H 2 O, to an argon ICP resulted in substantial increases in specimen
temperature over those obtained in the pure Ar plasma under the same
conditions. These results together with the results of the present calculation
lend strong support to the deposition of heat by atom recombination.
Pfender et al.!26'27!, on the contrary, attribute the heating entirely to the
ion flux impinging the specimen surface. The role of dopant gases and gases
in general were considered to play only a minor role. Additionally, heating
by atomic recombination was completely neglected. The sintering behavior
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208
at reduced pressures was therefore concluded to be due to the non-catalytic
nature of the surface, so that the negative charge established at the surface
increases the rate and energy of the ions colliding the surface. Our findings,
however, show otherwise.
The solid surfaces investigated in the present
sintering study were found to be catalytically active, resulting in significant
high surface temperatures. Calculation of relative energy fluxes arriving at
the surface also indicate that the ion and electron make negligible
contribution to the heating process under these reduced pressure conditions.
It is also abundantly clear from this and previous plasma sintering
studies^18'19'23! that gases, either use as support gas or present as im purity gas,
play a major role in the heating of a sample immersed in a plasma.
There is another heating mechanism we have neglected in the
microwave plasma heating of specimens. Although we have assumed that
heating of the samples was accomplished primarily by direct contact with the
discharge, partial coupling w ith the microwave energy may also take place if
significant penetration of the microwaves through the plasma occur. This
would help explain why the predicted temperature was so much less than
the observed temperature for SiC. Being a lossy material, SiC may receive >
additional heating from microwave energy, resulting in substantial increase
in the specimen temperature.
Thus, if the relative strength of the
microwave field in the discharges can be determined, then the cause of
enhanced heating of SiC in helium as postulated above would be confirmed.
As w ill be discussed further below, helium plasma was indeed less effective
in screening the microwaves than the other gaseous discharges employed in
this study.
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209
IV . F. Mechanisms of Surface Heating
s
The present analysis is obviously based on the hypothesis that heating by
recombination of atoms on the oxides/non-oxide surfaces is the dominating
energy transport mechanism. In order to account for the differences in the
temperatures attained among the different solids, w e now turn our attention
to the activities occurring on these surfaces. The following speculation on
the possible surface mechanisms focuses primarily on the activity of oxygen
atoms on various oxides since data such as catalytic efficiency and bond
energy of the adsorbed gas w ith a given surface are relatively more abundant
for oxygen than other gases used in this study.
Inspection of Table 9 indicates that insulators appears to obtain higher
specimen temperature than semiconducting oxides.
This trend is in exact
opposite to the order of recombination coefficient measurements tabulated
in Table 4, which lists transitional metal oxides having a higher catalytic
activity than the insulating oxides.
From the values of recombination
efficiencies on these oxides, we should, therefore, expect higher specimen
temperatures to be associated with the transition metal oxides rather than
the insulators. As may be recalled in the background section, the abovementioned catalytic recombination efficiencies were determined by the sidearm method in which the number of atoms that have reconstituted to form
molecules out of the total number of atoms, from a known constant source,
im pinging onto a given surface was measured.
These experiments were
performed in the absence of a plasma. Hence, the presence of a plasma may
play
an im portant role
in
offsetting the catalytic mechanism of
recombination on a solid surface. To understand this disparity we need to
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210
examine the nature of the interface, the strength of the surface bond, and the
processes of chemical reactivity at these interfaces more closely.
IV. F. 1. Electronic Factors
IV. F. 1. a. Semiconductivity
It is noteworthy that the trend for oxides in Table 4, showing the room
temperature recombination coefficient of oxygen atoms on a variety of
surfaces, pointed to a parallelism between recombination activity and other
heterogeneous catalytic reactions on oxide surfaces. In studying chemisorption and catalysis on metallic oxides, Stone!108! summarized the relative
activities of the metal oxides as
p -type oxides > n -type oxides > insulating oxides,
which coincides w ith the pattern found above by Greaves and Linnettl104'105!.
The activity series for the decomposition of N 2 O!166'167! and CO oxidation!108!
showed a similar trend o f p -type oxides very much more active than n -type
oxides.
Dickens and Sutcliffe!106! supplemented their recombination studies with
measurements of the electrical conductivities of the oxides in order to
correlate the catalytic activities to the semiconductor types o f the oxides.
They found that the conductivities of p -type oxides, e.g., CuO, N iO , Fe2 0 3 ,
and C 03 O 4, increased and that of n -type oxides (e.g., CdO) decreased when
exposed to oxygen atoms, the half-times of the changes being about
1
min.
On subsequent removal of the oxygen atom flux, the original conductivities
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211
were recovered, but with half-times of about
1
hr, indicating that the gaseous
species were quite strongly adsorbed. The rise in conductivity upon exposure
to oxygen showed that the concentration of current carriers, positive holes in
the case of N iO , has increased which suggests that an electronic charge
transfer mechanism was involved. Apparently, in the chemisorption step,
oxygen is chemisorbed in the form of a negative ion, O-(ads), the electron
being donated by the solid lattice.
The holes produced in the electron-
transfer step then give rise to the observed changes in conductivity.
The
invariant chemisorption of oxygen in the acceptor form also provided these
authors a useful means of classifying oxide surfaces of doubtful n - o r p -type
character (e.g., Fe2 C>3 ) under the experimental conditions.
IV . F. 1. b. Fermi Level
The position of the Fermi level uniquely determines the concentration of
free electrons and holes on the surface of the crystal.
This explains the
physical significance of the part played by the Fermi level in the phenomena
of chemisorption and catalysis, and at the same time establishes a
characteristic correlation between the adsorptivity and catalytic activity of the
surface, on the one hand, and the surface concentration of electrons and
holes on the other.
The change of the electrical conductivity o f the oxides during the
recombination reaction discussed above is primarily due to the change of the
concentration of electronic defect in the region near the surface, i.e., the
boundary layer.!168-170! The concentration of electron holes in the boundary
layer was thus increased by the chemisorption of oxygen on p -type solids.
Such an increase in the catalytic activity with a corresponding increase in the
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212
hole concentration is indicative of a p -type reaction. These observations are
consistent w ith the predictions of Wolkenstein's electron theory of
catalysisJ171! According to rigorous analysis of the model, the rate of p -type
reaction, in which a free hole from the catalyst is localized and attached to
the adsorbed particle, is accelerated during the displacement of the Fermi
level downward, corresponding to increasing the concentration of holes (i.e.,
hole conductivity).
The Fermi level thus acts as a regulator of the
chemisorptive and catalytic properties of the surface. By altering the position
of the Fermi level on the surface of the catalyst, we can, in principle, change
the chemisorptive and catalytic properties of the surface.
IV. F. 1. c. d -Electron Configuration
Greaves and Linnettt105^ sought to correlate the catalytic activity of
transition metal oxides with d -electron configuration, since there is much
experimental support for this view in the field of chemisorption and
catalysis on metals. They noted that the most active catalysts also correlate
with the presence of cations w ith unpaired d -electrons, from d 9 (Cu2+)
down to d 5 (Fe3+) and d 4 (Mn3+). But chromia (d 3) was relatively inactive.
Krylov^81!, on the other hand, has shown that for most reaction involving
oxygen and other gaseous species minimum activity corresponds to d °, d 5,
and d 10, w hile maximum activity corresponds to d
3
and d 7. Moreover,
Stonet108l pointed out the lack of sound support for a simple correlation of
the catalytic activity of transition metal oxides w ith the number of
d electrons.
Therefore, one cannot establish an unequivocal connection
between the number of vacancies in the d band, or the d character of the
conduction electrons with the catalytic recombination of atoms on transition
metal oxides.
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7
213
It is dear from the foregoing discussion that the catalytic mechanism was
controlled by electronic factors. The electronic structure of the solid has a
particular influence on the heterogeneous reactions at the interface. But, the
p -typeness in oxides is not of itself a suffident criterion to differentiate their
relative catalytic activities.
There is, however, another "chemical" factor
which we must consider in order to elucidate the dependence of the reaction
variables upon the properties of the oxides.
IV . F. 2. Chemical Factors
The regularity in changes of catalytic activity of oxides in oxidation
reaction are often correlated to changes in the strength of the metal-oxygen
bond in oxides.!81'172! Since the heterogeneous recombination is in some
respects similar to oxidation reactions, or it may indeed be thought of as a
higher form of oxidation, we shall examine the catalytic activity in oxygen
atom recombination by a similar approach, dependence upon the same
parameter - the energy of the M -O bond in the surface layer of the oxide.
IV . F. 2. a. Surface Oxygen Bond Energy
Golodetsl172! has tabulated in his book values of the bond energy of the
surface oxygen, qs, for a variety of simple metal oxides. Systematic studies on
the bond energies of surface oxygen for metal oxides have been carried out
using calorimetric measurements!173-175!, the method of adsorptionchemical equilibrium !176-178!, and the temperature dependence of the
equilibrium pressure of desorbed oxygen!179-181!. The values of the surface
oxygen bond strengths can also be estimated by using kinetic characteristics
such as reaction rates or activation energies of the isotopic heteroexchange
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214
reaction between O 2 and the surface oxygen of metal oxides!182! or those of
the surface reduction reaction.!183'184! Golodets has noted that though the
bulk thermochemical properties such as the standard heats of formation,
-AH°298 per g-atom of O, cannot characterize the bond strength of the surface
oxygen, there is some correlation between this value and qs, as shown in Fig.
52. There appeared to be some qualitative correlation between qs and the
type of conductivity of the metal oxides. Oxides w ith low values of qs are
predominantly p -type semiconductors and, according to Dzisyak et al.!185!,
seem to have less stable configurations in the d -shell of the cation,i.e., d 3
(M n 0
2
), d 6, d 7 (C 0 3 O 4 ), d
8
(NiO ), and d
9
(CuO).
The oxides with
interm ediate qs values are n -type semiconductors and have stable d electron configurations, i.e., d 0 (Ti0 2 , V 2 O 5), d 5 (Fe2 C>3 ), and d 10 (ZnO). The
oxides with very strongly bound oxygen are evidently insulators.
IV. F. 2 . b. Correlation of qs with Catalytic Activity
Following the arguments in the previous section, we can now relate the
catalytic activity, y, of various oxides in the recombination of O atoms with
the surface oxygen bond energy, qs, similar to that outlined by Golodets!172!.
Using y values from Table 4 and qs values from either Ref. [172], whenever
possible, or estimates based on the standard heats of formation, we obtain the
plot of log y versus qs shown in Fig. 53. There appears to be two distinct
curves in Fig. 53, one corresponding to semiconductors and the other to
insulators. Furthermore, the dependence of log y upon qs passes through a
maximum for both group of oxides, suggesting a certain optimum strength
of metal-oxygen bond in these oxides. As we have alluded to in previous
paragraphs, the catalytic activity of semiconductors in oxygen recombination
proceeds by way of an electronic mechanism. Therefore, the evidence from
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215
140 -I
120
-
100
-
•
T i0 2
T i0 2
M15O3®
/"““N
o
cd
■
:>
cd
O
•
80 •
&
•
cr
40 -
•
Qt°2
CdO •
60 -
•
W 03
ZnO
•
Zr0 2
•
U 03
V20 5
•
r «2°3
CuO •
C03O4
20 -
M a02
NiO
0
- ----- 1------1----- 1------1----- .------1----- r ---- 1--- “»--- 1
- —1---- 1-----1---20
40
60
80
100
120
140
160
AH 298 (K cal/g-atO )
Figure 52.
Variation of the surface oxygen bond strength with the heats
of formation of the metal oxides (values of qs adopted from
ref. [172]).
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216
Atom Recombination Coefficient, y
CuO
NiO
▲ f «2°3
MgO
CaO
ZnO
0
20
40
60
80
100
120
140
Bond Energy, qs (Kcal/g-at O)
Figure 53.
The dependence of catalytic activity of various oxides in the
recombination of O atoms upon the bond energy of the sur­
face oxygen (adapted from refs. [103-106,172]).
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217
these two groupings of recombination efficiency perhaps suggests that the
catalytic mechanism m ay be controlled by two dominant factors, one
electronic and the other ionic.
IV. F. 2. c. Correlation of qs with Electronegativity Difference
If we replot the recombination data against the electronegativity
difference, Ax, of the oxides we obtain Fig. 54.
Pauling!186] defines the
electronegativity, x, as the capability of atoms in a molecule to attract
electrons to themselves. The degree of ionization of the bonds can often be
characterized by the difference in the electronegativity between the two
constituents of a binary compound.
It is known that acidic oxides have
mainly a covalent bond and basic oxides an ionic bond.!81! The greater the
effective charge on the oxygen atom and, therefore, the larger the difference
in electronegativity, the higher the ionic character in the bonds. Thus, as it
was shown, acidic oxides have small values and basic oxides have large
values of electronegativity difference, Ax:181,172] Figure 54 shows that while
the correlation between the recombination activity and Ax is relatively poor
for the semiconductors, the insulators seem to exhibit some regularity in the
catalytic activity for oxygen atom recombination as a function of the
difference in electronegativity. Reaction rates tend to increase, in the case of
insulators, with enhanced basicity of the surface, though an optimal
alkalinity seems to be suggested. Krylov!81! pointed out that the active center
for base catalysts in a majority of cases appears to be the surface ion of O2-.
Figure 54, thus, indicates that there may be a distinctly different catalytic
mechanism operating in the insulating oxides, which is possibly ionic in
character.
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218
Atom Recombination Coefficient, y
lO '1 !
CuCT
NiO
CaO
[dO
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Ax
Figure 54. Correlation between the logarithm of catalytic activity for oxy­
gen recombination and the difference of electronegativity
(adapt from refs. [103-106,186]).
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219
IV . F. 3. Rate Equation for a Recombination Process
To understand the maximum in Figs. 53 and 54 we must consider the
elementary processes occurring at the interface.
Atom recombination on
surfaces, whether poisoned or not, have been found unambiguously to be of
the first order over a wide range of temperatures.tt01' 107'109'113'159-160! Many
investigators have looked into mechanisms that would account for this
observation. Ehrlicht187! has given a good treatment on a phenomenological
approach to the determination of the detailed mechanism of surface
reactions.
By far the most probable mechanism postulated involves
chemisorption of atoms followed by recombination during collisions
between gas atoms and surface-adsorbed atoms.
Thus, the catalytic
recombination of oxygen atoms may proceed according to the following
scheme
1) O + (
) -> (O )
2) 0 + ( 0 ) - » 0 2 + ( )
2 0
where
~ -7 o 7 ~
( )denotesan active center on
surface-adsorbedatom,
and k\ and
(79)
the surface ofthe catalyst,
arethe respective
(O ) a
rateconstants
associated with the elementary steps 1 and 2 in Eq. (79).
If we take it one step further, and find the expression for the rate equation
for the above recombination process, we then arrive at the following
r
= k2 p0 6
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(80)
220
where pQ is the partial pressure of the atom in the gas phase.
But, the
fraction of surface coverage with oxygen, 6, is simply the ratio of the number
of O atom adsorbed to the total number of available surface sites for
adsorption,
e = .— h is —
(si)
fcl Vo + f a Vo
Thus, the corresponding rate equation becomes
r
= f
- Vo
( 82)
fa + fa
IV . F. 4. Bronsted-Temkin Relation
W e can further express the rate constants in terms of the BronstedTem kin relation in order to relate the heats of formation of surface
intermediates and surface activities.!172! The Bronsted-Temkin relation has
proven to be valid in numerous surface reactions such as adsorption and
heterogeneous catalysis. This is evidenced by data presented on the exact and
strict correlations between the surface oxygen bond energy, qs, and specific
catalytic activities.
Basically, the Bronsted-Temkin relation establishes the
relationship between thermodynamic and rate characteristics of reactions
when ions or radicals participate in a process. Thus, we have the relation
k = g Ka
( 84)
where k is the rate constant, K is the equilibrium constant for an elementary
step, and g and a are constants.
The constants k and K can also be
represented in another form
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221
k
=
( 85)
K
and
K = K„
(8 6 )
where E is the activation energy, Q is the heat of the elementary step and kQ
and K0 are pre-exponential factors. Equation (84) can be transformed into
E = A - aQ
(87)
where A and a are constants.
Consequently, on the basis of the Bronsted-Temkin relation we can
express the rate constants fci and ki of the elementary steps in Eq. (79) as
*■ - “ ' i - j f i
- - « ■ ( -r *t )'
( 88 )
where a and fi are constants. In the first step, oxygen-catalyst bonds are
formed and in the second one they are broken. For small values of oxygen
bond energies, qs, we have
»
h and the corresponding rate equation (Eq.
82) reduces to
r
= h p0
(89)
Since k\ increases as the the value of qs is increased, the catalytic activity
should, therefore, increase w ith qs . At high values of qs, on the other hand,
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222
when the removal of surface oxygen is slow, fci »
and the rate equation
becomes
r
(90)
= h p0
As a result, we should expect the rate to decrease with increasing strength of
the surface oxygen bond, qs . Moreover, on the basis of Eq. (87), we have
E
= E2
where p ' is some constant.
(91)
= const + P 'q s
Hence, in this region, the activation energy
should increase w ith increasing qs .
Sim ilarly, corresponding to the
ascending branch of the curve of the rate versus qs, the activation energy
should decrease with increasing values of qs according to
E
= Ei
= const' - 2 a q s
(92)
Thus, an optimum strength of bonding of oxygen to metal in the oxide
catalysts is implied such that when qs > (qs )opt, the activity decreases with
increasing values of qs .
The activation energy corresponds to E2 and
increases as the bond energy is increased. When qs < (qs )opt, the activity is
determined by oxygen adsorption ( r = k\pQ) and increases w ith qs since, in
this step, the oxygen-catalyst bond is formed.
At the same time, the
activation energy, Ei, in this stage decreases with increasing qs .
According to the above analysis, the regularity in changes of catalytic
activity of oxides in recombination reactions may be explained in terms of
changes in the strength of the metal-oxygen bond in oxides. Figure 53 shows
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223
that the catalytic activity does indeed pass through a maximum for both
groups of oxides, i.e., semiconductors and insulators. Where the maximum
occurs in the curve we should also observe a minimum which corresponds
to the optimal catalyst when the activation energy is plotted against the
surface oxygen bond energy. W ith activation energy values obtained from
the literature!106'112! for catalytic recombination of oxygen, we were able to
plot the curve of E vs qs , as shown in Fig. 55.
Indeed, we observe a
correspondence between the minima in Fig. 55 and the maxima in the curve
of y vs qs . As indicated in Fig. 55, the two curves on the left-hand side are
those of the semiconductors, the upper curve being room temperature
values and the lower curve high temperature measurements. The curve for
the insulating oxides remains distinct and does not change w ith
temperature.
Therefore the above correlations of the experimental recombination data
with the surface oxygen bond energy, electronegativity, and activation energy
indicate that there may be a duel mechanism for the catalytic recombination
of atoms or radicals on the surface of metal oxides. Semiconducting oxides,
w ith the ability of the cation to exhibit variable valency, tend to be
dominated by a recombination mechanism controlled by electronic factors
(e.g., electroconductivities and Fermi levels).
Hole conducting (p -type)
semiconductors appears to be the most active with the highest efficiency
being characterized by an optimum qs . The highly stable insulating oxides,
on the other hand, without the availability of multivalency, tend to favor a
catalytic process which proceeds by an ionic mechanism. Basic oxides show
greater activity than the more acidic oxides with the relative catalytic
efficiency being determined by both the surface oxygen bond energy and
surface acidity.
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224
Activation Energy, E (Kcal/mole)
CdO
10 -
NiO
'& ZnO
CuO
NiO
CdO
I MgO
CuO
0
20
40
60
80
100
120
140
qs (Kcal/g-at O)
Figure 55.
The dependence of the activation energy of the atom recom­
bination proess on the bond energy of the surface oxygen
(values of E obtained from ref. [106,112]).
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225
IV. F. 5. Effect of Charging on Recombination Activity
Since the catalytic process on semiconducting oxides involved an
electronic mechanism, it is conceivable that the excess charge generated by
the discharge during plasma sintering accumulates on the surface of the
semiconductors and may be expected to have a negative effect on the density
of adsorption sites (assumed to be surface cations) and, thus, the rate of
catalytic recombination.
IV. F. 5. a. Retardation of Reaction Rate
There is numerous experimental evidence that supports the view of an
adsorbed oxygen as 0 - (ads) adion. The change in conductivity accompanied
by uptake of an excess of oxygen!106/188"189!, isotopic exchange of
oxygen!190/191!, and chemisorption and catalysis studies!81/108'172'192! indicate
that the adsorbed species is in an anionic form.
Thus oxygen is always
adsorbed as a negatively charged species, the electron being donated by the
solid catalyst to the adsorbed oxygen and compensated by formation of a hole
in the surface zone.
The interaction involving electronic charge transfer
between chemisorbed molecules and the electronic structure of the solid
during the chemisorption process is described by the electronic boundary
layer theory of chemisorption.!193'194!
The theory essentially treats the chemisorption process involving
molecules A on a solid B to be represented by a contact of materials A and
B, i.e., in a manner analogous to the surface process upon contact of a metal
and semiconductor to form a rectifying contact. In this theory, the gas being
adsorbed is represented solely as a donor or acceptor of electrons; the
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226
adsorbent is represented by a conventional semiconductor with a given
concentration of ionized donor or acceptor centers and whose ability to
participate in chemisorption is otherwise uniquely determined by the height
of the Fermi level.
One of its main predictions is that for depletive
chemisorption, i.e., chemisorption which involves the removal of the
majority carriers from the semiconductor, coverage at equilibrium should be
severely restricted.
The boundary layer theory of chemisorption, thus,
predicts that acceptor gas oxygen w ill be adsorbed depletively to low coverage
on n -type oxides (e.g., ZnO ), and cumulatively to high coverage on p -type
oxides (e.g., CuO). This is in fair agreement w ith experimental data and may
be one of the factors that contributed to higher recombination coefficients of
p -type semiconductors.
The accumulation of free electrons on the surface of the semiconductor
w ill diminish the concentration of electron holes by recombination at or
near the surface and, consequently, deplete the number of chemisorbed
oxygen atoms. The electrons created by the effect of a plasma, in fact, act as a
catalytic poison.
Their effect in reducing the number of positive holes
parallels the effect of impurities added to a semiconductor which are of the
opposite type to those initially producing semiconductivity. This effectively
reduces the concentration of holes and, as a result, the excess negative
charges on a p -type semiconductor surface can retard the rate of p -type
reactions.
In addition, the poisoning action of surface impurities, according to the
more fundamental treatment of the electron theory of catalysis^171!, is noted
to be critically dependent on the position of the Fermi level on the surface of
the crystal.
The word "impurity" does not necessarily denote chemically
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227
foreign atoms, but any agent which may either raise or lower the activity of
the catalyst. As mentioned above, the rate of p -type reactions is greater the
lower the Fermi level because these reactions are accelerated by holes. The
theory also predicts a change in the adsorptivity and catalytic activity by the
application of an external electric field to a semiconductor. By shifting the
Fermi level (other conditions being fixed) due to surface charging the
adsorptivity can be vary depending on the character of the reaction.
Therefore, by placing the semiconductor in a plasma field, the electron
concentration on the surface of the oxide w ill be increased as compared with
the case of no field, i.e., the Fermi level will be raised in the presence of the
field.
In other words, the surface is negatively charged. Thus, under the
influence of the field, the adsorptivity of the surface should decrease. At the
same tim e, the catalytic activity of the sample should also diminish. We
may expect a reduction in the reaction rate in the presence of a plasma
environm ent.
IV . F. 5. b. Destabilization of the Adsorbate-Adsorbent Bond
Surface charging also produces a deleterious effect on the existing surface
oxygen bond.
We may expect the excess surface charges to exert some
influence on the strength of the adsorbate-adsorbent bond.
Take, for
example, the situation in which an electron hole (here identical w ith N i3+
ion) is localized and attached to an O atom adsorbed on the (100) face of
NiO:t106!
o-
... CP-NiS+O2- . ..
. . . N i 2+0 2-N i2+. . .
(I)
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228
In the case of excess negative charges on the surface under discharge
conditions, underlying holes may be attracted towards the surface and give
rise to
o. . . 02-N i3+02- . .
. . . N i 3+0 2- N i2+. ..
(n)
The electrostatic repulsion between the two electron holes renders the N i3+O-(ads) bond in (II) to be weaker than that in (I). Similarly, the N i3+- 0 - (ads)
bond would be destabilized by the recombination of a free electron w ith a
hole, as in
o. . . 0 2 -N i 2+0 2- . . .
. . . N i 2+0 2- N i2+. ..
(in)
From electrostatic considerations, the surface-O-(ads) bond should be
stronger when a N i3+ state is localized at the adsorption site than in form (II)
and (III).
Therefore, excess negative surface charges may lead to the
generation of some weakly bound adanions which are particularly
vulnerable to rupture of the bond and eventual desorption from the surface.
Thus, from the theory of the electronic boundary layer, the electron
theory of catalysis, and qualitative electrostatic considerations discussed
above, the effect of excess negative charges on the surface resulting from an
electric field imposed to the sample is to reduce the adsorptivity and catalytic
activity of a semiconductor. The excess surface charges essentially produces a
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229
p o is o n in g
e ffe c t.
c o n s is te n t
w it h
th e
r e c o m b in a t io n
g e n e r a l,
th e
th e
in
a s s o c ia te d
w it h
a c tiv it y
in
th e
a c tiv it y
fo r
p r e d ic te d
a
v a r ie ty
c a ta ly t ic
o x id e s ,
o b s e rv e d
N iO )
o f
s u p e r io r
u n d e r
o b s e r v a tio n
e ffe c t
s tu d ie s
in s u la tin g
re v e rs e d
O u r
th e
a s
T h e
o f
o f
e x h ib itin g
g re a te r a c tiv it y
s till
o x y g e n
4 .
B a s e d
n u m e ro u s
th e
d u r in g
o f
th e
N e v e r th e le s s ,
p re s e rv e d ,
o x id e s
th e
th a t o f
p a tte rn
w a s
s in te r in g ,
as
te m p e ra tu re s
d e p re s s e d
tre n d
p-ty p e
i.e .,
o v e r
th is
s a m p le
is
o b s e rv e , in
o x id e s
p la s m a
fir e d
r e s u lt
o n
a to m s , w e
H o w e v e r,
lo w e r
n- t y p e
th a n
r e s u lts
s e m ic o n d u c t in g
p la s m a .
w a s
fo r
T a b le
b e
s in te r in g
th e o r ie s .
d is c h a r g e
m a y
th e
s e m ic o n d u c t o r s
o f
in
a
p la s m a
th e s e
g e n e r a lly
s e m ic o n d u c t o r s
th e
o f o x id e s
p re s e n te d
9 .
p re s e n c e
b y
a c tiv it y
in f lu e n c e
T a b le
o f
c a ta ly t ic
o f
c a ta ly t ic
( F e 2 C>3 ,
o x id e s
(Z n O ).
IV . F. 6 . Discussion on Dopant Effect in AI2 O3
C a lc u la t io n s
th a t
c a t a ly t ic
s u rfa c e
o f s p e c im e n
a c tiv it y
d u r in g
p ro c e e d s
b y
In
o f
o n
e ffe c t
K n o w
lt o n l14]
s m a ll
a d d itio n s
d o n o r s i195!,
a ls o
th e
Y 2O 3,
I f
p -ty p e n e s s
in
th e
th e
o b s e rv e d .
d o p e d
s p e c im e n
to
th is
la tte r
o x id e
o f th e
K n o w lt o n 's
d e c re a s e d
tw o
fa c to rs
s h o u ld
in
th e
s in te r in g
v ie w .
a n d
im p a r t
h a v e
th e
o f
o n
A I 2O
in a
N iO .
th a t
th e
T h e
fir s t
tw o
c h a ra c te r
th e n
th e
th e
to
th e
o f th e
p ro c e s s
e a r lie r
d o p e d
th e
in
th e
a n d ,
o p p o s ite
te m p e ra tu re s
o r d e r o f Y 2O 3, M g O , T i0 2 , a n d
a re
a lu m in a
a c tiv it y
H o w e v e r, th e
b y
w it h
d o p a n ts
in c r e a s e
c a ta ly t ic
in
in v e s tig a tio n
o u t
w e re
fa c t
a p p a r e n t ly
c a ta ly z e d
s a m p le s
th e
c h a r g in g
c a r r ie d
a lu m in a .
s h o w e d
s u p p o rts
b y
5 3 -5 5 ,
3
a c c e p to r
e n h a n c e d
9
in s u la to r s
F ig s .
c o n t r o llin g ,
a c c e p to r-d o p e d
r e s u lts
a ffe c te d
e le c tr o n
in
A lu m
w e re
T a b le
a c tiv it y
s h o w n
M g O ,
in
n o t m u c h
fro m
p lo ts
T iC > 2 ,
e le c t r o n ic
c o n s e q u e n t ly , h e a t in g
w a s
th e
s h o w n
C a ta ly tic
p la s m a
s u p p o rts
o f
w e re
d if f e r e n t
a d d itio n
w h e re a s
s p e c im e n s .
fir in g .
m e c h a n is m
s e m ic o n d u c t o r s .
d o p a n t
o f in s u la to r s
p la s m a
a
te m p e ra tu re
N iO .
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o f
th e
T h e s e
230
results, therefore, do not support the role of an electronic mechanism as the
dominant factor in chemisorption and catalysis on insulating oxides.
The order of dopants listed in the above paragraph was found to correlate
w ith the formation energy, The effect of dopants in
A H °2 9 8
A I2O 3
per g-atom of O, of the dopant oxides.
may be explained on the hypothesis that the
catalytic activity is characterized by having a certain optimum strength of
bonding of oxygen in oxides, qs, together w ith an optimum basicity, as
reflected by the electronegativity difference, Ax. Since any im purity dopants
added to the alum inum oxide w ill increase the activation energy, in
accordance with the curve of E vs qs shown in Fig. 55, we should expect
greater resistance to catalysis. This is confirmed by the plasma sintering data
cited above which reported that all of the dopants added to alumina
consistently exhibited lower specimen temperature than those of pure
alumina samples under identical power conditions.
The poisoning effect
may not be due to a decrease in the number of reaction sites, though this may
also contribute to a retardation in the catalytic activity, but to the additional
energy required to form the reaction complex on the surface. The extent of
reductions in specimen temperature caused by the dopants is therefore
determined entirely by qs and Ax. As pointed out earlier, the energy of
formation has a qualitative correlation with the surface oxygen bond energy.
Thus, on the basis of Fig. 53 the dopants that decrease the strength of M -O
bonds to the left of alumina (i.e., belonging to the ascending branch of the
curve of y vs qs) as well as those that increase the value of bond energy of
surface oxygen to the right of the maximum w ill decrease the activity of the
oxide. The influence of dopant on the electronegativity difference can be
explained in a sim ilar fashion (see Fig. 54).
The values of the
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231
electronegativity difference as well as the surface oxygen bond energy for
these dopant oxides are tabulated below in Table 15 for comparison.
Table 15
Values of the strength of bonding of surface
oxygen and the electronegativity difference
of dopant oxides.
Material
qs (Kcal/g-atom O)
Ax
Y2 O 3
122
2.3
MgO
115
2.3
T i0 2
93
1.9
N iO
13
1.8
The lowering of specimen temperatures as a result of dopant additions
generally paralleled the patterns in the surface oxygen bond energy and the
electronegativity difference except for yttria, whose qs value falls to the right
p
of the maximum on the descending branch of the y vs qs curve. Although
the surface temperatures during plasma sintering of Y 2 O 3 and MgO doped
specimen were comparable, we would expect yttria to depress the specimen
temperature more than magnesia.
This may have been affected by the
presence of a smaller concentration of yttria, at half the concentration, than
magnesia.
Knowlton reported that the temperature measurements were
subject to some variability.
If the sample rods were sintered slightly off
center or if the diameter of the rods were slightly smaller the measured
surface temperature would vary. These experiments can be repeated using
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232
the more accurate optical fiber thermometer together with the thimble
assembly to verify the dopant effect on insulating oxides.
IV . F. 7. Ionic Factors
According to Fig. 54, recombination efficiency on the refractory oxides is
enhanced with increased alkalinity of the surface and passes through a broad
maximum. There are essentially two types of alkaline centers on the surface
of stable oxides: the strongly basic centers (anions of O2-) and the weakly basic
centers (OH groups) of the surface. In most cases involving basic catalysts the
active center appears to be the O2- surface ion, whereas the O H groups are
catalytically inactive or only slightly active.!81)
Warren had also noted that
the ability of a surface to destroy various chain-carriers and intermediates
(e.g., H O 2 and H 2 O 2 ) in a combustion process seems to depend on the degree
of alkalinity (O2- and OH~) at the surface. Walsh and coworkers!196'197) from
their studies of the oxidation of methane by several refractory oxides also
concluded that more acidic surfaces are less active than the more alkaline
surfaces. Linnett et al.!105'112) suggested that the hydroxyl groups are not the
active sites for oxygen atom recombination on Pyrex and silica, but rather the
electronically saturated oxygen atom of the anionic =S i-0~ group and =S=0
group which result from dehydration of two adjacent hydroxyl groups on the
surface. Consequently, the oxygen bridge formed w ill be under some sort of
strain and some of the silicon atoms are only associated with three oxygen
atoms. In fact, according to studies of vibrational spectra, as the surface strain
increases with the dehydration, the surface siloxane bridges were shown to
contain very weakly bridging oxygen atoms.!198) Hence, recombination can
take place by abstraction of these relatively loosely bound oxygen atoms from
the surface by another atom. Thereafter, a new oxygen atom adsorbs on the
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233
surface defect resulting from the previous reduction reaction, and the process
is carried on.
Alternatively, the electrons available from the surface may serve to bind
adsorbed oxygen atoms to the surface until they are attacked by a gaseous
atom. Krylov!81! attributed die high catalytic activity of the solid bases to the
greater number of "negative free valences" or O5- resulting from
dehydration of their surfaces. It is also believed that the surface oxide ions of
lower coordination, i.e., O2- which are located on steps, kinks, comers, etc..,
are expected to be the source of electrons available for catalysis and have
enhanced reactivity at these centers.!198'1" !
Another possible ionic
mechanism may involve the interaction of a gaseous atom w ith surface S
center, which is analogous to the bulk F centers (one electron trapped in an
0 2~ vacancy). The adsorbed oxygen atom, O-(ads), can subsequently react
w ith an incoming atom. The support for this view was found in the work
presented by Che!1" ! who noted that oxygen adsorption destroyed the surface
S centers on several alkaline earth oxides. Thus, the basic centers appears to
play an important role in the catalysis of atom association on refractory nonmetals. Catalytic activity was found to depend on surface alkalinity as well as
on the strength of the surface oxygen bond.
However, more conclusive
results are needed in order to identify the dominating catalytic mechanism
occurring on these insulating oxide surfaces.
In Table 16 below, we have constructed a table similar to that of Table 9
summarizing the efficiencies with which various oxide surfaces catalyze the
recombination of H , O , and N atoms.
The catalytic efficiencies were
determined by using Eq (65), assuming a neutral temperature o f 1200 °K, to
obtain the value that would reproduce the same temperature as that of the
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234
observed specimen.
As we discussed previously, the activities of the
semiconductors were diminished due to excess negative charging in the
plasma environment, resulting in decreased adsorptivity and catalytic
activity on the surfaces. The insulators, on the other hand, were not affected
for other mechanisms were operative. For instance, the extrapolated values
of recombination efficiencies of oxygen on both alum ina (y = 0.0263) and
magnesia (y = 0.0315) from published data yielded fair agreement with those
calculated in Table 16. The similarity in the catalytic efficiencies for atomic
oxygen and atomic nitrogen on alumina was also observed by Goulard^116!.
Linnett et al.U12! noted in their work that the activity of hydrogen atoms on
alumina begin to increase considerably above 700 °K . This observation is
consistent with the result presented here for hydrogen.
Table 16
Summary o f estimated values of atom recombination
coefficient, y x
1 0 3,
on various oxide surfaces in differ­
ent gaseous discharges.
Gas
MgO
Al20 3
T i0 2
Z r0 2
Fe2 C>3
N iO
ZnO
h2
20
28
8
7
14
8
—
02
32.5
25.5
27
27
17
10
10
n
23.5
24.5
17.5
20
18.5
21
14
2
The results for magnesia indicate decreasing recombination activity in the
order: y (0+ 0) > y (N + N ) > y (H + H ). The support for these results is lacking in
the literature, however, the pattern appeared to correspond with the trend of
the correlation between the heats of chemisorption o f oxygen, nitrogen, and
hydrogen and the heats of formation of the oxides, nitrides, and hydrides!172!
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235
Catalytic activity on semiconductors, on the contrary, generally follow the
sequence of nitrogen, oxygen, and hydrogen. These surfaces were reduced, to
some extent, in nitrogen and more so in hydrogen plasma. Since reduced
surfaces increases the degree of surface imperfection, catalytic activity should
therefore be enhanced. This is confirmed by the work of v.d. Berg et aU192]
who observed higher density of active sites for adsorption and catalysis on
reduced CuO and V 2 O 5 . Thus, the increased surface activity in nitrogen
plasma for the semiconductors may be explained. Both hematite and nickel
oxide were reduced to their metallic state during plasma firing in a strongly
reducing hydrogen plasma.
It may be that these m etallic phases are
catalytically inferior to their oxides. The smaller recombination efficiencies
shown for nickle is consistent w ith the lower specimen temperatures.
As indicated in the above table, titania and zirconia exhibited similar
activities for each of the three gaseous species, with the highest recombining
efficiency shown towards atomic oxygen, followed by atomic nitrogen, and
then atomic hydrogen. The ranking of catalytic activities among the gases
paralleled that of MgO.
The similarity in their catalytic behavior may be
related to their closeness in physical and electronic structure properties. Both
crystallize in the fluorite structure (or derivatives of it) and display similar
electrical conductivities, being insulators at low temperatures and acquiring
n -type conductivity at high temperatures as oxygen is lost.!200'201! On the
basis of the above discussion on catalytic mechanisms, we would not expect
these oxides to show greater activity than alumina for recombination of
oxygen atoms since they both have lower values of electronegativity
difference and surface oxygen bond energy. But, the surface catalyzed atom
association reaction may be enhanced as a result of increasing loss of oxygen
from the surface at high sintering temperatures and, therefore, a
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236
corresponding increase in the number of active center for adsorption and
catalysis.
Though the catalytic efficiency for silicon carbide is not indicated in the
table, the sintering data tabulated in Table 9 show that SiC consistently
exhibits lower surface temperatures in the polyatomic gas discharges. For
obvious reasons, silicon carbide was not fired in the oxygen plasma. Halpem
and Rosnert160! noted low values of atom recombination coefficient and
energy accommodation coefficient for N atom reconstitution on SiC surface.
The lower activities at the carbide surface thus explain the generally lower
specimen temperature observed for silicon carbide.
Again, it would be pertinent to examine the relation between catalytic
activity and the energy of the bonds of the atoms w ith the surfaces and the
nature of the surfaces as we have done for the case of oxygen if we are to
resolve the differences in surface catalytic activity. The present analysis of
heating of solids in diatomic gas plasmas is, of course, speculative.
The
factors contributing to the catalytic recombination and energy deposition at
the surfaces may be very different from that depicted and possibly much
more complex.
IV . G. E-field Probe Measurement
IV . G. 1. Probe Characterization
By using the configuration of the high-resistance transmission wires as
depicted in Fig. 23, the characteristic response of the EM field probe for an
empty cavity was obtained. The measured probe output voltage as a function
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237
of absorbed power is shown in Fig. 56. The power absorbed in the empty
cavity as determined by calorimetric measurements was correlated with the
applied power and is presented in Fig. 57. The detected output dc voltage
apparently has an approximately linear response to the absorbed power for
the range tested. Since the microwave apparatus was operated without any
tuning devices, most of the input power was reflected in the absence of a
discharge, thereby resulting in the low power absorption in the cavity as
indicated in Fig. 57. The presence of a discharge would act as a sink for the
microwave energy and greatly enhances the absorption of microwave power
in the cavity, w ith efficiencies greater than 80%, as w ill be seen below.
Though the probe signal could only be characterized in a lim ited range of
absorbed power, the E-field probe was a useful tool in serving as a relative
measure of the electric field strength in various gas plasmas. A ll of the probe
data presented were averages of two separate runs.
IV . G. 2. Helium Plasma
The power absorption increases linearly w ith the incident power for the
helium plasma, as shown in Fig. 58. The probe response as a function of
absorbed power in helium appears in Fig. 59. The detected output voltage
decreases gradually with increasing absorbed power to about 900 W , at which
point the probe signal makes an upturn, indicating the presence of a
minimum. Since the probe characterization showed that the detected output
voltage was an increasing function of absorbed power, it is not clear why the
probe signal exhibited a decrease initially. The applied power can be thought
of as a direct means of altering the plasma characteristics, such as the electron
density.
When the gas is sufficiently ionized, the plasma behaves as an
electrical conductor.
The electrical conductivity is proportional to the
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238
3.0
Probe Voltage (mV)
2.5
2.0
1.5
1.0
0
20
40
60
80
100
Power Absorbed (watts)
Figure 56.
E-Field probe output as a function of absorbed microwave
power in the absence of a plasma.
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Absorbed Power (watts)
239
60-
40-
20 -
0
200
400
600
800
Applied Power (watts)
Figure 57.
Variation of the microwave power absorbed by the empty
cavviity as a function of applied power without a plasma.
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240
1500
. 1200
900
600
300
0
300
600
900
1200
1500
Applied Power (watts)
Figure 58.
Power absorption as a function of applied power in a micro­
wave excited helium plasma at a pressure of 25 torr.
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241
6
Probe Voltage (mV)
5
4
3
2
1
0
200
400
600
800
1000
1200
Power Absorbed (watts)
Figure 59.
E-Field probe output as a function of absorbed power in a
microwave excited helium plasma at a pressure of 25 torr.
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242
number of charge carriers in the plasma. The skin depth can thus be related
to the conductivity as shown before (see Fig. 17). The lower the electrical
conductivity, the larger the skin depth, and therefore, the greater penetration
of the electric field through the plasma medium.
The initial reduction of the induced ac voltage w ith applied power may,
in effect, indicate an increased screening of the E-field due to higher electrical
conductivity of the plasma as a result of increased degree of ionization. A
point is reached, however, when the skin depth becomes a constant as
electrical conductivity obtains saturation, the output dc voltage begins to
level out.
Figure 60 shows a plot of electrical conductivity curves as a
function of electron
temperature for He, A r, N 2 , and H 2 at one
atmosphere. 1981 The conductivity increases sharply w ith temperature and
reaches a lim iting value at
1 0 '1
(Q cm ) -1 until second ionization occurs.
According to Fig. 17, this would correspond to a skin depth of 0.1 mm. A t the
same temperature, H e exhibits a low er conductivity due to its high
ionization energy.
Since electron temperature increases w ith decreasing
pressure, the temperature at which saturation in the conductivity occurs is
consistent with those calculated in Table
8.
The observation is also in fair
agreement with the calculated electron density. Figure 61 presents the result
of computed electron number density as a function of applied power for
several pressures. The electron concentration appears to slowly approach a
lim iting value at higher power levels. The upward turn at higher power
levels may be due to a direct increase of probe signal w ith power, since the
screening effect by the plasma has become constant.
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243
Nitrogen
Helium
Hydrogen
T(kK)
Figure 60.
The dependence of electrical conductivity of hydrogen,
nitrogen, argon, and helium plasma upon the electron
temperature at one atm (from Winters [98]).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Electron Density
(cm -3)
244
□ 5 torr
O 25 torr
& 40 torr
0
500
1000
1500
2000
2500
Applied Power (watts)
Figure 61.
Electron density as a function of applied power for a microwave
excited helium plasma at several pressures.
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245
IV . G 3. Hydrogen Plasma
The probe response for the hydrogen plasma, as illustrated in Figs. 62 and
63, exhibited a similar effect as in the previous case. The detected output
voltage again passes through a minimum with respect to the applied power.
The m inimum now occurred at a smaller power level than that in He.
Indeed, calculation of electron density as a function of applied power showed
that the electron density approaching a constant value at lower power
values, as shown in Fig. 64. High signals at low powers may be indicative of
greater penetration of the microwaves, when the number of charge carriers is
less, and also at higher powers, as the electric-field strength increases
proportionally with absorbed power.
A t a constant input power, the detected output voltage showed an initial
monotonic decrease w ith increased pressure, as shown in Fig. 65.
Also
plotted in the same figure is a curve corresponding to an increase in power
absorption by the hydrogen plasma. The signal continues to decrease, at a
slower rate, with further increase in pressure and appears to have reached a
minimum at the same time as the power absorbed approached a maximum
value. Determination of the electron concentration as a function of pressure
suggests that as the absorbed power approaches a plateau, the ionization
degree, thus the electrical conductivity may also reach a maximum, as
indicated in Fig.
66.
This calculation is consistent w ith the theory of power
absorption for an electron as discussed above in section IV .f118! The theory
predicts that the power absorbed passes through a maximum at a pressure
characteristic of a gas, in a range of 1 to 80 torr. Hence a minimum in the
probe signal is observed.
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246
1200
1000/—N
800-
600-
400-
200 -
0
200
400
600
800
1000
1200
Applied Power (watts)
Figure 62. Microwave power absorbed as a function of applied power
in a hydrogen plasma at a pressure of 25 torr.
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247
6
Probe Voltage (mV)
5
4
3
2
1
0
0
200
400
600
800
1000
1200
Power Absorbed (watts)
Figure 63. E-field probe output as a function of absorbed power in a
microwave excited hydrogen plasma at a pressure of 25
torr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Electron Density
(cm-3)
248
□
5 torr
O 25 torr
A 40 torr
200
400
600
800
1000
Applied Power (watts)
Figure 64.
Electron density as a function of applied power for a micro­
wave excited hydrogen plasma at various pressures.
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249
3.0
-325
M
;>
I
-315
2 .0 -
Oh
-305
295
0
10
20
30
40
Pressure (torr)
Figure 65.
E-Field probe output and power absorbed as a function of
pressure for a microwave excited hydrogen plasma at a
constant input power of 360 W.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A b s o rb e d
D
00
P o w e r
!
-335
2.5-
(w a tts )
-345
250
12
10
Electron Density
(10 'ncm *3)
14
8
6
4
0
10
20
30
40
50
Pressure (torr)
Figure
66.
Average electron number density as a function of pressure
for a hydrogen plasma at a constant input power of 360 W .
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251
IV . G. 4. Oxygen Plasma
The oxygen plasma results resembled those of hydrogen, as evidenced in
Figs. 67 and
68.
W ith an increase in the power supplied to the plasma, the
output signal decreases, signifying a drop in the measured electric-field
strength. Thus the skin depth may be decreased because of higher electrical
conductivity. In the range of power measured in the oxygen experiment, the
probe response curve is apparently approaching a minimum, resembling the
left-handed portion of the curve of voltage versus absorbed power for
hydrogen plasma. Although pressure dependence o f the output dc voltage
was not monitored, we would expect analogous results to hold.
IV . G. 5. Nitrogen Plasma
The E-field response of the detector as a function of power for nitrogen
plasma appeared to display an opposite trend from that in an oxygen plasma.
Both the induced probe response and the power absorbed curves were shown
to increase w ith power applied to the cavity, as shown in Figs. 69 and 70. The
result of electron density calculations, as plotted in Fig. 71, does not suggest
constant electron concentration at low powers. It is not easy, however, to
understand on the above basis, why the detector signal exhibit an increase at
low power level as shown in Fig. 70. The dependence of the detected output
voltage on pressure, on the other hand, behaved like that of the hydrogen
gas plasma. Figure 72 shows that the absorbed power increased to a plateau
as the pressure was increased at constant applied power.
A t the same time
the E-field probe output decreased, indicating a reduction in the penetration
of the microwaves at higher pressures. Again the result of electron density
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252
600
Absorbed Power (watts)
500-
400-
300-
200 -
100
-
0
100
200
300
400
500
600
Applied Power (watts)
Figure 67.
Power absorption as a function of applied power in a micro­
wave excited oxygen plasma at a pressure of 25 torr.
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253
6
Probe Voltage (mV)
5
4
3
2
1
o
100
200
300
400
500
600
Power Absorbed (watts)
Figure
68.
E-Field probe output as a function of absorbed power in a
microwave excited oxygen plasma at a pressure of 25 torr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
254
1200
Absorbed Power (watts)
1000-
800-
600-
400-
200 -
0
200
400
600
800
1000
1200
Applied Power (watts)
Figure 69.
Power absorption as a function of applied power in a micro­
wave excited nitrogen plasma at a pressure of 25 torr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
255
7
Probe Voltage (mV)
6
5
4
3
2
1
0
200
400
600
800
1000
1200
Power Absorbed (watts)
Figure 70.
E-Field probe output as a function of absorbed power in a
microwave excited nitrogen plasma at a pressure of 25 torr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Electron Density
(cm*3)
256
□ 5 torr
O 25 torr
A 40 torr
0
300
600
900
1200
Applied Power (watts)
Figure 71. Average electron number density as a function of power for a
microwave excited nitrogen plasma at various pressures.
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I
6
660
5
-650
4
-640
<D
a
>
I
3
Power Absorbed (watts)
257
630
0
10
20
30
40
50
Pressure (torr)
Figure 72. E-field probe output and power absorbed as a function of
pressure for a microwave excited nitrogen plasma at a
constant applied power of 740 W.
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258
calculation shown in Fig. 71 suggests that electron concentration approaches
a constant at higher pressures.
The probe measurements also served as a means of determining the
relative strengths of microwave penetration through the gaseous discharges.
Table 17 below shows the result of electric field signals measured by the probe
in various plasma at the conditions employed during the plasma sintering
study. The probe signals can be ranked in the following decreasing sequence:
He > N 2 > O 2 > H 2 . The inert gas appears to be the most transparent to the
microwaves in this series.
Though Table 17 suggests the possibility of
coupling of the microwave energy w ith samples placed in the polyatomic gas
plasmas, microwave heating may only be a secondary factor. Results of the
temperature calculation indicate that heating by deposition of recombination
energy may be the dominating factor due to their greater reactional enthalpy.
However, increasing importance of heating by microwaves may occur in
helium, as evidenced by higher specimen temperature obtained for SiC in
helium .
Table 17
E-field probe output voltages measured for
various gaseous discharges operated at a an
average peak power density of 34 W /cm 3.
Plasma gas
Probe voltage (mV)
He
4.8
n
2
4.4
O2
4.2
h
1.8
2
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259
Relative microwave power absorption of various materials was also
measured in the helium plasma. Power absorbed in He was first determined
for the configuration of the alumina sample stage itself in the plasma. Then,
total power absorbed in the applicator with the specimen + stage + He plasma
was measured again at the same power density. The net microwave power
absorbed by the specimen was taken as the difference of these two separate
determinations.
Table 18 shows the result of the calculation for the
additional microwave power absorbed by various specimens over that
measured for an empty helium plasma plus a sample stage. The higher net
gain in the microwave power for silicon carbide may partially explain the
observed temperature anomaly in helium. The low power absorption by
titania is perhaps surprising. We would expect TiC>2 to absorb more power,
though not as much as SiC, since titania also possesses good dielectric
properties.
Table 18
The net gain in microwave power absorbed
relative to that in an empty plasma for var­
ious samples placed in a helium plasma op­
erating at a power density of 36 W /cm 3.
Material
Net power gained, %
SiC
4.6
MgO
3.6
Fe2 0 3
3.0
AI2O3
2 .8
T i0 2
2 .2
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CHAPTER V
CONCLUSIONS
A ll three plasma systems, namely, MEP, ICP and HCD, were employed to
sinter both a and p silicon carbide at high power levels in a variety of plasma
gases. The best sintered density obtained was 89% of the theoretical value for
silicon carbide doped w ith boron and carbon in a mixture gas consisted of Ar,
He, N 2 , and H 2 . Since plasma heating is believed to be caused by surface
catalyzed atom recombination reaction, the lack of heating exhibited by SiC
may be due to the low catalytic efficiency for recombining atomic hydrogen
and nitrogen.
Microwave and radio frequency plasma sintering of Si3N 4 in nitrogen
indicated that silicon nitride is not a suitable m aterial for this processing
technique. Even at atmospheric pressure, Si3 N 4 still decomposed easily, as
x-ray analysis of fired surfaces showed.
Steady-state specimen temperature during firing was measured in situ
using an optical thermometer. Thimble-shaped ceramic samples were fired
in four different gas plasmas, where sample temperature was found to be a
strong function of the gas composition. In general, specimen temperature
decreases in the following sequence of discharge environment: N 2 > O 2 > H 2
> He.
Thus for any given material, polyatomic gases which possess the
greatest reactional enthalpy attained the highest specimen temperatures.
Accordingly, pure monatomic gases do not provide sufficient heat for
sintering.
260
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261
Effectiveness of heating for a particular plasma gas varied with material
composition.
Insulating materials generally achieved higher specimen
temperatures than semiconducting solids. Heating of the semiconductors
was attributed to the release of chemical energy at the surface by atom
recombination catalyzed by an electronic mechanism.
According to this
theory, adsorption and catalytic activity on semiconducting oxides depend
critically on the position of the Fermi level. The excessive negative charging
of the surface in the plasma raises the Ferm i level and consequent
diminishes both chemisorption and catalytic activity on oxides. Thus, the
reduced heat transfer effects to a semiconducting surface immersed in a
plasma can be understood in this way.
The insulating oxides were not
affected by charging since catalytic recombination occurred by an ionic
mechanism. On the basis of this analysis, simple ranking of catalytic activity
obtained fair agreement w ith the observed pattern of specimen temperatures
among the oxides.
A very simple, first order approximation showed that kinetic energy
transfer and chemical energy of association of atomic species may be the
dominant factor in the heat transfer process under present experimental
circumstances.
Estimation of specimen temperatures using energy flux
equations together w ith literature data yielded fair agreement w ith the
observed values measured experimentally with an OFT for oxygen and less
satisfactory agreement for both nitrogen and hydrogen.
Besides the
uncertainty in the neutral gas temperature, the recombination coefficients
for atomic hydrogen and nitrogen on most of the tested surfaces were
unknown. Nevertheless, general trends for the diatomic gases were correctly
predicted.
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262
P la s m a
p ro d u c e s
r e a c t io n s .
c o n ta c t
H ig h ly
w it h
th e
a c tiv e
c h e m ic a l
n it r o g e n
a tta c k e d
m o re
o p e n
d is p la y e d
Z n O ,
o x id e s
a n d
fo r
a n d
N iO
ir o n ,
h ig h ly
m o s t
Z rC > 2 .
w a s
th e
e x p o s e d
w e re
r e d u c in g
a n d
o c c u rre d
to
b y
g a s
o n e s
p ro n o u n c e
in
to
v a r io u s
th a n
re d u c e d
n ic k e l,
r e s u ltin g
s u rfa c e
In d u c e d
o b s e rv e d
r e a c t iv e
r a d ic a l s p e c ie s
e t c h in g
s tru c tu re
th e
e x tr e m e ly
d is c h a r g e
e x a m p le ,
m o r p h o lo g ie s
a n
z in c
in
r e a c t r e a d ily
c h a n g e s
N 2/ A
fo r m
H e
o x id e s
o x id e s ,
e n t
w it h
s u rfa c e
A IN .
to
a tm o s p h e re ,
a ll
r e d u c t io n
to
s y s te m
r e d u c t io n
th re e
p u re
s o lid
in
o f
F o r
w h ic h
s u rfa c e
p la s m a
A I 2O 3,
o f th e
in
d e g re e s , a
N it r o g e n
a tta c k in g
F o r
c h e m ic a l
g iv e n
v a r y in g
c o n v e n tio n a lly .
in
a
E x a m in a t io n
s h o w e d ,
p la s m a s .
fo r
to p o g ra p h y .
I 2O 3 g a s - s o lid
p la s m a s
r e a c t iv e
in
p h y s ic a l s p u t te r in g ,
lo w e r
a tm o s p h e re ,
in
fir e d
N 2, H 2, a n d
to
c a n
e n v ir o n m
le s s
T i0 2 ,
s ta b le
i n s t a n c e , T iC > 2 , F e 2 0 3 ,
g a s
p la s m a s .
m e ta ls
M o re o v e r,
o c c u rre d
in
th e
H 2 p la s m a .
Finally, direct heating by microwaves is apparently not significant under
most circumstances, w ith the exception of SiC in the He plasma.
The
contribution of microwave heating in diatomic gas plasmas appeared to be
negligible compared to the large chemical recombination energy released at
the surface. However, E-field probe measurements of relative field strength
showed that inert gases were more transparent to the microwave energy
than the polyatomic gases in this study.
Thus increased coupling of the
microwaves with SiC may explain the unexpected high sample temperature
observed in helium.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER VI
RECOMMENDATIONS FOR FUTURE STUDIES
Thus far, the discussion on the action of a given plasma at an interface
has been, more or less, a phenomenological one. Heating by deposition of
chemical energy due to surface catalyzed atom recombination reactions is, of
course, only speculative.
The lack of understanding of the detailed
mechanisms involving the interactions of plasma species w ith the surfaces
and the detailed surface states prohibited quantization of the reaction rates.
There are several studies, however, which should be performed that would
further elucidate the nature of the plasma/surface interaction and either
confirm or refute these speculations. Other experiments are suggested that
would enhance our understanding of the gaseous discharge in general.
According to the model calculations, heating of solids immersed in the
plasma by the kinetic energies of the neutral species also played a significant
role, in addition to the heat of association.
In this study, neutral gas
temperature was determined from extrapolation of published experimental
correlation of gas temperature with the average power density. Therefore, a
more accurate determ ination of the gas tem perature is essential.
Construction of a small gas thermometer similar to that described by
Veprekl54'153! would provide a most suitable instrument for measuring the
neutral gas temperature.
Another method is to em ploy emission
spectroscopy to sample the light emission corresponding to the neutral
species population, thereby obtaining information concerning their kinetic
263
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264
temperature.
These determinations would thus verify our temperature
estimation and ascertain its functional dependence on the power density.
Due to rapid thermal equilibrium between heavy particles, the ions and
the neutrals have similar kinetic temperatures.
Measurement of the ion
temperature provides another means of verifying the accuracy of our gas
temperature estimation.
The Langmuir probes employed in the present
study proved to be inadequate under high power, high temperature
conditions. However, with the availability of a better electric probel202! we
should be able to obtain more accurate discharge characteristics under the
intense plasma sintering conditions.
The experimentally determined
parameters can be compared to those estimated from the theory of discharge
physics. Moreover, the obtained microscopic parameters such as electron
concentration and temperature should enable us to compute other discharge
characteristics, e.g., degree of dissociation, etc.
The power density was calculated on the basis of uniform microwave
power dissipation in the whole discharge. This is unlikely to be realized in
the present experimental setup, particularly when the field was known to be
most intense in the narrow section of the microwave applicator where the
discharge tube passes through. The high power electric double probe noted
above can be used to measure the axial electric field strength along the
discharge tubeJ203i
Consequently, the average power dissipated per unit
volume of the discharge can be more accurately determined.
A more suitable electric field probe should be used to measure the degree
of transparency of various discharges to microwaves. It must be capable of
sustaining high power loadings and respond to EM fields at the appropriate
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265
frequencies. Furthermore, the probe should be calibrated against fields of
known intensity to allow absolute determination of the microwave energy
coupled to specimens present in the microwave plasma. The E-field probe
measurements can thus be repeated to confirm the present findings and, in
particular, to determine whether the anomalous effect of the response of the
field with applied power in nitrogen plasma is a real effect.
Continuing a fu ll im plem entation of a thorough spectroscopic
investigation of the discharge w ould yield valuable information of
heterogeneous as well as homogeneous processes occurring during plasma
sintering. Emission study could be performed with both an empty discharge
and a discharge w ith a solid submerged. Not only w ill such an examination
yield information regarding the populations, energies, and various excited
species, but with increased spatial resolution, it would also reveal helpful
insights into the nature of surface reaction by the evolution of species at or
near the interface.
D o p a n t
s h o u ld
b e
e ffe c ts
re p e a te d
o b t a in
b e tte r
d o p e d
w it h
S i0 2 ,
a n d
s im p le
a n d
c a n
B 2 O 3
t r u ly
e x p e r im e n ta l
a
g iv e n
u s in g
th e
in
A s
p o in te d
N 2) s h o u ld
c a n
th e
b e
b e
N iO
w it h
T h e
to
th e
o b t a in e d .
e s tim a te d
s u rfa c e
e n e r g ie s
T h e
b y
o f
fir in g
w o u ld
o u t e a r lie r , s im p le
b o n d
s tu d ie d
a s w e ll a s p u re
re s p e c t
th e
as
c o n f ig u r a tio n
d is c h a r g e
c h a r a c te r iz e
o f
a lu m in a
m e a s u re m e n ts .
o x y g e n
p o s t u la te d
d a ta
s u rfa c e
a n
o f
p re s e n t
Y 2O 3, M g O , T i 0 2 , a n d
a lk a lin ity .
H 2, a n d
te m p e ra tu re
te m p e ra tu re
r a n k in g
n o t
o n
th im
o f
s u rfa c e
it
a d s o r p tio n
a n d
b o n d
w it h
a
w e a k
to
s p e c im e n s
v e r if ic a t io n
o x y g e n
s tre n g th
O F T
o f Y 2O 3, Z r 0 2 ,
o f fo r m a tio n
o x y g e n
a n d
a lu m in a
o f s u rfa c e -a d s o rb e d
n u m b e r
K n o w lto n l14!
b le
s a m p le s
p e r m
h e a ts
b y
b o n d
o f
th e
e n e rg y
o f th e
o x id e
s tre n g th ,
th u s
s p e c ie s
o f b a s ic
L e w is
(e .g ., O 2,
c e n te rs
a c id
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s u c h
o n
as
266
phenol. t81l This however does not give direct indication of their nature. The
methods discussed below can help identify the specific nature of these
centers.
Unlike the semiconductors, whose active centers for adsorption and
catalysis are known to be at the cation sites, the center of activities for atom
recombination on insulators are thought to concentrate at the more basic
surface oxygen anion sites. It is believed that the surface oxide ions in low
coordination (like those present on edges, steps and comers) are the most
probable sites where catalysis is occurring. With the help of both UV-VISN IR diffuse reflectance and transmission IR spectroscopies we may be able to
detect the interaction of adsorbed gaseous species w ith these coordinatively
unsaturated centers.t198l
Such an spectroscopic examination could also
reveal activities at weakly bonded oxygen atoms caused by dehydration and
subsequent surface strain. It would be extremely fruitful, though admittedly
not trivial, to characterize the insulating oxide surfaces regarding the type of
exposed planes in the surface, the nature, and density of surface
imperfections. Single crystals may also be used as the starting point and
progress to simulate polycrystalline solids by artificially creating surface
defects on low-index faces or by exposing high-index (step) faces.
We may also employ isotopic oxygen to obtain information concerning
the mechanism of recombination.
The exposure of
* 80 2
would reveal
whether atom recombination on the surface involves lattice oxygens or the
process occurs simply by collision of a gaseous species with an adsorbed
oxygen ion. If the product is predominantly
small amount of mixing of
160 180
and
18 C>2 ,
18 C>2
then the latter is true. A
would indicate that some
catalytic recombination took place at weak oxygen bridges.
The effect of
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267
isotopic exchange of oxygen w ith the insulating oxide system may be
neglected because the activation energy of the heteroexchange process is
considerably higher than that of catalytic recombination.t1721
The catalytic mechanism of atom recombination on semiconductors is
believed to be controlled by the electronic structure of the surface and its
Fermi level. The hypothesis that the catalytic activity of semiconductors is
retarded in the presence of a discharge may be tested by applying an external
electric field to a semiconductor and measure the changes in its adsorptivity
and catalytic activity. A slab of semiconductor would be placed in an external
homogeneous transverse electric field. The electron concentration on one of
the surfaces w ill be increased as compared with the absence of a field;
consequently, the Fermi level w ill be raised. Conversely, on the opposite
surface, the electron concentration w ill be reduced; i.e., the Fermi level will
be lowered. Thus on the basis of the electron theory of catalysis, under the
influence of the external field, the adsorptivity of one of the surfaces should
increase, while that of the other decreases, though may not be the same
amount.
Therefore, the adsorptivity of the sample as a whole should
change. This effect may be detected by a change in pressure in the adsorption
volume.
We would also expect a change in the reaction rate under the
influence of the external field.
The enhanced sintering rates in a plasma environment experienced by
several oxide materials may also be related to other factors that affect
diffusion in these solids. For instance, the increased surface defects due to
action of the discharge w ill have some bearing on diffusivity.
The
deposition of considerable quantities of energy into localized electronic and
phonon states of the solids may also induce significant increase in short-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
268
range diffusion. Therefore, it would be worthwhile to pursue along these
lines.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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V. A. Sazonov, Thesis, Inst. Catal., SO A N SSSR, Novosibirak (1969).
182.
V. V. Popovski and G. K. Boreskov, "Kinetics of Isotope Exchange of
Molecular O 2 w ith Oxide Surfaces of Fe, Co, N i, and Cu," Kinetika i
Kataliz 1,566 (1960).
183.
G. I. Golodets, "Relation between the Reduction of Oxide Catalysts and
Their Catalytic A ctivity in Oxidation-Reduction Reactions," Theor.
and Exp. Khimiya L 755-61 (1965).
184.
W. M . H. Sachtler and N . H. de Boer, "Catalytic Oxidation of Propylene
to Acrolein," in Proc. 3rd In t. Congress on Catalysis. V o l. 1, NorthHoli. Publ. Co., Amsterdam (1965) p. 252.
185.
A. P. Dzisyak, G. K. Boreskov and L. A. Kasatkina, "Homomolecular O
exchange on Metal Oxides of the Fourth Period (I) Exchange Kinetics
and Mechanism," Kinetika i Kataliz 4, 388 (1963).
186.
L. Pauling, The N a tu re of the Chem ical Bond, Cornell U niv. Press,
Ithaca (1948).
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187.
284
G. Ehrlich, "Molecular Dissociation and Reconstitution on Solids," J.
Chem. Phys. 31, 1111 (1959).
188.
T. J. Gray and P. W . Darby, "Semi-Conductivity and Catalysis in the
Nickel Oxide System," J. Phys. Chem. 60,209 (1956).
189.
R. Glemza and R. J. Kokes, "Transient Species in Oxygen Take-Up by
Zinc Oxide," J. Phys. Chem. 66,566 (1962).
190.
F. S. Stone and T. I. Barry, "Reactions of O at Dark and Irradiated ZnO
Surfaces," Proc. Roy. Soc. A. 255,124 (1960).
191.
E. R. S. W inter, "Reactivity of Oxide Surfaces," Advances in Catalysis
10,196 (1958).
192. J. v.d.Berg, A. J. v.Dillen, J. v.d.Meijden and J. W. Geus, "The Activity
of Metal Oxides in the Oxidation of Hydrogen and Carbon Monoxide,"
in: Surface Properties and Catalysis by Non-metals, J. P. Bonnelle, B.
Delmon and E. Derouane, eds., D. Reidel Publishing Co, Dordrecht
(1983).
193.
P. B. Weisz, "Effects of Electronic Charge Transfer between Adsorbate
and Solid on Chemisorption and Catalysis," J. Chem. Phys. 21, 1531
(1953).
194.
F. S. Stone, "Chemisorption on Semiconductors," in Chem isorption,
W. E. Garner, ed., Academic Press, New York (1957) p. 181.
195.
M. M. El-Aiat and F. A. Kroger, "Yttrium, an Isoelectric Donor in aAI2 O3 ," J. Am. Cerm. Soc. 65 [6 ], 280-283 (1982).
196.
D. E. Cheaney and A. D. Walsh, "HF Treatment of SiC>2 and Pyrex
Vessels Used for Combustion Studies," Fuel 35, 258 (1957).
197.
D. E. Cheaney, D. A. Davies, A. Davis, D. E. Hoare, J. Protheroe, and A.
D. Walsh, "Effects of Surfaces on Combustion of Methane and Mode of
Action of Anti-Knocks C ontaining Metals," 7th In t. symp.
Combustion, Butterworths, New York (1959).
198.
A. Zecchina and D. Scarano, "Electronic and Vibrational States at the
Surface of Ionic and Covalent Solids," in: Adsorption and Catalysis on
Oxide Surfaces, M Che and G. C. Bond, eds., Elsevier, Amsterdam
(1985) p. 71.
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199.
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M . Che, "Characterization and Reactivity of Oxide Surfaces," in:
Adsorption and Catalysis on Oxide Surfaces. M Che and G. C Bond,
eds., Elsevier, Amsterdam (1985) p. 11.
200.
M . D . Beals, "Single-Crystal Titanates and Zirconates" in: H i gh
T e m p e ra tu re O xides, Part II. Oxides of Rare Earth, Titanium ,
Zirconium , Hafnium, Niobium , and Tantalum , A. M. Alper, ed.,
Academic Press, New York (1970) p. 99.
201.
R. C. Garvie, "Zirconium Dioxide and Some of Its Binary Systems," in:
H ig h Tem perature Oxides. Part II. Oxides of Rare Earth, Titanium,
Zirconium , Hafnium, Niobium , and Tantalum , A. M. Alper, ed.,
Academic Press, New York (1970) p. 117.
202.
Dr. Jonathan Storer, senior research specialist at 3M , private
communication.
203.
S. R. Goode and D. C. Otto, "Some Fundamental Measurements of the
Atmospheric-Pressure, Microwave-Induced Discharge," Spectrochimica Acta 35B, 569 (1980).
204.
S. Chapman and T. G. Cowling, The M athem atical Theory of N o n Uniform Gases , Cambridge University Press, London (1960).
205.
W. E. Olmstead, Professor of Meas. Engg. Sci. & Applied M ath,
Norwestern University.
206.
M. Mitchner and C. H. Kruger, Jr., Partially Ionized Gases , John W iley
& Sons, New York (1973).
207.
R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena.
John W iley & Sons, Inc., New York (1960) p. 531.
208.
V. L. Tal'rose and G. V. Karochevtsev, "Elementary Reactions in LowTemerature Plasma," in: Reactions under Plasm a Conditions, M .
Venugopalan, ed., Interscience, New York (1971) pp. 35-139.
209.
H. E. Petschek and S. Byron, "Approach to Equilibrium Ionization
behind Strong Shoch Waves in Argon," Ann. Phys. i , 270-315 (1957).
210.
A. E. Nasser, H. M . Sofrata, and A. Sharaf, "Transport Phenomena of
Mixtures of Hydrogen, Oxygen and Argon at H igh Temperatures,"
Warme-und Stoffubertrangung 15,135-143 (1981).
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286
211. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of
Gases and Liquids , John Wiley & Sons, N ew York (1954).
212. I. Am dur and E. A. Mason, "Properties of Gases at Very High
Temperatures," Phys. Fluids I [5], 370-383 (1958).
213. H . W . Drawin, "Plasma Properties and Atomic Processes at Medium
and High Pressures," J. de Physique C 7 ,149-170 (1979).
214. V. E. Golant, A. P. Zhilinsky, and I. E. Sakharov, Fundamentals of
Plasma Physics. John W iley & Sons, New York (1980).
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A P P E N D IC E S
287
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288
APPENDIX A
POWDER MATERIALS AND SOURCES
AI2O3
Baikowski CR 30
Specific surface area = 30 m2/g
Baikowski International Corp.
Charlotte, NC
BaTi0 3
Ticon HPB BaTi03
Specific surface area = 3 m 2/g
TAM Ceramics, Inc.
Niagara Falls, N Y
Fe203
Pfizer a-Fe2 0 3
Specific surface area = 45 m2/g
Pfizer Pigments Inc.
Easton, PA
MgO
Baikowski M30 CR
Specific surface area = 30 m2/g
Baikowski International Corp.
Charlotte, NC
NiO
J. T. Baker 2794 NiO
Specific surface area = 20 m2/g
J. T. Baker
Jackson, TN
SiC
Ibiden P-SiC
Mean particle size = 0. 32 pm
Mitsui & Co., Ltd.
Tokyo, Japan
Superior Graphite Co.
Chicago, IL
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289
Si3N 4
Denka Si3 N 4
Mitsui & Co., Ltd.
Tokyo, Japan
TiB2
HPF TiB 2
Specific surface area = 1 m2/g
Advanced Refractory Tech., Inc.
Buffalo, N Y
T i0 2
H P T i0 2
Specific surface area = ? m2/g
TAM Ceramics, Inc.
Niagara Falls, N Y
ZnO
Kadox-911 ZnO
Specific surface area = 9 m2/g
Zinc Corporation of America
Monaca, Pa
Z r0 2
TZ-3Y Z r0 2
Specific surface area = 17 m2/g
Tosoh Corporation
Atlanta, GA
ZYP Z r0 2
Specific surface area = 37 m2/g
Zircar Products, Inc.
Florida, NY
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290
APPENDIX B
DERIVATION OF BOUNDARY LAYER EQUATIONS
This section discusses the equations governing the balance of charged
particles and their energies of a weakly ionized plasma in the neighborhood
of a solid wall. The ideas presented here extend from those of Chapman and
Cow ling!204! w ith generous assistance from Professor Olmstead!205!. The
main processes concerned here are the directed motion of the charged
particles (particle transport), the directed transport of energies, and the
particle energy exchange in collisions. In considering the transport processes
we know that mass, momentum, and energy are conserved as the plasma
species are transported from one location to another, in a microscopic sense.
Thus the plasma conservation laws are used for the calculations of the
motions of the constituent species.
From simultaneous solution of these
conservation equations it is possible, in principle, to find the distribution of
the density and electron and ion temperatures in the plasma volume.
When studying millions upon millions of particles with many collisions
moving in a chaotic motion, one has to resort to the tools of statistical
mechanics. Rather than calculating the motion of each particle separately,
the probability of different motions is calculated collectively. A probability
distribution function is therefore used to describe their motions. Thus the
fundamental kinetic description of a partially ionized gas is provided by the
velocity distribution function for each species.
This function can be
determined from a certain integral equation first given by Boltzmann. The
species distribution function J ( c , r , t ) is defined through the statement
thatf2°4/206]
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291
/ (c, r ,t ) d c dr
( B .l )
denotes the probable number of species in question, in time t, contained in
the differential volume element r, dr that have velocities in the range c, dc.
The boldface type r and c represent the "position vector" r which has (x, y,
z) as it components in the Cartesian coordinates and the vectorial velocity c
of a particle having (u, v, w) as its components relative to Cartesian
coordinates, respectively. Thus the average number density of the species in
the element dr of the gas is given by integrating f d c d r
throughout the
whole velocity space,
n
( B.2)
Im plicit in any such "probabilistic" description, of course, is some sort of
averaging process.
Given that <Z> is some molecular property which may be a function of
position, time, and velocity. The aggregate contribution for each of the j{c, r,
t ) dc dr particles in dr, whose velocities are in the range c, dc, is O f d c dr. By
integration over the whole velocity space we obtain
( B.3)
O is the mean value of the molecular function <Z>for the particles at (or near)
the point r.
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292
Consider now that each particle in the gas which is subject to an external
force F (e.g., gravity or electromagnetic forces).
During and between
collisions some of the particles lose energy and some gain energy. Hence, in
a time 6 t, the number of particles of a given species per unit volume in the
velocity range c, dc composed of j{c, r , t ) dc dr w ill have changed to the set
/(c + F d t ,r + c dt,t + dt) dc dr
(B .4)
owing to the net rate of increase from the sum of the effects of flow of
particles into the volume element dr, the acceleration of particles as a result
of force fields, and collisions with particles of the same and differing species.
Thus the rate of change of the velocity distribution / due to collisions can be
expressed by the differential equation
This is also known as Boltzmann's equation for f. The quantity (S f /d t ) dc
,then, measures the rate of change in the number of particles w ith velocities
in the range c, dc, within the stationary volume element at r, as a result of
collisions. Consequently, the rate at which collisions change
0
is equal to
( B.6)
where AC is the rate of change of C by molecular encounters. Incorporating
Eq. (B.5) into the above equation we obtain
( B.7)
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293
Performing integration for the various terms in the right-hand side of Eq.
(B.7) we get the relation
fI 0rtx 8 / dc
a
=
J
8f
dn&
d -n-r—
id&
90
r + F • ——
- + —
0 c - n — + c •—
9t
9r
\ 9t
9r
dc)
(/ u
B.8o )\
Equation (B.8 ) is also referred to as a moment of the Boltzmann equation
when the species Boltzmann equation is m ultiplied by some function of
particle velocity and integration of the resultant equation over velocity space.
Combining Eqs. (B.6 ) and (B.8 ) and after rearranging terms we m ultiply both
sides by dr
The left-hand side represents the total rate of change of Z 0 for the species
situated in the volume element dr. This change is reflected by various rates
of change due to the net rate of increase from convection of particles into and
out of the volume, the dependence of 0 for each particle species on the time,
the position of the particle, and its velocity, and the effects of collisions.
Sometimes it is more convenient to express Eq. (B.9) in terms of D /D f, or
the time-derivative following the motion, as in hydrodynamics.
In other
words, the Boltzmann equation is recast in terms of the peculiar particle
velocity, defined as C = c - c0, in place of the laboratory frame velocity c,
where c0 is the mass average velocity of the gas stream as one would
measure by means of a pitot tube. Thus C is the diffusion velocity of the
species in question relative to the local motion of the gas stream.
On
changing of variables from j{c, r, t ) to J{C, r , t ) and replacing 9 0 / dc, 9 0 / dr,
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294
and dO/dt by their appropriate derivatives we arrived at the transformed
species Boltzmann equation
/
| £ dc =
of
Df
+
I Df
n0
d . Co + A . n O C
dr
dr
9r
*
Df I dC
(
9C
9r
B.10)
I
where
= JL + c . JL
Df
9f
Now let us take 0 to be the particle mass. We then have nO = p, DO/Dt
= 0, 3 0 /dr = 0, and dO/dC = 0. The resultant moment equation for species s
becomes
Df
+ f t I " Co + I "
dr
dr
= a,
( B.11)
where as is the mass rate of production per unit volume of species s due to
collisional processes such as ionization. The collision term vanishes by the
summation of Eq. (B .ll) over all species of the gas mixture since the mass of
the gas is not changed by collisions. Noting that E psCs - 0, we obtain the
resulting equation
<B12)
This is the equation of continuity, which describes the rate of change of
density resulting from the net rate o f mass efflux per unit volume.
simply a statement of conservation of mass.
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It is
295
When 0 is taken as the particle momentum or energy, the resultant
moment equation becomes the corresponding conservation equation.
The
resulting conservation equations follow from similar calculations
Di
"
\9r ’
Ps
+
D ip M
Dt
I
0*H
19
Q J 0 )
c
l
PsHs\dr I
+ PsCs
dr
dr
( B.13)
c 0
+
dr qs
— 25{°)
=
Vs
Di
( B.14)
’ dr
=
where p is the pressure force, % the shear stress tensor, H the enthalpy, and q
the heat flux vector.
tjs and e5 are the respective collision terms for the
momentum and energy equations of species s.
Complementary to the
conservation of mass, the momentum and energy are also preserved in an
individual two-body collision, thus all collision terms again vanish by the
summation of equations (B.13) and (B.14) over all species in the gas. The
resulting global conservation equations for the gas as a whole are
p5m
= - f r
-
+ pF
(B15)
Equation (B.15) represents a balance of forces over a small volume element.
The rate of change of momentum is balanced by the pressure force, viscous
force, and external force on the element per unit volume.
In the energy
conservation equation (B.16) the net rate of gain of thermal energy is
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296
equivalent to the rate of gain of thermal energy by convection, by
conduction, by viscous dissipation, and the energy increase per unit volume
due to either expansion or compression. Equations (B.12), (B.15), and (B.16)
are identical w ith the equations of continuity, momentum, and energy
derived for a continuous fluid in hydrodynamics.!207!
We assume that the plasma under study is a monatomic gas, in which the
frequency of collisions of electrons and ions with atoms greatly exceeds that
of collisions of these particles w ith one another. The plasma thus consists of
electrons, single-charged positive ions, and neutral atoms. We now apply
the conservationequations to the plasma in the vicinity
of a wall.
The
balance equations for the electron, ion, and atom mass densities are
b
t + p' b
b t * P,i r
b i t + p‘ b
c° + b
^
■
C° * Jr P‘C> =
c° + b
0
I
PaC* =
<B 17)
(B .18)
(B -19)
where the p's are the partial mass densities and the subscripts e, i, and a refer
to electrons, ions, and atoms, respectively. The particle concentrations per
unit volume is therefore related to the mass densities by
P - (na + «;) ma
pi = n-{ma
pe = nem e = p im e/m a
n = na + m + ne = na + 2 m
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( B.20)
297
The above relations im plicitly assume that the plasma is quasi-neutral, i.e. ne
= m. The electron, ion, and atom temperatures can be determined from their
respective energy equations
D ( p ji.) . „ H
Df
+
+
Id
3 „ Dp.
.
P e C .F . ~ PeCe
+ *
*
-
Dt
"** 'Ce ■^
or
OT
(B 2 1 ,
Co — — CCfEf
“
Eel
Since ions and neutral atoms exchange energy efficiently on collision, they
are assumed to have the same temperature. Thus we combine their energy
equations
D-(p,Hi + PoH.) + (pH , +
- j^ (P , + P«) + p,C,F, - (p,Ci + PeCa) ^ ~
+ (Ti + Ta) : -r—C0 =
Or
( B.22)
E ei
The collision term in Eq. (B.21) contains two contributions. One is the loss of
energy to the ions in the ionization reaction, which is represented by a; E j,
where E* is the ionization energy per unit mass of the ions. The second
contribution is the loss of energy by elastic collisions between electrons and
the heavy particles, expressed by Ee/. The latter collision term also contribute
to the increased energy of the heavy particles due to collisions, Eq. (B.22).
The shear stress term on the left of Eq. (B..21) depends on me * /
therefore can be dropped.
2
and
Since Z p sCs = 0 and only the heavy particles
contribute to this sum, peCe is proportional to me and can be ignored, the
energy equations becomes
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298
( B.23)
+ PeCg Fj —
OJ/Ej
Eei
The force term may be approximated from sim plification of the
momentum equation for the electrons, Eq. (B.13).
have the electron mass as a factor.
All except three terms
The shear momentum carried by
electrons depends on me 1/ 2.and is therefore negligibly small. The remaining
two terms, the electron pressure gradient and the external force, are
independent of me , since Fe = eE /m e , where e is the electronic charge and E
the electric field. The electron momentum equation becomes
( B.25)
Substituting the above for the external force terms in Eqs. (B.21) and (B.22)
and noting the ambipolar diffusion condition Ce = Ct , we obtain the
resulting energy equations
( B.26)
+ paH a) + (p,H, + pJHa) { § - c 0) + %-{q, + q.)
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299
To sim plify further, consider the plasma/solid situation to be a one
dimensional problem where the x axis is taken normal to the w all and
assume that variations occur in x and t alone. Assume also that there is no
flow parallel to the wall surface, so the tangential forces are of no
significance. Since only a single component concentration need be specified
for this monoatomic gas mixture, we shall use the ion equation for the
species conservation equation. Thus the equations necessary to determine
the plasma species concentrations and temperatures are reduced to the
following
( B.28)
( B.29)
For a m ixture of atoms, singly-ionized ions, and electrons the
thermodynamic expressions for the enthalpies and constant pressure specific
heat cp are
H i — CpfTi
= _5Jl
2 ma
H e = CpeTe
( B.31 )
Cp = £cpe&-( B.32)
where k is the Boltzmann constant. The usual expression for the heat flux
has the form!207!
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where the first term is the Fourier heat conduction w ith thermal
conductivity
k
and the second is the transport of energy due to mass
diffusion of species s. Assuming that the ion and atom temperatures can be
represented by a single heavy particle temperature T/, and substituting the
above relations into Eqs. (B.29) and (B.30), we obtain
^{PtfipeTe) +
| Ke'fa~ + PeCeCpeTej
(B.34)
_D £e_
Dt
C ||
1
dx
.
-a m -E *
p t (Pi + P*)CpkTk
( B.35)
- § ( p , + P.) ♦ C , . ^ = Ee[
Making use of relation (B.20) and the fact that the mixture pressure is a
constant, and letting re?, = *}• + Ka, we get
^{PiCpkTe) + ^[pC ep hT . - * i | ^ )
.
p § t (c^
- J
^
.
Dt
^ l r ) + i
CM
- - aiEi-Ee,
dx
<“ 6>
r
(B37)
+Ci
=
E“
The mass rate of production of ions a; is determined by the ionization
reaction by electron impact. In a nonequilibrium situation the reaction rate
depends directly only upon the electron energy and is given by
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301
[OQ
r
kfon
=
**
11
/o I
de
&------ ] 1/2 f <r{e)£ exp
[meJc{kTef \ J„
P \ kTe)
(B .38)
where fc/0/l is the ionization coefficient for electron-neutral atom collisions, e
the kinetic energy of the electrons, and o(e) is the ionization cross-section as
a function of electron kinetic energy. When evaluated over a wide range of
ionization cross-section for various atoms, the rate constant becomes
kion = .1 .8 5 b N T ™ exp ( -
J f-J
( J f j2
( b.39 )
where b is the numerical coefficient characteristic of the given atom and N
the number of equivalent electrons in the outer atomic shell. Values of b
and N for a number of atoms are tabulated in Table 2 of Reference [208].
Thus for the elementary reaction of the type: e + A = A + + 2e, where A is a
neutral atom or molecule, the ion collision source term is proportional to ne
(Xi =
kion na ne mi
( B.40)
The rate of energy transfer per unit volume by elastic collisions from
electrons to single charged ions ist209l
F, _
Ea ~
n«2e 4 f ix m « f
n rri
, | 9 0 tT „ )3
k
(
b
-4
1
)
The energy transfer by elastic collisions from electrons to atoms is usually
much less than to ions.
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302
Before we can apply the energy equation, we also need to find appropriate
expressions for the thermal conductivity of the plasma gas . The thermal
conductivity for a monoatomic gas of species s the Chapman-Ensokog theory
yields!210!
ks
=
[=1 cal/on-sec-°K
4 ms
(B.42)
where R is the universal gas constant. iis is the coefficient of viscosity and
may be given by
us = 266.93 X 10’7
[=J g/cm-sec
( B.43)
af a ]
where as is the collision diameter, in A , and Q s is the collision integral as
tabulated in Reference [211]. For argon atoms, the thermal conductivity has
been calculated and represented by a power law!212!
Ka
= 5.8xlO '7 T fl3/4
(
B.44)
The electron and ion thermal conductivities are expressed as
(b -45>
where
A = 1.24 x 1014 -A£—
ne V2
( b.46 )
The electric field build up at the wall by the electrons causes the electrons
and ions to diffuse with the same ambipolar diffusion velocity.
The ion
diffusion velocity Q may be described byf213l
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303
WgCg — MjCj — D a ^ Me —
( B.47)
D a V tii
( B.48)
The coefficient D a is called the ambipolar diffusion coefficient and may be
expressed ast214l
( B.49)
where v/a is the average frequency of ion-atom collisions.
We now have specified the necessary physical quantities that appear in
the transport equations in terms of temperature, concentration, and the
physical constants of the electrons, ions, and atoms.
The boundary conditions are
B.C. 1:
at x ~ <*>
pt = p,«,
T/, = Th0
Te = Teo
( B.50)
where Pi0,Th0, and T eo and are bulk values of the ion density, heavies
temperature, and electron temperature. The continuum equations are only
valid up to the plasma sheath edge. W ithin the region of the plasma sheath
a collisionless approach or molecular description is used. Thus the second
set of boundary conditions established at the w all must involve matching
the continuum and the molecular descriptions.
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304
B.C. 2:
at x = 0
piQ = ™iML
Th = Tw
( B.51)
k^ - - p £ i cphTe = (2kTe + \e(ps\ ) ^ e x p \ - lj ^ l
where <ps is the sheath potential, c,- = 4 (kTe I mi I 1/ 2 and ce = (eTe f l i t me )V 2
are the respective thermal velocities of the ions and electrons that enter the
edge of the sheath.!120'150! Therefore, the first relation in (B.43) preserves the
continuity of the ion mass flux. The second relation assumes that the atoms
are in thermal equilibrium w ith the wall at the w all temperature. Since the
ions are assumed to be in temperature equilibrium w ith the atoms, this
boundary condition determines Th at the wall. The electron temperature Te
at the boundary wall is determined by the continuity of electron energy flux
at the sheath edge. Electrons diffusing toward the w all enter the sheath with
an average energy 2kTe + \e<ps\. This energy is carried by each electron across
the sheath w ith the flux (ne ce /4 ) exp ( - e(ps /kTe).
Thus the particle density and energy balance equations make it possible to
calculate the main characteristics of a monoatomic gas plasma. The particle
density distribution can be found by Eq. (B.28). The electron temperature Te
is obtained from the electron energy balance, Eq. (B.36), and the ion
temperature T* from the heavy particle energy balance, Eq. (B.37). We have,
as a result, a set of coupled, nonlinear partial differential equations which are
very difficult to solve analytically. Approximate solutions, however, may be
obtained by a numerical analysis approach.
Assuming that we have obtained values of the discussed plasma
parameters necessary for the temperature estimation, here we w ill show in
detail how the specimen temperature is calculated. First, we must determine
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305
expressions for the number flux of plasma species impinging the given
surface.
Electron Number Flux
SA
The number flux per unit area per
unit time normal to an element of
solid surface SA is
n0 v cos 0 f ( v ) dv dQ.
O
X
where n0 is the particle density, f ( v ) is Maxwell-Boltzmann's velocity
distribution, di2 is the element of solid angle subtended by SA, and <P is the
azimuthal angle about OX. However, because of the presence of a sheath, the
sheath potential acts as a barrier so that only electrons w ith kinetic energy
greater than e(ps can reach the surface, i.e.,
me(v cos 6 )2 £ e(f>s
therefore, we have
where /x = cos 6. According to Eq. (49) the integral for the electron number
flux, Fe, becomes
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306
,2»
Fe — lie
d&
r
H dii I
v f ( v ) dv
**mln
„ I me \3/2
c\2^fcTe)
f i d u i |[
v 3 e ~ mtv 2/ m ' t d v
Jvm
fvmin
If we let ~ e^
- x, then
2 kTe
Fe — Tie
2 m
arm,
\ 1/2
x e~x dx
where xm = eq>s / f i 1. Solving for Fe we obtain
Fe = „c[_ W k _ )1/2 rap( - e^
27rm,
kTP
Similarly for the atom and ion number fluxes, F a and F /, respectively, we
have
F.
-
kTa \V 2
(\27rma
r ^ FI
and
Fi =
t o m ,-/
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307
Energy Flux
The expression for the electron thermal energy flux was evaluated
according to Eq. (50), thus
mix
Qe
— He
dO
/x dfi f
• Vmin
mev 2) v f ( v ) dv
J 0
Hdp I
Jo
Again, letting
Qe
z Kl e
=
f
v
5
e ~ m‘v 2/ 2*t,
= x, we then have
2kTt j
M d f i j x 2 e~x dx
Jo
But, for each electron in crossing the sheath losses an amount of energy
precisely equal to e(ps in order to overcome the potential barrier posed by the
sheath, thus
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308
= Fe • 2kTe
So that on the average each electron arrives at the surface w ith kinetic energy
of 2kTe.
Likewise, the flux of kinetic energy transfer by atoms and ions are
similarly expressed. In addition, atomic species also carried with them the
potential energy of recombination,
Qa
= Fa‘
(2fcTtt +
yEd)
The ions are accelerated by the sheath potential and are efficiently
neutralized at the surface by combining with electrons, so that
Qi
=
F i'
{zkTi + Ej +
6(pg)
Example Calculation
The following is an illustrative calculation of the specimen temperature
estimation.
Assuming that we now have all the data needed for this
computation, let us determine how much a green alumina thimble w ill heat
up in a nitrogen plasma operating at a constant power density of 35 W /cm 3
and a pressure o f 25 torr.
The emissivity for alumina as well as other
materials used in this study were obtained from refs. [147,165] at the surface
temperature observed in these experiments.
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309
Gas = N 2
Material
T; = T a = 1200 K
em
A I
2O 3
0.42
Te = 1.82 x 104 K
y
.0263
ne = «,• = 8.45 x 1011 cm-3
<7
5.67 x 10-12 W /cm 2 K
m i = 2.325 xlO *26 Kg
Jfc
1.3806 x 10-23J/K
me = 9.109 x 10'31 Kg
Ed
4.9 eV
Et = 14.54 eV
The neutral species concentration was determined from the relation,
na =
(25 torr) (l.333 xlO '2— ^ — )
V = _______ 1_________ cm torr I
kTa f 1.381 x 10'21 -N cm..) (1200 K)
\
K atom/
na = 2.01 x 1017 cm-3
Now we can estimate the number fluxes of each plasma species according to
the expressions we just derived.
Assuming that all the molecules are
dissociated in the plasma, the flux of nitrogen atoms arriving at the surface is
V2
Jim,
1.381 x 10r 2 3
= 2 (2 .OIx 1017—
I
cm3/
K g
s2
m
2
x 1200 K
K
(loom)
27c x (2.325 x 10"26 Kg)
= 1.35 x 1022 cm-2 s_1
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310
Similarly, the ion flux is given as
Fi =
11 - ^ V 2 jctrii
m
= 2.85 x 1016 cm-2 S' 1
In order to evaluate the electron number flux, first we need to know the
sheath potential established at the immersed surface. This voltage can be
estimated from Eq (15)
<P == h i e in
2e
(2*
sh -)(i +
£1
1.381 x 10' 23 X (l.82 x 104 K )
1 eV
O = '__________ K /___________ \l.602 x 10' 19 T
v
2e
x In
2jr 9.109 x 10"31 Kgj/ ^ +
_\
2.325 x 10’26 Kg/ \
1200K
1.82 x 10* K /
<p = 6.47 V
Thus, from this we can determine the incident flux of the electrons which
have overcome the negative sheath potential
= 2.87 x 1017 cm*2 s_1
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311
The energy fluxes carried by plasma ions, electrons, and neutrals toward a
given solid surface is described previously by Eqs. 51-53.
Therefore, the
forward thermal flux delivered by the atoms is given by
Qa
=
Fa
(2 kTa + yE<f)
= 1.35x10,22
1
cm2 s
2 (l.381 x 10'23 ^ 4 1200 K
'
K I
+ 1.35 x lO 2 2 -4
cm2 s
0.0263 (4.9 eV) (l.602x 1049^ ) ]
= 729- 4 r
cm2
The ion thermal flux is computed by
Q i — Fi
(2
kTi
+
Ei
+
e(p)
= 2.85 x 1016 - 4 — \ 2 f1.381 x 10'23 ^-§-1 1200 K
cm2 s L '
K
2.85 x 1016 - 4 r - f ( 1 4 -5 4 eV + 6.47 eV) [l.602 x 104 9
1
cm2 s L
\
eV >1
= 0 .0 9 7 ^ cm2
And the electron energy flux is
Qe = Fe x 2 kTe
= 0.14- 4 r
cm2
The above calculation show that the electron and ion fluxes are negligibly
small compared to the neutral species flux because it is present at a greater
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312
concentration.
Thus, in the temperature estimation we assume that the
neutrals dominate the heat transfer process of a plasma w ith a given solid.
The overall energy balance on a sample, Eq. (77), is reduced to
Qa
+
Qe
+ Qi — Qo = G £fn Ts4
Hence,
Fa [ 2 k ( T a- T s) + yEd\ = a ^
Ts4
Solving for the specimen temperature by an iterative method, we obtain
Ts = 1870 K
Calculation of specimen heating for other materials used in this study
follows the same procedure outlined above.
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31
APPENDIX C
1200
1000
BOO
600
200
300
600
900
1200
1500
Time, t (sec)
Figure C l.
Temperature profile for A I2 O 3 fired in 25 torr O 2 plasma
at a power density of 31 W /cm 3 w ith the first 600 sec de­
voted to cleaning of adsorbed gases from the specimen at
low applied power levels (200 W ) in 3 torr Ar. The de­
sired power level was applied and O 2 admitted into the
system.
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314
1200
1000
800
600
200
400
800
1200
1600
Time, t (sec)
Figure C2.
Temperature profile for AI2 O 3 fired in 25 torr H 2 plasma
at a power density of 33 W /cm 3 w ith the first 800 sec de­
voted to cleaning of adsorbed gases from the specimen at
low applied power levels in 3 torr Ar. The desired power
level was applied and H 2 introduced.
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315
1200
1000
800
600
200
300
600
900
1200
1500
Tim e, t (sec)
Figure C3.
Temperature profile for A I2O 3 fired in 25 torr He plasma
at a power density of 36 W /cm 3. Low power (200 W) was
applied for the first 480 sec to remove adsorbed gases
from the specimen in 3 torr Ar. The desired power was
then applied and He admitted. The sharp rise in speci­
men temperature indicates that strongly chemisorbed
water was being removed. Except for some power fluc­
tuations in between, temperature was steadily obtained as
pressure continued to increase.
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316
1200
1000
800
600
200
300
600
900
1200
1500
1800
Time, t (sec)
Figure C4.
Temperature profile for A I 2 O 3 fired in 25 torr Ne plasma
at a power density of 36 W /cm 3. Low power (200 W ) was
applied for the first 570 sec to remove adsorbed gases from
the specimen in 3 torr Ar. The desired power was then
applied and Ne admitted. The sharp rise in specimen
temperature was due to the removal of tenaciously ad­
sorbed water. Except for some power fluctuations in
between, temperature was steadily obtained as pressure
continued to increase to the preset value.
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317
1400
1200
1000
-
800
600
400 j
200
400
800
1200
1600
Time, t (sec)
Figure C5.
Temperature profile for MgO fired in 25 torr He plasma
at a power density of 36 W/cm^ with the first 400 sec
devoted to cleaning of adsorbed gases from the speci­
men at low applied power levels in 3 torr Ar. The de­
sired power was then applied and extra cleaning of the
specimen continued for additional 6 min. Helium was
then bled into the system to obtain the preset pressure.
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318
1400
1200
1000
-
BOO
600
400
200 7
500
1000
1500
2000
Tim e, t (sec)
Figure C 6 .
Temperature profile for MgO fired in 25 torr Ne plasma
at a power density of 36 W /cm 3. Low power (200 W) was
applied for the first 400 sec to remove adsorbed gases
from the specimen in 3 torr Ar. The desired power was
then applied and Ne introduced. The sharp rise in speci­
men temperature indicates that strongly chemisorbed
water was being removed. Except for some power fluc­
tuations in between, temperature was steadily obtained as
pressure continued to increase.
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319
1400
1200
1000
-
BOO
400
200
200
400
600
800
1000
Time, t (sec )
Figure C7.
Temperature profile for Ti0 2 fired in N 2 plasma at a
power density of 35 W /cm 3. Low power (200 W ) was
applied for the first minute to remove adsorbed gases
from the specimen in 3 torr Ar. The desired power was
then applied and N 2 bled into the system to obtain a
pressure of 25 torr.
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320
1400
1200
1000
-
800
«J
600
200 7
200
400
600
800
1000
Time, t (sec)
Figure C 8 .
Temperature profile for TiC>2 fired in 25 torr O 2 plasma
at a power density of 31 W /cm 3 with the first minute de­
voted to remove adsorbed gases from the specimen at
low applied power levels in 3 torr Ar. The desired
power was then applied and O 2 admitted.
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321
1000
BOO
o
o
6-4
of
u
2
•p
cd
J*
600
400
03
CU
a
QJ
^
200
200
400
600
800
1000
Time, t (s e c )
Figure C9.
Temperature profile for TiC>2 fired in 25 torr Hfe plasma
at a power density of 33 W /cm 3. Low power (200 W) was
applied for the first 60 sec to remove adsorbed gases from
the specimen in 3 torr Ar. The desired power was then
applied and H 2 introduced. A sharp peak subsequently
appeared as residual adsorbed species were removed.
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322
1200
1000
oU
600
C
D
^
600
4J
u
C
D
p
.I 400
a
a)
E-*
200
2 00
400
600
800
1000
1200
Time, t (sec)
Figure CIO. Temperature profile for TiC>2 fired in 25 torr He plasma
at a power density of 36 W/cm 3 w ith the first 360 sec de­
voted to cleaning of adsorbed gases from the specimen
at low applied power levels in 3 torr Ar. The desired
power was then applied and He introduced. The sharp
peak arose as residual adsorbed water was further re­
moved.
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323
1200
Temperature, T (°C)
1000
800
600
400
200
0
200
400
600
800
1000
1200
Time, t (sec)
Figure C ll.
Temperature profile for TiC>2 fired in 25 torr Ne plasma
at a power density of 36 W/cm 3 with the first 500 sec de­
voted to cleaning of adsorbed gases from the specimen at
low applied power levels in 3 torr Ar. The desired power
was then applied and Ne admitted. Evolution of resid­
ual adsorbed water produced the initial sharp peak.
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324
1400
1200
,F 1000
H
:
-
0)
800 1
aj
600 r
S
400 7
u
3
u
0)
01
E-•
200
2 00
400
600
BOO
1000
Time, t (se c )
Figure C 1 2 . Temperature profile for ZrC>2 fired in 25 torr N 2 plasma
at a power density of 35 W /cm 3. Low power (200 W) was
applied for 2 2 0 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and N 2 introduced.
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325
1200
1000
800
600
a
u
0
ft
400
8
0
H
200
200
400
600
800
1000
1200
Time, t (sec)
Figure C13. Temperature profile for ZrC>2 fired in 25 torr O 2 plasma at
a power density of 31 W /cm 3. Low power (200 W) was
applied for 340 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and O 2 admitted.
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326
1000
800
u
O
^
600
6
u
4d
->
U
<D
«3
s
0)
*"*
400
200
200
400
600
800
Time, t (sec)
Figure C14.
Temperature profile for Z 1O 2 fired in 25 torr He plasma
at a power density of 36 W /cm 3. Low power (200 W) was
applied for 340 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and helium introduced. The sharp peak arose as
residual adsorbed water was further removed.
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327
1200
1000
oo
BO
O
600
eti
u
<D
a, 4oo
a
<D
H
200
200
400
600
BOO
1000
1200
Time, t (sec)
Figure C15. Temperature profile for SiC fired in 25 torr N 2 plasma at
a power density of 35 W /cm 3. Low power (200 W) was
applied for 160 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and N 2 admitted.
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328
1000
800
u
o
^
600
CO
I*
3
+>
cfl
u
400
(0
a,
S
cu
^
200
200
400
600
800
Time, t (sec)
Figure C16. Temperature profile for SiC fired in 25 torr H 2 plasma at
a power density of 33 W /cm 3. Low power (200 W) was
applied for 2 0 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and H 2 introduced.
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329
1200
1000
u
o
800
H
»
600
5*
V
O i 400
s
a)
H
200
200
400
600
BOO
1000
Time, t (sec)
Figure C l 7. Temperature profile for SiC fired in 25 torr He plasma at
a power density of 36 W /cm 3. Low power (200 W) was
applied for 30 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and He admitted.
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330
1400
1 30 0
1200
1100
O 1000
9 00
BOO
7 0 0
CL,
6 0 0
I
5 0 0
4 0 0
3 0 0
200
100,
500
1000
1500
2000
Time (sec)
Figure C18. Temperature profile for N iO fired in 25 torr N 2 plasma
at a power density of 35 W /cm 3 with the first 600 sec de­
voted to remove adsorbed gases from the specimen at
low applied power levels in 3 torr Ar. The desired
power was then applied and N 2 introduced.
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331
1000
900
Temperature
(°C)
600
7 0 0
6 0 0
5 0 0
3 0 0
200
100
5 0 0
1000
1500
2000
Time (sec)
Figure C19. Temperature profile for N iO fired in 25 torr O 2 plasma at a
power density of 31 W /cm 3 w ith the first 550 sec devoted to
remove adsorbed gases from the specimen at low applied
power levels in 3 torr Ar. The desired power was then
applied and extra cleaning of the specimen continued for
additional 4 min. O 2 was then admitted into the system to
obtain the preset pressure. Except for some power fluc­
tuations in between, temperature was steadily obtained as
pressure continued to increase.
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332
1000
900
BOO
eP 700
600
cti
U
<U
_ _ _
500
S
4 00
CL,
<D
Eh
300
200
100
4 0 0
BOO
1200
1600
Time (sec)
Figure C20. Temperature profile for NiO fired in 25 torr H 2 plasma
at a power density of 33 W /cm 3. Low power (200 W) was
applied for 460 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then
applied and H 2 introduced.
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333
1400
1200
033
a
S-i
0)
P<
0
0)
800 r
:
6oo
:
:
400 j
:
:
H
200
500
1000
1500
2000
Time, t (sec)
Figure C21. Temperature profile for Fe2 C>3 fired in 25 torr N 2 plasma
at a power density of 35 W /cm 3. Low power (200 W) was
applied for 600 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and N 2 admitted.
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334
1100
1000
900
800
700
600
^
500
400
300
200
100.
400
BOO
1200
1600
Time, t (sec)
Figure C22. Temperature profile for Fe2 C>3 fired in 25 torr O 2 plasma
at a power density of 31 W /cm 3. Low power (200 W) was
applied for 520 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then
applied and O 2 introduced.
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335
1200
1000
o
Temperature, T (
o
800
600
200
400
BOO
1200
1600
Time, t (sec)
Figure C23. Temperature profile for Fe2 C>3 fired in 25 torr H 2 plasma
at a power density of 33 W /cm 3. Low power (200 W) was
applied for the first minute to remove adsorbed gases
from the specimen in 3 torr Ar. The desired power was
then applied and further cleaning continued for 2.5 min.
H 2 was then admitted.
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336
900
BOO
700
Eh 600
500
U 400
<D 300
200
100
500
1000
1500
Time, t (sec)
Figure C24. Temperature profile for Fe2 C>3 fired in 25 torr He plasma
at a power density of 36 W /cm 3. Low power (200 W) was
applied for 570 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then
applied and He introduced.
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337
1200
Temperature, T (°C)
1000
BOO
600
400
200
200
400
600
800
1000
1200
Time, t (sec)
Figure C25. Temperature profile for ZnO fired in 25 torr N 2 plasma
at a power density of 35 W /cm 3. Low power (200 W) was
applied for 2 0 0 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and N 2 admitted into the system.
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338
1000
BOO
ou
EH
<U
u
3
+■>
cd
0)
Q*
U
600
400
a
CD
^
200
200
400
600
800
1000
Time, t (sec)
Figure C26.
Temperature profile for ZnO fired in 25 torr O 2 plasma
at a power density of 31 W /cm 3. Low power (200 W) was
applied for 60 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then
applied and O 2 introduced.
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339
800
700
600
-5 0 0
cd 400
2 300
200
100
200
400
600
800
Time, t (sec)
Figure C27. Temperature profile for ZnO fired in 25 torr H 2 plasma
at a power density of 33 W /cm 3. Low power (200 W) was
applied for 440 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then
applied and H 2 bled into the system.
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340
BOO
700
60 0
300
200 j
100
200
400
600
800
1000
Time, t (sec)
Figure C28. Temperature profile for ZnO fired in 25 torr He plasma
at a power density of 36 W /cm 3. Low power (200 W) was
applied for 180 sec to remove adsorbed gases from the
specimen in 3 torr Ar. The desired power was then ap­
plied and He introduced.
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341
1200
1000
ou
(0
Sm
3
d
u
<u
600
O i 400
a
(0
E-i
200
200
400
600
BOO
1000
Time, t (sec)
Figure C29. Temperature profile during a cleaning cycle for the opti­
cal fiber thermometer (OFT) fired in 25 torr N 2 plasma at
a power density of 35 W /cm 3. The power level was slow­
ly ramped to the desired value to obtained the preset
power density as N 2 was admitted.
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342
1200
1000
BOO
8)
600
4->
cti
(-i
<0
a, 400
a
0)
H
200
200
400
600
BOO
1000
1200
Time, t (sec)
Figure C30. Temperature profile for during a cleaning cycle for an
OFT light pipe fired in 25 torr O 2 plasma at a power
density of 31 W /cm 3. Low power (200 W) was applied
for the first 2 min in 3 torr Ar. The desired power was
then applied and O2 introduced. A higher power was
applied near the end of the cleaning procedure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
343
Length (cm)
APPENDIX D
*
5 torr
O
25 torr
□
AO torr
10"
0
500
1000
1500
2000
Incident Power (watts)
Figure D l.
Plasma length as a function of applied power for a micro­
wave excited helium plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
344
10-
L e n g th
(c m )
15-
o□
0
200
400
600
In c id e n t P o w e r
Figure D2.
800
A
5 to rr
O
25 t o r r
D
40 to r r
1000
1200
(w a tts )
Plasma length as a function of applied power for a micro­
wave excited hydrogen plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
345
25
Length (cm)
20
15
/\
10
5
A
5 to rr
*
10 t o r r
O
25 to rr
□
40 to rr
0
0
300
600
900
1200
1500
Incident Power (watts)
Figure D3.
Plasma length as a function of applied power for a micro­
wave excited nitrogen plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Average Power Density (W/cm3)
APPENDIX E
346
30
20
10
O
25 to r r
□
40 to r r
0
0
500
1000
1500
2000
Incident Power (watts)
Figure E l.
Average power density as a function of power for a micro­
wave excited helium plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Average Power Density (W/cm 3)
347
40-
30-
20-
OO
A 5 torr
O 25 torr
□ 40 torr
10-
0
200
400
600
800
1000
1200
Incident Power (watts)
Figure E2. Average power density as a function of power for a micro­
wave excited hydrogen plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Average Power Density
(W/cm 3)
348
60-
A 5 torr
O 25 torr
□ 40 ton-
40-
20
-
0
300
600
900
1200
Incident Power (watts)
Figure E3.
Average power density as a function of power for a micro­
wave excited oxygen plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
349
2
o
•
o
o
o
Average Power Density (W/cm3)
40
A
o
20°
o
•
A
A
h
A
10■
0
t
0
1
i
300
A
5 to rr
©
2 5 to r r
□
40 to rr
-•------ 1------ 1-------1-------1------- 1------ ------600
900
1200
1500
Incident Power (watts)
Figure E4.
Average power density as a function of power for a micro­
wave excited nitrogen plasma at various pressures.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
350
ne/Pd A x 10
(watts-cm)
APPENDIX F
pA (torr-cm)
Figure F I.
Plots of ne/P d A and E /p as a function of pA for a micro­
wave excited helium plasma. Curves were generated for
the present experimental conditions from microwave
breakdown and electron drift velocity data (refs. [60,120,
149-151]).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(watts-cm)’■
351
2.0
20
1.5
15
fc
2
1.0
10
CO
ne/Pd A x 10'
O
w
0
0
5
10
15
20
pA (torr-cm)
Figure F2.
Plots of ne/Pd A and E /p as a function of pA for a micro­
wave excited hydrogen plasma. Curves were generated
for the present experimental conditions from microwave
breakdown and electron drift velocity data (refs. [60,120,
149-151]).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
352
(watts-cm)
10
8
15
fc
0
PdA
4->
1
I
ne/Pd A x 10
10
o
W
2
0
0
10
5
1 5
20
pA (torr-cm)
Figure F3.
Plots of ne/Pd A and E /p as a function of pA for a micro­
wave excited nitrogen plasma. Curves were generated for
the present experimental conditions from microwave
breakdown and electron drift velocity data (refs. [60,120,
149-151]).
35556020820106
3 5556 020 820 106
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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