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Microwave processing of reaction-bonded silicon nitride

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NORTHW ESTERN UNIVERSITY
M icrowave Processing of Reaction-Bonded Silicon Nitride
A DISSERTATION
SUBM ITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLM ENT OF THE REQUIREM ENTS
for the degree
DOCTOR OF PHILOSOPHY
Field o f Materials Science and Engineering
by
J
Jeffrey John Thom as
//
'
EVANSTON, ILLINOIS
December 1994
'
'
'
UMI Number: 9521820
UMI Microform Edition 9521820
Copyright 1995, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
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ABSTRACT
M icrowave Processing o f Reaction-Bonded Silicon Nitride
Jeffrey John Thomas
Silicon compacts were nitrided in a microwave applicator using m inim um insulation
in order to maximize the temperature gradients. Rod-shaped specimens exhibited very nonuniform conversion to RBSN, in that the degree o f reaction was much higher in the middle
than near the ends, and the fully-nitrided areas contained regions o f high- and low-density
RBSN. The microwave-heated specimens also exhibited a significant weight loss. The
poor microstructures and weight loss were caused by high temperatures and temperature
gradients in the areas of m aximum nitridation rate, which caused silicon vapor to diffuse
within and out of the specimens.
The progress of the nitridation reaction was attributable to large changes in the
microwave heating characteristics o f the specimens as they nitrided. W hen the
com pacts first reached nitriding temperatures o f 1200-1300°C, the silicon pow der
sintered together via a coarsening process which created necks between adjacent
particles and caused the specimens to be electrically conducting. As a result, the
heating efficiency was low and the heating was not volumetric because microwave
pow er was absorbed only near the specimen surface. Therefore, no significant
temperature gradients developed initially.
Between 50% and 70% conversion to RBSN, the necks connecting the silicon
particles disappeared as the silicon phase was converted to silicon nitride. This caused
a large increase in both the heating efficiency and the penetration depth because the
ii
specim en as a whole was no longer electrically conducting. After 80% conversion the
penetration depth increased rapidly and the heating efficiency decreased. According to
an empirical model of the microwave heating process, the maxim um power absorption
occurred at a conversion level o f 72% for the specimen geometry used.
Compacts made from a mixture of silicon pow der and silicon nitride pow der did not
sinter when the initial volume ratio o f silicon nitride to silicon was at least 1. These
specimens nitrided uniform ly with inside-out composition profiles. Although the
mechanical properties o f these specimens were inferior, these results indicated that
microwave heating would be beneficial for the nitridation of pure silicon pow der com pacts
if neck formation between adjacent particles could be eliminated.
ACKNOW LEDGMENTS
I w ould first like to thank my advisors, Professor D. Lynn Johnson and Professor
H am lin M. Jennings, for their guidance, support, and encouragem ent throughout this
study. I would also like to thank Dan Skamser for his invaluable help in the com puter
m odelling aspect o f this work and for his friendship.
Special thanks to my parents, Jack and Lois Thomas, for their love and
encouragem ent and for their assistance in editing this manuscript.
Finally, I would like to thank my wife, Ana Vazquez, who is also my best friend.
Her love and emotional support saw me through the tough times and made my experience
as a graduate student infinitely more rewarding.
iv
TABLE OF CONTENTS
A BSTRA CT
......................................................................................................................
ii
.............................................................................................
iv
ACKNOW LEDGM ENTS
L IS T
OF
F IG U R E S
.....................................................................................................
viii
L IS T
OF
TABLES
.......................................................................................................
xvi
..................................................................................................
1
......................................................................................
5
...................................................................................................
5
1
IN T R O D U C T IO N
2
RBSN
BACKGROUND
2.1
In tro d u c tio n
2.2
R eaction m echanism s and m icrostructure
2.3
2.4
...............................................
7
2.2.1
Nitridation in pure nitrogen
10
2.2.2
Nitridation with added hydrogen
12
2.2.3
Form ation and m icrostructure o f a - S i - ^
15
2.2.4
Form ation and m icrostructure of J3-Si3N4
18
2.2.5
Effect o f cation impurities in the silicon powder
19
Effect o f processing conditions on the nitridation reaction ...................
22
2.3.1
Silicon particle size
22
2.3.2
Effect of temperature on the nitridation reaction
24
2.3.3
Gas com position and nitrogen partial pressure
28
R e a c tio n
2.4.1
k in e tic s
.........................................................................................
Intrinsic nitridation kinetics
v
31
33
2.4.2
2.5
3
4
Bulk diffusion of nitrogen
35
p ro p e rtie s
38
RBSN
.........................................................................................
2.5.1
M echanical properties at room temperature
39
2.5.2
High-temperature mechanical properties
42
M IC R O W A V E
H E A T IN G
...................................................................................
...................................................................................................
44
3.1
In tro d u c tio n
3.2
M icrow ave processing o f ceram ic m aterials
3.3
M icro w av e p ro cessin g o f R B SN
3.4
M icro w av e-m aterial in teractio n s
.............................................
53
3.5
D ielectric pro p erties o f m ixtures
.............................................................
62
3.6
V o lu m e tric
......................................................................................
66
h eatin g
E X P E R IM E N T A L P R O C E D U R E S
4.1
p re p a ra tio n
...........................................
47
............................................................
52
..................................................................
M aterial and atm osphere selection
..........................................................
4 .2
S p ecim en
4.3
A p p a ra tu s
..........
4 .4
R eac tio n -b o n d in g p ro ced u re
4 .5
T em perature m easurem ent and calibration
4 .6
T ag u c h i
4.7
S p ecim en c h a ra c te riz a tio n
71
71
72
........................................................................................................
e x p e rim e n ts
44
....................................................................
75
80
.............................................
82
.................................................................................
84
vi
........................................................................
87
5
RESU LTS
A N D D IS C U S S IO N
......................................................................
92
5.1
N itridation o f disk-shaped silicon com pacts
.........................................
92
5.2
N itridation o f rod-shaped silicon com pacts
............................................
101
5.2.1
M icrowave nitridation of rod-shaped com pacts
103
5.2.2
Taguchi experiments
114
5.3
Experim ental analysis o f m icrow ave heating phenom ena .......................
124
5.4
M icrowave heating characteristics o f silicon/silicon nitride mixtures .......
137
5.4.1
M icrowave heating model for nitriding com pacts
137
5.4.2
Nitridation o f silicon/silicon nitride pow der mixtures
147
5.4.3
Possible ways to avoid silicon neck formation
152
5.5
5.6
N um erical m odel o f m icrow ave RBSN processing
...............................
155
5.5.1
Material parameters and control equations used in the model
155
5.5.2
Computational procedure
161
5.5.3
Simulation o f the nitridation o f a standard silicon com pact
162
5.5.4
Simulation o f the nitridation o f a m ixed-powder com pact
171
5.5.5
Simulation o f the nitridation o f a non-sintered silicon com pact
177
A nalysis of silicon vapor transport and reaction band formation ............
182
.....................................................................................................
192
6
C O N C L U S IO N S
7
R E C O M M E N D A T IO N S
REFERENCES
FO R FU T U R E W O R K
............
..................................................................................................................
vii
195
200
LIST OF FIGURES
2.1
Effect o f oxygen on the reaction kinetics. The M o lining reduced the
am ount of oxygen in the furnace, thereby slowing the nitridation rate (after
Pigeon et al., 1993).
14
2.2
M echanism for the formation of the a-m atte, showing silicon evaporating
and the remaining vacancies coalescing into micropores (after Atkinson et al.
1974).
16
2.3
Formation mechanisms for the a-needles. A liquid forms either at the tip o f
the needle (top) or at the base (bottom), allowing silicon nitride to form at
the interface (after Jennings and Richman, 1976).
17
2 .4
Form ation o f ^-spikes in silicon liquid (after Jennings and Richman, 1976).
19
2.5
Effect o f various iron additions on the nitridation kinetics o f pure silicon
(after M oser e ta l., 1986).
20
2.6
Effect of particle size on the nitridation kinetics (after Atkinson et al. 1973).
23
2.7
Intrinsic nitridation kinetics as a function o f temperature: (o) 1350°C, (A)
1300°C, (□) 1275°C, (0) 1250°C, (+) 1200°C (After Pigeon and Varma
1993).
25
2.8
Effect o f He, H 2 , and Ar gas additions on the diffusivity (left) and the
thermal conductivity (right) o f N 2 gas (after Kim and Kim 1985c/, 1985/?).
29
2.9
Effect o f various pretreatments and gas compositions on the nitridation
kinetics, demonstrating the importance o f the native SiC>2 layer (after
Raham an and M oulson, 1984).
32
2.10 Effect o f average pore radius on the rate of sulphation o f calcined limestone
particles, dem onstrating the decrease in gaseous diffusion rates with pore
size (after Reyes and Jensen, 1987).
37
2.11 Variation in Young's m odulus, E, with total porosity P (after M oulson,
1979).
41
viii
2.12
Fracture strength o f various types o f RBSN plotted as a function of the total
porosity (after Rice, 1977).
41
2.13
Fracture strength o f RBSN as a function of temperature, for three different
densities (after Fleinrich and Bunk, 1981).
43
3.1
Schematic diagram o f the interaction of microwaves with different types of
m aterials (after Sutton, 1989).
46
3.2
Density versus temperature for conventional and microwave (28 GHz)
sintering of alum ina (after Janney and Kimrey, 1989).
51
3.3
Arrhenius-type plot of alumina sintering rate versus temperature, showing
the apparent activation energies for microwave and conventional heating
(after Janney and Kimrey, 1989).
51
3.4
Propagation of an electromagnetic plane wave in a lossy material (after
M etaxas and Meredith, 1983).
56
3.5
N orm alized power absorption versus loss tangent for a planar slab o f
thickness 1 cm, using f = 2.45 GHz and £r = 10.
58
3.6
Relative dielectric constant versus temperature for selected ceramic materials
at 8-10 GHz (after W alton, 1970).
60
3.7
Loss tangent versus temperature at 2.45 GHz for different grades of alumina
(after Spotz et al., 1994).
60
3.8
Plot o f normalized specimen temperature versus normalized applied
microwave power for a model material, showing the stable and unstable
regions (after W atters, 1989).
61
3.9
Pow er transmission coefficient versus volume fraction o f iron inclusions for
an iron / CaC 0 3 mixture at 9.6 GHz (after Neelakanta, 1994).
65
3.10
a) Effect of thermal conductivity on the radial temperature profile of an
infinitely long cylinder with uniform power deposition,
b) Effect of radius on the radial temperature profile of an infinitely long
cylinder with uniform power deposition and K(h = 10 W n r 1 K 1.
69
ix
3.11
Effect o f outer surface temperature on the required power density and the
maximum specimen radial temperature difference, for a uniformly heated
infinite cylinder with radius 1 cm and Kth = 10 W n r 1 K '1.
70
4.1
Tube assembly used for isostatic pressing of pow der into rods.
74
4.2
a) Configuration for nitriding disk-shaped silicon compacts.
b) Configuration for nitriding rod-shaped silicon compacts.
76
4.3
Schematic diagram of the microwave processing apparatus.
77
4.4
Tunable microwave cavity. The specimen is suspended from a balance.
79
4.5
L4 orthogonal array with 3 factors and 2 levels for each factor (top). L9
orthogonal array with 4 factors and 3 levels for each factor (bottom).
85
5.1
a) Hardness profile o f a 52% dense disk-shaped silicon com pact nitrided
to 65% conversion using microwaves.
b) Hardness profile o f a 52% dense disk-shaped silicon com pact nitrided
to 65% conversion at 1350°C using conventional heating.
94
5.2
Data from the nitridation o f 19 mm diameter disk-shaped silicon compacts
at 1350°C using conventional heating.
95
5.3
Data from the microwave processing of a silicon compact. A programm ed
conversion rate o f 12% per hour was used. Each data point is an average
value from the previous 5 minutes. The temperature measurements were
taken on the outer edge o f the disk, which was the coolest part of the
specimen.
97
5.4
a) Hardness profile of a 62% dense disk-shaped silicon com pact nitrided
to 70% conversion using microwaves.
b) Hardness profde of a 62% dense disk-shaped silicon com pact nitrided
at 1350°C using conventional heating.
98
5.5
Polished cross-section o f a 62% dense disk-shaped com pact which was
nitrided to 70% conversion using microwaves. Note the reaction bands.
99
5.6
Polished cross-section o f a 62% dense disk-shaped com pact which was
nitrided to 70% conversion using conventional heating.
99
x
5.7
Data from the nitridation of the 15 mm diameter and 23 mm diameter rodshaped silicon compacts using conventional heating.
102
5.8
Cross-section of 15 mm diameter (left) and 23 mm diameter (right) rodshaped silicon compacts after conventional nitriding.
102
5.9
Cross sections o f rod-shaped silicon compacts nitrided using microwave
heating: a) asymmetric radial nitridation, b) asymmetric axial nitridation,
c) typical profile with more conversion in the middle o f the rod.
105
5.10
Hardness profile along the center axis o f a 15 mm diameter rod-shaped
silicon com pact nitrided to 70% conversion using microwaves.
106
5.11
Data from the microwave processing o f a 15 mm diam eter rod-shaped
silicon com pact using a programm ed conversion rate o f 3% per hour.
Each data point is an average value from the previous 5 minutes.
108
5.12
Data from the conventional nitridation o f 15 mm diameter rod-shaped
silicon compacts with and without a 1% hydrogen addition.
110
5.13
Change in the reaction rate with nitrogen partial pressure, for a constant
insulation surface temperature of 865°C. A: pure nitrogen, B: 67 vol%
nitrogen, C: 50 vol% nitrogen.
112
5.14
Change in the insulation surface temperature with nitrogen partial pressure,
for a constant reaction rate o f 3% conversion per hour. A: pure nitrogen, B:
67 vol% nitrogen, C: 50 vol% nitrogen.
112
5.15
Processing conditions for the L9 Taguchi experiment.
115
5.16
Top: data from the L9 Taguchi experiment. Bottom: F-values from the L9
Taguchi experiment. F-values which are larger than the 95% confidence
level appear in boldface type.
117
5.17
Plots showing the effects o f the different factors on the hardness of the
specimens. Top: radial hardness. Middle: axial hardness. Bottom:
radial + axial hardness.
119
xi
5.18
Plots showing the effects o f the different factors on the specimens. Top:
ratio o f interior to surface hardness. Middle: ratio of middle to end
hardness. Bottom: am ount o f overheating.
120
5.19
Processing conditions for the L4 Taguchi experiment.
122
5.20
Top: data from the L4 Taguchi experiment. Bottom: F-values from the
L4 Taguchi experiment. F-values which represent a significant effect
appear in boldface type.
123
5.21
Cross section of the configuration used for the internal temperature
m easurement experiments.
125
5.22
Data from the nitridation o f 23 mm diameter compacts using the lightpipe
to monitor the internal temperature while the surface temperature was
held constant. Each data point represents the average temperature over a
15 minute period.
127
5.23
X-ray diffraction scan taken on a section o f the outer crust which forms
around the microwave-nitrided specimens. The presence o f a large silicon
peak indicates that the crust is formed by silicon vapor diffusing out o f the
specimens and condensing in the cooler pow der bed.
131
5.24
Photograph o f the cross-section o f a 15 mm diameter rod which was
nitrided as it was translated through the microwave cavity. Note the
closely-spaced reaction bands.
134
5.25
Hardness trace taken along the center axis o f a specimen which was
translated through the microwave cavity as it nitrided.
134
5.26
SEM photograph taken at the boundary between a dark reaction band
(top) and a white reaction band (bottom), The grey areas are RBSN and
the black areas are pores.
136
5.27
Dielectric constant and loss factor as a function o f silicon volume fraction,
using the equations for a conductor-loaded dielectric.
140
5.28
Normalized power absorption of a silicon/silicon nitride mixture as a
function o f composition, using the equations for a conductor-loaded
dielectric material.
xii
142
5.29
M icrowave penetration depth of a silicon/silicon nitride mixture as a
function o f composition, using the equations for a conductor-loaded
dielectric material.
142
5.30
Normalized power absorption o f a silicon/silicon nitride mixture as a
function o f com position, using the equations for a homogeneous
conducting material.
145
5.31
M icrowave penetration depth of a silicon/silicon nitride mixture as a
function of composition, using the equations for a homogeneous
conducting material.
145
5.32
Normalized power absorption o f a silicon/silicon nitride mixture as a
function o f composition, using the com bined model.
146
5.33
M icrowave penetration depth of a silicon/silicon nitride mixture as a
function o f com position, using the combined model.
146
5.34
Cross sections o f m ixed-powder specimens nitrided to 60% conversion
using microwave heating: a) mixture 2 (50 vol% silicon), b) mixture 3
(25 vol% silicon).
149
5.35
X-ray scans of a m ixed-powder specimen nitrided to 60% conversion using
microwaves. The top scan was taken with the specimen masked to scan
only the center area, and has no visible silicon peak. The bottom scan was
taken with the specimen masked to scan only the outside o f the middle part
o f the specimen, and has a large silicon peak.
151
5.36
Diagram o f the configuration used to represent the specimen and insulation
for the finite-difference model. Symmetry allows the entire specimen to be
represented by one 2D quadrant, as shown.
156
5.37
5.38
Computational procedure used for the com puter simulations.
Simulated temperature values in a standard silicon com pact from the middle
o f the specimen to the end. The solid line is the center of rod and the dotted
line is the surface, a) 10% conversion, b) 30% conversion, c) 40%
conversion.
xiii
163
165
5.39
Simulated composition values for a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and the
dotted line is the surface, a) 10% conversion, b) 30% conversion, c) 40%
conversion.
166
5.40
Simulated temperature values in a standard silicon compact from the middle
of the specimen to the end. The solid line is the center of rod and the dotted
line is the surface, a) 45% conversion, b) 50% conversion, c) 75%
conversion.
167
5.41
Simulated composition values for a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and the
dotted line is the surface, a) 45% conversion, b) 50% conversion, c) 75%
conversion.
168
5.42
Simulated nitrogen pressure values for a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center, and the
dotted line is 1 mm from the surface, a) 30% conversion, b) 45%
conversion, c) 75% conversion.
169
5.43
Simulated temperature values for a mixed-powder com pact from the middle
of the specimen to the end. The solid line is the center of rod and the dotted
line is the surface, a) 10% conversion, b) 50% conversion, c) 80%
conversion.
174
5.44
Simulated composition values for a mixed-powder com pact from the middle
of the specimen to the end. The solid line is the center o f rod and the dotted
line is the surface, a) 10% conversion, b) 50% conversion, c) 80%
conversion.
175
5.45
Simulated nitrogen pressure values for a m ixed-powder specimen from the
middle o f the specimen to the end. The solid line is the center, and the
dotted line is 1 mm from the surface, a) 10% conversion, b) 50%
conversion, c) 80% conversion.
176
5.46
Simulated temperature values for a non-sintered silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and the
dotted line is the surface, a) 10% conversion, b) 50% conversion, c) 80%
conversion.
178
xiv
5.47
Simulated composition values for a non-sintered silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and the
dotted line is the surface, a) 10% conversion, b) 50% conversion, c) 80%
conversion.
179
5.48
Sim ulated nitrogen pressure values for a non-sintered silicon com pact from
the middle o f the specimen to the end. The solid line is the center, and the
dotted line is 1 mm from the surface, a) 10% conversion, b) 50%
conversion, c) 80% conversion.
180
5.49
Geometric representation o f a nitriding specimen used to calculate the silicon
flux required for reaction band formation. Nitridation occurs only within
the reaction zones defined by the disk-shaped volumes of thickness w and
area A which separate fully nitrided and unreacted material.
183
5.50
Plot o f the equilibrium silicon vapor pressure over a condensed silicon
surface as a function of temperature, using the data o f Dushm an (1962).
189
5.51
Volatility diagram for the silicon-nitrogen system at 1480°C. The horizontal
line represents the silicon vapor pressure, and the angled line represents the
decom position of silicon nitride. Solid lines give the equilibrium
conditions.
190
xv
LIST OF TABLES
1.1
Selected properties o f silicon and silicon nitride.
4.1
Properties o f the silicon powders used, as reported by the manufacturers.
72
4.2
Silicon and silicon nitride diffraction peaks in the range 20 = 26° - 37°.
90
5.1
Average weight loss values after 50% and 75% conversion using different
processing conditions.
130
5.2
Composition o f the silicon/silicon nitride pow der mixtures, by volume and
by weight.
148
xvi
3
Chapter 1
Introduction
Silicon nitride, Si.3 N 4 , has been established as a prom ising material for high
temperature structural applications such as turbine blades for advanced heat engines due to
its low thermal expansion, high elastic modulus, and high-temperature stability. However,
commercial development has been limited because high quality components can not be
produced economically. Improved processing techniques are needed before many o f the
potential applications can be realized.
As with most ceramics, silicon nitride is strongest when the specimen approaches
full theoretical density. Dense silicon nitride is formed by sintering fine silicon nitride
pow der m ixed with sintering aids. Solid state sintering o f silicon nitride can occur only at
temperatures above the atmospheric decomposition temperature (1875°C) when atom
m obilities become sufficiently high. Therefore, sintering additives such as M gO, AI 2 O 3 ,
and Y 2 O 3 are added to the silicon nitride powder in order to form a liquid phase. In order
to achieve near-theoretical densities, nitrogen overpressures are typically used to prevent
decom position. Hot pressing can also be used to achieve full theoretical density, but this
method is expensive and is limited to the formation of simple com ponent geometries;
machining o f fully dense silicon nitride is also very expensive. The greatest disadvantage
to both o f these techniques is that the oxide sintering aids create a glassy grain-boundary
phase which leads to a degradation in strength and creep resistance at high temperatures.
Reaction-bonded silicon nitride (RBSN) is produced by heating silicon to
1
2
temperatures in the range o f 1250°C to 1450°C in a predominantly nitrogen atmosphere. To
fully convert silicon to silicon nitride, the specimen must be in a the form o f a silicon
pow der compact with an average particle size less than about 30 pm in order to allow all of
the unreacted silicon to come into contact with nitrogen. As the reaction proceeds, the total
porosity decreases as new material expands into the pores to accommodate the 22% volume
increase associated with the conversion from silicon to silicon nitride. Because oxide
sintering aids are not required, RBSN does not have a glassy grain boundary phase and
therefore retains its mechanical properties to temperatures in excess o f 1400°C. Another
advantage to RBSN is that there is very little dimensional change to the com pact during the
reaction, which allows com plex shapes to be readily formed. However, RBSN is
generally w eaker than sintered or hot-pressed material due to the residual porosity, which is
typically about 20%. Various properties o f silicon and silicon nitride are listed in Table
1.1.
M icrowave processing o f ceramic materials offers several potential advantages over
conventional processing, including reduced manufacturing costs due to energy savings,
reduced processing times, and im proved properties and microstructures. However, these
advantages have rarely been realized due to the complex nature o f microwave-material
interactions. M icrowave heating is fundamentally different from conventional heating, in
that heat is generated volumetrically within the specimen instead o f being applied only at the
surface. A unique feature of volumetric heating is the formation o f steady-state temperature
gradients with the interior hotter than the surface. These temperature gradients offer a
potential advantage for the processing o f RBSN. The large decrease in the average pore
size caused by the nitridation reaction tends to prevent nitrogen from reaching the interior of
the compact, and to fully convert from silicon to RBSN often requires very long processing
times. For large compacts with a relatively high green density, the porosity near the
surface can close off completely, leaving a core containing unreacted silicon. In the
presence o f a thermal gradient the center of an RBSN compact would react faster than the
3
Table 1.1.
Selected properties o f silicon and silicon nitride.
Property
Value
M elting point (Si)*
1413°C
D issociation temp. (SiaN,*)
1875°C
Density
Si*
pure Si 3 N 4 *
2.33 g cm -3
RBSN*
2.2 - 2.8 g cm -3
C oefficient o f thermal expansion (Si 3 N 4 )*
3.18 g cm '3
3 x 10-6 K-'
Flexural strength (RT)
dense S i 3 N 4 *
RBSN*
400-950 M N m -2
150-350 M N n r 2
Fracture toughness
dense S i 3 N 4 *
3.4 - 8.2 MN n r 3/2
RBSN*
1.5 - 2.8 M N mr3/2
Young's m odulus (RT)
dense S i 3 N 4 *
300 - 330 GN n r 2
RBSN*
120 - 220 GN n r 2
* From M oulson (1979).
* From Ziegler et al. (1987).
surface, and so more silicon in the interior would nitride before the porosity closed off.
T he temperature difference within the sample would also build a beneficial residual stress
state into the final product, with the surface under compression. This residual stress state
should help prevent surface cracks from forming and growing during service.
The objectives o f this work were to demonstrate an advantage to the use o f
microwave heating for the RBSN process by using the temperature gradients inherent to
volumetric heating to increase the amount o f conversion in the interior o f nitriding
com pacts, to optimize the microwave process so as to produce fully reacted RBSN with a
high relative density and good properties, and to gain a better understanding of the change
in the microwave heating properties as the composition o f an RBSN specimen changes
from silicon to silicon nitride.
Chapter 2
RBSN Background
2.1
Introduction
Reaction-bonded silicon nitride (RBSN) was first studied as a potentially valuable
engineering ceram ic in the late 1950's in the United Kingdom (Parr et al. 1959, 1960)
where m uch o f the research on RBSN continued in the 1960's and 1970's (Parr and M ay
1967, Jack 1973, 1976, Riley 1983). The first major research effort in the United States
began in 1970 when the Advanced Research Project Agency (ARPA) funded a program
w hich had as its primary goal the construction of a gas-turbine engine using RBSN
com ponents. This project stimulated interest in RBSN, and since the late 1970's there has
been extensive research into the processing methods and properties o f RBSN. This early
w ork is described in two com prehensive review papers (M oulson 1979, W eiss 1981).
The focus o f RBSN research is to produce material with good high temperature
properties. This requires an understanding o f three general areas: the formation and
com paction o f silicon powder, the effects o f the numerous processing variables on the
reaction kinetics and final microstructure, and the relationship between the microstructure
and the mechanical properties.
Silicon nitride exists in two hexagonal phases, designated as a and (3. In both
cases, the basic structural unit is the silicon-nitrogen tetrahedron, where each nitrogen atom
is shared by three tetrahedra. The first structural determination was made by Ruddleson
and Popper (1958). Until the mid 1970's it was believed that the p-phase was
stoichiometric Si 3 N 4 , and that the a-phase was a defect structure with oxygen replacing
nitrogen on some sites and nitrogen vacancies to maintain electroneutrality, as was first
suggested by Grievson et a l . (1968). It is now clear, based on further structural analysis,
that the a-p h ase does not contain oxygen (Priest et al. 1973, Niihara and Hirai 1976).
W hen oxygen is present in significant amounts, another com pound, silicon oxynitride
(Si 2 N 2 0 ), can form. This com pound is often amorphous and is difficult to detect, which
may explain the earlier confusion. The p~Si3 N 4 phase has a slightly lower free energy of
formation, and it is considered the more stable phase because a -S i 3 N 4 can be converted to
p-Si 3 N 4 at temperatures above 1500°C, but the transform ation from P-S 1 3 N 4 to a - S i 3 N 4
has never been observed (Bowen et al. 1978). The amount o f each phase that forms
depends on the particular nucleation and growth mechanisms rather than on thermodynamic
considerations, as will be discussed in the next section.
Like most polycrystalline ceramics, RBSN with the best mechanical properties is
obtained with a high density, uniform microstructure, and small grain size. As described
by the Griffith theory, the strength of a brittle material is determined by the stress needed to
propagate the largest flaw (Davidge and Evans 1970). In many cases, the largest flaws in
an RBSN specimen are caused by localized melting of silicon during nitridation (Arundale
and M oulson 1977). These flaws can result from large silicon particles, iron or other
cation impurities, or improper temperature control during nitridation. If these flaws are
avoided, generally by using good quality silicon powder, then the strength o f the RBSN
increases with decreasing pore size. The a /p ratio can also affect the mechanical properties
o f silicon nitride. Hot-pressed silicon nitride has a higher fracture toughness when it is
mostly P-phase (Heinrich 1987), but the opposite is true for RBSN. The fine-grained
fibrous nature o f the a-phase provides superior strength and toughness by reducing the
average pore size of the product. Also, RBSN with a large am ount of the P-phase is often
inferior because it was formed in the presence o f a liquid phase, which causes large flaws
7
(M oulson 1979).
An important requirement for high-temperature structural applications is creep
resistance. High-tem perature creep in RBSN is caused by internal oxidation o f grain
surfaces (Grathwohl and Thiim m ler 1978). If the pore size is small enough, this process
can be limited to the outer surfaces o f the specimen, where oxidation seals off the pores and
protects the interior o f the specimen (Porz and Thiimmler 1984). A fine pore size can be
achieved by using a small particle size and a high green density.
2.2
Reaction mechanisms and microstructure
M uch research into the nitridation process has been done during the last 20 years,
and the effects o f many o f the processing variables on the kinetics and product morphology
are well docum ented (Jennings et al. 1983, 1988a). However, some questions rem ain,
such as the exact role o f cation impurities during nitridation and the dom inant reaction
mechanism during the later stages of the reaction. One of the critical factors affecting both
the reaction mechanisms and kinetics is the presence o f oxygen. Oxygen generally exists
as a native silica layer on the starting silicon particles, and also as an impurity in the reactant
gas. Oxygen can also enter the system through leaks in the nitriding apparatus and through
oxide impurities derived from alumina or mullite furnace tubes (Pigeon et al. 1993). W ater
vapor is also present as an im purity in the reactant gas.
Several researchers have concluded that o c - S f ^ forms from gas phase reactions,
and that P-Si3 N 4 forms from solid-state and liquid-phase reactions, based on the
m icrostructure o f the phases (Guthrie and Riley 1973, Dalgleish et al. 1980, 1981,
G regory and Richm an 1982, Jennings et al. 1988). The a-p h ase forms as a random array
o f needles which grow into the porosity o f the com pact as an interlocking matte. This
m orphology strongly suggests a CVD process involving either Si(g) or SiO(g) (Longland
8
and M oulson 1978). The P-phase forms as a coherent product layer around the silicon
particles, indicating a reaction with solid silicon. It has also been dem onstrated (M oulson,
1979) that reactions with liquid silicon form the P-phase exclusively. Jennings et al.
(1983) has suggested that the a-phase is formed by reaction with molecular nitrogen and
that the P-phase forms by reaction with atomic nitrogen.
There are three fairly distinct stages in the nitridation o f a silicon pow der compact:
1. Devitrification and removal o f the native SiC>2 layer accompanied by a period
o f fast gas-phase nitridation which stops when a passivating layer forms around the
particles. The com position o f this layer depends on the presence o f hydrogen.
2. The period o f main nitridation, characterized by continuously decreasing
reaction kinetics. There are two significant rate-controlling mechanisms during this period:
diffusion through micropores in the product layer surrounding the individual particles and
bulk diffusion o f nitrogen into the com pact through interconnected macropores.
3. A period o f very slow reaction, where bulk diffusion o f nitrogen into the
com pact is rate controlling.
Nitrogen can react directly with silicon to form silicon nitride by any of the following
reactions (M oulson 1979):
3Si(g) + 2 N 2(g) = S i,N 4(s)
(AG° = -851 k J /m o l) ,
2.1
3Si(l) + 2 N 2(g) = S i3N 4(s)
(AG° = -217 k J/m o l) ,
2.2
3Si(s) + 2 N 2(g) = S i3N 4(s)
(AG° = -2 1 2 k J /m o l) ,
2.3
where the AG° values are for 1350°C. As discussed above, reaction 2.1 forms a -S i 3 N 4
while reactions 2.2 and 2.3 form P -S ijN ^ For reaction temperatures below the melting
point o f silicon, where most RBSN processing occurs, reaction 2.1 tends to dom inate, as
evidenced by the fact that the cx/p ratio o f the product is always greater than unity.
Nitrogen can also react with SiO, forming either a -S i 3 N 4 (Pigeon et al. 1993) or silicon
9
oxynitride (Barsoum et al. 1991) according to
3SiO (g) + 2 N 2(g) = S i3N 4( a , s ) + 1 .5 0 2(g)
(AG° = 502 k J/m o l)
2.4
(AG° = -6 .6 k J /m o l) .
2.5
or
2SiO (g) + N 2(g) = S i2N 2Q(s) + 0 .5O 2(g)
Since AG° for reaction 2.4 is positive, there has been some doubt as to w hether it is a viable
reaction path. M oulson (1979) showed that vaporization o f silicon is rapid enough to
support any observed nitridation rates by reaction 2.1, and he dism issed reaction 2.4 on
therm odynamic grounds. Dervisbegovic and Riley (1981) concluded on the basis o f
experimental evidence that SiO was not involved in the nitridation process. Jennings et al.
(1983) concluded that SiO nitridation could occur only with the addition o f hydrogen. On
the other hand, Lindley et al. (1979) stated that SiO nitridation was a significant source o f
the a-phase under all nitriding conditions. Recent work by Pigeon eta l. (1993) seems to
provide convincing experimental evidence that SiO nitridation contributes to the overall
nitridation kinetics in the presence of hydrogen, and these authors further suggest that the
process is also important during nitridation without hydrogen. Barsoum et al. (1989,
1991) claim that formation of the oxynitride (reaction 2.5) is thermodynamically favored
over a -S i 3 N 4 when reacting in pure nitrogen, and in fact the presence o f the oxynitride has
been reported after nitridation in pure nitrogen (Pompe eta l. 1985).
In order to understand the nitridation process, the equilibrium conditions with and
without hydrogen will be analyzed in the following sections. To do this, these additional
reactions (Pigeon eta l. 1993) must be considered:
2 Si(s) + 0 2(g) = 2SiO (g)
(AG° = -477 k J /m o l) ,
2.6
Si(s) + 0 2(g) = S i0 2(s)
(AG° = -6 2 0 k J /m o l) ,
2.7
10
S i 0 2 + Si(s) = 2SiO (g)
(AG° = 147 k J /m o l) ,
2.8
Si(s) + H 20 (g ) = SiO(g) + H 2(g)
(AG° = -8 4 k J /m o l) ,
2.9
2 H 2(g) + 0 2(g) = 2 H 20 (g )
(AG° = -314 k J /m o l)
2.10
S i 0 2(s) + H 2(g) = H 20 ( g ) + S i0 (g )
(AG° = -314 k J/m o l)
2.11
where the free energies are given for 1350°C.
2.2.1
Nitridation in pure nitrogen
Upon initial heating, the silicon particles are separated from the nitrogen gas by an
am orphous layer of SiC>2 which m ust be removed before nitridation can begin. As was
first established by Boyer et al. (1977, 1978), the presence o f iron as an im purity catalyzes
the crystallization o f the Si 0
2
and disrupts the layer, which is then removed by active
reduction according to reactions 2.8 and 2.11, both o f which liberate SiO. O nce the silica
is removed, nitrogen can adsorb onto the exposed silicon surfaces and nucleate reaction
sites, form ing small am ounts o f (3-Si3N4 by reaction 2.3 (Atkinson et al. 1974, 1976). A
period of fast reaction ensues as the SiO reacts with nitrogen to form a-Si_3 N 4 and Si2N20
by reactions 2.4 and 2.5, both o f w hich liberate oxygen. The presence o f this oxygen
slows the rate at which the silicon surface is exposed via the removal o f Si0
2
by reaction
2.7, and this limits the extent o f reaction during initial nitriding (Barsoum et al. 1991). The
period o f fast reaction ends after a passivating layer consisting primarily o f either a -S i 3 N 4
or Si 2 N 2
0
forms around the particles.
To determine the composition of this initial layer, the viability o f nitriding SiO by
reactions 2.4 and 2.5 must be evaluated. U nder typical high-purity conditions, w here
careful attention is given to removing oxygen and water, the bulk concentrations o f O 2 and
H 2 O im purities will be about 1 x Kb6 atm. The formation o f SiO by reactions 2.6 and 2.9
is limited to this impurity level, so under high-purity conditions the partial pressure o f SiO
will be determ ined by the removal o f surface SiC>2 via reactions
2 .8
and 2 . 1 1 , which give
SiO partial pressures o f 4.3 x 10' 3 atm and 4.9 x 10' 3 atm respectively (Pigeon et al. 1993).
Since reactions 2.8 and 2.11 occur at the particle surfaces, they are heterogeneous reactions
which form a local equilibrium inside the compact.
U sing a value o f 4.3 x lO 3 atm for ^SiO’ the maximum allowable P 0
for
reactions 2.4 and 2.5 can be calculated (Barsoum et al. 1991). For the formation o f a Si 3 N 4 by reaction 2.4 the requirem ent is (assuming 1 atm o f nitrogen)
%
< 7 x 10 - 1 7
and so p o 2 m ust be < 3 x 10' 1 6 atm. Similarly, for the formation o f Si 2 N 2
2.12
0
by reaction
2.5 the requirem ent is
y2
O,
and so p o 2 m ust be < 9.1 x 10'
10
< 3 x 10J
2.13
atm. Clearly, reaction 2.5 is much m ore tolerant o f
oxygen. The value o f AG for reaction 2.5 is more negative than AG for reaction 2.4 unless
the PG, *n the reaction zone falls below
1 0 ' 19
impurity levels o f oxygen and w ater vapor o f
atm, which is unlikely considering the bulk
1 0 -6
atm or higher in the reactant gas.
Therefore, it seems probable that for nitridation in pure nitrogen the initial passivating layer
on the silicon particles consists primarily o f Si2 N 2 0 , as concluded by Barsoum et al.
(1991).
D uring the second nitridation stage, which requires higher temperatures, the
reaction rate is determined by diffusion of the reactants through the product layer. The
oxygen that was released as SiO from the disruption o f the silica layer is now tied up in the
Si 2 N 2
0
layer and is no longer available for the gas phase. The SiO partial pressure
therefore is reduced to the level o f that o f the oxygen and w ater impurities, on the order of
10" 6 atm for high purity conditions. This lowers the m aximum allowable oxygen partial
pressure for nitridation o f SiO to
8
x lO 2 3 atm for a -S i 3 N 4 and 2 x lO 2 4 atm for the
oxynitride, using equations 2.12 and 2.13. Because of the product layer surrounding the
silicon particles, active and passive oxidation will no longer lower the oxygen partial
pressure significantly in the reaction zone between the particles, so nitridation o f SiO will
no longer be possible. The primary gas-phase reaction during the main nitridation period is
therefore nitridation o f silicon vapor diffusing out o f the product layer to form oc-Si3 N 4 via
reaction 2.1 (Barsoum e ta l. 1991). The vapor pressure o f silicon at 1350°C is 10' 7 atm
(M oulson 1979), which implies an evaporation rate o f 10' 6 kg n r 2 s e c 1 using Langm uir's
equation (Langm uir 1913). This is fast enough to support the maxim um nitridation rates
reported in the literature. Nitrogen diffusing into the product layer will react with solid
silicon to form (3 -Si 3 N 4 via reaction 2.3. As the nitrogen atom is smaller than the silicon
atom, nitrogen diffuses more readily and hence towards the end of the reaction, when the
product layer around the particles is thickest, the (3-phase is favored.
2.2.2 Nitridation with added hydrogen
The reaction mechanisms in the presence o f hydrogen are somewhat different. The
prim ary effect of hydrogen is to react with oxygen to form H 2 O via reaction
2
. 1 0 , which
greatly reduces the bulk P0 i , as was first pointed out by M oulson (1979). A ssum ing a
1% hydrogen / 99% nitrogen mixture, the equilibrium bulk P0 ^ is determined by
13
Assuming typical high-purity conditions as before, the bulk P h ,o
which fixes the bulk
at
8
be about 10
6
atm,
x 10' 1 9 atm. This value is som ew hat conservative, since the
PHi inside the compact will be somewhat greater than the bulk P Hi due to the fact that the
nitrogen consumed by the reaction is continuously replaced by the bulk mixture.
Some early work speculated that hydrogen reduced the silica layer, in order to
explain the increased reaction rate that was observed when small amounts o f hydrogen are
added to the nitrogen (Lindley et al. 1979, Heinrich 1980a). However, it has since been
dem onstrated that the disruption o f the layer occurs at 1215°C regardless o f the gas
com position (Barsoum et al. 1991), indicating that the primary catalyst is iron. Instead, the
increase in the initial reaction rate can be attributed to the fact that oxygen is no longer
com peting with the nitrogen for the exposed silicon surfaces, which greatly increases the
am ount o f reaction during the initial nitridation stage.
The SiO partial pressure will again be determined by reduction o f the Si 0
layer via
2
reactions 2.7 and 2.11. Previous researchers, including M oulson (1979), have theorized
that the addition o f H 2 would increase ^*SiO by shifting reaction
2 .1 1
to the right.
However, as pointed out by Pigeon et al. (1993), reaction 2.9 is shifted to the left, w hich
increases the local P h ,o near the exposed silicon surfaces. The net result is that the
hydrogen addition has very little effect on the ^SiO from reaction
2
. 1 1 , and the PSiO will
be the same as in the pure nitrogen case, about 4.3 x 1 0 -3 atm.
U sing this value, and assuming a ^ 0 , of
8
x 10' 1 9 atm as calculated above, AG for
reaction 2.4 is more negative than AG for reaction 2.5, which means that the formation o f
a -S i 3 N 4 is favored over the oxynitride in the presence o f added hydrogen. This has at
least two important ramifications. First, as discovered by Barsoum et al. (1991), the main
nitridation stage begins at a lower temperature, presumably due to the fact that the
oxynitride is a better barrier to diffusion than a -S ijN ^ Second, nitridation o f SiO remains
an important reaction mechanism during the main nitridation stage, because the oxygen
present in the system is not removed from the gas phase as is the case with Si 2 N 2
0
14
80
Mullitc—no liningO
O
Mullite-with Mo lining
0
2
4
6
8
10
Time (h)
12
14
16
Figure 2.1. Effect of oxygen on the reaction kinetics. The M o lining reduced the
amount o f oxygen in the furnace, thereby slowing the nitridation rate (after
Pigeon et al., 1993).
form ation. Several researchers (e.g. Elias and Lindley 1976, Raham an and M oulson 1984,
Pigeon et al. 1993) have noted that the presence o f oxygen enhances the reaction kinetics,
as shown in Figure 2.1. Barsoum et al. (1991) has suggested the following reaction
sequence for nitridation in the presence of hydrogen:
1.5Si(s) + 1.5Si0 2 (s) = 3SiO(g)
3SiO(g) + 2 N 2 (g) = S i 3 N 4 ( a ,s ) + 1 .5 0 2(g)
1 .5 0 2(g) + 3H 2 (g) = 3H 2 0 (g )
3H 2 Q(g) + 3Si(s) = 3SiO(g) + 3H 2 (g)
4.5Si(s) + 1.5Si0 2 + 2 N 2 = 3SiO + S i 3 N 4 ( a ,s )
2.15
Besides increasing the reaction kinetics, the addition of hydrogen also creates a fine­
grained, uniform microstructure (M angels 1975, Jones and Lindley 1976a ). The a /p ratio
of the final product is much higher when hydrogen is present, regardless of the other
15
processing param eters (Lindley et al. 1979), so hydrogen is alm ost always used in
commercial applications to improve the mechanical properties.
2.2.3 Form ation and m icrostructure o f a -S ijN 4
The a -S i 3 N 4 phase makes up more than 70% o f typical RBSN, with the rem ainder
being (3 -Si3 N 4 and unreacted silicon. There is significant evidence that the a-phase forms
from gas-phase reactions. The presence o f oxygen or water vapor in the gas along with
hydrogen, which creates SiO gas, significantly increases the oc/(3 ratio o f the product (e.g.
M essier et al. 1973). This indicates that the nitridation o f SiO forms primarily the a-phase.
On the other hand, flowing the reactant gas over a smooth silicon surface inhibits the
form ation o f a -S i 3 N 4 on that surface, presumably because the gaseous Si and SiO are
carried away from the specim en (Jennings and Richman 1976). The a-p h ase forms with
two different microstructures: a-w hiskers and a very fine-grained a-m atte. The a-m atte
forms around the surface o f the silicon particles as a dense layer o f silicon nitride with very
small pores. The a-w hiskers, which form on sample surfaces and grow into the porosity
o f the original compact, are thin fibers with a high aspect ratio.
The following m echanism for the formation o f the a-m atte was first proposed by
Atkinson, et al. (1974), and was later m odified by Jennings and Richm an (1976). After
initial nucleation o f silicon nitride on the particle surfaces, silicon is transported through
evaporation-condensation or surface diffusion to the nuclei, rapidly forming a coherent
product layer around the particles. To continue the reaction, silicon vapor m ust diffuse
through this product layer where it can react with nitrogen within the original porosity of
the com pact. New porosity develops in the places w here silicon has evaporated away, as
silicon vacancies coalesce. This allows the Si/Si 3 N 4 interface to advance into the silicon
particles. This mechanism is illustrated in Figure 2.2. It should be noted that this model
correctly predicts that the compact dimensions will remain the same while the volume of
16
(a)
(b)
NITROGEN
\ \ \ \
Si
Si
Si
V v v AA \ AA A \ A A A AAA A \ Aa A K\A
v « v v V V V v y
y
S i 3 N4 LAYER
S ILICON
(C)
Si
( d! Si
A
A A A A
v v— > ( p o r e /
« _ V
\
V
Figure 2.2. M echanism for the formation o f the a-m atte, showing silicon evaporating
and the remaining vacancies coalescing into micropores (after Atkinson et
al. 1974).
solid increases by 22% . If, for instance, the reaction took place at the Si/Si 3 N 4 interface,
the particle centers would move apart and the compact would increase in size as it reacted.
T he rate-controlling step for the formation of the a-m atte is the diffusion of Si through the
product layer.
The a-w hiskers are most probably formed by a vapor-liquid-solid m echanism, as
was first proposed by Gribkov et al. (1972). A small globule o f liquid first forms on the
surface o f the silicon where there is an impurity such as Fe which lowers the melting
temperature. Silicon is transported to the melted area in the vapor phase, where it dissolves
in the liquid. Gaseous nitrogen then reacts with silicon at the solid-liquid interface to form
silicon nitride, thus lengthening the needle. M icroscopic evidence (Jennings and Richman
1976) indicates that the liquid may remain as a puddle at the base o f the needle, or it may
form a bead which remains at the tip o f the needle as it grows, as illustrated in Figure 2.3.
This mechanism is supported by the observation that the needles are most numerous when
17
LIQUID
GROWTH
DIRECTION
BEAD
NITROGEN
SI LI CON
NITRIDE
NEEDLE
NITROGEN
SILICON
LIQUID
Figure 2.3
PUDDLE
Formation mechanisms for the a-needles. A liquid forms either at the tip
o f the needle (top) or at the base (bottom), allowing silicon nitride to form
at the interface (after Jennings and Richman, 1976).
18
a less pure silicon pow der and a high reaction temperature are used, thus increasing the
am ount o f liquid phase. However, this mechanism may contradict the generally accepted
theory that only gas-phase reactions produce oc-Si3 N 4 , while liquid and solid-state
reactions produce P-Si 3 N 4 .
2.2.4 Form ation and m icrostructure o f fi-Si^N 4
The P-phase of silicon nitride forms from a reaction between nitrogen and solid
silicon. P-Si 3 N 4 grains are usually much larger than a - S i 3 N 4 grains, and they typically
form as spikes which grow into the silicon particles along the < 0 0 1> direction . As the
reaction goes to com pletion these spikes meet and fuse together. A schematic o f a P-Si 3 N 4
spike appears in Figure 2.4.
There are two difficulties that must be overcome in the formation o f P-Si 3 N 4 .
First, nitrogen must be transported to the reaction site, which is the Si 3 N 4 /Si interface at the
tip o f the spike (M ukerji and Biswas 1981). Since diffusion o f nitrogen through solid
silicon is very slow, another diffusion path must exist. Second, since there is a 22%
volum e increase as silicon reacts to form Si 3 N 4 , new space for the product m ust be created
before the reaction can proceed. The most likely reaction mechanism for P-Si 3 N 4
formation involves the formation o f a liquid phase. Nitrogen can diffuse rapidly through
liquid silicon to reach the reaction site, and melted silicon will not impede the growth o f the
P-spike (Boyer and M oulson 1978). This mechanism is supported by the observation that
factors which promote the formation o f a liquid, such as a high temperature and cation
impurities, tend to increase the rate o f formation o f P-Si 3 N 4 .
Another mechanism for the transport o f nitrogen to the tip o f the P-spike which was
suggested by Jennings and Richman (1976) is diffusion down the large hexagonal tunnels
which run along the c direction of the grain. Diffusion o f nitrogen down these channels
would be significantly slower than diffusion through a liquid phase (Jennings et al. 1983),
19
NITRIDE LAYER
t
REACTION
NITRIDE
FORMING
GROWTH DIRECTION <OOI>
Figure 2.4.
Form ation o f P-spikes in silicon liquid (after Jennings and Richman,
1976).
but it is a necessary reaction path, as P-Si 3 N 4 has been detected in significant am ounts on
pure single-crystal silicon under conditions where melting can be ruled out (Dalgleish et al.
1981). W hen no liquid phase is present, space for the p-Si 3 N 4 grains to grow m ust be
created by the formation o f new porosity as silicon vaporizes.
W hether nitrogen diffuses through a liquid phase or down the channels in the P~
Si 3 N 4 grains, it m ust first dissociate. As suggested by Jennings et al. (1983), it appears
likely that the less strained p-Si 3 N 4 structure forms when atomic nitrogen reacts with
silicon.
2.2.5 Effect o f cation impurities in the silicon pow der
Cation impurities, primarily iron, are found in virtually all commercial silicon
powders, and these impurities have important effects on the nitridation reaction. As was
first suggested by Boyer et al. (1977, 1978), iron helps remove the protective silica layer
20
1400
Q •D■
iLl
h~
u
<U • °b
L
m
m
■■
700
o
. 4--
Ll
0
1 0 0
200
TIME
300
400
(MINUTES)
Figure 2.5. Effect o f various iron additions on the nitridation kinetics o f pure silicon
(after M oser et al., 1986).
on the silicon particles, probably by providing nucleation sites for devitrification. This
devitrification process occurs at 1215°C regardless of the gas composition (Barsoum et al.
1991), which confirms that it is iron and not hydrogen that catalyses the reaction.
M oser et al. (1986) deposited iron on spectroscopically pure silicon pow der using
the incipient wetness technique, a method which provides a very even distribution. They
found that the addition o f iron eliminated the initial induction period o f slow nitridation
associated with the pure powder, and accelerated the nitridation kinetics, as shown in
Figure 2.5. They further observed that the instantaneous nitridation rate was proportional
to the percentage of the silicon surface coated with iron until the entire surface was coated,
at which point further iron additions decreased the kinetics. This confirms the
observations o f Dervisbegovic and Riley (1981), who noted that large amounts o f iron
added as poorly-distributed particulates had little effect on the nitridation kinetics. The
21
effect o f iron on the reaction kinetics depends primarily on the percentage o f silicon surface
that is coated, rather than on the amount o f iron present.
A nother important result o f iron at impurity levels is the formation o f FeSix liquid at
tem peratures as low as 1200°C (Chart 1970, Boyer and M oulson 1978). This liquid
provides a m edium for the growth o f p-Si 3 N 4 by providing a rapid nitrogen diffusion path
into the silicon particles. It should also be noted that large iron particulates can cause
localized melting and this causes large pores to form as the liquid migrates away. These
pores then becom e strength-limiting defects in the resulting RBSN.
The presence o f a liquid phase, which is always associated with the presence o f
iron, has generally been felt to increase the (3 -Si 3 N 4 content (M essier and W ong 1973,
M itom o 1977). However, iron also promotes the formation o f atomic nitrogen by
catalyzing the dissociative chem isorption o f the N 2 molecule (Jennings 1988), which may
also increase the am ount o f the P-phase. Jennings (1988) found that iron filings placed
upstream o f a semiconductor-grade silicon wafer dramatically increased the percentage of
P-Si3 N 4 in the resulting product, even though the iron was not in direct contact with the
specim en.
Pigeon and Varma (1993) attempted to separate the effects of the liquid phase from
the effects o f atomic nitrogen formation by the addition o f various cation impurities to pure
silicon powder. They found that impurities that formed a liquid phase and also dissociated
nitrogen increased the nitridation rate more than impurities that did only one or the other,
and they concluded that both effects increased the nitridation kinetics significantly. They
also noted that impurities such as Ca, which forms a liquid phase at low tem peratures but
does not dissociate nitrogen, yielded very high ot/p ratios, indicating that the presence o f a
liquid phase favors the form ation of a -S i 3 N 4 more than it favors P-Si 3 N 4 .
22
2.3
Effect of processing conditions on the nitridation reaction
2.3.1
Silicon particle size
Changes in the silicon particle size have a significant impact on the nitridation
reaction. As the silicon surface area per gram o f powder increases, the am ount o f initial
conversion at low temperature increases due to the increased amount o f silicon vapor.
Also, as the particle size becomes larger, the thickness of the product layer separating the
unreacted silicon from the porosity increases, and the am ount of time needed to finish the
reaction increases. Thus, as the particle size decreases, the time required to com plete the
reaction and the final temperature also decreases (Heinrich 1978, Jones and Lindley
1976a). For example, silicon pow der with particle diameters in the range 15-30 pm
requires processing times on the order o f 1-2 days (M oulson 1979), while particles in the
range 1-5 p m can be usually be nitrided in 6-10 hours (e.g. Pigeon et al. 1993). Recently,
a technique has been developed to create extremely fine silicon powder by using a laser to
pyrolize silane gas (Cannon eta l. 1982, Flint and Haggerty 1987). This powder, which
has a particle size of 70-300 nm, can be fully reacted in a little as 10 min at 1250°C
(Sheldon eta l. 1989, 1992). Figure 2.6 illustrates the effect of particle size on the
processing time.
The microstructure o f RBSN is also strongly affected by the starting particle size.
The grain size o f both the a - and (3-phase increases with the silicon particle size (Heinrich
and Streb 1979). This can be explained by the fact that the m aximum size o f the a-needles
is limited by the pore size, while the maximum size o f the (3-spikes is limited by the particle
size (Ziegler et al. 1987). The phase composition of the RBSN is also a strong function of
the particle size. W ith a fine starting powder, the ot/(3 ratio is higher than with a coarse
starting powder. This is because a high surface area favors silicon evaporation and gasphase reactions, which form a -S i 3 N 4 .
23
29//m
20 //m
cs
o
C
5c?
<3
47
61ftm
Time [h]
Figure 2.6. Effect o f particle size on the nitridation kinetics (after Atkinson et al.
1973).
There are two distinct porosity regimes found in RBSN. The macropores, which
can be seen in a light microscope, are the result of the initial spaces between the silicon
particles, and the size o f the macropores is a direct function o f the starting particle size.
The m icropores are much finer and can only be seen using electron microscopy. They are
associated with the pores between the a-needles and with the pores formed during the
formation o f the a-m atte. The size o f the micropores has also been shown to increase with
the starting particle size, apparently because o f the associated increase in the average size of
a - S i 3 N 4 grains.
In general, the size o f the starting powder has a strong relation to the pore size and
grain size o f the final product and thus has a strong effect on the mechanical properties
(Kleebe and Ziegler 1985). Sm aller particles result in stronger, tougher RBSN, and also
require less time to process. However, the ultrafine silicon pow der prepared by laser
24
pyrolysis has a strong tendency to agglomerate (Pigeon and V arm a 1993), which m akes it
unsuitable at this time for commercial use.
2.3.2 Effect o f temperature on the nitridation process
All o f the reaction mechanisms have a positive temperature dependence, so the
overall reaction kinetics always increase with increasing temperature regardless o f the ratecontrolling step. The formation o f a -S i 3 N 4 by gas-phase reactions requires that silicon be
vaporized and removed from the silicon surfaces. The equilibrium vapor pressure over a
condensed material can be written as
2.16
w here P Si is the silicon vapor pressure and L is the heat o f sublimation, which is 438
kJ mol ' 1 for silicon at 1410°C (Emsley 1991). PSi is strongly temperature dependent, but
does not depend on the pressure o f other gases. M oulson (1979) has calculated that ^Si =
10' 7 atm at 1350°C. The rate o f removal o f silicon, which depends on the silicon surface
area, can be calculated as 1O' 6 kg n r 2 s e c 1 using Langm uir’s equation. This rate is more
than fast enough to support the observed maximum nitridation rates, which occur in the
initial stages o f the reaction when m ost of the silicon surface is exposed. However, in the
intermediate and later stages o f the reaction, when most of the silicon surface is covered
with a layer of product, the rate o f removal o f silicon may well become rate controlling for
gas-phase reactions.
M any of the reaction mechanisms have diffusion as their rate-controlling step,
which results in a strong temperature dependence. The diffusion o f nitrogen in liquid
silicon or in solid Si.3 N 4 is rate controlling for the formation o f (3 -Si 3 N 4 , while the
diffusion o f adsorbed silicon along silicon nitride surfaces is an important step for the
25
100
e
o
*5
*
>
60
- -
40
- -
C
o
°
0
2
4
6
8
10
12
14
Time (h)
Figure 2.7. Intrinsic nitridation kinetics as a function o f temperature: (o) 1350°C, (A)
1300°C, (□) 1275°C, (0) 1250°C, (+) 1200°C (After Pigeon and Varma
1993).
formation o f the a -S i 3 N 4 matte (Atkinson et al. 1974). The effect o f temperature on the
overall reaction rate o f a silicon powder compact is illustrated in Figure 2.7. It can be seen
that there is a period of initial reaction which is fairly independent o f temperature within the
range 1200-1350°C, after which there is a period of almost linear reaction kinetics which is
strongly temperature dependent. The initial temperature-independent regime is associated
with the removal o f the native SiC> 2 layer (Pigeon and Varma 1993). This layer prevents
silicon from vaporizing and limits the nucleation o f Si3 N 4 on the silicon surfaces, thus
effectively masking the intrinsic temperature dependence. The overall activation energy for
the reaction during the period of rapid linear kinetics in Figure 2.7 is 301 kJ m o l'1.
The nitriding temperature also affects the morphology of the RBSN product,
particularly the temperature at the beginning o f the reaction. The initial reaction step is the
26
nucleation o f
8
^ 4
grains on the silicon surface, which then grow as adsorbed nitrogen
diffuses to the reaction sites (Atkinson et al. 1974). At higher temperatures, the nucleated
grains grow quickly, depleting the surrounding surface o f adsorbed nitrogen and resulting
in a relatively low er density o f Si_3 N 4 grains than at lower temperatures (Atkinson et al.
1976). The end result o f fewer nucleation sites is a larger grain size in the final product. In
general, a smaller grain size is beneficial to the mechanical properties. However, when the
silicon particle size is larger than about
10
pm a very fine-grained microstructure with small
pores can seal off unreacted silicon at the center of the individual particles, thus prematurely
stopping the reaction (Riley 1989). After the initial product layer is formed, the m icro­
structure is less sensitive to the reaction temperature.
The nitridation rate o f a silicon compact is generally controlled by adjusting the
time-temperature program of the furnace. The program used depends primarily on the
nature o f the silicon powder and on the size o f the compact. One important factor that must
be considered is the heat generated by the reaction. The reaction between nitrogen and
silicon is exothermic, with 723 kJ released for each mole o f Si 3 N 4 formed. This creates
temperature gradients, with the interior o f the specimen hotter than the surface, and this can
cause localized melting and reduced strength if the gradients are large enough. The
magnitude o f the temperature gradients will depend primarily on the com pact size, the
nitriding rate, and the amount o f insulation around the specimen (if any). Atkinson and
Evans (1974) measured the temperature rise in the center o f nitriding compacts and found a
maximum change o f 38°C above the ambient furnace temperature at the center o f 5 cm
diam eter compacts. This occurred at the beginning o f the run, when the reaction rate was
highest.
The exotherm is a particularly important issue for ultrafine silicon particles, which
react very quickly. Sheldon (1989) studied the nitridation o f laser-derived silicon pow der
with an average particle size o f 0.3 pm which could be fully nitrided in 10 minutes. He
estimated temperature rises of up to 150°C over the furnace temperature due to the reaction
27
exotherm , even though his specimens were only a few mm thick.
For cylindrical specimens in an isothermal furnace, the difference between the
surface temperature and the furnace temperature (ATS) and the temperature difference from
the surface to the center (ATC) can be estimated fairly easily. The heat released by the
reaction is given by (Atkinson et al. 1974)
2.17
w here Q is the heat released per unit volume o f the specimen, AH is the reaction exotherm,
M n is the m olecular weight of nitrogen, p is the density o f the com pact, and X is the
fractional conversion o f Si to Si3 N 4 per second. For a 2.5 cm diam eter by 3 cm long green
com pact reacting at a rate o f 10% conversion per hour, Q = 0.36 W cm '3, and the heat
released is 5.3 W.
This heat is dissipated at the surface o f the sample by convection and radiation. At
nitriding temperatures, convective heat loss is negligible compared to radiative loss, so the
increase in surface temperature can be estimated from
H rad = 4se(T 3 ATs)A
,
2.18
w here H rad is the heat dissipated by radiation, s is the Stefan-Boltzm ann constant, e is the
em issivity, T is the furnace temperature, and A is the surface area o f the specimen. For the
above param eters, and a furnace temperature o f 1350°C, ATS - 6.5°C.
If we assume that the heat is generated uniformly throughout the specimen, then the
difference between the surface temperature and the center temperature is given by
2.1 9
28
where a is the specimen radius and Kth is the thermal conductivity. Using a conservative
value of Kth for silicon o f 0.03 W cm ' 1 K ' 1 (Atkinson and Evans 1974), ATC= 4.7°C.
From the above analysis it appears that the macroscopic temperature gradients in
conventionally heated compacts are not a significant factor unless the initial reaction is
extremely fast. However, if the reaction rate is not uniform local temperature excursions
can occur which can cause melting.
2.3.3 Gas composition and nitrogen partial pressure
The composition o f the nitriding gas is an im portant variable for RBSN processing.
The m ost com m on gas addition is hydrogen, which greatly lowers the
thus increasing
the kinetics by allowing for the gas-phase nitridation o f SiO, as discussed in Section 2.2.2.
However, there is considerable evidence that the addition o f hydrogen can also affect the
microstructure o f the product. Several researchers have reported that even small additions
o f H 2 can make the microstructure more uniform and increase the average strength of
RBSN (Jones and Lindley 1976a, 1976/?, Cam poz-Loriz and Riley 1979, Lindley e ta l.
1979). Dalgleish et al. (1980) found that single-crystal slices with no Si0
2
formed deeper
layers of Si 3 N 4 in a N 2 /H 2 mixture than they did in pure N 2 . Furtherm ore, M angels
(1981a) observed similar effects when He was added to the nitrogen instead o f H 2 , despite
the inert nature of helium.
Kim and Kim (1985a, 1985/?) have successfully explained the above results in
terms o f the effect that second-component gases have on the transport properties o f the
nitriding gas. Using the Chapm an-Enskog theory for the kinetic behavior o f gases, the
authors demonstrate that added gases will alter the molecular diffusivity and thermal
conductivity o f the resulting mixture. The addition o f lighter gases such as H 2 or He will
increase the diffusivity and thermal conductivity, while the addition o f heavier gases such
as Ar will have the opposite effect, as shown in Figure 2.8 . The diffusivity o f the gas
29
18171615-
12 -
Q
1200 1300
1400
1500
1600 1700
TEMPERATURE ( K )
0
20
40
60
60
100
SECOND-COMPONENT GAS (mol % )
Figure 2 .8 . Effect o f He, H 2 , and A r gas additions on the diffusivity (left) and the
thermal conductivity (right) o f N 2 gas (after Kim and Kim 1985a, 1985b).
mixture is a function o f temperature, but is virtually independent o f the am ount o f secondcom ponent gas added. According to Kim and Kim (1985a), in the temperature range of
1200-1700 K, even small (> 0.1% ) additions o f H 2 or He will increase the diffusivity by a
factor o f 2.65 or 3.3, respectively. The thermal conductivity is a strong function o f
com position, and is not significantly altered at very low concentrations o f H 2 or He.
However, the concentration o f a second-component gas inside a rapidly reacting com pact
can be significantly higher than the bulk level, due to a "pile up" effect as nitrogen is
consum ed and then replaced by viscous flow o f the bulk mixture.
Heat conduction inside the silicon compact will depend primarily on the thermal
conductivity o f the gas phase during the initial reaction stages, because the rate-controlling
step is at the point contacts between the silicon particles where the heat will be conducted
by the adjacent gas (Kim and Kim 1985/?). Therefore, the result o f additions o f a lighter
gas is that the heat generated by the reaction exotherm will be more efficiently dissipated,
30
thus reducing thermal gradients. Since the strength o f an RBSN specimen is often limited
by large pores created by melts resulting from localized temperature excursions (Mangels
1981a), it follows that the strength o f RBSN is enhanced by H 2 .
An important result o f the secondary gas piling up in the interior o f the com pact is
that the nitrogen partial pressure is reduced. Atkinson et al. (1976) demonstrated that in the
early reaction stages the nitridation rate decreases with decreasing nitrogen pressure for a
given temperature. Therefore, the added gas tends to prevent the reaction from proceeding
too rapidly by reducing the nitrogen partial pressure in the interior o f the compact. This
reduces the thermal gradients in the specimen and results in a more uniform microstructure.
The result o f an increase in the nitrogen diffusivity is unclear. Some studies have
suggested that the distribution o f nitrogen in the com pact is non-uniform when the reactant
gas is flowing past the specimen (e.g. Elias and Lindley 1976). The addition o f a lighter
gas would tend to produce a more uniform distribution o f nitrogen, which could lead to a
more uniform microstructure. Another important consideration is the rate at which nitrogen
is supplied to a faster reacting area o f the specimen. If nitrogen is supplied more rapidly,
more heat will be released and there is a higher probability of melting. However, the
effects o f an increased diffusivity are probably offset by the piling up of the lighter gas in
fast-reacting areas. In the later stages of the reaction, when bulk nitrogen transport is ratecontrolling, the increase in diffusivity will be beneficial in allowing the interior o f the
com pact to become fully nitrided.
31
2.4
Reaction kinetics
There has been much confusion regarding the global kinetics o f the nitridation
reaction, because o f the extrinsic effects o f trace impurities in the silicon pow der and in the
nitriding gas and because o f the effects o f bulk nitrogen diffusion into the compact. Early
researchers reported zero-order (Hiittinger 1969,1970), logarithmic (Evans and Chatterji
1958), parabolic (M essier and W ong 1973), and continuously decreasing kinetics
(Atkinson et al. 1976). Little attention was given to the relative formation kinetics for the
a - and P-phases, although Jennings and Richmond (1976) concluded that a - S i 3 N 4 and PSi 3 N 4 were form ed by different reaction mechanisms.
In recent years, it has becom e clear that the intrinsic kinetics involving the reaction
between nitrogen and a single silicon particle can be studied only if very pure silicon
pow der and nitriding gases are used. In particular, the native oxide layer on the silicon
particles must be removed prior to nitriding. Rahaman and M oulson (1984) were the first
to realize this, and they performed careful experiments using very pure silicon pow der
which was pretreated in hydrogen to remove the silica. They found that the reaction rate
was much higher when the oxide layer was removed, and that the hydrogen in the nitriding
gas no longer had a significant effect on the reaction kinetics, as shown in Figure 2.9. This
result affirms that the primary effect of hydrogen is to reduce the p o , , thereby increasing
the rate o f removal o f the native SiC>2 layer.
The nitridation kinetics of a pure silicon powder compact will depend both on the
intrinsic single-particle kinetics and on the bulk diffusion of nitrogen through the open
porosity, and these will be discussed separately in the next two sections. The important
effects o f cation impurities and the native silica layer were discussed in previous sections.
32
SAMPLE
PRETREATMENT
N ITR IO IN G GAS
□
PARTICLE
SIZE
* 8 /< m
Nj
0
N2 / 5 % H 2
•
PR ETR EA TM ENT a n d
NITRIO ING
TEMPERATURE = 1623 K
h2
X
,, 1h
1h
■
Ar,
1h
a
Hz.
1h
n
2
N2 / 5 % H 2
n
2/
s
%
h2
S0%N2 /5 0 % H 2
%
NITRIDATION
Hz.
OUT— I
0
I
1
I
2
L
.
I
- J
3
I
Ia
U
I
I
I
I
12
16
20
TI ME ( h)
Figure 2.9. Effect o f various pretreatments and gas compositions on the nitridation
kinetics, demonstrating the importance o f the native SiC>2 layer (after
Raham an and M oulson, 1984).
33
2.4.1 Intrinsic nitridation kinetics
Using the data from the above-m entioned work o f Raham an and M oulson (1984),
Rossetti and Denkewicz (1989) have provided a convincing kinetic analysis which
separates the formation o f oc-Si3 N 4 and (3 -Si 3 N 4 into separate and parallel reaction paths,
as was first suggested by Jennings and Richman (1976). They use a general m ethod for
the treatment o f isothermal solid-state kinetics based on the Johnson-M ehl-Avrami equation
(Johnson and M ehl 1939, Avrami 1939):
2.20
where (p is the fraction reacted in tim e t, p is a constant based on nucleation frequency, and
m is a constant that depends on the system geometry. As was shown by Hancock and
Sharp (1972), the value o f m, which is determined by measuring the slope o f plots o f -In
ln( 1 -(p) versus In t, can reveal the general reaction mechanism operating on the system.
Rossetti and D enkewicz (1989) m easured m for the conversion o f silicon to a - S i 3 N 4, (3Si 3 N4, and the com bined overall conversion to Si 3 N4. For the case o f the overall
conversion, the value o f m was outside the ranges of all the possible mechanisms,
indicating that there is more than one rate-controlling process contributing to the global
kinetics. W hen they looked at the conversion to the individual phases, however, the m
values both fell into a range which indicates zero-order, first-order, or phase-boundary
controlled rate expressions.
W hen they tested the rate expressions for the individual phases on the data, they
found that a -S i 3 N 4 formation was described by a first-order rate expression and that [3Si 3 N 4 formation was described by a phase-boundary controlled rate m echanism. The
reported linear least-squares correlation coefficient for both fits was greater than 0.999 over
the entire conversion range tested, which makes their treatment quite convincing. The
34
individual rate expressions can be written as
=
2.21
’
2.22
w here (pa and cpp are the norm alized conversions to a -S i 3 N 4 and (3 -Si 3 N 4 and ka and kp
are the m easured rate constants (conversion/time) at a given temperature.
These rate mechanisms are consistent with the microstructural evidence. A firstorder rate law has physical significance for geometry-independent reactions where the rate
is proportional to the volume o f material unreacted, such as homogeneous liquid or gasphase reactions. This is consistent with the previously accepted reaction mechanism for a Si 3 N4, which is a CVD process involving Si(g) and N 2 (g), providing that the volatilization
o f silicon exceeds the observed reaction rates, which has been shown (M oulson 1979). A
phase-boundary controlled reaction implies the movement o f a reaction interface, which
matches well the evidence that (3 -Si 3 N 4 forms by a solid-state reaction at the interface
between the product layer and the silicon particles.
One difficulty with the above analysis is that no dependence on the particle size or
surface area is considered, which means the model cannot be used as a general description
o f the intrinsic kinetics. Pigeon and Varma (1993) studied the intrinsic single-particle
kinetics for various sizes o f equiaxed particles, and they found that the initial kinetics were
nearly linear and could be described by the general intrinsic rate equation
2.23
where Rj is the intrinsic rate (moles o f Si reacted per unit time), Sa is the specific surface
area o f the pow der (m 2 g '1)* Ea is the activation energy (kJ m o k 1), and ko and y are
constants. By varying the temperature and particle size, the authors were able to calculate
values for y, ko, and Ea o f 0.843, 5 x 10'7, and 301.5 kJ m o k 1 respectively. They then
found that eq. 2.23 accurately describes the maximum initial rate as a function o f surface
area and temperature under high-purity conditions.
The above treatments, while useful for gaining an understanding o f the nitriding
process, are not truly applicable to normal nitriding conditions where the oxide layer is
present on the particles, along with impurity levels o f iron. As is abundantly clear from the
early research into the nitridation reaction, the observed kinetics will depend strongly on the
thickness o f the oxide layer and the presence or absence o f hydrogen, particularly in the
early stages o f the reaction.
2.4.2
B ulk diffusion o f nitrogen
Another factor which can affect the reaction kinetics, and which is important for this
work, is the effect o f nitrogen transport through the interconnected porosity o f the compact.
As the reaction proceeds, the porosity decreases from about 40% in the green com pact to
about 20% in the finished ceramic. More importantly, the average pore size decreases by
2-3 orders o f magnitude during the reaction (Atkinson et al. 1973) as the a -S i 3 N 4 needles
grow outwards into the pores, which greatly reduces the permeability. U nder some
conditions, the flow o f nitrogen to the reaction site becomes the rate-limiting step in the
reaction, resulting in preferential reaction at the surface o f the compact. If the porosity at
the surface is reduced to the point where nitrogen does not penetrate into the com pact at a
reasonable rate, then the reaction will stop prematurely, leaving unreacted silicon at the
center o f the compact. W hether gas flow into the com pact becomes rate-limiting depends
prim arily on the com pact dimensions and the starting porosity. To a lesser extent the
permeability can be affected by the reaction rate and particle size.
Because o f the inherent complexities o f the pore structure, the exact mechanisms for
the transport o f nitrogen through the reacting compact are difficult to describe. Due to the
36
wide variety o f applications o f this type of reaction, much work has been done with the
goal o f m odeling gas transport through a porous matrix (e.g. Peterson 1957, Szekely and
Evans 1970, 1971, Bhatia and Perlm utter 1980). Although describing these models in
detail is beyond the scope o f this work, some o f the general results are useful to consider.
There are two mechanisms which can cause incomplete reaction in a porous system where
the volum e is increasing. First, pores can plug, which isolates partially reacted particles
from the rest o f the porosity, preventing further reaction. This is referred to as reduced
connectivity o f the pore structure. Second, the effective diffusion lengths for reactants to
reach the unreacted material can increase to the point where the reaction essentially stops.
This "tortuosity" arises from narrowing of the necks through which the gas m ust pass and
from "dead ends" in the pore structure. For a given amount o f total porosity, the am ount o f
conversion that will take place depends strongly on the initial pore size distribution. Reyes
and Jensen (1987) examined the sulphation of calcined limestone particles, a reaction with a
large volum e increase, and found that the overall conversion decreased substantially as the
starting average pore radius decreased (see Fig. 2.10). They attribute this to the increased
likelihood that a small pore will plug and to the greater number o f small necks found
between small pores.
Gaseous diffusion through a porous medium can occur by two different
mechanisms. If the mean free path o f the gas is much smaller than the pore diameter, then
the gas diffuses primarily by interatomic collisions giving normal viscous flow. If the
mean free path is much larger than the pore diameter then the gas diffuses by collisions
with the pore walls, a condition known as Knudsen or m olecular diffusion.
The pore size o f an RBSN compact will depend strongly on the degree o f reaction.
The pore size o f a green compact can be estimated as being on the order o f the particle
radius, w hich for the silicon powders used in this study is 1-5 pm . As the a - S i ; ^ grows
into the porosity the pore size decreases dramatically. The average pore size of fully
reacted material has been estimated as being .0 1 -0 . 1 pm , for a starting particle size o f
10
37
0.20
z s 6
c
o
*5
>
ooc
O
m
O
0 . 10 -
0.050.5 1.0 2.0 3.0
av arag a p o ra rad iu s , r <^im)
0.00
tlm« . t x 1 0"3 (s a c )
Figure 2.10.
Effect of average pore radius on the rate o f sulphation o f calcined
limestone particles, demonstrating the decrease in gaseous diffusion
rates with pore size (after Reyes and Jensen, 1987).
Jim
(Evans and D avidge 1970).
The mean free path o f a gas is given by
° - 7 0 7
X = -------na
,
2.24
w here n is the atomic density and a is the collision cross section (Tipler 1969, pg. 76).
The mean free path of nitrogen at room temperature and pressure has been calculated to be
.063
Jim
(Lee et al. 1963). For a fixed pressure, as the tem perature increases n will
decrease. At a typical nitriding temperature o f 1350°C, the mean free path at 1 atm is
estim ated to be 10 Jim (Sheldon 1989).
From this analysis we can see that at the beginning o f the reaction nitrogen
diffusion will have a contribution from both viscous flow and Knudsen diffusion, but that
towards the end o f the reaction, when nitrogen transport becomes an issue, the dom inant
m echanism will be Knudsen diffusion.
38
An important consideration then for RBSN processing is to calculate the m aximum
com pact size that can be fully nitrided. Atkinson et al. (1973) studied the effect o f com pact
size on the reaction kinetics, and concluded that the onset o f gas flow control would be
with com pacts 4-5 cm in diameter. However, they used silicon pow der sizes in the range
of 20-60 jim for their experiments, which is an order o f magnitude larger than is typical for
current applications and would affect their results in two ways. First, the starting pore size
is large, which reduces the num ber o f blocked pores and narrow necks later in the reaction
making diffusion faster. Second, with large particles the rate-controlling mechanism is the
gas-particle reaction, as nitrogen m ust diffuse through the product layer surrounding the
individual particles. This means that the nitriding rates are quite slow, even in the
beginning o f the reaction. Also, the smaller specific surface area o f the large particles
reduces the amount o f the a-phase growing into the porosity. All these factors indicate that
the m axim um com pact dimensions for 1-5 pm starting pow der would be considerably
smaller. In fact, conventional processing o f RBSN done in the present w ork indicate that
the m axim um com pact size is less than 3 cm and that gas flow is a critical factor for 1.5 cm
com pacts.
2.5
RBSN Properties
As with most materials, the properties o f RBSN are influenced primarily by the
microstructure. The important microstructural parameters for RBSN are the total porosity,
the size and distribution o f the m icropores and macropores, the a -S i 3 N 4 and p-Si 3 N 4 grain
size, the a /p ratio, and the am ount of unreacted silicon. The relative importance o f these
parameters on the mechanical properties will be different depending on whether the roomtemperature or high-temperature properties are being considered. In particular, the
oxidation o f RBSN is a critical factor at high temperatures.
39
2.5.1 M echanical properties at room temperature
The mechanical behavior o f a brittle ceramic material such as RBSN is described by
the critical flaw theory, whereby the strength o f the material is a function o f the size o f the
largest pore or other microstructural inhomogeneity (Davidge and Evans 1970). This can
be written in terms o f the Griffith equation:
w here Of is the fracture stress, E is Young's modulus, y\ is the specific fracture energy, c is
the critical flaw size, and Y is a geometrical constant. The specific fracture energy and the
Young's m odulus are directly related to the fracture toughness, Kjc, by the Irwin equation:
K?c = 2YjE
.
2.26
The above equations, which describe the stress necessary to extend a sharp-tipped crack in
a material subject to a stress normal to the plane containing the crack, clearly indicates the
param eters influencing the strength of RBSN.
The Young's modulus is a bulk property that depends on the am ount and
orientation o f the phases in the material but is relatively insensitive to sample surface
conditions and to the presence of scattered large-scale defects. There is a considerable
range o f values reported in the literature, with the total porosity being the most important
characteristic. M oulson (1979) found a reasonably good fit to the data using the
relationship
E = 3 0 0 ex p (-3 P )
(G N n r2)
2.27
40
where P is the fractional porosity (see Fig. 2.11). M oulson (1979) attributes much o f the
remaining variability in the reported values for E to the presence o f unreacted silicon. The
specific fracture energy, which is rather difficult to measure experimentally, also depends
primarily on the fractional porosity and increases with increasing density. Typical values
o f yi for RBSN range from 4 J n r 2 to 10 J n r 2 (Dalgleish and Pratt 1975, Evans and
D avidge 1970).
The param eter that has the greatest influence on the strength o f RBSN is c, the
critical flaw size. The critical flaws in RBSN are generally the largest pores, which are
often areas where localized melting has occurred due to cation impurities. If the silicon
pow der is very pure, or if the cation impurities which can cause localized melting are well
distributed, then the size o f the largest pores will scale with the starting particle size. Under
some conditions, machining damage at the surface of an RBSN com ponent can create
critical flaws.
The effect of the Si 3 N 4 grain size and the o/(3 ratio on the strength is difficult to
determine. In general, a smaller grain size and a high ot/(3 ratio correspond to a high
strength (Heinrich and Hausner 1980), but this is due in part to the processing conditions.
M aterial with small grains and more a -S i 3 N 4 would be created using lower nitriding
temperatures, which would mean less localized melting and a smaller critical flaw size.
The strength o f RBSN does increase with increasing density as a general trend, but
there is a large amount of scatter because of the large difference in critical flaw size that can
exist in materials o f the same fractional porosity (Rice 1977). In general, it has been found
that a narrow pore-size distribution and a moderate density is preferable to a high density
with scattered large voids (Kleebe and Ziegler 1985). A plot o f the fracture strength versus
the total porosity for various RBSN materials appears in Figure 2.12.
41
300
f = 3 0 0 „ p <-3P>
2.4
250
2.3
o oo
l/l
‘u 2.2
13
O
150 5
o
o
100
0.1
0
0.3
0.2
0.4
FRACTIONAL POROSITY, P
Figure 2.11.
Variation in Young's modulus, E, with total porosity P (after M oulson,
1979).
y...................
3cco
500 sJJo o
>s v
o o° ^
„ o o ^
oo°
o
200
o0
<
cr
$—
50
3 I
: >0 i
5
O
o
5
5
1
1
1
i
i[
cc
i/i
O
S
z>
-3.9 P)
•<c O
°O U
0
c
0 °
0 o
•
0
o O O
100
a = 4 0 0 exp
o /
■s. _
•n.
o
20
0.1
0.2
0.3
0.4
0.5
FRACTIONAL POROSITY, P
Figure 2.12.
Fracture strength o f various types of RBSN plotted as a function o f the
total porosity (after Rice, 1977).
42
2.5.2 High-temperature mechanical properties
One o f the primary applications for RBSN is in high-temperature structural
com ponents. This is because RBSN maintains its strength to temperatures in excess o f
1400°C, as illustrated in Figure 2.13 (Heinrich and Bunk 1981), and because the thermal
expansion coefficient is very low, which provides good thermal stress resistance. The
prim ary draw back to the use of RBSN at high temperatures is oxidation, which can occur
at both external and internal surfaces due to the open porosity.
Oxidation occurs as Si3 N 4 decomposes and the Si re-reacts with O 2 to form Si0
Because Si 0
2
2
-
has a larger volum e than Si3 N 4 , oxidation leads to a reduction in the pore
diam eter as well as a decrease in the total porosity. As a result, very small pore channels
near the surface will be closed off by the Si0
2
layer, limiting the oxidation o f internal
surfaces (Grathwohl and Thum m ler 1978). For this reason, the am ount o f oxidation that
occurs under given conditions will depend on the size o f the micropores, with the amount
o f oxidation decreasing with decreasing pore size (Porz et al. 1981).
The maximum amount of oxidation that takes place in a given specimen will depend
on the temperature. From 900°C, where oxidation begins, up to about 11Q0°C, the SiC>2
layer will form slowly, allowing oxidation to take place throughout the specimen. Above
1200°C, the open pores near the surface will be closed quickly, protecting the interior and
reducing the total amount o f SiC>2 formed (Grathwohl and Thum m ler 1978).
Oxidation does not affect the high-temperature strength o f RBSN, but it does
reduce the creep resistance. The Si 0
2
layer changes the composition o f the grain
boundaries, facilitating grain-boundary sliding by viscous flow (Birch and W ilshire 1978).
Since surface oxidation will not affect the grain boundaries in the interior of the specimen,
the best high-temperature creep resistance is achieved under conditions where the internal
oxidation is minimized (Heinrich et al. 1982).
43
400
~
300
1
x.
/o=2.2gc»*:
o"
O': 8|itn
x
*
—
oz
«t—
200
UJ
U
oel
3* 100
h
U
<
ac
Li-
0
400
.0 0 0
1200
1600
TEMPERATURE, T (*C)
Figure 2.13.
Fracture strength o f RBSN as a function o f temperature, for three
different densities (after Heinrich and Bunk, 1981).
A specimen that undergoes oxidation at high temperatures and is then cooled to
room temperature will be affected in more than one way. The crystalline form o f SiC>2
which forms during high-temperature oxidation (cristobolite) undergoes a phase
transformation at around 250°C causing a 5% decrease in volume. The result is that
m icrocracks form at the boundary between the SiC>2 surface layer and the Si 3 N 4 , which can
decrease the room-temperature strength (Evans and D avidge 1970). However, oxidation
can also round off internal flaws and blunt crack tips, both o f which can increase the
strength (Davidge and Evans 1970). The net effect on the strength is com plex and depends
on the particular oxidation conditions and on the RBSN microstructure. Both increased
and decreased room-temperature strength have been observed experimentally after
oxidation (Ziegler 1981).
Chapter 3
M icrowave Heating
3.1
Introduction
The use o f microwave energy for heating began in the 1950's, following the
developm ent o f the magnetron during W orld W ar II. Although much data on the dielectric
properties o f materials has been gathered and significant developments in the design o f
microwave generators and applicators have been made, the science o f microwave
processing is still in its early stages o f development.
M icrowave heating is fundamentally different from conventional heating in that the
heat is generated within the specimen instead o f being applied from an external source.
This volumetric heating has several advantages. Specimens can be heated rapidly and
uniformly, thus reducing processing times and m inimizing thermal stresses for applications
such as drying and binder burnout. Very high specimen temperatures can be reached,
m aking microwave heating attractive for ceramic processing. In particular, microwave
sintering has received m uch attention because o f the apparent reduction in the activation
energy. The reverse steady-state temperature gradients that result from volumetric heating
(hotter in the interior, cooler near the surface) can be beneficial for processes such as
reaction bonding and chemical vapor infiltration (CVI) where gaseous reactants must be
transported from outside the specimen to the interior through a diminishing pore structure.
Specific exam ples o f the use o f microwaves for ceramic processing are discussed in the
44
45
next section.
M icrowaves are coherent, polarized, electromagnetic waves with wavelengths
betw een 1 mm and 1 m, and corresponding frequencies ranging from 300 to 0.3 GHz.
M icrowaves can be transmitted, reflected, or absorbed at an interface as with visible light.
M icrowave heating occurs when the electric field generated within the material induces
charged species such as electrons and ions to move. The resistance to these movements
due to inertial, elastic, and frictional forces attenuates the electric field and generates heat.
Different types o f materials interact with microwaves in different ways, as illustrated in
Figure 3.1. Good conductors such as metals reflect microwaves and cannot be heated. At
the other extreme, some highly insulating materials transmit microwaves without absorbing
any energy. The fundamentals o f microwave-material interactions are reviewed in Section
3.4.
The degree o f interaction between the microwaves and the material is clearly
dependent on the properties o f the material, which makes microwave heating much more
com plex than conventional heating. These material properties are strongly dependent on
temperature and the microwave frequency and are often affected by impurities. As the
temperature increases, the dielectric constant, electrical conductivity, and thermal
conductivity all change, sometimes very rapidly. M any ceramic materials, such as AI 2 O3 ,
M gO, and Si0 2 , are virtually transparent to microwaves near room temperature but become
more absorbing when heated above a certain critical temperature. Other ceramic materials,
including M n 0
2
, CuO, and NiO, are good absorbers at room temperature. For many
ceramic processing applications, including sintering and reaction bonding, the com position,
density, and microstructure o f the specimen changes with time.
M icrowave heating also creates steady-state thermal gradients within the specimen,
which can cause the material properties and the composition to become inhomogeneous.
The equations governing the temperature distribution in a volumetrically heated specimen
are given in Section 3.6. It is usually impossible to understand fully how the microwaves
46
Material ty p e
P e n e t r a t io n
TRANSPARENT
(Low lo s s
insulator)
T otal
OPAQUE
(Conductor)
None
(R e fle c te d )
ABSORBER
(Lossy insulator)
P artial
to T otal
ABSORBER
(Mixed)
(a) Matrix = low lo s s insulator
(b) F i b e r / p a r t i c l e s / a d d i t i v e s =
(abso rbin g m a te ria ls )
P artial
to Total
A/WWW
A A A aaaa*
Figure 3.1. Schematic diagram of the interaction o f microwaves with different types of
m aterials (after Sutton, 1989).
47
are interacting with a specimen, because of the complexity o f the relevant electromagnetic
wave equations and because o f the lack o f accurate values o f material properties.
However, microwave processing can be modeled numerically using a finite-element
analysis, as discussed in Section 5.5.
3.2
Microwave processing of ceramic materials
M icrow ave processing o f ceramic materials began in the early 1960's with some
com m ercial applications in the foundry industry such as curing and drying, where large
tim e savings were achieved with the use of microwaves. Through the 1970's other
applications to the heating o f ceramics were developed, including high-temperature
applications such as sintering. At the present time there are many diverse applications o f
m icrowave processing o f ceramic materials under development. As first suggested by Roy
et al. (1985), these applications can be divided into four general areas: process control,
liquid-state processing, plasm a processing, and solid-state processing. The first three
categories will be discussed briefly in this section, and then solid-state ceramic processing
will be discussed in more detail.
The application o f microwaves to process control involves using the microwave
energy for making measurements or detecting flaws rather than for heating. Because many
ceramic materials are virtually transparent to microwaves near room temperature,
microwaves can be used to detect internal defects in dense ceramic parts as a method of
quality control (Campbell and Shrivers 1973). M icrowaves can also be used during
processing to m onitor param eters which affect the lossiness o f the material, such as the
moisture level (Barr 1979).
Liquid-state microwave processing generally involves the heating o f solutions or
suspensions, with advantages such as reduced processing times due to volumetric heating
48
and the lack o f contamination from conventional heating elements. One particularly
important application being developed is the vitrification of high-level radioactive waste.
By using microwaves to evaporate a radioactive solution and vitrify the remaining solid
waste in a single step, the efficiency and safety o f the process is increased. M icrowave
heating is also used successfully for the casting, setting, and drying o f suspensions. A
total production scheme for the whiteware industry called the Tobin process, which was
developed by Tobin (1981) and Chabinski and Eves (1986), uses m icrowave heating for
many o f the processing steps, from slip-casting to firing. Experiments have dem onstrated
improved product quality and a reduction in the processing time for the total casting cycle,
am ong other advantages.
A plasm a is a partially ionized gas consisting of positive ions and electrons in
approximately equal proportions. A plasm a is usually generated by applying
electrom agnetic energy such as microwaves to a cham ber at reduced pressure. Because the
plasm a is conductive, a large am ount o f energy can be deposited into a small volume,
which makes extremely high temperatures and heating rates possible. Plasmas have
becom e an important tool for materials processing because o f their unique properties. The
formation o f free radicals greatly increases the reactivity of the ionized species, w hich is
useful for such applications as the synthesis o f polymers. Even more success has been had
with high-temperature ceramic processing. In particular, the use of a microwave-induced
plasm a for the sintering o f ceramic materials such as alumina has led to greatly reduced
processing times (K em er and Johnson 1985). Another use for microwave-generated
plasm as is in chemical vapor deposition, where the plasma assists in decom posing gaseous
precursors to produce reactants with highly excited electronic states (Kamo et a l . 1983).
Applications o f microwaves to the processing of solid ceramics are typically divided
into two categories: low-temperature (< 500°C) and high-temperature (> 500°C). W hile
high-temperature applications are mostly in the research and development stage, there are
two low-temperature applications in widespread commercial use: drying and binder
49
burnout. W ater absorbs microwave energy very efficiently, and microwave heating is
often more economical than conventional heating for drying, particularly for low w ater
contents (< 5%) and large volum es (Smith 1974). Because microwaves heat
volumetrically, water is driven out of the hotter interior o f the specimen towards the
surface, which reduces drying times and lowers energy costs. The organic binders that are
used to give strength to green ceramic bodies are usually burned out before the part is fired.
Volumetric microwave heating can often lower the burnout temperature and reduce
breakage (M etaxas and M eredith 1983). Also, the binder-burnout and firing steps for
materials such as alumina spark plug insulators and polycrystalline lead zirconate titanate
can be com bined because the same applicator is used for both, thus increasing processing
efficiency (Schurbring 1983, Harrison et al. 1988).
Several high-temperature processing steps have been investigated using microwave
heating, including calcining, melting, and sintering. In particular, microwave heating has
been found to increase the sintering rate of some materials, and most o f the research in
high-temperature ceramic processing has focused on the sintering of oxide materials,
particularly alumina. The fundamentals of the microwave sintering process have been
reviewed by Tinga (1988) and Varadan e ta l. (1988).
Schurbring (1983) conducted some o f the earliest microwave sintering experiments
using alum ina spark plug insulators. He used a multimode cavity to sinter as many as 186
parts at a time at 1600°C, and he was able to prevent thermal runaway by controlling the
pow er input. The quality of the microwave-sintered parts was comparable to that o f
conventionally heated parts. Johnson and Brodwin (1987) sintered rod-shaped alum ina
com pacts using 2.45 GHz microwaves in a rectangular cavity. The rods were heated to
1500-1800°C in only 10 minutes and were then sintered at a rate o f 2 mm per minute. An
extremely fine average grain size of 0.78 pm was achieved. This is a very significant
result, as a small grain size generally corresponds to good mechanical properties.
50
M eek eta l. (1987a, 1987/?) conducted similar experiments on alumina pow der
com pacts using both 2.45 GHz and 60 GHz microwave energy and also reported very fine
grain sizes. They found that high-purity submicrometer alumina pow der could be densified
from 50% to 95.7% o f theoretical density in a matter o f minutes by heating from room
temperature to 1700°C using 60 GHz microwaves. To achieve the same density using
conventional heating required 20 hours at 1600°C. Clearly, the small grain size o f
microwave-sintered specimens is a direct consequence of the short processing times, as the
grains grow rapidly at sintering temperatures.
Janney and Kimrey (1988, 1989) used 2.45 GHz and 28 G H z radiation to sinter
99% A l 2 0 3 / 1 % M gO and reported increased power deposition at 28 G Hz due to the
sensitivity of the microwave loss mechanisms to the frequency. They also conducted
sintering experiments using both conventional and microwave heating and found that
microwave sintering was much more rapid than conventional sintering (see Fig. 3.2).
They calculated the activation energies for these two processes, as shown in Figure 3.3,
and found that the apparent activation energy for m icrowave sintering was only about one
third o f the value for conventional sintering.
This controversial result seems to indicate an athermal "microwave effect" whereby
m icrowave energy provides a stimulus to the densification process that is independent of
temperature. One obvious explanation is that microwaves enhance diffusion. However,
because the atomic jum p frequency is much higher than the microwave frequency, the
m echanism by which microwaves would increase diffusion rates is not yet apparent. One
problem with quantifying the magnitude o f a microwave effect is the difficulty in measuring
temperature in a microwave cavity. A standard thermocouple cannot be used because the
m icrowave field interacts with the metal wires. There are two ways that temperature in a
m icrowave cavity can be measured: optical pyrometry and shielded thermocouples. These
methods both have problems, as will be discussed later, and this makes quantitative
assessm ents such as that in Figure 3.2 som ewhat suspect. However, as other researchers
51
100
90
£
Microwave
80
c7>
I
70
Conventional
60
50
80 0
100 0
12 00
1400
Temperature (°C)
Figure 3.2. Density versus temperature for conventional and microwave (28 GHz)
sintering o f alum ina (after Janney and Kimrey, 1989).
6.0
O —Microwave
Q —Conventional
4 .0 -
170 kJ/mol
<l)
c5
U.
O)
2 .0 -
c
1—
)
c
■(/)
0
0 .0 -
c
-
2 .0 5 7 5 kJ/moi
-4 .0
5 .0
6.0
7 .0
8.0
10,000/T (1/K)
Figure 3.3. Arrhenius-type plot o f alumina sintering rate versus temperature, showing
the apparent activation energies for microwave and conventional heating
(after Janney and Kimrey, 1989).
52
have reported similar results, particularly with the sintering o f alumina, the microwave
effect on sintering is generally accepted.
3.3
Microwave processing of RBSN
M icrowave processing of silicon nitride has been investigated in a program at Oak
Ridge National Laboratory since 1990, using 2.45 GHz and 28 G Hz m ultim ode ovens.
The initial focus o f the study was to investigate possible athermal microwave enhancements
o f either the nitridation reaction or of silicon nitride sintering. Specimens were well
insulated to avoid temperature gradients, and temperatures were measured using shielded
therm ocouples embedded within the specimen.
Tiegs et al. (1991a) reported increased nitridation rates for silicon com pacts heated
w ith 2.45 G Hz microwaves, as com pared to conventionally heated compacts. M icrow ave
specimens could be fully nitrided in around
2 0
hours, while conventional heating required
more than 50 hours. Kiggans et al. (1991) reported that the onset o f the nitridation reaction
occurred at a lower temperature when heating with 2.45 GHz microwaves than with
conventional heating. The conclusion o f both studies was that microwave heating enhances
some o f the nitridation mechanisms.
Similar results were obtained for microwave sintering (Tiegs et al. 1991a, 1991 b).
M icrowave heating was found to increase the shrinkage rate and the rate of grain grow th as
com pared to conventional heating, although the magnitude of the enhancement was
significantly less than with sintering o f alumina. Also, the heating efficiency and
densification were found to be better with 28 GHz microwaves than with 2.45 GHz
microwaves. These microwave effects appealed to be caused in part by preferential heating
at the grain boundaries. Recent work at Oak Ridge has concentrated on sintered RBSN
(Tiegs et al. 1993a, 1993b). Normally this is done by first nitriding a silicon com pact and
53
then sintering it in a Si 3 N 4 pow der bed. By using microwave heating the two steps can be
com bined, thus simplifying the operation and reducing the total processing time.
3.4
Microwave-material interactions
W hen microwave energy is applied to an insulating material, the electric field
polarizes the charges in the material. The electric field reverses its direction rapidly, and the
induced polarization current is unable to follow at the frequency o f the wave. The
com ponent o f the polarization current that is in phase with the electric field attenuates the
electric field and generates heat within the material. This induced polarization can take the
form of electronic polarization, where electrons are displaced around the atomic nuclei, or
atomic polarization, where the atomic nuclei are displaced because o f the unequal
distribution o f charge within a molecule.
If the material is conducting rather than insulating, the applied field can create direct
conduction paths which cause charged particles such as ions or electron to flow. These
currents create a large amount of dissipated power and cause rapid attenuation of the electric
field. The response o f a material to an applied field is described by the complex dielectric
constant e* (also called the complex permittivity) which is made up o f a real part (e1, the
dielectric constant) and an imaginary part (£", the dielectric loss factor):
e* = e - je " = £0(£r - j e 'eff)
,
3.1
where j is the square root o f -1, £q is the permittivity o f free space ( 8 . 8 6 x 1 0_1 2 F/m ), £r
is the relative dielectric constant, and £"ff is the effective relative dielectric loss factor. The
dielectric constant represents the amount of stored energy in the material caused by
polarization under an applied field, while the dielectric loss factor represents the am ount of
54
energy dissipated within the material by all o f the loss mechanisms relevant to highfrequency heating. The param eter that is usually used to describe the degree o f microwave
energy absorption for a material is the loss tangent:
tan 5 = ^
£r
g .
27tf£0£r
,
3.2
where a is the total ac conductivity (S/m) due to conduction and displacement currents and
f is the microwave frequency (Hz). Materials with tan
considered lossy, while materials with tan
8
8
much larger than one are
much less than one are considered to be low-
loss.
The quantity that is o f primary interest in most microwave heating applications is
the am ount o f pow er absorbed by the material. To derive an expression for the pow er
absorbed requires the use of M axw ell’s equations; such a derivation can be found in
m icrowave heating texts (e.g. M etaxas and M eredith 1983). The time-average pow er Pav
(W ) is given by
P av = i(B E 0 B;frJv (E * .E )d V
,
3.3
where E is the electric field (which can be complex), CD= 2 n f is the angular frequency, and
V is the volume o f the specimen. The power generated at a specific point within the
specim en increases linearly with frequency and the relative loss factor and varies with the
square o f the electric field. This expression is difficult to calculate exactly, because the
electric field varies within the microwave applicator and also within the specimen due to
attenuation. The electric field can be written in the form
3.4
55
which represents a periodic plane wave traveling in the x direction with a complex
propagation factor y given by
3.5
w here p* is the com plex permeability and po is the permeability o f free space (1.23 x lO 6
H/m). The phase factor P measures the change in phase when the wave passes into the
dielectric material, while the attenuation factor a measures the decrease in the magnitude o f
the field with distance into the dielectric material. Using eq. 3.5 in eq. 3.4 gives the
following simplified form for the electric field:
E = E m a x - a x j(cot-Px)
3.6
This type of propagation is illustrated in Figure 3.4. The electric field attenuates with the
first exponential term, and therefore the dissipated power, which varies with the square o f
the electric field, takes the general form
P(x) = P 0 ( l - e - 2“ )
.
3.7
In an actual system, some o f the incident microwave power is reflected at the
surface o f the specimen. The am ount o f reflection depends on the conductivity o f the
specim en (which is proportional to the loss tangent) and the specimen geometry. For a
planar homogeneous surface the reflection coefficient is (Jordan and Balm ain 1968)
3.8
z
Figure 3.4. Propagation o f an electromagnetic plane wave in a lossy material (after
M etaxas and M eredith, 1983).
For specimens w ith a high loss tangent, the reflection coefficient approaches one and most
o f the incident power is reflected. For a low loss tangent the reflection coefficient
approaches a constant value determined by the relative dielectric constant. The pow er
absorbed into the specimen, in terms o f the incident power and the reflection coefficient, is
3.9
For the case o f a planar slab, the reflection coefficient takes the following form calculated
by Chao (1981):
3.10
w here d is the thickness o f the slab and a is the attenuation constant defined in eq. 3.5.
The pow er absorbed by a slab-shaped specimen as a function o f loss tangent based on eqs.
3.9 and 3.10 is shown in Figure 3.5. W hen the loss tangent is very high, the pow er
57
absorption is low because much o f the incident pow er is reflected. W hen the loss tangent
is low, the pow er absorption is low because the microwaves are transm itted through the
specimen with very little attenuation o f the electric field. The value o f the loss tangent that
gives m axim um power absorption depends on the thickness o f the slab, but will generally
be around
1
.
The attenuation constant a for a homogeneous material is given by
3.11
w here a has the units o f n r 1. The attenuation constant of a mixture is discussed in Section
3.5.
The attenuation o f the electric field within a material is characterized by the penetration
depth D, which is defined as the distance from the surface o f the material at which the
pow er drops to e _1 of its surface value and is given simply by
D =
2
For the case o f a very lossy material (tan 5 »
3.12
a
1) the penetration depth can be approximated
by
r
D =
3.13
^ 2 a) 2 p.0 p,r£oer ta n 8 y
while for the case o f a low-loss material (tan 5 «
D =
1) D can be approximated as
3.14
58
Absorbed Power / Incident Power
1.0
0.8
0.6
0.4 -
0.2
01
.1
1
10
100
1000
Loss Tangent
Figure 3.5. Norm alized pow er absorption versus loss tangent for a planar slab o f
thickness 1 cm, using f = 2.45 G Hz and er = 1 0 .
10000
59
During heating e r and tan
8
change with temperature. The relative dielectric
constant increases slowly with temperature from room temperature to 1400°C for most
m aterials, generally changing by less than 10% for ceramic materials. This change in e r
has been shown by Ho (1988) to be due to an increase in polarizibility caused by
volumetric expansion. The dielectric constants o f selected ceramic materials as functions o f
tem perature are shown in Figure 3.6. The loss tangent is affected by temperature much
m ore than is e r . For most ceramic materials, tan
is reached, at which point tan
8
8
rises slowly until a critical temperature
increases rapidly. The increase in the loss tangent is
generally attributed to additives and impurities that form intergranular phases. These
phases soften at elevated temperatures, causing a large increase in the local conductivity.
The change in tan
8
at 2.45 GHz with temperature for alumina with varying amounts of
additives is shown in Figure 3.7 . Note that the increase in tan
8
for the 92% pure alum ina
is much greater than the increase for 99.5% alumina, demonstrating the effect o f impurities.
The loss tangent for insulating ceramic materials such as alumina is usually much
less than one, as can be seen in Figure 3.7. This means that the penetration depth at the
standard m icrowave frequency o f 2.45 GHz is much larger than the size o f the specimen,
so that much o f the microwave energy is transmitted through the specimen without
generating heat. Therefore, as tan
8
rises, the material absorbs m icrowave energy more
efficiently, which further raises the temperature. This can cause a condition called thermal
runaway, whereby a specimen w hich reaches a certain critical temperature undergoes a
sudden exponential increase in temperature. This phenomenon was studied by W atters
(1989), who used exponential forms for the loss tangent based on experimental data.
Figure 3.8 shows the variation o f temperature with pow er for a model material. The
temperature increases with the applied power along the lower branch o f the curve until the
critical temperature is reached, at which point a further temperature increase does not
require an increase in power and the specimen will rapidly heat up until it reaches the stable
temperature on the upper branch. Points on the unstable branch cannot be maintained in a
60
Temperature (°C)
200
12
__l
'
11
600
I
I
I
1000
I
I
1400
I
I
99%
p u re
a i 2o 3
c
<0 10
V)
c
o 9
o
9 7 % p u re AI2 O 3
o
8
o
0)
<D
7
_
6
—--------9 6 0 6 (G lass- c eram ic)
_ _________
f a r n M i r R r p 2 . 4 5 g /c m 3 R e a c tio n -b o n d e d S i 3 N4
------------2 .1 4 g /c m 3
W ' 2 .0 6 g /c m 3
1.94 a /c m 3
% jP u s e d s ilic a #
1 2 0 °/o i(p o ro sity) slip c a s t
TD
0)
>
5
CD
cr
4
3
^ P y ro ly tic Si 3 N 4
r 315 9 /c m 3
X
1000
2000
3000
Temperature (°F)
Figure 3.6. Relative dielectric constant versus temperature for selected ceramic
materials at 8-10 GHz (after W alton, 1970).
0 .0 2 0
92%
99%
97%
0 .0 0 5
99.5%
0 . 0 0 0
500
1000
1500
2000
T e m p e r a tu r e , °K
Figure 3.7.
Loss tangent versus temperature at 2.45 GHz for different grades of
alumina (after Spotz et al., 1994).
61
10.00
<u
3
8.00
O
VQ)
E 600
CD
C
E
O
2.00
c
0.00
o.ooo
0 .0 0 5
o.oio
normalized
0 .0 1 5
0.020
power
Figure 3.8. Plot o f normalized specimen temperature versus normalized applied
microwave power for a model material, showing the stable and unstable
regions (after W atters, 1989).
real system at steady state. The upper stable branch may be above the melting temperature
o f the material, in which case it is only theoretical. The temperature Tcrit where runaway
occurs differs widely in different materials.
62
3.5
Dielectric properties of mixtures
Determining the complex dielectric properties of a composite mixture o f two or
more phases is a complicated problem which depends on the dielectric properties o f the
individual phases, the relative volum e fractions, the shape o f the phases, and the spatial
distribution o f each phase. To understand the microwave heating properties o f an RBSN
com pact containing both Si 3 N 4 and silicon requires a theoretical model that can predict the
effective dielectric properties o f the compact based on the volum e fractions o f the phases
(which is equivalent to the percent conversion). Considering the nitriding mechanisms
discussed in Chapter 2, it is reasonable to consider the silicon nitride phase to be an
interconnected layer of insulating material, and the silicon phase to consist o f roughly
spherical conducting inclusions. This allows the RBSN com pact to be m odeled as a
conductor-loaded dielectric material, for which treatments exist in the literature.
Recently, Neelakanta (1990) developed analytical equations to describe the complex
dielectric behavior o f a mixture o f conducting inclusions in a dielectric, insulating host
material. His formulation uses an order function, U, which takes into account the
geometry of the inclusions and the frequency range o f the electric field. The relative
complex dielectric constant is given by
3.15
as discussed in the previous section. The following equations describe the relative
dielectric constant and dielectric loss factor o f the mixture, with subscript
inclusions and subscript
2
1
referring to the
referring to the host:
u
+1 r
,
3.16
63
3.17
where:
a = conductivity (S/m)
0
,
) = angular frequency (Hz) ,
9 = volum e fraction of conducting inclusions ,
U = order factor = 1/6 for spherical inclusions at m icrowave frequencies.
To determine the microwave propagation characteristics o f a conductor-loaded
dielectric mixture, an exponential attenuation constant a mix for the mixture m ust be derived
(N eelakanta 1994). For the case o f a pure conductor (0=1) the pow er absorbed per unit
volum e is
3.18
where E is the magnitude o f the electric field inside the material. For the case o f the
mixture, the pow er can be assumed to be deposited only within the conducting phase,
which gives
s *
= E2a miIe
.
3.19
The pow er deposited can also be written in terms o f an exponential attenuation constant as
with eq. 3.7. Taking the ratio o f the power deposited in the mixture to the pow er deposited
in the pure conductor gives the following relation:
Pmix = gmixQ = P o ( i - e x p ( - 2 a mixx)
P]
a,
P 0(l - e x p ( - 2 a j x )
3.20
64
w here x is the distance into the material. Solving eq. 3.20 for a mix using the penetration
depth o f the conductor, l / 2 ct], for x gives
3.21
w here oci is determ ined using eq. 3.11, which is valid only for a hom ogeneous medium.
The attenuation o f the mixture will be much less than the attenuation o f the pure conductor,
because it is assumed that the conducting inclusions are not in contact with one another.
This means that charge transport cannot take place, and the microwave attenuation will be
prim arily from displacement currents as with an insulating material. A conductor-loaded
dielectric heated with microwaves behaves like a lossy dielectric material rather than a
conductor, as has been shown experimentally by Neelakanta (1994) using iron particles
distributed random ly in an insulating CaCC >3 host (see Fig. 3.9). W hen the volume
fraction o f iron is low enough so that the inclusions were not touching, the penetration
depth is relatively large, with m ost o f the incident power passing through the specimen.
H owever, when the volume fraction increases to about 0.3 there is a transition in the
heating behavior and the penetration depth quickly drops to a few hundred m icrons as the
iron inclusions began to touch each other and charge transport can take place.
65
1
©
2
A .
0.3 -
@)
E
.
3 (g
B
T
Region Hi
(Metat-tike)
Regie n I
(Dielectric-like)
0.5
Volume Fraction (9)
Figure 3.9. Power transmission coefficient versus volume fraction o f iron inclusions
for an iron / CaC 0
3
mixture at 9.6 GHz (after Neelakanta, 1994).
66
3.6
Volumetric Heating
Microwaves heat volumetrically, meaning that heat is deposited within the specimen
rather than directly at the surface, which leads to the formation o f steady-state temperature
gradients. Temperature variations within the specimen must be taken into account when
processing materials with microwaves, because they can lead to density or com position
gradients as well as residual stresses.
The heating o f a specimen is governed by the heat equation, which in its general
form is
V -(K thVT) - c pp ^
= -Q v
3.22
w here Kth is thermal conductivity, cp is the heat capacity, p is the density, and Qv is the
heat generated per unit volume. Heat is lost to the surroundings from the surface o f the
specim en or o f the insulation through radiation and convection:
3.23
where Q a is the heat lost per unit surface area, s is the Stefan-Boltzm ann constant (5.67 x
lO 8 W n r 2 K '4), e is the em issivity, h is a convective heat loss constant, T surf is the
surface temperature o f the specimen or o f the insulation, and To is the ambient temperature,
which for a microwave applicator is usually room temperature. U nder steady-state
conditions, the heat generated in the specimen and the heat lost from the surface are equal,
so
3.24
v
A
67
where V and A represent the total volume and total surface area o f the specimen,
respectively.
To calculate the temperature profile exactly would require solving M axw ell’s
equations to find the field distribution in the specimen, and to solve eq. 3.22, which is very
difficult because Qv and Kth vary with temperature and composition. One approach is to
model the temperature distribution in the specimen numerically using a finite-element
analysis, and this m ethod will be discussed in Section 5.5. A general estimate o f the
m agnitude o f the radial temperature gradients found in a specimen can be made by
sim plifying eq. 3.22 and assuming a simple specimen geometry. For an infinitely long
cylinder, the steady state heat equation can be written as
=
r 3r ^ dr J
Qv
K th
3.25
w here the thermal conductivity is assumed to be constant. This geom etry also corresponds
to a finite cylindrical specimen with its ends well insulated to prevent heat loss. If we
assume that the dielectric loss is constant within the specimen, and that the penetration
depth is much larger than the specimen radius, then Qv is a constant and eq. 3.25 can be
solved directly to give (Watters 1989)
3.26
w here a is the radius o f the cylinder. By using eqs. 3.23 and 3.24 as boundary conditions,
Tsurf can be found by solving
3.27
68
Note that the surface temperature is independent o f the thermal conductivity and is a
function only o f the input power, the specimen dimensions, and the emissivity. For
surface temperatures greater than about 1Q00°C the convective heat loss is much less than
the radiative heat loss and is often ignored.
To get an estimate o f the radial temperature profile found in a specimen where the
m icrowave pow er is deposited uniform ly throughout the volume, eq. 3.26 can be plotted
for various values o f Kth and a. Figure 3 .10(a) shows the radial temperature profile inside
a 1 cm diameter cylinder with a surface temperature of 1200°C, for three different values of
the thermal conductivity. As the thermal conductivity decreases, the temperature gradient
increases and the center o f the cylinder gets hotter. Figure 3 .10(b) shows the variation in
the temperature profile with specimen radius, for a surface temperature of 1200°C and Kth
= 1 0 W m - ' K 1.
The magnitude o f the temperature gradient is greatly influenced by the am ount of
insulation around the specimen, because the heat is lost from the insulation surface rather
than the specimen surface. As insulation is added the temperature o f the surface o f the
insulation decreases, which reduces the amount o f microwave pow er needed to reach a
given specimen temperature and decreases the temperature gradients within the specimen.
Figure 3.11 shows the maximum radial temperature difference and the required microwave
pow er density as a function o f insulation surface temperature for a =
1
cm and Kth =
10
W n r 1 K_1. The absolute specim en temperature will depend on the am ount o f insulation.
W hen the microwave penetration depth is comparable to the specimen size or
smaller, the assumption o f uniform power deposition is no longer valid and the temperature
gradients will be sm aller because less power is deposited in the interior of the specimen.
For a highly lossy material, the microwaves will be absorbed at the surface and the radial
temperature profile will be essentially isothermal.
69
1450
Kth = 5 W /m K
1400
U
t
U
3
2
<v
a
g
«
1350
Kth = 10 W /mK
1300
1250
Kth = 20 W /m K
1200
1150
2
0
6
Distance from center (mm)
4
10
8
Figure 3.10(a). Effect o f thermal conductivity on the radial temperature profile of an
infinitely long cylinder with uniform pow er deposition.
1400
1350
a = 1.5 cm
U
o
Qi
i-
<s*>*
«
|
B
<u
H
1300
a = 1.0 cm
1250
a = 0.5 cm
1200
1150
0
2
4
6
8
10
12
Distance from center (mm)
14
Figure 3.10(b). Effect o f radius on the radial temperature profile o f an infinitely long
cylinder with uniform pow er deposition and Kth = 10 W n r 1 K 1.
70
-80
30 -60
20
-
-40
10-20
650
750
850
950
1050
1150
1250
1350
Center Temp.- Surface Temp. (°C)
Power density (W/cm3)
100
1450
Surface Temperature (°C)
Figure 3.11. Effect o f outer surface temperature on the required pow er density and the
maxim um specimen radial temperature difference, for a uniformly heated
infinite cylinder with radius 1 cm and Kth = 10 W rrr1 K '1.
Chapter 4
Experimental Procedures
4.1
Material and atmosphere selection
Almost all of the RBSN experiments were conducted using H Q/10 grade silicon
pow der (Elkem M etals Co., Pittsburgh, PA) which has a mean particle size o f 2-3 pm ,
m axim um particle size of 10 pm , and is 99.6% pure. The primary im purities are iron,
alum inum , calcium , and carbon, as listed in Table 4.1. For com parison purposes, two
other silicon powders were used for a few experiments: Sicomill grade KN5C and grade
K N5E (Kem aNord Industrikemi, Stockholm, Sweden). The average particle size o f the
Sicom ill KN5C grade is 7 pm , while that o f the KN5E grade is 3 pm , and both grades
have a m axim um particle size of 20 pm. The Sicomill powders have somewhat lower
impurity levels than the Elkem pow der (see Table 4.1). Well characterized silicon powders
with small particle sizes were chosen for this study in order to reduce the number of
variables affecting the reaction kinetics. In particular, the powders are fine enough to
nitride com pletely in a few hours in 1 atm o f N 2 . Significantly slower kinetics were
observed for most silicon compacts, because bulk diffusion o f nitrogen through the
porosity was rate controlling in the later stages o f the nitridation reaction. All o f the
experiments reported in this work were conducted using the Elkem H Q/10 grade silicon
pow der.
For the experim ents involving silicon nitride powder, SN-9FW grade (Denka,
71
72
Table 4.1.
Properties of the silicon powders used, as reported by the manufacturers.
Elkem H Q /10
Sicomill KN5C
Sicomill KN5E
Average diameter (pm)
2-3
7
3
M axim um diameter (pm)
10
20
20
Fe (ppm)
<500
180
250
A1 (ppm)
<600
70
50
C a (ppm)
< 100
20
25
C (ppm)
< 1200
600
250
Tokyo, Japan) was used. This pow der has an average particle size o f about 1pm and an
oc/p phase ratio o f about 9.
All o f the gases used were high purity. M ost o f the nitridation experiments were
conducted in a 1% hydrogen / 99% nitrogen mixture, with some experiments also
conducted in a 10% hydrogen / 90% nitrogen mixture and in pure nitrogen. High purity
helium / nitrogen mixtures were used for experiments requiring lower nitrogen partial
pressures. The thermal conductivity and diffusivity properties o f helium are sim ilar to
those o f hydrogen, as discussed in Section 2.3.3.
4.2
Specimen Preparation
Silicon compacts were prepared either by die pressing or by isostatic pressing. Diepressed com pacts were made in a 19 mm diameter stainless steel die using uniaxial pressure
at 25 M Pa to form disk-shaped compacts 19 mm in diameter by 7 mm high, with a green
density o f 52%. This was the highest pressure that could be used without the com pacts
breaking as they were pushed out o f the die. Before pressing, a release agent (stearic acid)
73
was applied to the interior o f the die to allow the compacts to be removed intact. Some
disks were isostatically pressed at 275 M Pa, which increased the green density to 62%.
This was done by placing the disks into latex, tubes which were then evacuated and knotted
at both ends to protect the compacts from the oil bath o f the isostatic press.
All o f the later experiments were conducted with rod-shaped com pacts form ed by
wet-bag isostatic pressing, because of the higher green density and larger com pact size
afforded by this method. A brass tube 25 mm in diam eter and 200 m m long with pinholes
spaced about 2 cm apart along its surface was used to provide a stable form for the
compact. Latex tubing about 20 mm in diameter was stretched inside the brass tube and
folded back over the ends, and a rubber stopper was wedged into one end. A vacuum was
then applied to the outside o f the brass tube, forcing the latex tube to expand against the
inner wall. At this point the silicon pow der was poured into the open end o f the tube,
using a vibrating mechanism to achieve a maximum tap density. W hen the tube was full,
the open end was stoppered and the vacuum was removed. The tube assembly is illustrated
in Figure 4.1. The assembly was then isostatically pressed at 275 M Pa to form silicon
com pacts 250 mm long by 15 m m in diameter, with a green density o f 64%. These rod­
shaped com pacts were then cut to the desired specimen length using a hacksaw blade. The
standard specimen length was 40 mm, but a few later experiments were conducted using
com pacts up to 100 mm in length.
Some experiments were conducted using a mixture o f silicon pow der and silicon
nitride powder. To assure good mixing, the powders were weighed into a plastic ja r and
then ball milled for several hours in research grade methanol using zirconia milling media.
The slurry was then dried and passed through a 200 p m sieve before isostatic pressing into
15 m m diam eter rods.
Before being heated in the microwave cavity, the silicon com pact was placed into an
insulation shell made o f alumina fiberboard (AL-30, Zircar Products, Florida, NY) with a
wall thickness of 1 mm. The configuration used was different depending on w hether the
74
Latex tube
Rubber stopper ■
Brass Tube.
Holes for oil to enter
Powder
Figure 4.1. Tube assembly used for isostatic pressing o f pow der into rods.
75
specim en was a die-pressed disk or an isostatically pressed rod, as illustrated in Figure 4.2.
The disk-shaped compacts were placed into an insulation basket which was cut so that
much o f the outer edge o f the specimen was exposed. The specimen was sandwiched
between disks o f pressed silicon nitride powder to provide axial insulation and support.
Initially, rod-shaped specimens were heated in the microwave cavity using a similar
configuration, but this resulted in uneven heating patterns and the formation o f an opaque
condensate on the quartz tube surrounding the specimen. These problems were alleviated
by placing the rod-shaped specimens into an insulation cup which com pletely covered the
specimen. Alumina pow der (RC-H P DBM, Reynolds Chemicals, Richm ond, VA ) was
then poured around the rod to form a pow der bed (see Fig. 4.2 (b)). This insulation
reduced the amount of heat radiated from the surface of the rod, but was thin enough to
allow sizable temperature gradients to form during volumetric heating.
4.3
Apparatus
A schematic o f the microwave processing apparatus appears in Figure 4.3. The
microwave heating experiments were conducted using a tunable cylindrical cavity
(W avem at Inc., Plymouth, MI) which was connected via a rectangular waveguide to a 2.45
GHz microwave power source with a maximum power output o f 3 kW (Astex/Gerling
Laboratories, M odesto, CA). The circulator diverts pow er reflected from the cavity away
from the pow er source into a water-cooled dummy load. The insulation cup holding the
specimen was suspended inside the cavity from an analytical balance (M odel B120S,
Sartorious Instruments, Goettingen, Germany) to provide weight gain measurements.
Before entering the microwave reactor, the input gas was passed through an oxygen
getter consisting o f copper filings with a high surface area maintained at 750-800°C, and
then through molecular sieve material to remove w ater vapor. The gas delivery system,
Silicon nitride powder compact
Figure 4.2(a).
Configuration for nitriding disk-sipped silicon compacts.
Alumina insulation cylinder
--------- ^
Figure 4.2(b). Configuration for nitriding rod-shaped silicon compacts.
Figure
4.3.
G as
Tank
Schematic diagram
B alan ce
D u m m y Load
P yrom eter
F low m eters
of the microwave processing apparatus.
M ic r o w a v e
G enerator
T unable
C avity
Pressure G auge
C irculator
O xygen
Getter
N e e d le
V alves
R ough
P um p
78
including the quartz tube which passed through the microwave cavity and the Plexiglas
cham ber holding the balance, could be sealed off by a series o f valves and O-ring seals in
order to prevent oxygen from reaching the specimen during the run. An optical pyrom eter
(M odel 100, Accufiber, Beaverton, OR) was focused either on the outside of the specim en
or on the outside o f the insulation cup, depending on which configuration was used.
The tunable microwave cavity is shown in more detail in Figure 4.4. By adjusting
the height o f the cavity and the position o f the launch probe, different resonant modes
(standing wave patterns) can be set up. The TM 012 mode, which has a radially symmetric
electric field and a fairly large and uniform hot zone, was used for most o f the microwave
experiments. For a few experiments the TEq] \ mode was used, which has a sm aller hot
zone and provides more focused and intense heating. The forward and reflected
microwave power levels were measured by meters which used crystal detectors to convert
the field strength in the waveguide to a standard dc voltage. The cavity was considered to
be tuned when the ceiling and probe positions resulted a minimum amount o f reflected
power. To prevent microwaves from escaping from the top and bottom o f the cavity or
from the viewing port, brass choke tubes are attached to the outside o f the cavity. These
tubes are narrow enough so that microwaves cannot propagate, and are long enough to
attenuate the field to a safe level.
The pyrometer and balance were connected to a com puter which inputted the
specimen temperature and weight at regular intervals during the run. The com puter could
then adjust the microwave power by sending a digital signal to a controller (M odel 575,
Keithley DAC, Cleveland, OH) which converted the signal to an analog voltage between 0
and 1 volt before passing it to the microwave pow er supply, which interpreted the signal as
a desired forward pow er level.
Conventionally nitrided RBSN specimens were also made, using an alum ina muffle
tube furnace with a SiC heating element. Temperature control was provided by a
program m able PID controller (M icristar Control Systems, M inneapolis, M N) using an R-
79
A djustable
ceiling
Specim en
V iewing port
W aveguide
Launch probe
Q uartz tube
Figure 4.4. Tunable microwave cavity. The specimen is suspended from a balance.
80
type therm ocouple. A gas delivery system similar to the one described above was used, so
that the only significant difference between the microwave and conventionally processed
specim ens was the heating method used.
4.4
Reaction-bonding procedure
The first step in a microwave processing run was to weigh the green specimen.
The specimen was then placed into the insulation cup, and either silicon nitride pow der or
alum ina pow der was poured around the specimen to form the pow der bed. The cup was
placed in a drying oven for approximately 30 minutes to remove adsorbed w ater from the
insulation, and then weighed. The cup was suspended inside the microwave cavity so that
the specimen was midway between the floor and ceiling o f the cavity and the cup was not
touching the quartz tube (see Fig. 4.4). The gas delivery system was then evacuated using
the mechanical pump and backfilled to one atmosphere with the reactant gas. A gas flow
rate o f approximately 50 seem was maintained through the system during the run.
The m icrowave power source was then turned on, and the pow er was slowly
increased to about 200 W while the cavity was tuned to minimize the reflected power.
W hen the surface temperature of the insulation cup was high enough for an orange color to
be observed (550-600°C) the pyrom eter head was focused onto the center o f the hot zone.
A BASIC com puter program was then activated so that the current surface temperature and
weight were displayed on the screen every few seconds. After the weight readings reached
a steady state value, the balance was tared so that further weight readings would represent
the weight gain o f the specimen. The forward power was then increased manually until the
specim en began to nitride, as observed by increasing weight values.
A second BASIC program was then activated to control the experiment in one of
two ways. The simplest method was temperature control, which mimicked the operation of
a conventional furnace controller. The program would maintain the surface temperature so
that it followed a preprogrammed time-temperature profile which would generally consist
o f alternating temperature ramps and isothermal holds. The temperature was maintained by
comparing the actual surface temperature to the current setpoint and then increasing or
decreasing the microwave power as needed. A more efficient method of process control,
which was used for most of the microwave RBSN experiments, is reaction rate control. In
this case, the computer program altered the temperature setpoint every 5 minutes to
maintain a programmed weight gain rate. Reaction rate control prevented internal melting
by keeping the reaction from proceeding too quickly, and it reduced the total processing
time by increasing the temperature setpoint as needed later in the reaction. This method of
controlling the RBSN process is particularly suitable to microwave heating because o f the
ability to change the specimen temperature quickly and accurately.
At the conclusion of the run the insulation assembly and the specimen were each
weighed again to determine the final weight gain. The percent conversion o f an RBSN
specimen can be determined from the weight gain by
100 AW
conversion (%) = --------------0 .665W g
,
4.1
w here AW is the weight gain and W g is the green weight. In many cases the weight gain
o f the specimen was somewhat less than the weight gain o f the basket assembly, which
was an indication that silicon vapor had diffused out o f the specimen and condensed in the
pow der bed. This weight loss, which was at most 3% of the original weight o f silicon,
caused the actual reaction rate to be slightly higher than the measured rate.
The procedure for conventional nitridation was very similar. Some specimens were
loaded into insulation baskets as with the microwave specimens, but this tended to cause
internal melting due to the reaction exotherm, so most specimens were nitrided while lying
exposed on an alumina boat. The furnace tube was evacuated and backfilled before
heating. Typical conventional nitridation schedules included a 4-6 hour hold at 1250°C
82
followed by a second hold at 1350°C. The duration o f the second hold was varied
depending on the desired final conversion percentage. To nitride specimens fully, a third
temperature hold at 1425°C was often added.
4.5
Temperature measurement and calibration
Temperature measurement in a microwave environment is complicated by the fact
that standard thermocouples cannot be used because o f electromagnetic interference. There
are two generally accepted methods for measuring the temperature o f a microwave-heated
specimen: a shielded thermocouple and optical pyrometry. A shielded thermocouple is
simply a standard thermocouple that is surrounded by a layer of conducting material which
isolates the metal wires from electromagnetic fields. This method has two significant
disadvantages. First, the therm ocouple interferes with the microwave field, which makes it
impractical for use in tuned cavities. Second, it requires good thermal contact with the
specimen, which means that the temperature distributions of small specimens will be
perturbed by the thermocouple. However, shielded therm ocouples have been successfully
used when heating relatively large, well insulated specimens in multimode cavities (Tiegs et
al. 1991a, 1991/7, Kiggans et al. 1991).
Tem perature measurement in this study was done with optical pyrometry, a
technique which determines the temperature of a source from the intensity o f the emitted
radiation using the principle of Planck's law. Optical pyrometry is very attractive for use in
microwave environments because it does not interfere with the electromagnetic fields or the
specim en itself. The optical pyrometer used in this study (Accufiber model 101,
Beaverton, OR) measured the intensity of the radiation emitted at a single wavelength (950
nm) and converted it electronically to a temperature reading which could be read by the
com puter controlling the experiment. The manufacturer claims a precision o f 0.2 °C and an
83
accuracy o f 1-2°C for this device.
Tw o different methods of gathering the radiation from the specimen were available,
a pyrom eter head and a lightpipe. The pyrometer head has optical lenses which allow it to
measure the temperature o f a 1-2 mm diameter spot on the specimen at a distance o f about
30 cm. This was the method used to measure the surface temperature of the insulation
basket or specim en (see Fig. 4.3). The lightpipe consists o f a 30 cm -long single-crystal
sapphire detector enclosed in a 3 mm diameter protective sapphire sheath. This device was
designed to be inserted into a specimen to measure internal temperatures, and it does not
interact with microwaves.
The major disadvantage to optical pyrometry is that the energy emitted by a flat
surface at a certain temperature varies depending on the material. The emitting power o f a
material is determined by its emissivity, and this param eter varies with temperature. A
radiation source with the maxim um emissivity value o f 1 is called a black body. M ost
m aterials have emissivity values in the range 0.4 - 0.95. In order to accurately measure
surface temperatures using optical pyrometry, the emissivity o f the material as a function o f
temperature must be known, either from published data or from calibration.
For this study, the pyrom eter was calibrated using a conventional furnace. An
insulation basket was placed in the furnace with a type-R therm ocouple inside it, and
allowed to reach a steady isothermal state. The optical pyrometer was then focussed on the
insulation and calibrated to the thermocouple using the internal electronics o f the device.
This procedure was repeated at several different temperatures. Similar calibrations were
also performed on silicon com pacts and fully reacted specimens. Fortunately, the
em issivity o f an RBSN specimen was found to remain relatively constant as it nitrided.
No practical method for monitoring internal specimen temperatures was available.
Any internal measurements required that a hole be drilled into the specimen. Because o f the
relatively small specimen size which could be uniformly heated in the tunable cavity, the
size o f the hole needed for the lightpipe was relatively large and tended to change the
84
microwave heating characteristics as well as the temperature distribution. Some runs were
conducted using 25 mm diameter compacts with a 7 mm diameter hole for the lightpipe.
These specimens did not nitride uniformly, but they did provide internal temperature data.
4.6
Taguchi experiments
The Taguchi method of experimental design was used in this study to analyze the
effects o f various processing variables on microwave RBSN. This method has two major
advantages over traditional experimental methods when a process or product is to be
optimized. First, the number of experiments which need to be run is minimized by using a
predeterm ined orthogonal array to set the conditions for each experiment. Second, the
results o f the experiments can be analyzed using the analysis of variations (ANOVA) to
determine the relative importance o f each factor. The Taguchi method was developed in
Japan in the 1960’s as a method o f improving quality, particularly in the automobile
industry. The orthogonal arrays and ANOVA equations described here are from the book
by Ross (1988).
The first step in designing a Taguchi experiment is to select the factors which may
be important for the process, and the levels that should be used for each factor (generally
two or three). For example, the temperature at which an experiment is conducted would be
a factor, and temperatures o f 1000°C and 1100°C would be two levels for that factor. The
selection of the levels for each factor is very important and should be based on some
previous knowledge o f the process.
The second step is to select an orthogonal array that prescribes the different trials
that are to be run. Tw o examples o f orthogonal arrays appear in Figure 4.5. The L4 array
has three factors with two levels for each factor, and requires four trials. For exam ple, the
second trial would be conducted with factor 1 at level 1, factor 2 at level 2, and factor 3 at
Factors
Trial no.
1
2
3
1
1
1
1
2
1
2
2
3
2
1
2
4
2
2
1
Factors
Trial no.
1
2
3
4
1
1
1
1
1
2
1
2
2
2
3
1
3
3
3
4
2
1
2
3
5
2
2
3
1
6
2
3
1
2
7
3
1
3
2
8
3
2
1
3
9
3
3
2
1
Figure 4.5. L4 orthogonal array with 3 factors and 2 levels for each factor (top).
orthogonal array with 4 factors and 3 levels for each factor (bottom).
level 2. The L9 array has 4 factors with three levels for each factor, and requires 9 trials.
The third step is to analyze the results o f the experiment, which means choosing
one or more responses which can be measured for each trial. For exam ple, if the process
being studied is sintering, then likely responses would be the density and the strength of
the sintered specimens. For each trial, the measurement o f a response is called an
observation (i.e. a density o f 2.34 g crrr3 for trial 4 would be one observation).
Finally, the results of the experiment can be analyzed using ANOVA. The main
objective is to determine which of the factors had the largest effect on the process. This is
done by calculating how much of the total variance in the observations o f a response is
caused by each o f the individual factors. The following equation determines V a , the
amount o f variance caused by changes in the level of factor A:
1
where:
fA n
I
i=l
T
~n ~
kA = number o f levels for factor A ,
Aj = sum o f the observations made when factor A was at level i ,
nAi = number o f observations made when factor A was at level i ,
T = sum o f all observations ,
N = total num ber o f observations ,
Da = degrees o f freedom for factor A = kA-1.
The other statistical value that must be calculated is the amount o f variance in the
observations that occurs while factor A is held at a fixed level. This is known as the
variance due to error, and it is given by
4.2
87
where:
yj = individual observation made at level i ,
t)e = degrees o f freedom for error = N-kA .
W hat determines the importance o f factor A in affecting a given response is the
relative sizes o f V a and Ve. If factor A has an effect, then there will be more variance in the
observations made when factor A was at different levels than when factor A was held at the
same level, and so V a will be larger than Ve. This can be quantified by an "F-test" which
gives the level o f confidence that a factor is important. The F value for a given factor and
response is simply given by
There are published tables (e.g. Ross 1988) which then allow the confidence level
(expressed as a probability percentage) to be looked up based on the F value and the
degrees o f freedom associated with the experiment. For example, for an L9 orthogonal
array having 9 observations and 3 levels for each factor, an F value of at least 3.46 would
be required to have a 90% confidence level that a factor is affecting the response.
4.7
Specimen characterization
Specimens were cut in half using a water-cooled sectioning saw to reveal the
interior structure. The color o f a specimen changes from black to light tan as it converts
from silicon to silicon nitride, so simply inspecting the interior of a partially reacted
com pact provides useful information about its composition. One half o f the cut specimen
was mounted using a cross-linking polymer hot-mount and then polished using diamond
slurries. The specimen was first ground flat using a 30 pm slurry, and then polished using
88
6 |xm and 1 |am slurries. Because o f the high residual porosity, an extrem ely good polish
could not be achieved, but the microstructure could be observed using optical microscopy
at m agnifications up to 300x.
The final density of some specimens was measured using the three-weight
A rchem edes method, following the procedures outlined in Reed (1988). The specimen
was weighed dry and was then boiled in deionized water for 1-2 hours to saturate the open
porosity with water. After reaching room temperature, the specim en was weighed while
suspended in a basket immersed in water. The specimen was then removed from the water
and quickly weighed a third time after wiping away excess moisture. The bulk density of
the specimen,
D
r
,
was then calculated from
jHri;y - D*—* aq W
wt W
~~ dr
*” itrm m
^
_ Dw
vv
vv
U' Br —---- —-------—
W sat - W” imm
A c
,
‘tO
where Wdry is the dry weight, Wjmm is the immersed weight, W sat is the w eight saturated
with water, and Da and D w are the densities o f air and water. The degree o f conversion can
be calculated from the bulk density using
Db -D _
conversion(% ) = 100---------- 0.665D g
,
4.6
where Dg is the green density. The percent conversion values o f conventionally nitrided
specimens calculated using this method were within 3% o f the values calculated from the
w eight gain o f the specimen using equation 4.1, which indicated that the Archemedes
density measurements were accurate. One advantage o f the above method was that the
density and percent conversion values at different locations within a specimen could be
measured by sectioning it several times and then measuring the bulk density o f the
individual pieces.
89
In order to quantify composition gradients in partially reacted specimens, the
hardness o f the polished specimen was measured using the Vickers indentation method. A
diamond-tipped indenter was lowered onto the surface of the specimen with a known
am ount o f force, and then the diameter o f the resulting indent was m easured using an
optical microscope with a micrometer eyepiece. The hardness of the specimen (in Pa) at
that point was then calculated from
where P is the indenter load (N) and d is the diameter o f the indent (m). This m ethod was
useful because a series of closely spaced indents could be made across the specimen. The
resulting hardness trace gave a qualitative measure o f composition gradients, as the
hardness o f RBSN increases monotonically with the degree o f conversion.
Scanning electron microscopy (SEM) was used to observe the starting powders and
to observe the microstructure of some RBSN specimens. Fracture surfaces were mounted
and then sputter-coated with either carbon or gold to make the surface conducting and
prevent surface charging.
X-ray diffraction was used to measure the weight fractions of the a - and (3- phases
and o f residual silicon, and to analyze the composition of unusual deposits found in the
insulation basket and powder bed. The machine used was a com puter-controlled
diffractom eter (model 2400, Scintag, USA) using C u -K a radiation. The 20 and (hkl)
reflection values for the silicon and silicon nitride peaks which were scanned are listed in
Table 4.2. RBSN compacts with large composition gradients were masked with lead tape
in order to selectively measure one area of the specimen at a time.
Gazzara and M essier (1977) proposed the first method for determining the phase
com position from peak intensities, and several other researchers have since proposed
alternate methods. The method used in this study, which was developed by Jovanovic et
90
al. (1994), uses experimentally determined calibration constants which take into account the
possible effects o f preferred orientation and extinction. The weight fractions are
determ ined from the following equations:
Iq(102) + l a (210) _ 0 6 4 7 W«
L(101) + L (2 1 0 )
WP
4 8
Is i(H l) _ 5.523—
c c . o W si
—
4 .9
,
w here Ix(hkl) is the integrated intensity o f the (hkl) reflection o f phase x, and W x is the
weight fraction o f phase x. The integrated intensities were calculated automatically by the
software package running the diffractometer. The oc/P phase ratio is simply the value o f
W aAVp. The percent conversion o f an RBSN specimen can be calculated from the silicon
weight fraction according to
1 _ w ..
conversion(% ) = 100------------- —
1 + 0.665W Si
Table 4.2.
.
Silicon and silicon nitride diffraction peaks in the range 20 = 26° - 37°.
20
Phase
Peak
26.51
a-Si3N 4
(200)
27.07
p -S i3N4
(200)
28.48
Si
(111)
30.99
a - S i3N4
(201)
33.66
P-Si3N 4
(101)
34.58
a - S i3N 4
(102)
35.31
a - S i3N4
(210)
36.07
P-Si3N4
(210)
4 .1 0
91
The value for the percent conversion from equation 4.10 is based on the am ount o f
silicon actually present in the specimen, while the values calculated from the weight gain
and the bulk density are both based on the initial amount o f silicon. In general, some
w eight loss occurs during nitriding as silicon vapor diffuses out o f the specimen. If no
silicon is lost during nitriding, then the percent conversion values should agree; if there is a
silicon weight loss then the value based on the diffraction peaks will be higher. Typical
w eight loss values for conventional nitridation are less than 1% o f the green weight, but
much larger values have been observed for microwave nitridation in this study.
Some o f the nitridation runs were conducted using com pacts consisting o f a mixture
o f silicon pow der and silicon nitride powder. For these specimens, the following equation
was derived to calculate the percent conversion from the silicon weight fraction:
V - W
conversion(% ) = 150.4---------------- 51— r
V s (l.504 + W si)
,
where Vsi is the volume fraction o f silicon powder in the green compact.
4.11
Chapter 5
Results and Discussion
5.1
Nitridation of disk-shaped silicon compacts
The first set o f nitriding experiments was conducted using die-pressed disks 19 mm
in diam eter by 7 m m high with a green density o f 52%. There were two basic goals for
these experiments: to nitride the specimens fully using the microwave apparatus, and to
take advantage o f the steady-state temperature gradients associated with volumetric heating
to create an inside-out reaction.
In order to generate large temperature gradients it was necessary to maximize
radiative heat loss by using as little insulation as possible, so the first runs were conducted
with the outside edge o f the disk exposed, but with alumina fiber insulation on the faces.
The runs were controlled by focusing the optical pyrometer onto the exposed edge o f the
specimen and maintaining a chosen temperature setpoint. No information about the
reaction rate was available during nitridation. These experiments were seriously ham pered
by the formation of a dark condensate on the inside o f the quartz tube next to the specimen,
which affected the processing in two ways. First, the temperature measured by the
pyrom eter was artificially lowered, which caused the specimen surface temperature to
becom e higher than the setpoint. Second, the condensate eventually became so thick that it
began to couple with the microwaves, creating a hot spot on the quartz tube which ended
92
93
the run. The only vapor phase species which occur in the RBSN system in significant
quantities are Si(v) and SiO(g), and because of the dark appearance o f the condensate it
was assum ed to be silicon.
A different nitriding configuration was then used which consisted of a cup which
surrounded the outside edge o f the disk with a thin layer of insulation except for a small
hole where the temperature reading was taken. The condensate continued to form outside
the hole, affecting the temperature measurement, but it was reduced sufficiently to prevent
the formation o f hot spots on the quartz tube. W ith this configuration the specimen was
suspended from the analytical balance, which allowed the reaction rate to be monitored
during the run. It was found that by adjusting the temperature so as to prevent the
specim en from reacting faster than 15% per hour the condensate could be reduced, but not
eliminated. The heating configuration was then modified into the insulation basket shown
in Figure 4.2(a), which was found to reduce the condensate formation sufficiently to
prevent hot spots while maximizing radiative heat loss from the outside o f the specimen.
To see if the specimens were reacting preferentially in the interior, disks were
reacted to 50% -80% o f com pletion and then sectioned and polished. In all cases, there
appeared to be radial composition gradients, with more conversion in the center than near
the edges. This was quantified by doing hardness traces across the diameter, as discussed
in Section 4.7. The hardness profile o f a specimen nitrided to 65% conversion appears in
Figure 5 .1(a), confirming that the microwave-nitrided specimens are more reacted in the
center.
To provide a comparison, identical disks were nitrided isothermally using the tube
furnace. These specimens could be nitrided fully in 10 hours at a temperature of 1350°C,
indicating that nitrogen diffusion was not significantly slowed by the reduction in porosity,
as expected for specimens with this size and green density. However, a conventionally
nitrided disk reacted to 65% conversion was more reacted near the surface than in the
center, as shown in Figure 5.1(b). This indicates that nitrogen partial pressure dropped
94
(GPa)
3
Hardness
4
2
A
A
1
j
0
0
—
i—
2
i—
i—
4
i—
i _ _ i _____ i
i
8
10
6
i
i
i
12
i
i
14
16
■
i
18
Distance across specimen (mm)
re 5.1(a).
c
Hardness profile o f a 52% dense disk-shaped silicon com pact nitrided
to 65% conversion using microwaves.
-i-------.------- 1-------.-------1-------1------- 1-------1-------1-------1------- 1-------.-------1-------.------- p
Hardness
(GPa)
□
□
□
□
□
2 -
Q
-----------1 ------------ 1------------ ■
0
2
I
4
■
I
6
■
I
8
■
I ---------- 1
10
I
12
■
I
14
.
I
.
16
I
18
Distance across specimen (mm)
F igure 5.1(b ).
Hardness profile o f a 52% dense disk-shaped silicon com pact nitrided
to 65% conversion at 1350°C using conventional heating.
0>
u
0
O
52% green density
A
62% green density
—1
0
120
240
360
480
600
720
840
960
1080
Time (min)
Figure 5.2. Data from the nitridation o f 19 mm diameter disk-shaped silicon compacts
at 1350°C using conventional heating.
below 1 atm in the interior o f the com pact during nitridation.
The next set o f experiments was conducted using disks that were isostatically
pressed to increase the green density from 52% to 62%. This was done to see if the insideout reaction would occur in specimens where nitrogen diffusion through the porosity was
more difficult. Figure 5.2 shows the percent conversion versus time for the 52% and 62%
dense silicon compacts at 1350°C in the conventional furnace. The kinetics in the early
stage of the nitridation reaction are similar, but the denser compacts react more slowly later
in the reaction because of their lower permeability.
The microwave nitridation runs on the denser silicon com pacts were conducted by
controlling the reaction rate rather than the temperature. This was done for two reasons.
First, the nitriding rate in the initial stage could be slowed to prevent the reaction exotherm
from causing melting. Second, the specimen temperature could be increased as needed
96
towards the end of the reaction to keep the reaction proceeding at the desired rate. These
experim ents were conducted using constant nitridation rates o f 10-15% conversion per
hour. Figure 5.3 shows the data from the m icrowave processing o f a 62% dense disk.
The nitridation rate was held at 12%/hour up to 70% conversion, while the surface
tem perature o f the specimen was monitored using the pyrometer. Note how the surface
temperature increases throughout the experiment.
Figure 5.4(a) shows the radial hardness profile o f a microwave specim en nitrided to
70% conversion, dem onstrating a large com position gradient. The hardness profile o f a
conventionally nitrided specimen reacted to 85% conversion (see Fig. 5.4(b)) shows the
decreased conversion in the center associated with nitrogen depletion effects. The
m axim um hardness o f the disks with a 62% green density was about 6.0 GPa, as
com pared to about 3.3 G Pa for the disks with a 52% green density.
Tw o other observations characterized the m icrowave-nitrided disks. First, there
was an axial composition gradient with more reaction near the faces than in the center,
which gave the partially reacted specimens an "hourglass" profile (see Figure 5.5). For
com parison, the cross-section o f a conventionally-heated specimen is shown in Figure 5.6.
Because the maximum diffusion distance in the axial direction is only 3-4 m m (half the
thickness), the lack of an inside-out reaction indicates that significant axial temperature
gradients are not present. Even a small axial temperature gradient would be expected to
increase the reaction in the center as compared to the faces, because nitrogen depletion in
specimens this small should be minimal.
There are two possible explanations for the lack o f an inside-out reaction along the
axial direction o f the disks. First, the insulation on the faces o f the disks could reduce the
axial temperature gradient enough so that it would not significantly affect the composition
profile. Second, the microwaves may not have penetrated into the disks far enough to
cause volumetric heating. It should be noted that because the outside edge o f the disks was
exposed while the faces were insulated, radial temperature gradients would be expected to
97
1250
Temperature (°C)
1200
s
o
"3
fa
>■
oe
1150
40
U
ea>
uu,
v
CL
1100
1050
0
60
120
180
240
300
360
Time (minutes)
Figure 5.3. Data from the microwave processing o f a silicon compact. A programm ed
conversion rate o f 12% per hour was used. Each data point is an average
value from the previous 5 minutes. The temperature measurements were
taken on the outer edge o f the disk, which was the coolest part o f the
specimen.
98
7
6
Oh
O
w
l/i
c
TS
u
5
4
4
A
A
A
A
A
S3 2
1
_i
0
0
i
i
2
i
i
4
i
i
6
i
8
i
i
10
i
i
i
12
■
14
i
16
18
Distance Across Specimen (mm)
Figure 5.4(a).
Hardness profile o f a 62% dense disk-shaped silicon com pact nitrided
to 70% conversion using microwaves.
□
cs
□
O
5
^
A
4
vi
V
G
D
□
D
□ □
□ □ □
□ □
□
"G
« 3
S3
2 -i
0
L.
4
6
J
8
i
l_
10
■
12
14
■
i
16
18
Distance Across Specimen (mm)
F igure 5.4(b ).
Hardness profile o f a 62% dense disk-shaped silicon com pact nitrided
at 1350°C using conventional heating.
99
Figure 5.5.
Polished cross-section o f a 62% dense disk-shaped com pact w hich was
nitrided to 70% conversion using m icrowaves. N ote the reaction bands.
--------------------------------------
Figure 5.6.
19 mm
►
Polished cross-section o f a 62% dense disk-shaped com pact w hich was
nitrided to 70% conversion using conventional heating.
100
exist even if the microwave energy was absorbed only at the surface o f the disk. In a
larger, cylindrical specimen, significant temperature gradients would not form without
volumetric heating.
The second observation was the formation o f a banded microstructure, which can
be seen in Figure 5.5. These bands consist o f alternating parallel light and dark regions
within the fully nitrided areas o f the specimen. No reaction bands were ever observed in
conventionally nitrided specimens, and this type of microstructure has never been reported
in the literature, which indicates that microwave heating is causing this phenomenon. This
microstructure and the formation o f reaction bands will be discussed in detail later in this
chapter.
In order to demonstrate a significant advantage to the use o f microwave heating, it
is necessary to fully nitride specimens that are difficult or impossible to nitride fully in a
conventional furnace. The die-pressed disks were not adequate for this, because their
m axim um thickness o f about 7 m m allowed nitrogen to diffuse rather easily to all areas of
the specim en. Also, as discussed above, temperature gradients could form in the disks
without true volumetric heating taking place due to the insulation on the faces. For these
reasons, the remaining experiments were conducted using isostatically pressed rods, which
have a significantly larger maximum diffusion distance and which were much more difficult
to nitride fully in the conventional furnace.
101
5.2
Nitridation of rod-shaped silicon compacts
Rod-shaped silicon compacts were made with two different diameters. The
standard diameter, which was used for most o f the experiments, was 15 mm. A set o f
experim ents was also done using larger rods with a diam eter o f 23 mm. Both sizes had a
green density of 64%. The method of forming the rod-shaped com pacts by isostatic
pressing is discussed in Section 4.2.
These com pacts had less porosity and had significantly longer maxim um diffusion
distances than the disk-shaped compacts, which made them more difficult to nitride fully.
Conventional nitridation was done using a multi-step temperature program consisting o f a
four-hour hold at 1280°C followed by a hold at 1375°C and, in some cases, a hold at
1420°C. After 18 hours at 1375°C, the 15 mm diam eter rods were 85% reacted, while the
23 mm diam eter rods were 67% reacted. An additional 18 hour hold at 1375°C only
increased the conversion to 89% and 77% respectively, so a third temperature hold at
1420°C was added to try to fully nitride the rod-shaped compacts. The processing o f
RBSN above the silicon melting point (1410°C) is often necessary so that full nitridation
can be reached in a reasonable time. However, if a continuous layer o f nitride has not
formed around the silicon particles, then large melts will form in the interior o f the
specim en (M oulson 1979).
Figure 5.7 shows the percent conversion versus time for the two com pact sizes, as
well as the temperature profile used. After 10 hours at 1425°C the 15 mm diam eter rods
appeared to be fully nitrided, but the 23 mm diameter rods had internal melting (see Fig.
5.8). From these experiments it is clear that the isostatically pressed rods are large enough
and dense enough so that full nitridation is difficult under isothermal conditions due to the
reduced permeability. The 15 mm diameter rods can only be fully nitrided by raising the
furnace temperature above the silicon melting point, while it appears that the 23 mm
diameter rods cannot be fully nitrided at all without internal melting, although no significant
102
1450
□ r *.
□
□
1400
r ~ .g - -
60 -
i
i
i □
i
40 -
1350
9
~~
20
1
0
0
1— »
*
8
1
temperature profile
n
15 m m diameter rods
•
23 m m diameter rods
1300
Temperature (°C)
Percent Conversion
80
1250
1
12
16
20
24
28
32
Time (hours)
Figure 5.7. Data from the nitridation of the 15 m m diameter and 23 m m diam eter rod­
shaped silicon com pacts using conventional heating.
Figure 5.8. Cross-section of 15 mm diameter (left) and 23 mm diam eter (right) rod­
shaped silicon com pacts after conventional nitriding.
103
further efforts were made to do so. Therefore, if the rod-shaped silicon com pacts could be
successfully nitrided using microwave heating in a reasonable time, or if an inside-out
reaction profile were observed, then this would indicate true volumetric heating and
dem onstrate an advantage for microwave processing.
5.2.1 M icrowave nitridation o f rod-shaped compacts
Initial experiments concentrated on finding the optimum heating configuration for
the 15 m m diam eter compacts. A standard specimen length o f 40 m m was chosen to
provide reproducible results. W hen an open insulation basket was used, as w ith the disk­
shaped com pacts, the condensate formation inevitably led to hot spots on the quartz tube.
Therefore, a full layer o f insulation with a silicon nitride pow der bed was used, as shown
in Figure 4.2(b). W ith this configuration the rods could be nitrided to at least 75% overall
conversion. However, significant problems with the m icrowave processing o f rod-shaped
com pacts occurred over the course o f several runs:
i.
Asymmetric radial nitridation: many specimens developed a region o f full
nitridation on only one side o f the rod (see Fig. 5.9(a)).
ii. Asymmetric axial nitridation: many rods became fully nitrided either on the
top or on the bottom, while the other end o f the rod rem ained unreacted.
(see Fig. 5.9(b)).
iii. "Crust" formation: an uneven, dark layer o f material formed on the outside
o f the specimen within the powder bed.
iv. W eight loss: the weight gain o f the specimen was always less than the
weight gain o f the basket assembly.
v. Microstructural inhomogeneity: the fully nitrided regions o f the rod had
areas of different color, internal melts, and reaction bands.
104
The first processing param eter that was adjusted was the resonant heating mode
used. The only mode which would heat the disk-shaped compacts to nitriding temperatures
was the T E i l [ mode, which provides a small, intense hot zone. By adjusting the cavity
ceiling and the launch probe (see Fig. 4.4) several other modes were found to heat the rod­
shaped compacts. The most uniform heating was achieved with the TM 0 1 2 mode, which
has a larger axial hot zone than the T E i
1 1
mode, as well as a radially symmetric electric
field. The use o f the TM 0 1 2 mode eliminated the problem o f radially asymmetric
nitridation.
The position o f the specimen within the microwave cavity was also found to be
important. By using the TM 0 1 2 mode and placing the specimen midway between the
cavity ceiling and baseplate, the problem of asymmetric axial nitriding was avoided, and the
rods then reacted preferentially in the middle and developed a characteristic "hourglass"
reaction profile (see Fig. 5.9(c)). Full reaction across the diam eter o f the 15 mm rods was
reached in the middle o f the specimen while the ends were still unreacted. This seemed to
indicate that microwave heating increased the conversion in the interior of the compacts,
because when using conventional heating the interior o f the 15 mm diameter rods could be
fully nitrided only by raising the temperature above the silicon melting point. However, no
inside-out com position profiles were observed in the microwave-heated rods, which
indicated that significant temperature gradients did not occur early in the run when the
com pacts were mostly silicon.
The large axial composition profiles observed in partially nitrided rods clearly
dem onstrate that the middle o f the rod becomes much hotter than the ends during the run.
Figure 5.10 shows the hardness profile along the center axis o f a 70% reacted rod. The
corresponding heat distribution suggests that as the nitridation reaction progresses the
specim en absorbs more microwave energy, and so the region of the specim en that is
initially hottest becomes fully reacted at the expense of cooler areas. If the opposite were
true, then the less reacted areas o f the rod would absorb more microwave energy, and any
105
^.v?*£i^-, *■''
Figure 5.9. Cross sections o f rod-shaped silicon compacts nitrided using m icrowave
heating: a) asymmetric radial nitridation, b) asymmetric axial nitridation,
c) typical profde with more conversion in the middle o f the rod.
106
10
8
/es
aS
X
X
o
6
C
■2
05
s
4
O o o
o O
2 . o o
J____ 1____ I____ I____ I____ 1____ I____ I____ L.
0
0
4
8
12
16
20
24
Distance along center axis (mm)
Figure 5.10.
Hardness profile along the center axis o f a 15 mm diam eter rod-shaped
silicon com pact nitrided to 70% conversion using microwaves.
axial com position gradients which formed would tend to even out. The m icrowave heating
characteristics o f the compacts are discussed in more detail in Section 5.4.
Although the microwave processing o f rods was successful, in that the 15 m m
com pacts could be nitrided fully across their diameter, the problems of crust formation,
w eight loss, and m icrostructural inhomogeneities remained. The most obvious explanation
for these problem s was that the specimens were getting too hot in the interior, causing
silicon to be forced out o f the specimen into the powder bed. The next set o f experiments
had the goal o f adjusting the processing parameters so as to form fully dense RBSN
specimens. One concern was that the silicon nitride powder used as the pow der bed was
itself being heated by the microwaves. By switching to alumina powder, which is virtually
transparent to microwaves, the formation o f an outer crust was reduced somewhat.
However, the microstructure o f the specimens remained poor.
107
A possible cause of internal overheating was the reaction exotherm. As discussed
in Section 2.3.2, the heat released by the nitridation reaction can cause temperature
gradients to form and is therefore a potential cause of internal overheating and melting. For
the global conversion rates used during the microwave nitridation am s, the m aximum
temperature difference resulting from the exotherm would be only on the order o f 5°C if the
com pact were nitriding uniformly. However, the observed large axial com position
gradients indicate that the nitridation reaction was localized within the specimens during
m icrowave processing, causing the reaction rate in the hottest areas to be significantly
greater than the global programm ed rate. Since the reaction rate is a strong function of
temperature, the reaction rate in the fastest-reacting areas could feed off its own exothermic
heat, causing a sudden increase in the temperature which would last only until the available
nitrogen in that area was consumed.
There appeared to be three ways the process could be changed to prevent
overheating in the interior o f the specimens. First, the global reaction rate could be reduced
to prevent the internal nitridation rate from reaching the critical level that would cause
overheating. Second, the silicon compacts could be prenitrided in the conventional
furnace. This might cause the specimens to nitride more evenly, thus reducing the
difference between the maximum local reaction rate and the global programmed rate.
Third, the gas composition could be altered to make it less reactive.
M icrowave nitridation experiments were conducted using several different
conversion rates, ranging from 5% conversion per hour down to 1% conversion per hour.
Figure 5.11 shows the kinetic data from an experiment conducted at 3% conversion per
hour. At all o f these rates weight loss and crust formation were observed, and no
consistent im provement was found by decreasing the reaction rate. It is likely that the
m axim um local reaction rates and temperatures were too high even when the reaction rate
was as slow as 1% conversion per hour. Because it is desirable to minimize the processing
time, reducing the reaction rate is not a practical approach to preventing internal
108
100
925
Percent Conversion
Insulation Surface Temperature (°C)
950
900
875
850
825
0
4
8
12
16
20
24
28
Time (hours)
Figure 5.11.
Data from the microwave processing o f a 15 m m diam eter rod-shaped
silicon com pact using a programm ed conversion rate o f 3% per hour.
Each data point is an average value from the previous 5 minutes.
109
overheating.
Compacts were prenitrided by firing them at 1280°C for hold times which varied
depending on the am ount of conversion desired. For exam ple, a 4-hour hold was found to
consistently give 25% conversion. The prenitrided specimens were then further nitrided in
the microwave apparatus in the same way as the green compacts. Significant differences
were found between the green and prenitrided compacts. The com position was more
uniform along the axis o f the rod in the prenitrided compacts, with less difference in
conversion between the ends and the middle, confirming that the specimens reacted m ore
evenly after prenitriding. However, the prenitrided rods also reacted preferentially near the
surface, making them more difficult to nitride fully across the diameter than the green
specimens. The outer crust formation and weight loss were reduced, but w ere not
eliminated. In general, prenitriding the compacts made them react more like the
conventionally-heated specimens, and any advantages which may have resulted from
m icrowave processing when using green compacts seemed to be lost.
The other factor that could affect the reactivity o f the specimens is the gas
composition. The standard reactant gas used for the nitridation experiments was a 99% N 2
/ 1% H 2 mixture. As discussed in Section 2.2.2, hydrogen lowers the oxygen partial
pressure thus allowing for the gas-phase nitridation o f SiO and increasing the kinetics.
Additions o f lighter gases such as H 2 also increase the diffusivity and thermal conductivity
of the reactant gas mixture, which creates a fine-grained RBSN microstructure with better
mechanical properties.
Also, because the nitrogen is continuously consum ed by the reaction, it is possible
for the hydrogen to build up in the interior of the specimen to concentrations significantly
greater than that of the input gas, especially when the com pact is reacting quickly. This
"pile up" effect can be beneficial, as discussed in Section 2.3.3, in that it slows the reaction
rate in fast-reacting areas. However, it could also reduce the am ount o f conversion in the
interior o f the com pacts where the concentration of H 2 would be greatest. To determine the
110
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E
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H
1250
.
1
1
1
1
8
12
16
20
■ -i-----■ 1 ..i___
24
28
32
Time (hours)
Figure 5.12.
Data from the conventional nitridation of 15 mm diameter rod-shaped
silicon compacts with and without a 1% hydrogen addition.
effect o f small H 2 additions on the RBSN process, com pacts were nitrided in the
m icrowave cavity and in the conventional oven using pure N 2 . As can be seen from Figure
5.12, the reaction kinetics o f the conventionally nitrided 15 mm diameter rods are
significantly increased by the 1% hydrogen addition. This result is in good agreem ent with
previous studies (e.g. see Fig. 2.9). A sim ilar effect was observed for the m icrowaveprocessed compacts, in that the insulation surface temperature required to maintain the
program m ed conversion rate was higher when using pure nitrogen. This temperature
difference could not be accurately measured, however, due to small differences in the
thickness o f the insulation cylinder and the pow der bed from run to run. No consistent
differences were observed in the composition profiles or in the amount o f weight loss or
crust based on the presence o f 1% FF in the reactant gas. This indicates that hydrogen
buildup was not preventing nitrogen from diffusing to the center o f the compacts.
Ill
If the internal overheating is caused by the reaction exotherm, then it m ight be
beneficial to dilute the nitrogen with an inert gas. By reducing the nitrogen concentration,
the fastest-reacting areas o f the specimen would become starved o f nitrogen more quickly,
thus preventing the exothermic heat from causing large temperature excursions. As
discussed in Section 2.3.3, lighter gas additions are preferable because they increase the
diffusivity and the thermal conductivity o f the mixture. Because hydrogen is flammable in
high concentrations, high purity helium was chosen as the diluting gas. A second
flowm eter was installed and calibrated to helium so that the relative concentrations o f N 2
and He w ould be known.
To establish the effect o f nitrogen dilution on the reaction rate, specimens were held
in the microwave cavity at a constant insulation surface temperature or at a constant
nitridation rate while the amount o f helium in the input gas was changed. As shown in
Figures 5.13 and 5.14, lowering the nitrogen partial pressure reduced the reaction rate
dramatically. W hen the insulation surface temperature was held constant (Fig. 5.13) the
reaction rate dropped by about half when 33 vol% He was added to the nitrogen. W hen the
reaction rate was held constant (Fig. 5.14) the addition o f He forced the insulation surface
temperature to increase.
The effect o f nitrogen partial pressure on the reaction rate o f silicon pow der
com pacts was first discussed by Atkinson et al. (1976). They found that the initial
nitridation kinetics were linear, and could be written as
where AM is the mass o f nitrogen reacted in time t, A is the surface area o f the powder, and
k[ is a linear rate constant which was found to be proportional to the nitrogen partial
pressure. They also found that the grain size of the silicon nitride was a function o f the
nitrogen pressure, with sm aller grains developing at higher pressures. This can be
112
8
k.
os
6
=5
£'w'
CQ
U
4
S
o
• fW
+-»
o
OS
0)
as
2
0
0
120
60
180
240
Time (minutes)
Figure 5.13.
Change in the reaction rate with nitrogen partial pressure, for a constant
insulation surface temperature o f 865°C. A: pure nitrogen, B: 67 vol%
nitrogen, C: 50 vol% nitrogen.
U
o
840
a>
u
830
9
+■»
03
u
a>
a
sa>
I- —
820
A
r
B
B
810
800
H
v
u
iM
k
9
C»
S
o
a
780
c
750
790
, A
770
■
I
i
I
r
M
760
i l l
0
60
120
180
240
300
I
I
360
420
Time (minutes)
Figure 5.14.
Change in the insulation surface temperature with nitrogen partial
pressure, for a constant reaction rate o f 3% conversion per hour. A: pure
nitrogen, B: 67 vol% nitrogen, C: 50 vol% nitrogen.
113
explained by a nucleation and growth mechanism, with more nuclei developing at high
pressure because of the higher density o f chem isorbed nitrogen on the silicon surface at the
start o f the reaction.
Ziegler et al. (1987) have suggested that the dependence of the kinetics on the
nitrogen pressure is caused by the microstructure o f the nitride product, that is, that the
decrease in the reaction kinetics at low nitrogen partial pressures is due to the fewer num ber
o f grains that nucleate. H owever, the results shown in Figures 5.13 and 5.14, which
dem onstrate that the reaction rate changes quickly in response to changes in the nitrogen
pressure, indicate that the effect o f nitrogen partial pressure on the reaction kinetics is
independent o f the microstructure o f the initial product layer. A more likely explanation is
that the nitrogen pressure controls the first step in the nitridation reaction, which is the
chem isorption o f nitrogen onto a silicon or silicon nitride surface, where it then diffuses
and reacts with adsorbed silicon (see Section 2.2.3). The rate o f chem isorption o f a gas is
proportional to the number o f collisions between the gas molecules and the surface, and the
collision rate is proportional to the partial pressure o f the gas. This would explain why the
nitridation rate changes rapidly in response to changes in the nitrogen partial pressure.
Compacts which were nitrided in a dilute N 2 /He mixture using both m icrowave and
conventional heating had more conversion to silicon nitride near the surface, as with the
prenitrided compacts. There was also more melting in the center o f the compacts, although
the presence o f white overheated areas and reaction bands in the microwave specimens was
reduced. Lowering the nitrogen partial pressure apparently reduced the amount o f nitrogen
that could diffuse into the interior o f the specimens, leading to an outside-in reaction
profile. As with prenitriding, reducing the nitrogen partial pressure made the microwave
processed specimens react more like the conventionally processed specimens in that full
reaction across the diameter o f the 15 mm diameter rods was very difficult.
The above experiments indicate that internal overheating in the microwaveprocessed specimens occurs whenever extensive nitridation occurs in the interior o f the
114
compacts. This seems to indicate that microwave heating does not have any advantages for
the processing o f RBSN. However, the above experiments did not dem onstrate this
conclusively because they did not explore all possible combinations o f the relevant
processing parameters.
5.2.2
Taguchi experiments
The Taguchi method o f experimental design and its advantages were discussed in
Section 4.6. The goal o f the Taguchi experiments performed here was to optimize the
microwave processing o f the 15 m m diameter rod-shaped silicon compacts so as to utilize
the benefits o f volumetric heating while avoiding the problems o f crust formation, weight
loss, and other microstructural inhomogeneities which are apparently caused by internal
overheating.
The results presented in the previous section indicate that the relevant processing
param eters are the reaction rate, the presence of hydrogen in the reactant gas, the dilution of
the reactant gas with an inert gas, and the prenitridation treatment. An L9 orthogonal array,
w hich has four factors, three levels for each factor, and requires 9 trials, was chosen for
the first experiment. The basic form at for an L9 array appears in Figure 4.6.
The factors and levels w ere chosen as follows. The reaction rate was held constant
at 1% per hour, 2% per hour, or 3% per hour. The reactant gas was pure nitrogen, 99%
N 2 / 1% H 2 , or 95% N 2 / 5% H 2 . The reactant gas was diluted with helium in the am ounts
o f 0 vol%, 25 vol% , or 50 vol%. Finally, the silicon com pacts were prenitrided to 25%
conversion, 50% conversion, or were not pretreated. The L9 array with all o f the
experimental conditions is shown in Figure 5.15. The experimental conditions for each
trial are determined by the L9 orthogonal array in such a way that the effects o f each factor
can be analyzed separately. The trials were performed in random order using the standard
insulation configuration with an alumina powder bed, and all o f the specimens were
115
Trial
Prenitridation
Reaction rate
Helium dilution
Reactant gas
1
none
3% per hour
none
pure N 2
2
none
2% per hour
25 vol%
99% N 2 /1 % H 2
3
none
1% per hour
50 vol%
95% N 2 / 5% H 2
4
25%
3% per hour
25 vol%
95% N 2 / 5% H 2
5
25%
2% per hour
50 vol%
pure N 2
6
25%
1% per hour
none
99% N 2 / 1% H 2
7
50%
3% per hour
50 vol%
99% N 2 / 1% H 2
8
50%
2% per hour
none
95% N 2 / 5% H 2
9
50%
1% per hour
25 vol%
pure N 2
Figure 5 .1 5 .
Processing conditions for the L9 Taguchi experiment.
116
nitrided to 70% conversion.
To analyze the results o f the experiment, quantitative observations were made on
the specimens. As discussed earlier, the best way to measure com position gradients in the
specim ens is by performing hardness traces. The specimen from each trial was sectioned
and polished, and then two hardness traces were taken, one across the diam eter in the
m iddle o f the rod, and one lengthwise along the center axis. The average hardness value
from each o f these hardness traces was used as a response to the Taguchi experiment, as a
measure o f the overall quality o f the specimen. Since all o f the specimens were nitrided to
the same conversion, differences in the average hardness would indicate differences in the
microstructure o f the product.
The ratio o f the hardness in the center o f the specimen to the hardness near the
surface, using the values from the hardness trace across the diameter, was used to m easure
the am ount o f inside-out reaction caused by the microwave heating. The ratio o f the
hardness in the middle o f the specimen to the hardness at the ends, using values from the
hardness trace along the length, was used to measure the uniformity o f the nitridation. The
am ount o f overheating which took place was also used as a response. This was determ ined
subjectively by simply rating the amount of visible white areas and melted areas in each
specim en on a numerical scale from 0 to 10.
To determ ine how much effect each of the four factors had on the above responses,
the data were analyzed using the ANOVA equations 4.2 - 4.4. The F-value given by eq.
4.4 is a measure of the likelihood that a given factor affected a given response. The larger
the F-value, the more im portant the factor. For this experiment, an F-value o f 5.14
corresponded to a confidence level of 95% that a factor was significantly affecting the
m icrow ave processing responses.
The response values and the F-values from this experim ent appear in Figure 5.16.
The F-values which are larger than the 95% confidence level appear in boldface. Clearly,
the factor with the largest effect was the helium dilution. The average hardness values from
117
Trial
1
2
3
4
5
6
7
8
9
M ean hardness across
the diam eter (GPa)
7.99
5.93
3.03
6.81
4.05
6.31
3.58
4.84
5.23
M ean hardness along
the length (GPa)
4.9 6
3.86
2.66
3.07
2.62
3.73
3.04
3.62
3.90
Hardness o f interior
com pared to surface
1.00
0.87
0.38
0.71
0.63
0.75
0.48
0.76
0.81
Hardness o f middle
com pared to ends
5.43
1.45
0.43
2.60
1.95
2.04
0.98
1.74
2.23
Apparent amount o f
overheating (0-10)
4.0
3.5
2.0
4 .0
3.0
3.5
1.0
1.5
2 .0
Observation
Prenitride
Rx rate
He
h2
comments
M ean hardness
across the diameter
.43
.51
6 .2 5
.17
Helium dilution
lowers the hardness
M ean hardness along
the length
.58
.13
4 .9 4
.64
Helium dilution
lowers the hardness
Hardness o f interior
com pared to surface
.09
.20
7.47
.72
Helium dilution
lowers internal
hardness
H ardness o f m iddle
com pared to ends
.20
.92
1.67
1.60
No conclusive effect
Apparent amount of
overheating
6 .5 3
.12
.93
.12
Prenitriding reduces
overheating
F ig u r e
5 .1 6 .
Top: data from the L9 Taguchi experiment. Bottom: F-values from the
L9 Taguchi experiment. F-values which are larger than the 95%
confidence level appear in boldface type.
118
the two hardness traces were both lower when helium was used, indicating that lowering
the nitrogen partial pressure had a negative effect on the RBSN microstructure. The
hardness o f the interior as com pared to the surface was also lower with the helium dilution.
As discussed in the previous section, this is probably because all the nitrogen is consum ed
near the surface of the specimen before it can reach the interior. The am ount o f internal
overheating appeared to be lower when the specimens were prenitrided. This is because
the specim ens nitride more uniformly after prenitriding, and because less o f the nitridation
takes place by microwave heating.
The data from the L9 experiment can be shown graphically by plotting the average
value o f a response at a fixed level of a factor against the different levels o f that factor. In
Figure 5.17, the radial hardness, axial hardness, and the sum o f the radial and axial
hardness values are plotted in this manner for all four o f the factors. Sim ilar plots for the
ratio o f internal to surface hardness, the ratio o f middle to end hardness, and the am ount o f
overheating appear in Figure 5.18. For all of these plots, “low” refers to no prenitriding,
no helium, no hydrogen and a 1% per hour reaction rate, “medium” refers to 25%
prenitriding, 25% helium, 1% hydrogen, and a 2% per hour rate, and “high” refers to 50%
prenitriding, 50% helium, 5% hydrogen, and a 3% per hour rate.
In general, the specimens from the L9 Taguchi experiment were all poor in one way
or another. Those specimens that were processed from the green state were fully reacted in
the interior, but had large amounts o f microstructural inhomogeneities, while the
prenitrided specimens reacted preferentially near the surface. In particular, the trials
conducted at 50% helium dilution resulted in very poor specimens, and this somewhat
overshadow ed the effects o f the other factors when analyzing the data. A second Taguchi
experim ent was designed which did not use a high helium concentration. This experim ent
used an L4 orthogonal array, which has three factors, two levels for each factor, and
requires 4 trials (see Fig. 4.6). The factors were chosen as follows. The reactant gas was
pure nitrogen or 95% N 2 / 5% H 2 , the reactant gas was diluted with 25 vol% helium or not
Total Hardness (GPa)
Avg Length Hardness (GPa)
Ayg Radjal Hardness (GPa)
119
A
D
+
O
7
prenitride
rx rate
dilution
hydrogen
6
5
4
LOW
H IG H
MEDIUM
4.5
A prenitride
O rx rate
+ dilution
O hydrogen
4.0
3.5
3.0
2.5
LOW
MEDIUM
A
O
+
O
11
10
H IG H
prenitride
rx rate
dilution
hydrogen
9
8
7
Figure 5.17.
LOW
MEDIUM
H IG H
Plots showing the effects o f the different factors on the hardness o f the
specimens. Top: radial hardness. Middle: axial hardness. Bottom:
radial + axial hardness.
H-interior / H-surface
120
0.9
0.8
0.7
0.6
A prenitride
n rx rate
+ dilution
O hydrogen
0.5
0.4
I
0.3
LOW
MEDIUM
H IG H
4.0
A
O
+
O
H-middle / H-end
3.5
3.0
2.5
2.0
0.5
X
X
LOW
Amount of overheating
prenitride
rx rate
dilution
hydrogen
MEDIUM
H IG H
3.5
3.0
2.5
A prenitride
a rx rate
+ dilution
O hydrogen
2.0
X
LOW
Figure 5.18.
X
MEDIUM
H IG H
Plots showing the effects o f the different factors on the specimens. Top:
ratio o f interior to surface hardness. Middle: ratio o f middle to end
hardness. Bottom: amount o f overheating.
121
at all, and the conversion rate was either 3% per hour for the entire reaction or 4% per hour
initially and 2% per hour later in the reaction. The two-stage conversion program required
the same total processing time as the constant conversion rate, so this factor explored the
effect o f a faster early reaction. The conditions for this experiment are shown in Figure
5.19. All o f these specimens were prenitrided to 25% conversion and then nitrided to 90%
conversion using microwave heating. The 25% prenitridation treatm ent was chosen as a
com prom ise between the overheating that occurred with the green specimens and the
outside-in reaction profile that developed in the specimens with the 50% prenitridation
treatment.
As with the L9 experiment, two hardness traces were taken on the specim ens to
measure the average hardness, the relative amount of internal conversion, and the relative
uniform ity of the reaction along the center axis. For this experiment, the am ount o f silicon
w eight loss was also used as a response. This was measured by calculating the percent
conversion based on the weight gain of the basket assembly, and then subtracting the
percent conversion as calculated from the weight gain of the specimen only. The response
values and the F-values from the L4 experim ent appear in Figure 5.20. For an L4 array, an
F-value o f 8.5 corresponds to a confidence level o f 90%. Although m ost o f the factors had
maxim um F-values between 5.5 and 6.5, they are probably significant because the other Fvalues are m uch lower.
As with the L9 experiment, the amount o f conversion in the interior was lower
when the reactant gas was diluted with helium. The average hardness across the diameter
was higher when the reactant gas contained 5% hydrogen, as was the am ount o f reaction in
the middle as compared to the ends. W hen the reaction rate was held at 3% per hour, the
average hardness along the length was higher and the weight loss was lower. The results
o f this experiment indicate that a constant reaction rate and the presence of hydrogen are
beneficial, and that dilution o f the reactant gas is harmful. However, as with the first
experiment, all o f the specimens had some microstructural inhomogeneities such as melted
122
Trial
Reaction Rate
Reactant gas
Helium dilution
1
3% per hour
95% N 2 / 5% H 2
none
2
3% per hour
pure nitrogen
25 vol%
3
4% / 2%
95% N 2 / 5% H 2
25 vol%
4
4% / 2%
pure nitrogen
none
Figure 5 .1 9 .
Processing conditions for the L4 Taguchi experiment.
areas and reaction rings, and none o f them demonstrated an inside-out com position profile.
The results o f the two Taguchi experiments verified that there are serious problem s
with the m icrowave processing o f RBSN which cannot be solved by adjusting the typical
processing parameters. The focus o f the next section is to analyze m ore closely the
phenom ena such as weight loss, crust formation, and reaction bands which appear only in
the m icrowave specimens, to see how they are related.
123
Trial
1
2
3
4
M ean hardness across
the diameter (GPa)
6.48
5.72
7.80
4.82
M ean hardness along
the length (GPa)
4.89
4.48
3.93
4.20
Ratio o f interior to
surface hardness
0.92
0.57
0.74
0.58
Ratio of middle to end
hardness
1.72
1.63
1.77
1.94
W eight loss (%)
2.82
1.53
3.59
4.02
Observation
Rx rate
Fh
He
comments
M ean hardness
across the diameter
.02
5 .4
.70
Hydrogen gave
higher hardness
M ean hardness along
the length
6 .3
.02
.60
3% per hour gave
higher hardness
Ratio o f interior to
surface hardness
.16
.01
2 3 .8
Helium dilution
lowers internal
hardness
Ratio o f middle to
end hardness
.02
6 .4
.58
Hydrogen raises
middle hardness
5 .7 5
.10
.52
4% / 2% rate
increases weight loss
W eight loss
F ig u r e
5 .2 0 .
Top: data from the L4 Taguchi experiment. Bottom: F-values from the
L4 Taguchi experiment. F-values which represent a significant effect
appear in boldface type.
124
5.3
Experimental analysis of microwave heating phenomena
The microwave-nitrided specimens, particularly those made from rod-shaped
silicon com pacts, demonstrate internal melting and other unusual microstructures and have
a tendency to lose a significant am ount o f the original weight o f silicon during processing.
These effects appear to be caused by internal temperatures that are m uch higher than would
be needed to maintain the program m ed 3% per hour reaction rate. There appear to be two
possible mechanisms which could cause overheating in the interior o f the microwave
specimens. First, the microwave heating characteristics o f the nitriding com pact could be
such that certain compositions absorb microwave energy very efficiently, causing relatively
small areas o f the specim en to be much hotter. Second, the exothermic heat released by the
nitridation reaction could cause the temperature o f localized, fast-reacting areas to increase
suddenly, further increasing the nitridation rate and causing even more heat to be released.
In the latter case the temperature excursions would last only until the available nitrogen was
consumed. Attempts to decrease the amount of exothermic heat released by diluting the
nitrogen with an inert gas were unsuccessful, and those experiments did not provide any
insight into whether short-term temperature excursions were causing the internal
overheating.
To determine whether brief temperature excursions were occurring inside the
microwave heated specimens, some way o f monitoring the internal temperature was
needed. As discussed in Section 4.5, this was accomplished using an optical lightpipe.
Because the lightpipe was too delicate to be inserted directly into the specimen, a closedend alum ina tube was used as a protective sheath. This required that a hole 6 mm in
diam eter be drilled halfway into the silicon compact, so this set o f experiments was
conducted using the larger 23 m m diameter rods in order to have a significant thickness o f
material rem aining around the hole. Figure 5.21 shows the configuration used for the
internal temperature measurement experiments. The com pact was supported in the
125
V\
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
F ig u r e
5 .2 1 .
Alumina pow der bed
\
\
\
\
/
23 m m diam eter silicon com pact
\
\
\.
/" V
Alumina fiberboard insulation
\
\
\
\
\
\
\
S
\
C losed-end alum ina tube
\
\
s'
Optical lightpipe
\
Cross section o f the configuration used for the internal temperature
m easurement experiments.
m icrowave cavity by the alumina sheath, and was surrounded by a thin layer o f alum ina
fiberboard insulation and an alumina pow der bed. The lightpipe could be inserted into the
sheath during the run to measure the internal temperature. The optical pyrom eter was
focused onto the surface o f the insulation directly opposite the tip o f the lightpipe.
There were two drawbacks to these experiments. First, the tem perature at the
surface o f the com pact was not measured, so the temperature difference within the com pact
was not known. Second, the weight o f the specimen could not be m onitored in
conjunction with the lightpipe measurements, so the reaction rate was not known. For this
set o f experiments the insulation surface temperature was m aintained at a constant value by
the com puter program while the internal temperature was monitored to look for sudden
temperature changes and long-term trends. Sudden, short-term increases in the internal
temperature would be an indication of temperature runaway initiated by the reaction
126
exotherm, while long-term changes in the internal temperature would be evidence o f
changes in the microwave heating characteristics. The experiments were stopped every few
hours so that the com pact could be taken out and weighed to determine the percent
conversion. The experiments were continued, usually at increasing temperatures, until
significant nitridation had occurred or until no further nitridation appeared to be possible.
The data from one o f the experiments appear in Figure 5.22. During the initial
stages o f the reaction, the internal temperature is constant with time. However, after about
25% overall conversion the internal temperature increases with time while the insulation
surface temperature remains constant. No significant internal temperature excursions were
observed during the run, which lasted a total o f 30 hours. At the end o f the run the upper
part o f the specimen, including the top o f the hole, appeared to be fully nitrided across the
diameter; this was significant because it could not be accomplished using conventional
heating. This composition profile also indicated that the percent conversion in the area o f
the com pact where the temperature measurements were taken was higher than the overall
value.
The temperature data shown in Figure 5.22 clearly indicate that the radial
temperature gradient in the specimen increased during the run, especially in the later stages.
One reason for this is that the thermal conductivity o f the specimen decreases as it nitrides.
However, this does not explain why there is no increase in the internal temperature o f the
specimen over the first 25-35% conversion, or why the internal temperature increases most
rapidly at the end o f the reaction. The results o f these experiments strongly suggest that the
m icrowave penetration depth is small when the com pact is mostly silicon, but that it
increases with increasing conversion so that volumetric heating and temperature gradients
form later in the run. Because there were no short-term temperature fluctuations despite the
formation o f an inhomogeneous RBSN microstructure, it appears likely that internal
overheating is caused by changes in the microwave heating characteristics o f the specimens
w ith changing composition, rather than by the reaction exotherm. The microwave heating
properties o f nitriding silicon com pacts are discussed in Section 5.4.
0
Internal Temperature (°C)
1400
4
—
8
12
16
20
24
28
i-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------1-----------r-
* ,0 0 * —
1375
°* °°"” °
rCd° ,1P n°
nnCH
1350
1325
1300
Insulation Surface Temp. (°C)
1275 ocna
i
j
1250
880
i
i
■
i
i ------------1------------(------------1------------1------------1------------1------------1 -
QOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
870
79% conversion ^
°OOOoOOOOOOOOOOOOOOOo
\
860
y
52% conversion
23% conversion
OOOOOOOO
850
840
>. 10% conversion
6000
'
830
0
4
8
12
16
20
24
28
Time (hours)
Figure 5.22.
Data from the nitridation of 23 mm diameter compacts using the
lightpipe to monitor the internal temperature while the surface
temperature was held constant. Each data point represents the average
temperature over a 15 minute period.
128
The weight loss o f the microwave specimens during nitriding, along with the
formation o f an outer crust, strongly suggest that silicon is being transported out o f the
com pacts in the vapor phase. There are two vapor-phase species present during nitriding
that could conceivably form in concentrations high enough to cause the observed am ount o f
mass transfer: Si(v) and SiO(g). Silicon vapor is formed directly from solid or liquid
silicon surfaces and is necessary for the formation o f oc-SisN,*. The am ount o f silicon
vapor that forms depends strongly on the temperature; the evaporation rate o f silicon at
nitriding temperatures has been calculated to be more than enough to support the m aximum
observed nitriding rates (M oulson 1979).
SiO(g) can form directly from reactions between solid silicon and oxygen (eq. 2.6)
or from the removal o f the native SiC>2 layer on the silicon particles (eq. 2.8). The role o f
SiO(g) in the nitridation process is discussed in Sections 2.2.1 and 2.2.2. For SiO(g) to
diffuse out o f the specimen at a significant rate during nitriding would require a significant
source o f oxygen other than the native SiC>2 layer, and so the am ount o f w eight loss would
be strongly dependent on the amount of oxygen in the input gas and on the oxygen partial
pressure within the compact.
To determine whether the weight loss was being caused by silicon vapor or by
SiO(g), a series o f microwave nitridation experiments was conducted under conditions that
would give different oxygen levels within the com pact and in the reactant gas. As
discussed in Section 2.2, the presence of hydrogen in the reactant gas lowers the oxygen
partial pressure by forming H 20(v) by reaction 2.10. In order for SiO(g) to cause the
observed am ounts of weight loss, the bulk O 2 and H 2 O concentrations in the input gas
would have to be significantly higher than the high-purity conditions assumed in Section
2.2. This means that when nitriding in pure nitrogen the formation of the oxynitride by
reaction 2.5 would be favored, which would remove the oxygen from the gas phase.
W hen nitriding with added hydrogen, the formation of a -S fN 'a by reaction 2.4 is favored,
and the oxygen would remain in the gas phase where it could be carried out o f the specimen
129
as SiO(g). The O 2 level in the gas cylinders is about 10 ppm, and small leaks in the gas
delivery system could raise this level even higher. However, after the gas passes through
the pretreatm ent of the oxygen getter and the molecular sieve material, the partial pressures
are significantly lower. Therefore, increased weight loss would be expected with the getter
and sieves bypassed if the diffusing species is SiO.
M icrowave nitridation experiments using the standard 15 m m diameter com pacts
w ere conducted using pure nitrogen or 99% N 2 / 1% H 2 as the reactant gas, and with the
oxygen getter and molecular sieves in place or bypassed. The weight gain o f the basket
assem bly and of the specimen alone were measured at 25% conversion, 50% conversion,
and 75% conversion. The am ount of weight loss was defined as the percent conversion
calculated using the weight gain o f the specimen subtracted from the percent conversion
calculated using the weight gain o f the basket assembly. This provides a relative m easure
o f the am ount o f material transported from the com pact into the powder bed and does not
take into account any material that may escape into the exit gas stream. Because no
condensate formation was observed on the quartz tube after any o f these experim ents, the
am ount o f material escaping the insulation basket was assumed to be negligible.
The results of these experiments appear in Table 5.1. The average weight loss for
all the experiments after 50% conversion was 1.51 %, and the average weight loss after
75% conversion was 2.95%. Interestingly, there was no weight loss after 25% conversion
in any o f the 13 experiments. There was very little difference in the weight loss values
between the experiments conducted in pure nitrogen and those conducted using 99% N 2 /
1% H 2 , both with and without the gas pretreatment. The experiments conducted without
the gas pretreatment had slightly less weight loss than the experiments conducted with the
pretreatm ent, which is the opposite of what would be expected if SiO(g) were causing the
w eight loss. The difference is within the bounds o f random error, however, since the
am ount o f weight loss varied by up to 0.7% between runs conducted under the same
conditions. Overall, these results indicate that SiO(g) is not the species diffusing out o f the
130
Table 5.1
Average weight loss values after 50% and 75% conversion using different
processing conditions.
Experimental
conditions
number
o f runs
Avg. weight loss
(50% conversion)
Avg. w eight loss
(75% conversion)
99% N 2 / 1% H 2
getter
4
1.60%
3.12%
99% N 2 / 1% H 2
no getter
3
1.46%
2.85%
pure nitrogen
getter
3
1.70%
3.46%
pure nitrogen
no getter
3
1.25%
2.31%
Total
13
1.51%
2.95%
specim en, which leaves Si(v) as the only likely candidate.
Another way to investigate the weight loss phenomenon is to analyze the
com position o f the crust that forms around the outside of the specimens. If the crust
contains elemental silicon it would indicate that silicon vapor was diffusing out o f the
specim en and condensing into the pow der bed, because the areas of the specimen next to
the crust are fully nitrided when the crust is collected. Figure 5.23 shows an X-ray
diffraction scan taken on a section o f the crust material. A large silicon peak is present,
along with the expected oc-Si3 N 4 and (3-Si3N4 peaks. The fact that the am ount o f weight
loss is relatively independent o f the reactant gas composition and the gas pretreatment,
along with the presence o f elemental silicon in the outer crust, indicates that silicon vapor is
diffusing out o f the microwave-heated specimens while they are nitriding.
The silicon transported out of the nitriding compacts leaves behind less dense areas
131
1400
Counts per second
1200
1000
800
600
400
200
26
28
30
32
34
36
2 theta (degrees)
Figure 5 .2 3 .
X-ray diffraction scan taken on a section o f the outer crust which forms
around the microwave-nitrided specimens. The presence o f a large
silicon peak indicates that the crust is formed by silicon vapor diffusing
out o f the specimens and condensing in the cooler pow der bed.
132
which are white because they are pure RBSN with no residual silicon. These “overheated”
areas are sometimes large and nearly homogeneous, while in other specimens they contain
large silicon melts. Another unusual feature o f many o f the microwave-heated specimens is
the formation of “reaction bands,” which are narrow, alternating layers o f lighter and
darker material within the fully nitrided areas o f the specimen.
The hardness o f the white overheated areas was considerably less than the hardness
o f the fully dense RBSN found in some areas o f the microwave specimens and in the
conventionally heated specimens. For the 15 m m diameter rod-shaped com pacts, the
average hardness o f the normal RBSN was found to be 7.5 G Pa for both the m icrowave
and conventional specimens, while the average hardness o f the overheated areas was only
4.5 G Pa.
Because the hardness o f RBSN depends on the microstructure as well as the
density, this difference in hardness does not conclusively prove that the overheated areas
are less dense than the normal RBSN. In order to measure the bulk densities directly, a
large overheated area and a normal fully nitrided area were cut out o f a microwave
specim en with a sectioning saw. The densities of the two samples were then measured
using the Archemedes method, following the procedure described in Section 4.7. The
density o f the overheated sample was 2.21 g cm '3 and the density o f the normal sample
was 2.45 g cm '3, which is a large difference. Based on a green density o f 64% for the rod­
shaped silicon compacts, the percent conversion can be calculated from these bulk densities
using eq. 4.6 to be 72.5% for the overheated sample and 96.7% for the normal RBSN
sample. However, X-ray diffraction scans on the specimens revealed no elemental silicon
present in either. Therefore, the low density o f the overheated specimen is caused by the
loss o f some o f the original silicon rather than by incomplete conversion.
The reaction bands were present to some degree in most o f the microwave
specimens. In some specimens a regular pattern o f bands appeared, while in others only
one or tw o w ere observed. In general, the rings appeared to form at the boundary between
133
a fully nitrided area and an unreacted area. In order to create specimens with a purposely
sharp transition between fully nitrided and unreacted areas, a series o f experiments was
conducted using longer, 15 m m diameter specimens which were translated through the
microwave cavity as they nitrided. Because the specimens were longer than the “hot zone”
of the resonant microwave heating mode used, unreacted silicon was heated rapidly to
nitriding temperatures as it was introduced into the hot zone. The specimens were lowered
through the hot zone at a constant rate of 2 mm per hour, causing the nitridation reaction to
proceed along the main axis of the rod as a reaction front. The silicon compacts were about
10 cm in length and were surrounded by an insulation configuration sim ilar to that used for
the shorter specimens.
These specimens exhibited a continuous series o f reaction bands which developed
parallel to the com position boundary as it moved along the main axis o f the specimen, as
can be seen in Figure 5.24. The reaction bands were too narrow for the density to be
m easured directly. However, hardness traces taken along the center axis o f these
specimens clearly demonstrate the difference in microstructure between the bands (see
Figure 5.25). The white bands are relatively soft, which suggests that they are overheated
areas where silicon has diffused away leaving behind pure, low density RBSN. The
darker bands are much harder, w hich indicates that they have a higher bulk density. In
fact, the m axim um hardness o f the dark bands is nearly 10 GPa, which is harder than the
RBSN found in fully nitrided conventional specimens. This suggests that silicon vapor
diffused out of the white bands w here it reacted to form RBSN in the dark bands.
One of these specimens was vacuum impregnated with an epoxy material and then
given a very fine polish. It was then viewed in an environmental SEM, an electron
microscope that does not require insulating specimens to be coated with a conducting layer.
The photograph shown in Figure 5.26 was taken at the boundary between a white ring and
a dark ring. There is a large difference in porosity between the two areas, and the transition
from one microstructure to another is very shaip.
15 m m
T
Figure 5.24.
Photograph o f the cross-section of a 15 m m diam eter rod which was
nitrided as it was translated through the microwave cavity. Note the
closely-spaced reaction bands.
Hardness (GPa)
12
Dark bands
10
8
6
W hite bands
4
2
12
13
14
15
16
17
18
19
20
Distance along center axis (mm)
Figure 5.25.
Hardness trace taken along the center axis o f a specimen which was
translated through the microwave cavity as it nitrided.
135
The density variation shown in Figure 5.26 provides additional evidence that the
reaction bands and the overheated areas are both created by silicon vapor diffusing within
and out o f the specimen, indicating that large axial temperature gradients m ust exist within
the com pacts. The results presented in this section show that these temperature gradients
are caused by changes in the microwave heating characteristics o f the specimens as they
nitride rather than by brief, localized temperature excursions triggered by the reaction
exotherm. The m icrowave heating characteristics of the RBSN specimens are discussed in
the next section.
136
$sgmin4,
20k V
0QE
.
No r t h i » i « t # r n
Figure 5 .2 6 .
M3O0
Uni v t n l tw
SEM photograph taken at the boundary between a dark reaction band
(top) and a w hite reaction band (bottom). The grey areas are RBSN and
the black areas are pores.
137
5.4
Microwave heating characteristics of silicon/silicon nitride mixtures
The experimental results presented in the previous sections indicate that microwave
heating is creating non-uniform temperature distributions within the silicon compacts,
causing them to nitride unevenly and creating poor RBSN microstructures. The purpose o f
this section is to develop an understanding o f the microwave heating characteristics o f the
nitriding specimens as a function o f com position, and to explore ways to im prove the
m icrostructures o f the microwave-heated specimens.
5.4.1 M icrowave heating m odel fo r nitriding compacts
Success in m odeling the microwave heating characteristics of nitriding silicon
com pacts can be judged by how well the following observations are explained:
-
The middle o f the rod-shaped silicon com pact becomes fully nitrided
while the ends are unreacted, and there is a relatively sharp boundary
between the fully reacted and unreacted regions o f the specimen.
-
No inside-out reaction profiles were observed in the rods, indicating that
volumetric heating was minimal because the microwave penetration depth
was small.
-
Silicon was transported within the specimen as it nitrided, creating bands
o f high-density and low-density RBSN near the com position boundary.
In general, the incident microwave power can be reflected back from the surface of
the specimen, absorbed within the specimen, or transmitted through the specimen. W ithin
the hot zone o f a resonant heating mode such as the TM 0 1 2 mode, the electric field
surrounding the specim en can be considered uniform. Therefore, the regions o f the
specimen that absorb microwave energy most efficiently due to their com position will be
hottest.
138
The am ount o f pow er that is reflected from the surface o f the specimen is given by
P ref = P 2 p inc
.
5 .2
w here Pjnc is the incident pow er and p is a reflection coefficient which depends on the
com position o f the specimen and the geometry o f its surface. For a planar, hom ogeneous
surface, the reflection coefficient takes the explicit form
w here e* is the RM S value o f the complex dielectric constant. The am ount o f pow er
transm itted through the specimen can be written as
P.rans = ( P i „ c - P , e ( K 2ad
.
5.4
where a is the attenuation coefficient o f the material and d is a characteristic length
representing the thickness o f the specimen. Eqs. 5.2 and 5.4 can then be com bined to find
the pow er absorbed in the specimen:
P,bs = Pine - Pref “ P,n,ns = P inc ( l " P2 )(' “ e "2“ “ )
•
5 .5
It should be noted that eq. 5.5 is not an exact solution for the pow er absorbed by a rod­
shaped specim en in a tunable microwave cavity. Such a solution would require solving
M axw ell's equations to find the field distribution everyw here within the rod. Also, eq. 5.3
represents the reflection coefficient for a flat surface rather than for a cylinder. W atters
(1989) used numerical methods to approximate the heating characteristics o f a
139
homogeneous, infinite cylinder and concluded that analysis using a planar slab geometry
was sufficient to predict heating effects in a cylinder. For the purpose o f analyzing the
heating characteristics o f a rod as a function o f composition, only relative differences in the
pow er absorption need to be considered, and for this the use o f eqs. 5.3 and 5.5 is
adequate.
The microwave heating characteristics o f a silicon/silicon nitride mixture will
depend strongly on the distribution o f the phases, particularly o f the conducting silicon
phase. As discussed in Section 3.5, one reasonable approach is to consider a partially
nitrided silicon compact to be a conductor-loaded dielectric material consisting o f
conducting spheres o f silicon surrounded by a continuous insulating phase consisting o f
silicon nitride and porosity. In this case, the relative dielectric constant and the dielectric
loss factor o f the mixture, £'mjx and e " ix, are given by eqs. 3.16 and 3.17, and the
attenuation constant, a mjx, is given by eq. 3.21. The reflection coefficient o f a conductorloaded dielectric material can be calculated by replacing the RMS value o f the complex
dielectric constant with e'mix in eq. 5.3 (Neelakanta 1994).
To calculate the reflection coefficient and attenuation constant as a function o f the
silicon volume fraction, the relative dielectric constant of silicon nitride and the electrical
conductivity o f silicon at nitriding temperatures must be known. The conductivity o f
silicon nitride is much less than the conductivity of silicon and can be ignored. The relative
dielectric constant o f RBSN is a very weak function o f temperature, as shown in Figure
3.6. At 1350-1450°C the value o f e'r for RBSN is 5.1.
The conductivity o f silicon near room temperature is a strong function o f impurities
which supply extrinsic charge carriers, but at higher temperatures the conductivity is
dominated by intrinsic charge carriers and becomes independent o f the impurity level. For
typical commercial silicon powders such as the ones used in this work, the transition from
extrinsic to intrinsic behavior occurs between 400°C and 70Q°C (Touloukian 1967). The
intrinsic conductivity of silicon has been measured at temperatures up to 1650°C by Law
140
1.4e+5
1.2e+5
u
©
-10
G
©
1.0e+5
v
8.0e+4
SJ
©
]o>
*3
©
6.0e+4
4.0e+4
iS
2.0e+4
0.0e+0
0.0
0.1
0.2
0.3
0 .4
0.5
0.6
0.7
V o lu m e f r a c tio n silico n
F ig u r e
5 .2 7 .
Dielectric constant and loss factor as a function of silicon volume
fraction, using the equations for a conductor-loaded dielectric.
and Francois (1956). At typical nitriding temperatures of 1300-1450°C the conductivity o f
silicon varies from 2.5 x 104 S/m to 3.3 x 104 S/m.
Figure 5.27 shows the relative dielectric constant and the dielectric loss factor at
1350°C as a function of the silicon volume fraction, calculated using eqs. 3.16 and 3.17.
Both increase by about a factor o f 2 as the silicon volume fraction varies from zero to 0.7.
Figure 5.28 shows the normalized absorbed pow er as a function of percent conversion
calculated using eq. 5.5, where 0% conversion corresponds to a silicon volum e fraction of
0.64 and 100% conversion corresponds to no silicon. The m axim um pow er absorption
occurs at 72% conversion. At higher conversions the absorbed pow er drops o ff quickly as
more pow er is transmitted through the specimen. Below 72% conversion the absorbed
pow er increases gradually with increasing conversion as less power is reflected from the
surface o f the specimen. The formation of temperature gradients within the specimen
141
depends prim arily on the microwave penetration depth. W hen the penetration depth is on
the order o f the specimen size or larger the specimen will be heated volumetrically and
significant temperature gradients will form, but when the penetration depth is small then the
specim en will be heated from the surface and will be isothermal in the interior. Figure 5.29
shows the penetration depth, l/2 a , as a function o f percent conversion, calculated using
eq. 3.21. The penetration depth is less than 1 mm at low conversions, so true volum etric
heating would not be expected to develop until some nitridation occurs. At conversions
greater than 80% the penetration depth is larger than the specimen size and significant
temperature gradients would be expected.
If a nitriding silicon com pact behaved like a conductor-loaded dielectric material,
then radial temperature gradients would form, but only after significant nitridation had
taken place. This is in good agreement with the experimental observation that no inside-out
reaction occurs in partially nitrided compacts, but that full nitridation across the diam eter is
easier to achieve when using microwave heating as com pared to conventional heating.
However, the conductor-loaded dielectric theory also predicts that the pow er absorbed will
increase very gradually with conversion until the specimen is about 75% nitrided, at which
point it would decrease rapidly. This would tend to promote sm ooth axial com position and
tem perature gradients rather than the observed sharp com position boundaries. Also, the
plot o f absorbed pow er vs. com position (Fig. 5.28) does not suggest any reason why a
large am ount o f power would be deposited near a com position boundary, as appears likely
from the formation o f the reaction bands.
As discussed in Section 3.5, the conductor-loaded dielectric model assumes that the
conducting particles are isolated from each other so that no displacement currents can
develop in response to the microwave field. This causes the material to behave like a
hom ogeneous lossy dielectric material rather than a good electrical conductor. If the
conducting particles are in contact with each other, then charge transport within the
specimen will reflect and attenuate the microwaves as if the specim en were a homogeneous
142
0.8
o
a
S
0 .6
0.2
0.0
0
20
40
60
80
100
Percent conversion
Figure 5.28.
Normalized pow er absorption o f a silicon/silicon nitride m ixture as a
function o f com position, using the equations for a conductor-loaded
dielectric material.
100
E
a
-o
e
o
a>
C
a>
CU
.01
0
20
40
60
80
100
Percent conversion
Figure 5.29.
M icrowave penetration depth o f a silicon/silicon nitride mixture as a
function o f com position, using the equations for a conductor-loaded
dielectric material.
143
conductor. The above treatment o f a nitriding silicon com pact as a conductor-loaded
dielectric material is based on the assumption that the silicon particles become separated by
a layer o f insulating RBSN during the initial stages o f the reaction.
This assumption can be tested directly by measuring the conductivity o f a partially
nitrided com pact at room temperature using a laboratory resistance meter. If the silicon
particles are separated by a layer of RBSN, then the conductivity would be too low to
measure, but if the silicon particles are connected into a continuous phase then the
conductivity should be high enough to detect. These measurements gave the rather
surprising result that the silicon particles are connected, and that they remain connected well
into the nitridation reaction. The conductivity o f the green specimens was just barely high
enough to be detected, as would be expected from particle-particle contacts in a pressed
compact. However, the conductivity o f the specimens increased as they nitrided, reaching
a maxim um at 25% conversion. The conductivity then decreased with increasing
conversion, dropping below the detection limit at between 60% and 70% conversion,
presumably as the silicon phase became depercolated. This trend was the same for the
microwave and conventional specimens. An interesting note is that the transition from
conducting material to non-conducting material occurred at the boundaries between fully
reacted RBSN and less reacted material in the microwave specimens.
The above result is a clear indication that the silicon compacts sinter during initial
nitridation, forming necks between the particles which remain until the later stages o f the
reaction. Because the external dimensions o f the specimen remain unchanged, this
sintering is a coarsening effect whereby material is transported either by surface diffusion
or by a vapor-phase mechanism to the contact areas between the particles while the particle
centers remain a fixed distance apart.
To model the microwave heating of a compact with a connected silicon phase, eqs.
3.11 and 5.3, which give the attenuation constant and reflection coefficient of a
homogeneous material, should be used. The electrical conductivity o f a mixture containing
144
tw o continuous phases can be approximated by the rule of mixtures as (Landauer 1952)
a = V ,o , + V 2g 2
,
5.6
where Vi and V 2 are the volume fractions o f the two phases. The conductivity o f silicon
nitride is negligible, so the conductivity o f the mixture can be estimated as being the
conductivity o f silicon multiplied by the silicon volume fraction.
Figure 5.30 shows the norm alized absorbed power as a function o f com position
calculated using eq. 5.5 for a specimen with a connected silicon phase. The absorbed
pow er is less than 3% for m ost of the reaction and does not begin to increase rapidly until
the specimen is fully reacted. As expected, the penetration depth in this case is also very
small - below 300 pm for m ost o f the reaction (see Fig. 5.31).
Clearly, the silicon phase cannot remain connected until the end o f the reaction. A
reasonably accurate empirical model o f the microwave heating char acteristics can be
obtained by allowing the nitriding compact to behave like a homogeneous conductor at low
conversion levels and like a conductor-loaded dielectric at high conversion levels. At
intermediate conversion levels there is a large change in the heating characteristics as the
silicon particles lose contact with each other. Based on the room-temperature conductivity
measurements discussed above, the transition from conductor to lossy dielectric appeared
to take place between 50% and 70% conversion. In this transition region the reflection
coefficient and attenuation constant are found from empirical curve fits connecting the lowcon version and high-conversion regions.
Figures 5.32 and 5.33 show the absorbed power and penetration depth as functions
o f com position using this com bined model. There is now a significant increase in the
pow er absorption when the specimen composition reaches the transition region. This
means that small differences in the specimen composition will become greatly magnified
when any part o f the specimen reaches 50% conversion, because that area o f the specimen
145
0.10
0.08
w
C
K
0.06
VI
|
0.04
0.02
0.00
0
20
40
60
80
100
Percent conversion
Figure 5.30.
Normalized pow er absorption o f a silicon/silicon nitride mixture as a
function o f com position, using the equations for a hom ogeneous
conducting material.
1000
VI
G
O
u
u
E
800
600 -
Q*
<u
T3
s
400
u
V
c
a>
CW
200
o
0
20
40
60
80
100
Percent conversion
Figure 5.31.
M icrowave penetration depth o f a silicon/silicon nitride mixture as a
function o f com position, using the equations for a homogeneous
conducting material.
146
— 1--------- "—
1.0
"■r. -
... •—
— r .... .......■--------- 1--------- •---------
a>
I 0.8
-a
1 0.6
lossy dielectric
CA
J2
a
\
\
•
f
•
’S 0.4
oS
\
.•
model
conductor
•
z
-------- 1-------- ■
0.0
0
20
40
'
•
,*S,SS,^
0.2 -
\
•
60
1
- i --------
80
*-
____>
■
100
Percent conversion
Figure 5 .3 2 .
Normalized power absorption o f a silicon/silicon nitride mixture as a
function o f com position, using the com bined model.
0
20
40
60
80
100
Percent conversion
Figure 5 .3 3 .
M icrowave penetration depth o f a silicon/silicon nitride mixture as a
function o f com position, using the com bined model.
147
will absorb significantly more microwave pow er than less reacted areas, and this explains
the tendency for the microwave specimens to separate into fully reacted and unreacted areas
separated by a sharp com position gradient. The microwave pow er absorption drops off
rapidly after about 85% conversion as most of the power is transm itted through the
specimen, which means that the areas near the composition boundaiy that are 50% to 85%
nitrided will absorb most o f the microwave power and will therefore be the hottest areas of
the specimen. This provides a plausible mechanism for the formation o f the reaction bands
via silicon vapor transport, and this will be discussed in detail in Section 5.6.
The sudden increase in absorbed power with increasing conversion is accompanied
by a sim ilar increase in the microwave penetration depth, as shown in Figure 5.33. The
penetration depth is larger than the specimen size after about 70% conversion, w hich means
that significant radial temperature gradients will form due to volumetric heating. The
combination of volumetric heating and efficient power absoiption in the partially nitrided
reaction zones near the composition boundaries should create internal temperatures that are
significantly higher than standard nitriding temperatures. To predict the com position and
temperature gradients in the microwave specimens requires a com puter model, which is the
subject o f Section 5.5.
5.4.2 Nitridation o f silicon / silicon nitride pow der mixtures
To test the microwave heating theory developed in the previous section, some way
o f keeping the silicon particles from forming necks was needed to make the specimens
behave like a conductor-loaded dielectric material. According to the results shown in
Figures 5.28 and 5.29, this should prevent large axial com position gradients from forming
and should allow radial temperature gradients and an inside-out com position profile to
develop. This was accomplished by mixing silicon pow der with silicon nitride pow der at
various volume fractions to separate the silicon particles from each other. Three mixtures
148
w ere used, as shown in Table 5.2. The procedure for preparing the 15 m m diam eter
m ixed-pow der com pacts is discussed in Section 4.2. These com pacts were nitrided in the
m icrowave cavity using the same procedure that was used for the pure silicon compacts.
M ixture 1 (75 vol% silicon) showed little improvement over the pure silicon
com pacts. In a 70% nitrided com pact, there were sharp axial com position gradients as well
as some microstructural inhomogeneities in the fully reacted middle. However, mixture 2
(50 vol% silicon ) developed a dramatically different composition profile, as shown in
Figure 5.34(a) for a specimen reacted to 60% conversion. The interior o f the com pact is a
light tan color, indicating full conversion to RBSN, while the outer edges are dark. This
com position profile indicates that there were temperature gradients in both the radial and
axial directions, but in this case there are no sharp boundaries between fully reacted and
unreacted material. There is a dark band of material around the oval-shaped center area,
w hich suggests that some silicon transport took place. Figure 5.34(b) shows the
com position profile o f a com pact made from mixture 3 (25 vol% silicon) which was also
nitrided to 60% conversion. This specimen looks very similar to the mixture 2 specimen,
but no sharp gradients or reaction bands are present.
Because the strength o f an RBSN specimen depends on the grow th o f an
interlocking matte o f silicon nitride grains between adjacent silicon particles, the specimens
made from the pow der mixtures would not be expected to have good mechanical
Table 5.2.
Composition o f the silicon/silicon nitride pow der mixtures, by volum e and
by weight.
vol% Si
vol% Si3 N 4
wt% Si
wt% Si 3 N 4
mixture 1
75
25
68.7
31.3
mixture 2
50
50
42.3
57.7
mixture 3
25
75
19.6
80.4
149
15 mm
F ig u r e
5 .3 4 .
Cross sections o f mixed-powder specimens nitrided to 60% conversion
using m icrowave heating: a) mixture 2 (50 vol% silicon), b) mixture 3
(25 vol% silicon).
150
properties. For this reason, hardness profiles taken across the interiors o f partially nitrided
specim ens were inconclusive in verifying the apparent inside-out reaction profiles shown in
Figure 5.34. Instead, the residual silicon content o f the specim ens was m easured using
quantitative X-ray diffraction measurements, as discussed in Section 4.7. Figure 5.35
shows X-ray diffraction scans taken on the 60% nitrided specim en shown in Fig. 5.34(a),
along with the silicon weight fraction and percent conversion as calculated using eqs. 4.9
and 4.11. The scan taken o f the interior o f the specimen has no visible silicon peak and has
a calculated conversion value o f more than 98%. In contrast, the scan taken o f the outside
o f the specimen near the middle has a large silicon peak and has a calculated conversion
value o f 77.3%. The 20 values from 31° to 33.25° were not scanned to avoid a highintensity peak from the lead mask.
The X-ray diffraction results clearly demonstrate the development o f radial insideout reaction profiles in the specimens made from powder mixtures with a silicon volume
fraction o f 0.5 or lower. This does not necessarily mean that a pure silicon com pact with
no charge transport between adjacent particles would nitride in the same way. There were
two m ajor differences between the mixed-powder specimens and the pure silicon compacts.
First, the silicon particles did not sinter together because they were physically separated
from each other by the silicon nitride particles. This was verified by room-temperature
conductivity measurements; the specimens with 50 vol% and 75 vol% Si3 N 4 pow der did
not have a measurable room-temperature conductivity at any point in the nitridation
reaction, while the 25 vol% Si 3 N 4 powder specimens had conductivities sim ilar to the pure
silicon compacts.
Second, the initial silicon volume fraction was much lower than that o f a pure
silicon compact. This means that throughout the nitridation reaction the microwave
penetration depth, as calculated using the conductor-loaded dielectric model, would be
higher for the mixed-powder specimens than for a pure silicon com pact with the same
conversion value. Also, the reduction in porosity and poie size due to the nitridation
151
1200
Center area: 98.7% conversion
Counts per second
1000
800
600
400
200
26
28
30
32
34
36
34
36
2 theta (degrees)
Counts per second
800
Outer area: 11.3% conversion
600
400
200
26
28
30
32
2 theta (degrees)
Figure 5.35.
X-ray scans o f a mixed-powder specimen nitrided to
60% conversion
using microwaves. The top scan was taken with the specim en masked to
scan only the center area, and has no visible silicon peak. T he bottom
scan was taken with the specimen masked to scan only the outside o f the
middle part o f the specimen, and has a large silicon peak.
152
reaction was low er with the m ixed-powder specimens, m aking bulk nitrogen diffusion less
difficult and thus m aking the interior o f the specimens easier to nitride.
In general, the results o f the powder mixing experiments indicate that if neck
formation in pure silicon compacts could be prevented, the microwave specimens would
nitride more uniformly and beneficial temperature gradients would form in the later stages
o f the reaction.
5.4.3 Possible ways to avoid silicon neck form ation
As discussed in Sections 5.4.1 and 5.4.2, the m icrowave heating characteristics of
nitriding silicon com pacts are negatively affected by the formation o f necks between
adjacent silicon particles during initial nitridation. These necks prevent the insulating
silicon nitride product from separating the individual silicon particles, and thus charge
transport can take place within the specimen, which attenuates and reflects the incident
m icrow ave power.
The solid-state sintering o f silicon has been studied extensively because silicon is
considered a model material for other covalently bonded non-oxide ceramics (Coblenz
1990). These studies have typically had the goal o f sintering com pacts of fine silicon
pow der to full density (e.g. M oller and W elsch 1985). Solid-state matter transport can take
place by several different mechanisms. Grain boundary diffusion and lattice diffusion
cause densification, while surface diffusion and evaporation-condensation cause coarsening
which inhibits densification by reducing the surface area (Greskovich and Rosolowski
1976). As a covalent material, silicon is difficult to densify, and this is attributed to the fact
that the coarsening mechanisms tend to dominate the sintering behavior. Originally, the
dom inant coarsening mechanism was thought to be evaporation-condensation (Greskovich
and Rosolowski 1976). However, Coblenz (1990) has recently concluded that surface
diffusion is the dominant coarsening mechanism at all particle sizes o f interest, based on
153
surface diffusivity measurements done by Robertson (1981).
To fully densify silicon compacts requires that coarsening effects be minimized.
Coblenz (1990) showed that oxygen acted as a sintering aid because the thin oxide layers
that form on silicon pow der inhibit silicon surface diffusion and thus allow densification
via grain boundary and lattice diffusion to dominate the sintering. G reskovich (1981)
found that small additions o f boron had a similar effect.
It is unlikely, however, that inhibiting surface diffusion would prevent coarsening
during the initial nitridation o f silicon compacts, because the nucleation and growth o f
silicon nitride on the silicon surface during the initial reaction period also depends on
surface diffusion. This means that lowering the silicon surface diffusivity would low er the
initial nitridation rate, and therefore would not reduce the am ount o f coarsening that could
take place before a layer o f RBSN covered the exposed silicon surface. Also, since the
oxide layer that surrounds the silicon particles must be removed before nitridation can
begin, oxygen would not be expected to reduce the am ount o f coarsening in RBSN
specim ens, and, in fact, the experiments done in this w ork all used silicon pow der with a
native oxide layer in place.
In order to prevent coarsening, it seems likely that the silicon particles would need
to have an insulating coating that would prevent them from being in contact with each
other. In addition, this coating would have to allow nitrogen and silicon diffusion to take
place so as not to inhibit the nitridation reaction itself. The most obvious m ethod would be
to coat the individual silicon particles with a thin layer of RBSN before the pow der is
pressed into a compact. This would present difficulties, however, because o f the tendency
for the silicon pow der to stick together as it nitrides.
To nitride loose silicon pow der without forming a single agglom erated mass would
require a fluidized bed, which uses a gas stream to separate the individual particles from
each other (Kunii and Levenspiel 1991). The use of a fluidized pow der bed for the
preparation o f silicon nitride powder from silicon powder has recently been investigated by
154
Jovanovic et al. (1994). They found that a fluidized bed provided good heat transfer,
temperature control, and reaction rate control, and that the process could potentially be
scaled up to a continuous system. However, very fine particles could not be utilized
because o f their tendency to agglomerate into larger clusters which then caused the bed to
collapse. Instead, they fluidized large (400 pm ) porous particles consisting o f partially
sintered silicon pow der with an average particle size o f 2 pm , which were ground into a
fine silicon nitride pow der after nitridation in the fluidized bed.
The above method would not eliminate the problem o f coarsening during RBSN
processing, because the large porous particles are already interconnected by large necks.
Partially nitriding these large particles and then grinding them down into a fine power
w ould cause the silicon nitride layer to break up leaving the silicon surface exposed. Liu
and Kimura (1993) found that fine silicon particles could be fluidized at room temperature
by mixing them with large, easy-to-fluidize silicon or silicon nitride particles. These
authors are currently attempting to use this approach to form fine silicon nitride pow der
directly from a fluidized bed (K im ura 1994). If successful, this technique could potentially
be used to coat silicon pow der w ith a thin, uniform layer o f RBSN.
155
5.5
Numerical model of microwave RBSN processing
A nitriding silicon compact heated by microwaves is a complex system, and the
temperature and composition of the specimen cannot be solved for exactly. Instead, a
finite-difference model can be used to simulate the process. W ith this approach, the
specim en is represented by a simple geometry which is then divided into a num ber o f small
volum e elements referred to as control volumes. W ithin each control volum e the
temperature, composition, and nitrogen partial pressure are considered to be uniform ,
which then allows the equations governing the microwave power absorption, reaction
kinetics, temperature gradients, and nitrogen diffusion to be solved exactly. Using a
com puter program, the heat flow into the individual control volumes and out o f the
specim en is then balanced using global boundary conditions. As long as the size o f the
individual control volumes is sufficiently small, this provides an accurate model o f the
process.
The computer model used here was designed to simulate the microwave heating o f a
cylindrical rod. It was first used by Skamser and Johnson (1994) to find the tem perature
distribution inside an alumina fiber preform, and it was then m odified to find the
temperature, nitrogen partial pressure, and composition within a nitriding silicon com pact
surrounded by a thin layer of insulation. Symmetry allows the values for the entire
specim en to be calculated based on one 2D quadrant, as shown in Figure 5.36.
5.5.1
M aterial parameters and control equations used in the model
The equation governing heat transfer within the specimen is
i a /
dT'
/
dTN
dT
rK th
K th
+ Qabs =
r dr V
dz,
pc aT
dr , ) + dz V
'
156
Insulation
Specimen
2D area used by the
finite difference model
~ X \W
D = 1.4 cm
L = 4 cm
Figure 5.36.
Diagram of the configuration used to represent the specim en and
insulation for the finite-difference model. Symmetry allows the entire
specim en to be represented by one 2D quadrant, as shown.
where r is the radial coordinate, z is the axial coordinate, Kth is the thermal conductivity (W
n r 1 K-1), Q abs is the absorbed pow er density (W n r 3), p is the density (g n r 3), and c is the
heat capacity (J K_1 g '1)- The temperature in each control volume elem ent and the heat
transfer in the radial and axial directions are calculated using the tri-diagonal matrix
algorithm (Patankar 1980). This algorithm operates by making repeated small adjustments
to the temperature values until the heat transfer within each control volume according to eq.
5.7 is balanced. The specimen is in steady-state thermal equilibrium when the total power
absorbed is equal to the total power dissipated at the outer surface.
The thermal conductivity varies within the specimen depending on the composition,
decreasing as the am ount o f RBSN increases. The thermal conductivity o f the solid phase
is much higher than that of the gas phase, so the thermal conductivity o f the com pact can be
estimated as being the thermal conductivity of the solid material multiplied by the volume
fraction o f solids (Sheldon 1989). As a first approximation, the thermal conductivity o f the
157
solid phase can be represented by a weighted average o f the values for pure silicon and
silicon nitride, which results in the following empirical relation:
K th = (1 - e)[6.6X + 22(1 - X)]
(W n r ' K ' 1) ,
5.8
w here e is the porosity, X is the fractional conversion, and 6.6 and 22 are the therm al
conductivities o f silicon nitride and silicon at 1350°C, respectively. The thermal
conductivity is also a function of temperature, but because the values are relatively constant
over the temperature range of interest this was ignored.
The heat generated within a specimen by microwave heating was discussed in
Section 5.4. The pow er absorbed at a distance r from the surface can be written as
P m w M = P i „ c ( l - p 2 ) ( l - e - 2“ r)
5.9
w here P jnc is the incident m icrowave power at the surface o f the specimen, p is the
reflection coefficient, and a is the attenuation constant. An empirical model for the
m icrowave heating characteristics o f a nitriding compact was derived in Section 5.4.1. At
low conversions the specimen behaves like a homogeneous conducting material, and much
o f the incident pow er is reflected. At high conversions the specimen behaves like a
conductor-loaded dielectric material and the microwaves are transmitted into the specimen
causing volumetric heating. The pow er absorption and penetration depth as functions of
com position using this model are illustrated in Figures 5.32 and 5.33.
Heat is also generated within the specimen by the reaction exotherm. The heat
released within a control volume can be written as
P ex
5.10
158
where AH is the reaction exotherm (723 kJ m o b 1)* M n is the m olecular weight o f nitrogen,
V is the volume o f the control volume, p is the green density o f the silicon com pact, and x
is the reaction rate in fraction converted per second.
The partial pressure o f nitrogen will be higher near the surface o f the specimen than
in the interior, because the nitrogen that is consumed by the nitridation reaction can only be
replaced by bulk diffusion through the porosity o f the compact. As discussed in Section
2.4.2, the mean free path of gaseous species at 1 atm pressure and at nitriding tem peratures
is larger than the pore size, so the dominant diffusion mechanism in RBSN specim ens is
Knudsen diffusion. The concentration of nitrogen within the specimen is governed by the
following m olar conservation equation (written in cylindrical coordinates):
5( % t )
at
a
r ar
i
rD
a D 3( % t ) + B
3( % t ) + —
K ar
dz
K az
w here P is the nitrogen partial pressure (Pa), R is the gas constant, D « is the Knudsen
diffusion coefficient, and B is the consumption o f nitrogen by the reaction (mol s_1). Eq.
5.11 must be solved within each control volume. Under steady-state conditions the left
hand side is zero, so the consumption of nitrogen within the control volume is balanced by
the net diffusion o f nitrogen into it from neighboring control volumes. This equation has
the same form as the equation governing heat transfer within the specim en (eq. 5.7), so the
program calculates the nitrogen partial pressure distribution within the specimen using the
same algorithm that finds the temperature distribution.
The consumption o f nitrogen within a control volume can be written as
B = ^ -inc:V
Mn
(mol s_l)
,
5.12
where x is the reaction rate in fraction converted per second, V is the volume o f the control
159
volum e (cm 3), and pjnc is the total density of nitrogen added to the silicon com pact as it
nitrides to form RBSN. For a green density o f 64% , the bulk density o f the specim en
increases from 1.49 g cm -3 to 2.48 g cm '3, w hich gives
p j nc
= 0.99 g cm -3.
T he effective Knudsen diffusion coefficient was derived by M ason et al. (1967) as
D* - ! ( f r )
K° <m2s',) ■
w here M is the m olecular weight o f the diffusing species (28 g m ol-1 for N 2 ) and Ko is the
perm eability o f the porous medium.
The permeability is a strong function o f the total porosity and o f the pore size
distribution, and is rather difficult to estimate. Atkinson et al. (1973) measured the
permeability o f RBSN specimens made from silicon powder with an average particle size
o f 20 p m and found that Ko decreased exponentially with increasing conversion from 5 x
10-7 m for the green compacts to 1.2 x 1O'9 m for fully nitrided material. The volume
fraction porosity decreased from 0.36 initially to 0.22 in the fully nitrided material, while
the average pore size decreased by two orders o f magnitude.
Abbasi and Evans (1983) derived the following empirical formula for the
permeability by simulating diffusion in porous solids using calculated trajectories o f a large
num ber o f gas molecules:
^ 2 - = 0.0093 + 0 . 1 6 - 0 .0 1 8 1 d
d
,
5.14
w here e is the volum e fraction porosity, d is the average pore size, and o is the standard
deviation o f the pore size. Eq. 5.14 can be com bined with the experimental permeability
m easurem ents o f Atkinson et al. (1973) to find values appropriate for the silicon com pacts
used for these experiments, which had the same total porosity but had a starting particle
160
size o f 2 |im . By assuming that the starting pore size is half the average particle size, and
that it decreases by two orders o f magnitude during the reaction, the permeability o f the
RBSN specim ens used in this w ork can be estim ated as being 4.5 x lO 8 m for the green
com pact and to decrease exponentially with increasing conversion to 2.7 x 10'10 m for pure
RBSN.
As discussed in Chapter 2, the reaction rate increases with temperature and
decreases with increasing conversion, and the a -S i 3 N 4 and |3-Si3N4 phases form by
separate and parallel reaction paths. The reaction rate is also approximately proportional to
the nitrogen partial pressure, as was first noted by Atkinson et al. (1976) and was also
observed experimentally in Section 5.2. Rossetti and Denkewicz (1989) provided a kinetic
analysis o f the nitridation reaction which was discussed in Section 2.4.1, and this analysis
was used to model the reaction rate. The conversion rates to the a - and (3-phases can be
written as
( # / d t ) a = 3 k a ( l -<!>„)
5.15
5.16
w here (j)a and ())p are the norm alized conversions to a -S i 3 N 4 and p-Si 3 N 4 and ka and kp are
the rate constants (conversion/time) at a given temperature. The rate constants take the
forms
k a = C PN exp — —
“
N2
RT )
5.17
5.18
where Ea and Ep are the activation energies for the formation o f the individual phases, PN^
161
is the nitrogen partial pressure (atm), and C is a constant which depends on the particle size
and other processing conditions. Rossetti and Denkewicz (1989) estimated the activation
energies to be 498 kJ m o b 1 for a -S i 3 N 4 and 523 kJ m o b 1 for (3-Si3N4, and these values
are consistent with published estimates of the global activation energy for the silicon to
silicon nitride reaction (Hiittinger 1969, 1970). The pre-exponential constant, C, can be
estimated by measuring the maximum initial nitridation rate at a given temperature and at 1
atm nitrogen. For the silicon pow der used for the nitridation experiments presented in this
work, a pre-exponential constant o f 4 x 1012 s_l was calculated.
Heat is lost from the outer surface of the insulation which surrounds the specimen
according to eq. 3.23, which can be rewritten as
Q s„,r = * ( f o f - T S ) + 2.09(Tsurr- T o )125
( Wr a - 2 ) ,
5.19
where s is the Stephan-Boltzm ann constant, e is the emissivity, T surt- is the insulation
surface temperature (K), and To is the ambient temperature (K). The first term represents
radiative heat loss and the second term is an empirical relation describing convective heat
loss (Carslaw and Jeager 1989). The total heat loss from the surface o f the specimen
according to eq. 5.19 must be equal to the total absorbed power calculated from eqs. 5.9
and 5.10 for the specimen to be in thermal equilibrium.
5.5.2
Computational procedure
The finite-difference model was run on a desktop com puter using a specimen size
of 4 cm long by 1.4 cm in diam eter and an insulation thickness o f 0.3 cm on the sides and
0.5 cm on the ends. Several runs were conducted using different numbers o f control
volumes, and a 50 x 50 matrix corresponding to 2500 control volumes was found to give
accurate results while allowing the runs to be completed in a reasonable amount o f time (1-
162
2 days).
The program operated as follows. First, a global conversion rate (typically 3% per
hour), a time increment (usually 1 min), and an initial pow er level were chosen. The
program then calculated the equilibrium temperature profile in the compact. The reaction
rate in each control volume was then calculated based on its temperature and com position,
and on the nitrogen pressure calculated from the previous iteration. The com position was
then adjusted based on the fixed time interval and the appropriate reaction rate. The
program then calculated the new equilibrium nitrogen pressure distribution in the specimen,
based on the permeability and nitrogen consumption in each element.
The total conversion rate for the specimen during the previous time increment was
then calculated and com pared with the programmed rate. If the rate was too high, the
incident pow er level was lowered, and vice versa. The temperature profile was then
recalculated based on the new incident power level and composition values. This
procedure closely approximated the experimental microwave processing o f rod-shaped
silicon com pacts at a fixed reaction rate. The composition, temperature, and nitrogen
pressure in the elements were saved in data files during the run. A flow chart illustrating
the procedure used by the com puter program appears in Figure 5.37.
5.5.3 Simulation o f the nitridation o f a standard silicon compact
The temperature and composition profiles along the center axis o f the rod from the
m iddle to the end are shown in Figures 5.38 - 5.41, for a run with the conversion rate set at
3% per hour. The solid lines represent the centerline o f the specim en, and the dotted lines
represent the surface. The axial nitrogen partial pressure profile in the specimen is shown
in Figure 5.42. For this figure, the dotted line represents the pressure at a distance o f 1
m m from the surface o f the specimen.
At 10% conversion, the rod is slightly hotter in the middle because o f heat loss
163
Adjust incident powder based
on desired reaction rate
Calculate absorbed
M W power
Calculate reaction
exotherm
Calculate temperature
profile
NO
Is the heat flow
balanced?
Increment the time forward
Y ES
(Increase the conversion to
RBSN in the elements)
Calculate reaction
rates
Calculate nitrogen
consumption
NO
Is the N 2 conservation
equation satisfied?
YES
Figure 5 .3 7 .
Put data into
a file
Computational procedure used for the com puter simulations.
164
from the end (Fig. 5.38(a)), and this causes the middle to be slightly more reacted (Fig.
5.39(a)). Overall, the temperature and com position distributions are quite uniform. W hen
the percent conversion is below 50% , there is a gradual increase in the m icrowave pow er
absorption with increasing com position, and so the middle o f the rod begins to heat more
efficiently than the ends.
After 10 hours, when the specimen is 30% converted overall, the middle o f the rod
has becom e hotter while the end has remained about the same (Fig. 5.38(b)). A significant
axial com position gradient has formed at this time (Fig. 5.39(b)), with the middle
approaching 40% conversion while the ends remain at about 20% conversion. A t this
point, there is still very little difference between the temperature and com position values in
the interior o f the specim en and those at the surface, because the microwave penetration
depth is very small and the nitrogen pressure is fairly uniform. The nitrogen partial
pressure in the center of the com pact has dropped by at most 8% from the surface value of
1 atm (see Fig. 5.42(a)).
At 40% conversion, the axial temperature and composition gradients have becom e
m uch steeper and less uniform (see Figs. 5.38(c) and 5.39(c)), with a relatively small
region at the surface o f the rod near the middle becoming much hotter and more reacted
than the rest o f the specimen. This change in the heating characteristics is caused by the
rapid increase in the pow er absorption that occurs after 50% conversion. W hile m ost o f the
specim en has remained below 50% conversion, a small region near the surface in the
m iddle has reached 60-90% conversion and is absorbing microwave pow er very efficiently
(see Figure 5.39(c)). The m axim um temperature value is now greater than 1450°C, which
m akes the formation o f melts or overheated areas a possibility.
A short time later, at 45% overall conversion, the middle o f the rod has becom e
fully reacted across the diameter, and the composition gradient is extrem ely steep (Fig.
5.41(a)). The m iddle o f the rod is much hotter than the end (Fig.5.40(a)), and there is now
a radial temperature difference of more than 150°C in the middle o f the rod which is caused
165
---------------- 1
----------------'-----------------1
--------------
1350
'-------------1
--------
r
a) 3.3 hours, 10% conversion
1325
1300
1275
1250
0.5
1.0
1.5
2.0
1350
b) 10 hours, 30% conversion
1325
1300
1275
1250
i
0.5
1.0
1.5
2.0
0.5
1.0
1.5
Distance along center axis (cm)
2.0
T
1450'
n
c) 13.3 hours, 40% conversion
1350
1250'
1150'
1050'
950'
(
5.38
Simulated temperature values in a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and
the dotted line is the surface, a) 10% conversion, b) 30% conversion,
c) 40% conversion.
166
Fractional conversion
1----------1---------- 1— ...... '■
i
...— i-----------
a) 3.3 hours, 10% conversion
0.20
0 . 10-1
0.00 ..... .. .......1______ 1______ _______ 1______ 1______ 1______ 1_______
0.5
1.5
0.0
2.0
1.0
0 .5 0 Fractional conversion
b) 10 hours, 30% conversion
0.40
0 .3 0 -
0 .2 0 -
o.io 0.00
0.0
0.5
1.0
1.5
2.0
1.00
Fractional conversion
c) 13.3 hours, 40% conversion
0.80
0.60
0.40
0.20
0.00
0.0
0.5
1.0
1.5
2.0
Distance along center axis (cm)
F ig u r e
5 .3 9 .
Simulated composition values for a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and
the dotted line is the surface, a) 10% conversion, b) 30% conversion,
c) 40% conversion.
167
1600Temperature (°C)
a) 15 hours, 45% conversion
150014001300-
1200
-
1100
“
1000
0.0
0.5
1.0
1.5
2.0
1600Temperature (°C)
b) 16.7 hours, 50% conversion
15001400
1300-
1200 1100“
1000
0.0
0.5
1.5
2.0
1.0
1.5
Distance along center axis (cm)
2.0
1.0
1600Temperature (°C)
c) 25 hours, 75% conversion
15001400"
1300“
1200
-
1100-
1000
0.0
F ig u r e
5 .4 0 .
0.5
Simulated temperature values in a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and
the dotted line is the surface, a) 45% conversion, b) 50% conversion,
c) 75% conversion.
168
Fractional conversion
1.00
a) 15 hours, 45% conversion
0 .8 0 0 .6 0 -
■n .
0 .4 0 0 .2 0 -
0.00
0.0
0.5
1.0
1.5
2.0
1.00
Fractional conversion
b) 16.7 hours, 50% conversion
0.80 0 .6 0 0 .4 0 0 .2 0 -
0.00
0.0
0.5
1.5
2.0
1.0
1.5
Distance along center axis (cm)
2.0
1.0
Fractional conversion
1.00
0 .8 0 c) 25 hours, 75% conversion
0 .6 0 0 .4 0 0 .2 0 -
0.00
0.0
F ig u r e
5 .4 1 .
0.5
Simulated composition values for a standard silicon com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and
the dotted line is the surface, a) 45% conversion, b) 50% conversion,
c) 75% conversion.
169
Nitrogen pressure (atm)
1 .0 0 0.95 a) 10 hours, 30% conversion
0 .9 0 -
0.85 -
0.80
0.0
0.5
1.0
1.5
2.0
Nitrogen pressure (atm)
1.0 0 1
0 .8 0 b) 15 hours, 45% conversion
0 .6 0 -
0.20
0.00
0.0
0.5
1.0
1.5
2.0
Nitrogen pressure (atm)
1.00
c) 25 hours, 75% conversion
0.80
0.60
0.40
0.20
0.00
0.0
F ig u r e
5 .4 2 .
0.5
1.0
1.5
Distance along center axis (cm)
2.0
Simulated nitrogen pressure values for a standard silicon com pact from
the middle of the specimen to the end. The solid line is the center, and
the dotted line is 1 mm from the surface, a) 30% conversion, b) 45%
conversion, c) 75% conversion.
170
by volumetric heating. The middle o f the rod has reached 1620°C at the center, despite the
fact that the conversion rate is only 3% per hour. This can be explained by noting that the
areas o f the specim en which are very hot are nearly fully converted to RBSN while most of
the unreacted part o f the specimen is below 1250°C and is therefore reacting rather slowly.
The nitridation reaction is occurring primarily in the part o f the rod that has the largest
temperature and composition gradients. The nitrogen partial pressure in the interior o f the
specim en has dropped to zero in the middle of the rod (Fig. 5.42(b)). This reflects the fact
that the permeability o f the specimen has decreased due to the increased conversion,
m aking nitrogen diffusion slower. The depletion o f nitrogen is greatest in the middle o f
the rod because the local reaction rate is highest there. Near the end o f the rod the nitrogen
pressure at the center is still greater than 0.95 atm because very little nitrogen is being
consum ed.
At 50% overall conversion, the temperature m aximum has begun to move away
from the middle o f the rod (Fig. 5.40(b)), creating a local temperature peak which
corresponds to the transition between fully reacted and much less reacted material (Fig.
5.41(b)). This occurs because the pow er absorption decreases to near zero as the
com position approaches pure RBSN. The m aximum pow er absorption occurs at between
70% and 80% composition, which corresponds to a fairly narrow axial region located
betw een the fully reacted and less reacted regions o f the specimen.
After 25 hours the temperature peak has moved axially away from the middle o f the
rod tow ard the end, as can be seen in Figure 5.40(c). The m axim um tem perature is about
1500°C, while the middle and the end o f the specimen are both much cooler. The specimen
now consists o f a fully nitrided middle and unreacted ends, separated by a sharp
com position gradient (see Fig. 5.41(c)). The nitridation reaction is now proceeding as a
“reaction front” which is moving towards the end o f the rod. This is verified by noting that
the m inim um in the nitrogen pressure, which corresponds to the region o f maximum
reaction rate, has moved axially toward the end of the rod along with the composition
171
gradient (see Fig 5.42(c)).
The composition distributions predicted by this model closely match the
com position profiles observed in partially-nitrided compacts processed with microwave
heating. The increase in heating efficiency after 50% conversion causes the m iddle o f the
specim en to nitride first, and creates very high temperatures near the composition
boundary. Significant nitridation occurs only near the boundary, and this causes the
nitrogen pressure in the interior o f the specimen to drop to zero because nitrogen is
consum ed faster than it can be replaced. The large axial temperature gradients across the
com position boundary are a necessary condition for the formation o f reaction bands by the
diffusion o f silicon vapor within the specimen. The conditions under which silicon mass
transport w ould be rapid enough to cause the observed density variations between adjacent
reaction bands is discussed in Section 5.6.
5.5.4 Simulation o f the nitridation o f a mixed-powder compact
As discussed in Section 5.4.2, silicon com pacts made from a mixture o f silicon
pow der and silicon nitride powder exhibited smooth composition gradients and inside-out
com position profiles when nitrided using microwaves. This was attributed to the fact that
the silicon particles did not sinter into a continuous conducting phase during initial
nitriding, which made these specimens behave like a conductor-loaded dielectric. By
m odifying the parameters o f the com puter model the microwave heating o f a m ixed-powder
specimen can also be simulated numerically.
The reflection coefficient and attenuation constant of the mixed-powder specimens
are calculated using the conductor-loaded dielectric model, according to equations 3.21 and
5.3. The m icrowave pow er absorption and penetration depth as a function o f com position
using this approach are shown in Figures 5.28 and 5.29. The norm alized absorbed pow er
172
and penetration depth at low conversion values are much higher than with the empirical
model used for the pure silicon compacts.
The other model param eter which must be modified for the m ixed-powder com pacts
is the permeability. The permeability o f the green mixed-powder compacts is the same as
that o f the pure silicon com pacts because the green density is the same. However, the
volume increase during nitridation is much smaller because the starting silicon volume
fraction is much lower. This means that the reduction in both the total porosity and the
average pore size will be proportionally lower with the m ixed-powder compacts. This was
verified by conventional nitridation experiments which showed that the m ixed-powder
specimens could be fully nitrided in a shorter time than the pure silicon com pacts without
raising the nitriding temperature above the silicon melting point.
The permeability of specimens made from pure silicon com pacts was estimated in
Section 5.5.1 to be 4.5 x lO 8 m for the green compact, and to decrease exponentially with
conversion to 2.7 x 1CH° m for pure RBSN. One way to estimate the perm eability o f a
fully nitrided mixed-powder com pact is to assign to it the permeability o f a pure silicon
com pact which has had the equivalent amount of nitridation. For exam ple, a mixed pow der
com pact with 50 vol% silicon has a silicon wt% of 42.3% (see Table 5.2), so when fully
nitrided it would have a permeability value equivalent to that o f a pure silicon com pact with
42% total conversion, or 5.2 x lO 9 m. This estimate for the permeability values is rather
rough; the actual values would likely be higher because not all o f the pores will be filled
with RBSN, as would be the case with a partially nitrided compact.
The results o f the simulation of the microwave nitridation o f a mixed-powder
com pact consisting o f 50 vol% silicon powder and 50 vol% silicon nitride pow der appear
in Figures 5.43 - 5.45. As with the graphs from the first simulation, the tem perature,
composition, and nitrogen pressure profiles along the axis o f the specimen from the middle
o f the rod to the end are shown. For this run, the conversion rate was set at 6% per hour
rather than 3% per hour in order to have a mass-based nitridation rate similar to that o f the
173
previous simulation.
The progress o f the nitridation reaction is much different than the previous
simulation. N o sharp com position or temperature gradients occur at any point in the
processing, and the internal temperatures do not prematurely rise above the silicon melting
point. Figure 5.43 clearly shows that radial temperature gradients are present at the start o f
the reaction, and that they increase with increasing conversion. After 80% conversion,
there is a radial temperature difference o f about 70°C from the center o f the specimen to its
surface (see Fig. 5.43(c)) which is caused by the volumetric heating which occurs when
the specim en is a conductor-loaded dielectric. This causes an inside out reaction profile to
form , as can be seen from Figure 5.44. At 80% overall conversion (Fig. 5.44(c)), the
center o f the specimen has reached 95% conversion, while the surface remains near 65%
conversion. The temperature and composition values both decrease near the end o f the rod,
but these axial gradients are relatively gradual.
In contrast to the previous simulation, the nitrogen pressure in the interior o f the
specim en does not fall below 70% o f its surface value during the reaction (see Fig. 5.45).
This is mainly due to the lack o f localized regions o f fast nitridation that were observed
during the simulation o f the processing o f a pure silicon compact. The higher permeability
o f the m ixed-powder com pact also contributes to the higher nitrogen pressures observed
during this simulation by increasing the nitrogen diffusion rate. Overall, the results o f this
simulation agree well with the composition profiles observed experimentally in partially
nitrided m ixed-pow der specim ens (see Figs. 5.34 and 5.35).
—I-------------- i---------------- 1----------------.----------------1-----------------r
1400
a) 1.7 hours, 10% conversion
1375
1350
1325
1300
1275
\
1250
0.5
1.0
1.5
1400
b) 8.3 hours, 50% conversion
1375
1350
1325
1300
1275
1250
I
0.5
1.0
1.5
2
1425
1400
c) 13.3 hours, 80% conversion
1375
1350
1325
1300
1275
1250
5.43
i
0.5
1.0
1.5
Distance along center axis (cm)
Simulated temperature values for a mixed-powder com pact from iI
middle o f the specimen to the end. The solid line is the center of
the dotted line is the surface, a) 10% conversion, b) 50% conver
c) 80% conversion.
175
Fractional conversion
a) 1.7 hours, 10% conversion
1.00
Fractional conversion
b) 8.3 hours, 50% conversion
0.80
0.60
0.40
0.20
0.00
0.0
Fractional conversion
1 .0 0 -
0.5
—
-------------------------->
—......................"1--------------------------'
0 .8 0 -
-----------1
-------------
—'
2.0
—i--------------------------'--------------------------
c) 13.3 hours, 80% conversion
0 .6 0 -
■
s.
S
\
•
0 .4 0 -
\
0 .2 0 i
0.0
F ig u r e
1.5
1.0
5 .4 4 .
.
i
.
i
0.5
1.0
1.5
Distance along center axis (cm)
*
2.0
Simulated composition values for a mixed-powder com pact from the
middle o f the specimen to the end. The solid line is the center o f rod and
the dotted line is the surface, a) 10% conversion, b) 50% conversion,
c) 80% conversion.
Nitrogen pressure (atm)
Nitrogen pressure (atm)
176
a) 1.7 hours, 10% conversion
0 .9 -
b) 8.3 hours, 50% conversion
0.8 -
0.7
0.0
0.5
1.5
2.0
1.0
1.5
Distance along center axis (cm)
2.0
1.0
Nitrogen pressure (atm)
i.o -r
0 .9 -
c) 13.3 hours, 80% conversion
0.8 -
0.7
0.0
F ig u r e
5 .4 5 .
0.5
Simulated nitrogen pressure values for a m ixed-powder specim en from
the middle o f the specimen to the end. The solid line is the center, and
the dotted line is 1 mm from the surface, a) 10% conversion, b) 50%
conversion, c) 80% conversion.
177
5.5.5 Simulation o f the nitridation o f a non-sintered silicon com pact
Another useful aspect of the numerical model is that it can be used to predict the
m icrowave processing behavior o f RBSN specimens under different conditions, thus
allow ing the process to be optimized more easily. As discussed in Section 5.4, if the
formation o f necks between adjacent silicon particles could be avoided then microwave
processing should enhance the nitridation of pure silicon com pacts as was originally hoped.
The microwave processing o f a silicon com pact without a continuous silicon phase can be
simulated with this model by using the conductor-loaded dielectric model to describe the
microwave reflection coefficient and attenuation constant as with the simulation o f a mixedpow der specimen. The other model parameters, including the permeability, have the same
values used for the first simulation o f a pure silicon compact.
The results o f a simulation conducted at 3% conversion per hour appear in Figures
5.46 - 5.48. As with the previous graphs, the temperature, com position, and nitrogen
pressure along the center axis o f the specimen from the middle o f the rod to the end are
shown. The progress o f the reaction is similar to the m ixed-powder simulation in that no
sharp com position or temperature gradients appear. There is no significant radial
tem perature gradient after 10% conversion (see Fig. 5.46(a)), but after 50% conversion
there is a temperature difference o f nearly 25°C between the center o f the rod and the
surface (see Fig. 5.46(b)).
At 50% overall conversion the center of the rod is slightly more reacted than the
surface (Fig. 5.47(b)). This is significant, because it means that the radial temperature
gradient is counteracting the effect o f nitrogen depletion on the reaction rate. The minimum
nitrogen pressure after 50% conversion is 77% o f the surface value (see Fig. 5.48(b)).
After 80% conversion the center o f the rod remains more reacted than the surface
(Fig. 5.47(c)), despite the fact that the nitrogen pressure in the center has dropped to
slightly more than half o f its surface value (Fig. 5.48(c)). This can be attributed to the
T
1400
a) 3.3 hours, 10% conversion
1375
1350
1325
1300
. ---
1275
( 0
1400
i—
0.5
■
>
■
1.0
1
■
1.5
2.
1.5
2
1.5
2.0
b) 16.6 hours, 50% conversion
1375
1350
1325
1300
1275
i 0
0.5
1.0
1475
1450
1425
c) 26.6 hours, 80% conversion
1400
1375
1350
1325
1300
i 0
0.5
1.0
Distance along center axis (cm)
5.46
Simulated temperature values for a non-sintered silicon com pact fr
the middle o f the specimen to the end. The solid line is the center
and the dotted line is the surface, a) 10% conversion, b) 50%
conversion, c) 80% conversion.
179
Fractional conversion
0 .5 0 a) 3.3 hours, 10% conversion
0 .4 0 0 .3 0 -
Fractional conversion
Fractional conversion
.0 0 "
0 .8 0 -
b) 16.6 hours, 50% conversion
0 .6 0 0 .4 0 -
0 .2 0 -
c) 26.6 hours, 80% conversion
0 .2 0 0.00
0.0
F ig u r e
5 .4 7 .
0.5
1.0
1.5
Distance along center axis (cm)
2.0
Simulated composition values for a non-sintered silicon com pact from
the middle of the specimen to the end. The solid line is the center o f rod
and the dotted line is the surface, a) 10% conversion, b) 50%
conversion, c) 80% conversion.
180
Nitrogen pressure (atm)
1.00
0.99 0.98 a) 3.3 hours, 10% conversion
0.97 "
0.96 0.95
0.0
0.5
1.5
2.0
1.5
2.0
1.0
1.5
Distance along center axis (cm)
2.0
1.0
Nitrogen pressure (atm)
1.0
0 .9 "
0.8
-
0.7 -
0 .6
b) 16.6 hours, 50% conversion
-
0.5
Nitrogen pressure (atm)
0.0
0 .9 -
0.8
0.5
1.0
c) 26.6 hours, 80% conversion
-
0.7 '
0.6
'
0.5
0.0
F ig u r e
5 .4 8 .
0.5
Simulated nitrogen pressure values for a non-sintered silicon com pact
from the middle o f the specimen to the end. The solid line is the center,
and the dotted line is 1 mm from the surface, a) 10% conversion,
b) 50% conversion, c) 80% conversion.
181
increase in the temperature difference between the center and the surface as the conversion
increases (see Fig. 5.46(c)). The radial temperature gradient increases with increasing
conversion because the microwave penetration depth increases and the thermal conductivity
decreases.
The results o f this simulation indicate that the temperature gradients associated with
volumetric microwave heating would counteract the effects o f nitrogen depletion, leading to
an inside-out RBSN com position profile throughout the reaction for a 1.5 cm diam eter rod.
Because there are no sharp temperature gradients within the specimen at any point in the
reaction, the formation o f overheated areas and reaction bands would not be expected. It
appears likely that specimens significantly larger than 1.5 cm in diameter could be fully
nitrided with microwave heating using the conditions o f this simulation.
182
5.6
Analysis of silicon vapor transport and reaction band formation
The experimental results presented in Section 5.3 dem onstrated that the formation
o f high and low density bands in m icrowave-processed RBSN, along with w eight loss and
the formation o f an outer silicon crust, are all caused by silicon vapor transport within and
out o f the specimen. The purpose of this section is to analyze the conditions under which
silicon vapor would form and be transported at levels high enough to create the observed
density differences between adjacent reaction bands.
Silicon vapor will form by two mechanisms: the direct sublimation o f solid or
liquid silicon, which depends only on temperature, and the decom position o f silicon
nitride, w hich depends on temperature and the nitrogen partial pressure. Silicon vapor
transport is driven by gradients in the silicon vapor concentration, with silicon diffusing
tow ard the regions o f low er concentration. Silicon vapor gradients will form in the
presence o f temperature gradients due to the temperature dependence o f the silicon partial
pressure. The loss o f silicon from the specimen surface by external mass transfer and the
reaction o f silicon vapor with nitrogen will also contribute to concentration gradients within
the specimen. In addition, there will be a relatively small thermal gradient-driven
com ponent o f the net mass flow which is counter to the concentration gradient-driven
com ponent, and this should be taken into account.
To estimate the m olar flux o f Si required for the formation o f the reaction bands, a
simplified model o f the microwave nitridation reaction in a rod can be used, as shown in
Figure 5.49. The specimen is a rod with length 2L and cross-sectional area A; for a 15 m m
diam eter rod, A = 1.77 cm 2. The nitridation reaction occurs within two disk-shaped
volum es of thickness w which are at the boundaries between the fully reacted middle and
the unreacted ends. According to the microwave heating model developed in Section
5.4.1, the material near the com position boundaries will absorb microwave pow er much
more efficiently than the rest of the specimen due to its composition. For this reason,
183
— ---------------------
A
2L
►
\
\
\
A
\ J
F ig u r e
J
J ............ .........
J
.
y
j
5 .4 9 . Geometric representation o f a nitriding specimen used to calculate the
silicon flux required for reaction band formation. Nitridation occurs only
within the reaction zones defined by the disk-shaped volum es of thickness
w and area A which separate fully nitrided and unreacted material.
significant axial and radial temperature gradients would be expected to exist within the disk­
shaped volum es containing the nitridation reaction. This was verified by the results o f the
finite-difference numerical model presented in the previous section. As the specimen
nitrides, the com position boundaries move outw ard toward the ends of the rod. Because of
the sym m etry o f this model, only one disk needs to be considered.
The simple geometry shown in Figure 5.49 is consistent with the com position
profiles observed in the longer rods which were translated through the microwave cavity,
in that the reaction bands are disk-shaped and are perpendicular to the center axis of the
rod. This allows the process to be modeled in one dimension, so that only axial
tem perature and composition gradients are considered. It should be noted that in all o f the
specim ens where reaction bands were observed there was a boundary separating fully
reacted material from unreacted material, and that the reaction bands had formed parallel to
184
this com position boundary. This means that the silicon concentration gradients which
create the reaction bands are determined primarily by the composition profile, and so the
analysis based on the one-dim ensional composition profile should apply to all o f the
specim ens.
The proposed mechanism for the formation o f the reaction bands is that silicon
vapor is transported from the hotter side o f the reaction zone to the cooler side as the
nitridation reaction proceeds. Once all o f the original silicon has nitrided to form RBSN,
the reaction zone containing temperature and silicon partial pressure gradients moves
outw ard tow ard the end of the rod, leaving behind a pair of RBSN reaction bands. This
mechanism implies a time scale for the mass transfer to take place which can be calculated
from the global conversion rate.
The total mass o f silicon transported across the disk-shaped volum e can be written
as
Ap Aw
me; = — ------------,
bI
1.665 4
5.20
where Ap is the difference in density between the dense and porous bands at the end o f the
nitridation reaction. Although the densities o f individual reaction bands could not be
m easured directly, a reasonably accurate estimate based on observations o f the
microstructure and on Archemedes density tests done on large overheated areas is that Ap
is about 0.3 g cm '3. The disk width, w, represents the thickness o f a pair o f reaction
bands; although there is some variation in the size of the bands a reasonable average value
is 2 mm. It should be noted that the mass flux which will be calculated using eq. 5.22 is
independent o f w. Using the above values in eq. 5.20 gives ms; = 1.6 x 10'2 g.
The time required to fully nitride the silicon within the disk o f width w is given by
w
t = —
xL
(seconds)
,
5.21
185
where x is the nitridation rate of the specimen in units o f fractional conversion per second.
Equation 5.21 assumes that nitridation is occurring only within the disk-shaped volum e of
width w, so the resulting value o f t is conservative. Typical m icrowave nitridation runs
were conducted at a conversion rate o f 2% per hour, w hich is equivalent to x = 5.56 x 10'6
s_l. U sing w = 0.2 cm and L = 2 cm (corresponding to a 4 cm long rod) results in t = 1.8
x 104 s. The m olar flux o f silicon across the disk is
Nc: =
tMA
(m o lm -2 s-<) ,
5.22
w here M is the molecular weight o f silicon (28 g m o l'1). Using the above estimates for msi
and t gives Nsi = 1.8 x 10'4 mol irr2 s_1.
A s discussed previously, the mean free path of gaseous species at 1 atm pressure
and at nitriding temperatures is larger than the pore size, so the dom inant diffusion
m echanism in RBSN specimens is Knudsen diffusion. In the rapidly nitriding areas o f the
specim en the nitrogen partial pressure is significantly less than 1 atm due to nitrogen
depletion, which further increases the mean free path. The molar flux o f silicon vapor in
the presence o f one-dimensional pressure and temperature gradients under conditions of
Knudsen diffusion can be written as (Jackson 1977)
N s.
Si = - —
RT
dPSi
1 ^Si dT
dz
2 T dz
5.23
where Psi is the partial pressure o f silicon, z is the axial coordinate, Dsj is the effective
Knudsen diffusion coefficient for silicon vapor, and Nsi is the m olar flux per unit crosssectional area.
The second term inside the brackets in eq. 5.23 represents the m olar flux caused by
the presence of a temperature gradient. This effect, known as thermal transpiration, causes
gaseous species to diffuse from colder areas towards hotter areas. In the equilibrium
186
condition, Nsi = 0, the pressure difference d P Si generated by a temperature difference dT is
given from eq. 5.23 as
5.24
Since the maxim um temperature difference in a reacting specimen is generally very small
com pared with the absolute temperature, the pressure gradients caused by chemical
reactions in a porous catalyst are usually much larger than the pressure gradients caused by
therm al transpiration, and so the latter are often neglected (Jackson 1977). This
simplification can be justified in this case by noting that when the temperature changes by
100°C the equilibrium partial pressure o f silicon changes by about an order o f magnitude
(see Fig. 5.50), and so the resulting silicon concentration gradient is on the order o f the
absolute silicon partial pressure. The corresponding pressure gradient caused by thermal
transpiration for a 100°C temperature difference can be estimated from eq. 5.24 as being
about .03Psj, or only 3% o f the total silicon concentration gradient.
The effective Knudsen diffusion coefficient is given by M ason et al. (1967) as
5.25
w here M is the molecular w eight o f silicon (28 g m ob1) and K0 is the permeability o f the
porous m edium (m), which depends on the total porosity and on the pore size distribution.
The permeability o f the RBSN specimens was estim ated in the previous section as
being 4.5 x lO 8 m for the green com pacts and then decreasing exponentially to 2.7 x 10"10
m for fully nitrided material. This analysis was based on standard RBSN processing with
no transport o f silicon. The pore size in the low-density RBSN band that forms on the
hotter side o f the reaction zone will remain fairly constant, because the increase in volume
187
due to the nitridation reaction is offset by the net flux o f Si out o f the region, and so the size
o f the pore channels does not significantly decrease. The pore size and the permeability of
the dense bands will be much lower, as with a static nitriding system. According to the
proposed model
for the reaction
band formation, silicon vapor diffuses through the hotter
porous band, where the nitrogen partial pressure is low, and then condenses and reacts in a
cooler area forming a dense reaction band. The permeability value used to model silicon
vapor diffusion should therefore be the value that describes the porous reaction bands. A
reasonable estimate is to consider the porous bands to have the same permeability as the
green com pact. Using this value in eq. 5.25 results in a diffusivity o f Dsj = 6.7 x 10-5
m 2 s '1.
The silicon partial pressure gradient required to cause a given m olar flux can be
found by rearranging eq. 5.23 (and ignoring the effects o f thermal transpiration) to be
d^si _
dz
N SiRT
D Si
5 26
w here the minus sign indicates that the molar flux is in the direction o f decreasing pressure.
The silicon partial pressure drop in the specimen required to sustain a given m olar flux is
therefore given by
=
_N siR IA z
52?
D si
where Az is the distance over which silicon vapor must be transported to form the reaction
bands. A conservative estimate is that Az = w, which assumes that Si must be transported
across the entire thickness o f the disk-shaped volume containing the nitridation reaction.
U sing the previously estim ated values in eq. 5.27 results in a partial pressure drop o f 1.7 x
Kb4 atm across the reaction zone.
188
The equilibrium vapor pressure o f a solid or liquid material can be written as
P,vap
5.28
w here AHsub is the heat o f sublim ation and K is an integration constant. The vapor
pressure, P vap, is a strong function o f tem perature but is independent o f the total pressure
o f the system. The vapor pressure o f silicon has been experimentally m easured (Dushm an,
1962), and a plot o f the equilibrium vapor pressure vs. tem perature appears in Figure 5.50.
To have a silicon partial pressure gradient sufficient to form the observed reaction bands
requires a m axim um silicon vapor pressure o f 1.7 x 10'4 atm. U nder equilibrium
conditions, this corresponds to a temperature o f about 1480°C, which is about 100°C
higher than standard nitriding temperatures. The temperature distributions in nitriding
specimens calculated using the numerical model have maximum values near the
com position boundary which are at least 1500°C and are sometimes significantly higher
(see Fig. 5.40), which suggests that significant silicon vapor transport could take place.
Another important effect that was predicted by the com puter simulation o f a
nitriding silicon com pact is that the nitrogen partial pressure in the reaction zone drops to
near zero because the nitrogen is consum ed faster than it can diffuse in from the surface
(see Fig. 5.42). W hen the nitrogen partial pressure decreases, the tem perature at w hich
silicon nitride decom poses into silicon and nitrogen is also lowered. The equilibrium
nitrogen pressure over solid silicon nitride at 1480°C is defined by the following reaction
(H euer and Lou 1990):
S i3N 4 -» 3Si(v) + 2 N 2(g)
( l n K = -5 4 .1 )
.
5.29
W hen the nitrogen pressure is lower than the equilibrium value defined by reaction 5.29,
silicon nitride will decompose into silicon vapor and nitrogen. The relationship between
189
10 '2
10"3
?
w
1 0 '4
w
gM
10 '5
3
(n
su
a
i«
X
1 0 '7
r
10'8
10 '9
1000
Figure 5.50.
1200
1400
Temperature (°C )
1600
Plot o f the equilibrium silicon vapor pressure over a condensed silicon
surface as a function o f temperature, using the data o f Dushm an (1962).
Si(v) and N 2 (g) at a given temperature can be shown graphically in a form known as a
volatility diagram (see Fig. 5.51). The usefulness of this type o f diagram was advocated
by Lou e ta l. (1985) for gas-solid reactions in high-temperature ceramic systems.
The horizontal line in Figure 5.51 represents the equilibrium vapor pressure o f
silicon over liquid silicon, which is independent o f the nitrogen partial pressure. The
angled line represents the vapor pressure of silicon over a silicon nitride surface according
to reaction 5.29. At a higher temperature the crossover point A would move upward and to
the right. If the nitrogen partial pressure is less than about 1 x lO 3 atm (to the left o f the
crossover point) then some of the silicon vapor from the decomposition reaction will
condense into liquid silicon, and the silicon partial pressure will remain at the equilibrium
vapor pressure o f 1.7 x 10~4 atm (the solid horizontal line). If the nitrogen partial pressure
is greater than 1 x lO 3 atm (to the right o f the crossover point) then silicon vapor will react
190
a
<u
u
s
w
sn
a>
u
a
is
u.
es
a
osu
X
10'4
10
3
Nitrogen partial pressure (atm)
Figure 5.51.
Volatility diagram for the silicon-nitrogen system at 1480°C. The
horizontal line represents the silicon vapor pressure, and the angled line
represents the decomposition o f silicon nitride. Solid lines give the
equilibrium conditions.
with nitrogen to form solid silicon nitride.
There are two possible conditions in the system in the latter case. If the com pact is
mostly silicon nitride, then the silicon partial pressure will be at the equilibrium value
defined by the angled solid line in Figure 5.51. However, if there is significant unreacted
silicon, as with a normal nitriding compact, then there will be an excess o f silicon vapor
and the actual silicon vapor pressure will be somewhere between the solid line and the
dotted line because the system will not be in equilibrium. An important conclusion that can
be drawn from this analysis is that when the nitrogen partial pressure in the specimen is
significantly lowered by the nitridation reaction, the silicon partial pressure will be at or
near the equilibrium vapor pressure, even if all of the original silicon from the com pact has
191
nitrided.
The above calculations indicate that a significant silicon vapor flux will develop
during m icrowave processing o f RBSN specimens which have a continuous silicon phase,
and that the proposed mechanism for the formation o f the observed reaction bands by
silicon vapor diffusion is plausible. According to this m echanism, silicon vapor is formed
at relatively high concentrations in the hottest part o f the specimen near the com position
boundary. Because the nitrogen partial pressure is very low, the gaseous silicon does not
react to form silicon nitride immediately. Instead, it diffuses dow n the silicon partial
pressure gradient toward the cooler part o f the specimen where it either reacts with the
available nitrogen or condenses as solid or liquid silicon. In either case, there is a net
transfer o f mass out o f the hottest region o f the specimen into the adjacent cooler regions.
W hen the nitridation reaction is proceeding as a reaction front along the axis of the
specim en, a series o f high-density and low-density RBSN bands are formed. N ear the
surface of the specim en silicon vapor diffuses out o f the specimen and into the cooler
pow der bed, causing the w eight loss phenom enon discussed in Section 5.3.
Chapter 6
Conclusions
The use o f m icrowave heating for the processing of reaction-bonded silicon nitride
(RBSN) was investigated in this work, with the goal o f utilizing the tem perature gradients
associated with volumetric heating to create beneficial inside-out reaction profiles in the
nitriding specimens. However, the microwave-nitrided silicon com pacts exhibited very
non-uniform conversion to RBSN and the fully nitrided areas had poor microstructures
w hich included regions o f high-density and low-density RBSN.
The rod-shaped silicon com pacts used in this study first became fully nitrided in the
middle while the ends remained unreacted. The nitridation reaction then proceeded as
localized reaction fronts that moved toward the ends o f the rod. The poor RBSN
microstructures were caused by high temperatures and temperature gradients in the nitriding
areas o f the specimen, which caused silicon vapor to diffuse within and out o f the
specimen. The progress o f the nitridation reaction was attributable to a large change in the
microwave heating characteristics o f RBSN specimens as they nitrided.
The m icrowave RBSN process proceeded as follows:
• W hen the specimen first reached nitriding temperatures o f 12Q0-1300°C, the
silicon pow der sintered together via a coarsening process which created necks
between adjacent particles but did not cause any shrinkage or densification.
• The specimen behaved like an electrically conducting material during the initial
192
193
stages o f the nitridation reaction, because charge transport could take place
through the continuous silicon phase. As a result, the heating efficiency was low
because most o f the incident pow er was reflected from the surface o f the
specimen. The specimen was not heated volumetrically because the microwave
pow er was absorbed only at the surface o f the specimen. Therefore, no
significant temperature gradients or inside-out composition profile developed.
• Between 50% and 70% conversion the necks between the silicon particles
disappeared as the silicon phase was converted to silicon nitride. This caused a
large increase in both the microwave heating efficiency and the penetration depth
because the specimen as a whole was no longer electrically conducting. The
m axim um microwave pow er absorption occurred near 72% conversion for the
1.5 cm diam eter specimens used for this work.
• Once the com position reached 70% conversion to RBSN, the penetration depth
increased rapidly, becom ing larger than the specimen size. This caused the
microwave power absorption to decrease as more o f the incident microwave
pow er was transmitted through the specimen without being absorbed.
By making com pacts from a mixture o f silicon pow der and silicon nitride powder,
the silicon particles were prevented from sintering together. These specimens nitrided
uniform ly and exhibited inside-out composition profiles when the volume fraction of
silicon nitride pow der was 0.5 or greater. The mechanical properties o f these specim ens
were inferior to those o f standard specimens because the strength o f RBSN depends on the
interlocking Si 3 N 4 grains which form between adjacent particles. However, these results
indicated that m icrowave heating would be beneficial for the RBSN processing of pure
silicon compacts if the neck formation between adjacent particles could be eliminated. One
possible way to do this would be to form an insulating layer o f RBSN around the
individual silicon particles before forming the green specimens; this presents technical
194
difficulties, however, because o f the tendency for the silicon pow der to agglomerate as it
reacts.
A numerical finite-difference model o f the microwave RBSN process was
developed using the appropriate equations for heat transfer, nitrogen diffusion, and the
nitridation reaction. An empirical model for the microwave heating characteristics of the
pure silicon com pacts was used which followed the microwave process described above.
The results o f this mode! are in good agreement with the composition profiles observed
experim entally for both standard silicon compacts and the m ixed-powder compacts. The
model also predicts that microwave processing would provide a beneficial inside-out
reaction in pure silicon com pacts without a continuous silicon phase.
The formation o f alternating layers o f high-density and low-density RBSN in the
m icrowave-heated specimens is caused by silicon vapor transport. The regions o f the
specimen near the boundary between fully reacted and unreacted material are much hotter
and have a higher reaction rate than the rest o f the specimen, and this causes the nitrogen
pressure in these areas to decrease to near zero. Significant amounts o f silicon vapor form
in these areas by evaporation from silicon surfaces and from the decom position o f Si 3 N 4 .
The silicon vapor diffuses into the cooler areas o f the specimen where it reacts with
nitrogen to form RBSN. This mass transport creates the reaction bands and large areas of
low -density RBSN which were described in this work. Silicon vapor also diffuses out of
the specim en at a much higher rate than is observed in conventionally-heated specimens.
Chapter 7
Recommendations for Future W ork
A lthough this study demonstrated that the use of microwave heating for the
formation o f RBSN from standard silicon compacts did not provide beneficial temperature
distributions in the specimens due to the large change in microwave heating characteristics
that takes place during the reaction, some areas for future work are suggested by the results
presented here.
The experiments performed using silicon/silicon nitride pow der mixtures, along
w ith the com puter model predictions presented in Section 5.5, showed that microwave
heating would provide a beneficial inside-out reaction if the silicon particles could be
prevented from sintering into a continuous conducting phase during initial heating o f the
compact.
As suggested in Section 5.4.3, the best way to prevent necks from forming
between adjacent silicon particles would be to form a thin layer of RBSN around the
individual silicon particles before pressing the powder into a compact. This would form an
electrically insulating barrier between the particles without interfering with the nitridation
reaction and without introducing any potentially harmful additives into the specimens. The
use o f a fluidized bed to produce silicon nitride powder from silicon pow der has been the
subject o f recent research (Liu and Kimura 1993, Jovanovic et al. 1994), which has
dem onstrated that it is difficult to fluidize fine silicon powder. Another possibility would
be to use an aerosol reactor. By dispersing the particles in a gas stream before they entered
195
196
a hot furnace, the particles could be nitrided and then cooled before they agglomerated.
The am ount o f nitridation could be controlled by adjusting the residence time in the furnace.
This w ould be a good subject for further experiments.
The future o f silicon nitride as a high-temperature structural ceramic material almost
certainly does not lie with RBSN, however. Recent research on sintered and hot-pressed
silicon nitride has demonstrated progress in eliminating the amorphous grain boundary
phases which to this point have limited their high-temperature properties (Ziegler et al.
1987). Because dense silicon nitride has much better strength and oxidation resistance than
RBSN, future high-temperature applications for ceramic materials will likely focus on the
use o f sintered or hot-pressed material.
One significant advantage o f RBSN over dense silicon nitride that remains is the
low er cost. The high cost o f silicon nitride powder, along with the expense o f m achining
dense silicon nitride into the desired shape, make sintered silicon nitride parts extremely
expensive in comparison with metal parts (Sheppard 1991, Q uadir e ta l. 1991). A fairly
recent innovation in silicon nitride technology, which provides a less expensive method for
the formation o f dense silicon nitride, is sintered reaction-bonded silicon nitride (SRBSN),
which involves nitriding a silicon com pact to form RBSN and then sintering the RBSN
specim en to full density.
SRBSN has two significant advantages over sintered silicon nitride. First, the
densification step is accompanied by less shrinkage because the RBSN ceramic has less
porosity than a com pact of silicon nitride powder. SRBSN specimens undergo linear
shrinkage o f only 5-10%, as com pared to 15-20% for sintered silicon nitride specimens
(M angels and Tennenhouse 1980). This reduces m achining costs and allows closer
dim ensional tolerances to be maintained. Second, the use o f silicon pow der instead o f
silicon nitride powder as the starting material reduces costs. Tiegs et al. (1993a) have
calculated that the raw material costs of SRBSN are less than 25% that of high-purity
sintered silicon nitride, thus making SRBSN cost-com petitive with metal parts.
197
RBSN specimens were first successfully sintered by M angels and Tennenhouse
(1980). These authors created complex shapes such as turbine rotors by slip casting silicon
powder; they then nitrided and sintered the parts in separate steps, achieving densities
greater than 98% of theoretical. They concluded that the oxide additives required for
liquid-phase sintering o f the RBSN specimen, such as M gO, Y 2 O 3 , and AI2 O 3 , should be
added to the silicon pow der before processing to ensure an even distribution. One
disadvantage o f the SRBSN process is that two separate processing steps are required.
The silicon com pact is first nitrided without insulation in order to prevent the reaction
exotherm from causing internal melting. The RBSN part is then insulated in silicon nitride
pow der for the sintering step in order to prevent weight loss during densification. The
sintering step is often performed under increased nitrogen pressure, which reduces the
am ount o f additives needed for densification by allowing higher sintering temperatures to
be used (K leebe and Ziegler 1989).
Recently, Tiegs et al. (1993a, 1993b) have used microwave heating to process
SRBSN in a single step, thus reducing both the processing time and the cost. M icrow ave
processing allows the nitridation step to be carried out using an insulating pow der bed,
because the internal temperature can be controlled by adjusting the microwave power.
After the nitridation reaction is complete, the microwave power is increased to densify the
part at temperatures o f 1750-1800°C. Because the insulation package is used during the
nitridation step the problems associated with changes in the microwave heating
characteristics with com position encountered in this work are avoided. However,
significant temperature gradients cannot form in the specimens as a result o f the insulation.
A significant disadvantage o f this approach is that the sintering step is performed under
atmospheric nitrogen pressure and therefore relatively large amounts o f additives are
required to achieve high densities. As a consequence, these parts maintain their strength
only up to about 800°C (Tiegs et al. 1993b). Microwave furnaces that could operate under
increased nitrogen pressure might be designed for future use, however.
198
The promising SRBSN results mentioned above suggest an area for future
experim ents which also utilize the results o f this work. Additives to the silicon powder,
including the evenly-distributed additives used for liquid-phase sintering, could be used to
separate the silicon particles and prevent neck formation. The beneficial temperature
gradients associated with volumetric microwave heating could then be taken advantage of,
allowing larger and denser RBSN parts to be made. One m ajor difference between the
SRBSN process and the standard RBSN process is that the mechanical properties o f the
intermediate RBSN ceramic are not important. Therefore, specimens made from mixtures
o f silicon pow der and silicon nitride pow der (such as those discussed in Section 5.4.2)
w ould be suitable for post-RBSN sintering, although their mechanical properties are not
equivalent to those of standard RBSN.
It would be useful to explore further the microwave nitridation o f specimens made
from mixtures o f silicon powder, silicon nitride powder, and metal oxide sintering aids,
with the goal o f producing large parts with low residual porosity which could then be
sintered to full density. The oxide additives are typically added in the am ount o f 5-15 wt%,
depending on their molecular weight and the sintering temperature to be used. Silicon
nitride pow der consisting primarily of the a-phase is also sometimes added in the amount
o f 5-10 wt% to increase the am ount o f a -S i 3 N 4 in the intermediate RBSN ceramic (Tiegs et
al. 1993a). This is done because the microstructure o f the a-phase enhances the
densification process and encourages the formation o f elongated, strength-enhancing P~
grains in the final ceramic.
The results o f the powder mixing experiments discussed in Section 5.4.2 indicate
that the amount o f additives required to keep the silicon particles from sintering is between
25 vol% and 50 vol%, which is considerably higher than the total am ount o f additives
currently used to form SRBSN. However, as discussed above, the addition o f fine a Si3 N 4 pow der to the starting silicon powder would not affect the mechanical properties of
the dense ceramic.
199
Full densification of silicon nitride pow der by sintering requires that the starting
pow der have a very high surface area, and this limits the green density o f the starting
com pact to about 55-60% (M angels 1981h). The nitridation of silicon pow der produces a
fine-grained silicon nitride microstructure with a decrease in the average pore size o f up to 2
orders o f magnitude, which enhances the densification process considerably (Kleebe et al.
1988). Therefore, the surface area o f the starting silicon pow der is less critical. The
m axim um green density for silicon powder with an average particle size on the order o f 1
p m is about 70%. A 70% dense com pact consisting o f 50 vol% silicon pow der and 50
vol% additives would have a density o f 77% after complete nitridation. This indicates that
the use o f m ixed-pow der com pacts for SRBSN would provide a substantial decrease in the
am ount o f shrinkage during sintering as com pared to silicon nitride pow der compacts.
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