Synthesis of Nano-Sized
Silicon Nitride Powder
in Microchannel Reactors
AN ABSTRACT OF THE THESIS OF
Michiru Hirayama for the degree of Master of Science in Chemical Engineering
presented on July 28 , 2006.
Title: Synthesis of Nano-Sized Silicon Nitride Powder in Microchannel Reactors
Abstract approved:
Shoichi Kimura
Four types of microchannel reactors were built, using a combination of
smallest alumina-tubes commercially available, for testing the feasibility of
applying high-temperature microchannel reactors to the ammonolysis of SiO for
producing nano-sized silicon nitride powder. The innermost tube used for feeding
SiO vapor had an inner diameter (ID) of about 500 µm, while the outermost tube
used for ammonia feed had an ID of 3180 µm, and between these two was a
1600µm ID tube for argon flow to separate the two reactant gases: SiO and
ammonia.
The microchannel reactors were operated at temperature between
1300°C and 1350°C at pressure slightly above atmospheric pressure.
All the microchannel reactors built for this study could be operated without
any serious problems, such as clogging of micro-tubes with whiskers or nano-sized
powder.
The reduction of residence time and quenching of reactant/product
mixture decreased the average particle size down to about 10 nm.
The smallest
size for particles to grow was estimated based on thermodynamic consideration and
found to be on the same order of magnitude as those observed in TEM pictures.
Based on the successful operation of microchannel reactors, potential structures for
a scalable set of multi-microchannel reactors were proposed for future study.
©Copyright by Michiru Hirayama
July 28, 2006
All Rights Reserved
Synthesis of Nano-Sized Silicon Nitride Powder in Microchannel Reactors
by
Michiru Hirayama
A THESIS
Submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented July 28, 2006
Commencement June 2007
Master of Science thesis of Michiru Hirayama presented on July 28, 2006.
APPROVED
Major Professor, representing Chemical Engineering
Head of the Department of Chemical Engineering
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon
State University libraries. My signature below authorizes release of my thesis to
any reader upon request.
Michiru Hirayama, Author
ACKNOWLEDGEMENTS
There have been much help and encouragement from others to make this
thesis successful. Therefore, I would like to take this opportunity to express my
sincere appreciation to the following people:
Dr. Shoichi Kimura, my advisor, for his advice, encouragement, and
assistance in every aspect throughout this research and my study at Oregon State
University.
Dr. Mark Dolan, Dr. Chin-hung Chang, and Dr. Joseph R Zaworski, my
committee members, for their valuable help and suggestions.
All the professors in Chemical Engineering Department, who provided me
with valuable knowledge and experience during my study at OSU.
Dr. Michael Nesson for his help and advice during the period of this study as
well as his courtesy for taking TEM images.
My fellow graduate students in the Department of Chemical Engineering for
their friendship and help.
My parents and family, who have provided enormous encouragement as well
as the financial support throughout my study.
TABLE OF CONTENTS
Page
CHAPTER 1
INTRODUCTION ...................................................................
1
CHAPTER 2
LITERATURE SURVEY .........................................................
5
2.1 Synthesis via Chemical Vapor Deposition (CVD) .........
6
2.2 Ammonolysis of Silicon Monoxide (SiO) Vapor ...........
8
2.3 Ammonia Dissociation ...................................................
9
2.4 Macro-scale Reactor versus Microchannel Reactor ....... 12
2.5 Objectives of This Research ........................................... 13
CHAPTER 3 EXPERIMENTAL APPARATUS AND PROCEDURES ......... 15
3.1 Reactor Configurations ................................................... 15
3.1.1 Vertical microchannel reactors ........................ 15
3.1.2 Horizontal microchannel reactors .................... 20
3.2 Procedures of Reaction Experiment ............................... 23
3.3 Characterization of Product Powder .............................. 30
TABLE OF CONTENTS (Continued)
Page
CHAPTER 4
EXPERIMENTAL RESULTS AND DISCUSSIONS ............... 31
4.1 SiO Vapor Generation versus Product Yields ................. 31
4.2 Nano-Sized Si3N4 Power Synthesis ................................ 32
4.2.1 Product morphologies ...................................... 32
4.2.2 Effects of residence time ................................. 38
4.2.3 Effects of temperature ..................................... 42
CHAPTER 5
DISCUSSION ........................................................................... 43
5.1 Critical Size for Stable Growth ...................................... 43
5.2 Scalable Microchannel Reactors .................................... 51
CHAPTER 6 CONCLUSIONS AND RECOMMENDATION FOR FUTURE
WORK ...................................................................................... 57
6.1 Conclusions .................................................................... 57
6.2 Recommendation for Future Work ................................. 58
TABLE OF CONTENTS (Continued)
Page
BIBLIOGRAPHY .............................................................................................
59
APPENDICES .................................................................................................... 62
LIST OF FIGURES
Figure
Page
3.1 Dimensional details of individual tubes used for vertical
microchannel reactors. ................................................................................. 16
3.2 (a) Schematic diagram of vertical microchannel reactor set-up
with no collection coupler. ..................................................................... 18
3.2 (b) Schematic diagram of vertical microchannel reactor set-up
with collection coupler. ........................................................................... 19
3.3 Dimensional details of individual tubes used for horizontal
microchannel reactors. .................................................................................. 21
3.4 Detailed structure of horizontal microchannel reactor with its own
heating unit. .................................................................................................. 22
3.5 (a) Schematic diagram of horizontal microchannel reactor set-up
with no collection coupler. ..................................................................... 24
3.5 (b) Schematic diagram of horizontal microchannel reactor set-up
with collection coupler. .......................................................................... 25
3.6 Picture of horizontal microchannel reactor with its own heating
unit. .............................................................................................................. 26
LIST OF FIGURES (Continued)
Figure
Page
4.1 (a) TEM picture of particles obtained in the vertical microchannel
reactor with no collection coupler. ......................................................... 34
4.1 (b) TEM picture of particles obtained in the vertical microchannel
reactor with collection coupler. .............................................................. 35
4.1 (c) TEM picture of particles obtained in the horizontal microchannel
reactor with no collection coupler. ......................................................... 36
4.1 (d) TEM picture of particles obtained in the horizontal microchannel
reactor with collection coupler. .............................................................. 37
4.2 Mean particle size varying with mean residence time. ................................ 41
5.1 (a) Schematic diagram of multiple microchannel reactors. ......................... 54
5.1 (b) Unit component for multiple-layer microchannel reactors. ................... 55
5.1 (c) A set of multiple microchannel reactors. ................................................ 56
LIST OF TABLE
Table
Page
4.1 Correlations between mean residence time and mean particle
size obtained in different types of microchannel reactors. .......................... 40
5.1 Physical properties needed for Kelvin’s equation. ....................................... 48
NOMENCLATURE
G
Gibbs free energy
i*
critical number of molecules in a cluster that can grow
KP
equilibrium constant for the ammonolysis of SiO
M Si 3 N 4 molecular weight of silicon nitride
J
g/mol
nSi 3 N 4
moles of silicon nitride in a cluster
mol
Pi
partial pressure of species i
Pa
P0
operating pressure
Pa
R
universal gas constant
J/mol ⋅ K
r
radius of a cluster
cm
r*
critical radius of cluster that can grow
cm
T
operating temperature
K
Vm
volume of silicon nitride molecules
cm3
v*
volume of cluster that can grow
cm3
∆G
change in Gibbs free energy
J
µi
chemical potential of species i
J/mol
µ io
chemical potential of species i at its standard state
J/mol
ρ
density of silicon nitride
g/cm3
σ
surface tension of silicon nitride
N/cm
(dynes/cm)
SYNTHESIS OF NANO-SIZED SILICON NITRIDE POWDER IN
MICRO-CHANNEL REACTORS
CHAPTER 1 INTRODUCTION
In 1896, the earliest reference of silicon nitride was made by Mehner [1896]
in Germany.
Silicon nitride was founded in the 1960s as a good temperature
insulation material and used in its film form.
Silicon nitride was then identified as
an excellent high temperature material and used in huge amounts because of its
high temperature capabilities and low thermal expansion coefficient. During the
1960’s and 1970’s, use of silicon nitride was further developed because of the need
for materials able to stand the high-temperature zones in turbine engines.
Some methods for synthesizing silicon nitride include carbothermal
nitridation of silica, direct nitridation of silicon powder, and liquid- and gas-phase
reactions. To obtain silicon nitride in its film form, the gas phase reaction, such as
the chemical vapor deposition (CVD) process, is usually used.
Most of these
processes require high temperatures ranging from 1350°C to 1800°C, except some
2
liquid- and gas-phase reactions.
Silicon nitride has two forms (α and β), and both the forms are of hexagonal
crystal structures. The sequence of α-silicon nitride is in A, B, A, B, etc., while that
of β-form is in A, A, A, A ,etc. Because α-silicon nitride requires a lower Gibbs
free energy of formation, having larger pockets, silicon nitride usually forms in its
α-phase [Wilcox, 1982; Hisao, et. al., 1994].
It has been known that controlling the quality of sintered parts becomes easier
as the size of raw material silicon nitride powder decreases.
It has been expected
that use of nano-sized silicon nitride powder (smaller than about 100 nm) widens
the range of its applications.
In this light, it is attempted to synthesize nano-sized
silicon nitride powder in this research.
It has been found, using a macro-scale reactor, that nano-sized silicon nitride
powder can be synthesized via the ammonolysis of SiO vapor [Lin and Kimura,
1996; Vongpayabal and Kimura, 2005]. However, the products obtained in the
macro-scale reactor have a wide range of size distributions, because of the wide
range of residence time distributions of reactants in the reactor [Vongpayabal,
2003].
3
It is expected that microchannel reactors enable to achieve rather uniform
residence time distributions because of their configurations in confined micro-sized
dimensions. The micro-sized dimensions automatically provide very short mean
residence time, leading to narrowly distributed, smaller nano-sized powder.
The main objective of this research is to test the feasibility of synthesizing
nano-sized silicon nitride powder in microchannel reactors.
It is also attempted to
characterize products obtained in microchannel reactors of different configurations
not only for making comparisons between macro-scle and microchannel reactors in
terms of mean particle size but also for finding some directions to designing
scalable microchannel reactors.
There are 6 chapters in this thesis that present the development of reactor
configurations for the synthesis of nano-sized silicon nitride powder using
microchannel reactors.
The literature survey in Chapter 2 shows the history of the
synthesis of silicon nitride powder and the present knowledge surrounding it. The
details of the experiment and the design of the devices used are in Chapter 3.
In
Chapter 4, results of nano-sized silicon nitride powder synthesis using four
different types of microchannel reactors are presented and discussed. Chapter 5
4
presents an estimate for the critical size for stable growth of nano-sized silicon
nitride particles and discusses the result in comparison to particle sizes observed.
Finally, Chapter 6 includes the conclusions and recommendation for future work.
5
CHAPTER 2
LITERATURE SURVEY
Recently, the demand of Silicon nitride (Si3N4), especially in its pure powder
form, has dramatically increased for making materials that require toughness,
strength and temperature resistance [Andrievski, 1994; Barsoum, et. al., 1989,
1991; Gleiter, 1989; Lee, et. al., 1999; Maalmi and Varma, 1996].
Because it is
rather easy to equalize the quality of Si3N4 when it is manufactured as powder, the
demand for technologies to synthesize Si3N4 of uniform, small particle size at lower
cost has become much stronger [Danforth, et. al., 1981, 1988; Orthner, et. al., 2000].
There
are
several
methods
to
produce
Si3N4
powder:
carbothermal
reduction/nitridation of silica, direct nitridation of silicon powder, and
liquid-/gas-phase reactions.
The gas-phase reactions, usually identified as
chemical vapor deposition (CVD) with or without laser or plasma, yield high purity
Si3N4 powder at rather low temperature.
However, the gas-phase reactions
assisted with laser or plasma are, in general, costly and inappropriate for mass
production.
The carbothermal reduction/nitridation of silica is for low grade
6
silicon nitride production. Though the direct nitridation of silicon powder and the
liquid phase reaction such as the reaction of SiCl4 in liquid ammonia are suitable
for mass production, nano-sized powder cannot be produced.
A unique process that uses SiO-vapor and ammonia has been developed for
synthesizing nano-sized silicon nitride powder at large quantities [Lin, 1995;
Vongpayabal, 2003]. The process has been tested using macro-scale reactors, and
it has been proved that nano-sized powder can be produced.
However, the
particles obtained have wide size distributions.
The following sections describe processes for nano-sized silicon nitride
synthesis, focusing on the CVD reactions with no assistance by laser or plasma.
2.1 Synthesis via Chemical Vapor Deposition (CVD)
Advantages of CVD processes include high purity and controlled composition
as well as stoichiometry, leading to high degree of structural perfection, good
electrical properties, and low defect density of sintered materials.
A CVD process can be summarized in the following sequence of steps:
7
1. Reactant gases (frequently diluted in carrier or inert gas) are introduced
into a reaction chamber, where they flow through from inlet to outlet by
convection.
2. The reactant gaseous species are transferred by gas-phase diffusion and
forced convection, and react to form solid products and gaseous by-products, if any.
CVD reactions occur by supplying energy, as thermal energy, protons, or
electrons, among which the thermal energy is the most common energy used.
Products from CVD processes either precipitate as powder in the vapor phase
(homogeneous reaction) or deposit on solid surface (heterogeneous reaction) [;
Allaire, et. al., 1991]. The heterogeneous CVD reactions are mostly used for
creating a firm form of product film to cover the surface of solid, such as wafer.
Most CVD techniques to obtain silicon nitride usually use the reaction
between silane or silicon halides and ammonia at high temperature, mostly above
1000℃ when neither plasma nor laser is used.
Some example reactions are
[Wilcox, 1982]:
3SiH4 (g) (Silane) + 4NH3 (g) = Si3N4 (s) + 12H2 (g)
3SiCl4 (g) + 4NH3 (g) = Si3N4 (s) + 12HCl(g)
8
3SiF4 (g) + 6NH3 (g) = Si3N4 (s) + 2NH4F (g) + 10HF (g)
3SiH4 (g) + 3N2H4 (g) (hydrazine) = Si3N4 (s) + 2NH3 (g) + 9H2 (g)
3SiO(g) + 4NH3 (g) = Si3N4 (s) + 3H2O(g) + 3H2 (g)
The physical properties of product (Si3N4) depend on several factors and
parameters, such as residence time, reactor types and dimensions, temperature, and
gas flow rates.
2.2 Ammonolysis of Silicon Monoxide (SiO) Vapor
The stoichiometry of SiO ammonolysis is represented as
3SiO(g) + 4NH3 (g) = Si3N4 (s) + 3H2O(g) + 3H2 (g)
SiO is solid at room temperature and sublimates at temperature higher than about
1200°C.
Hence, its ammonolysis reaction takes place at temperature around
1300℃ or higher, at which SiO has high enough vapor pressure and the rate of
reaction with ammonia is reasonably high. The ammonolysis of silicon monoxide
was first proposed by Lin and Kimura [1996] as a process to produce nano-sized
silicon nitride powder at low cost.
9
The ammonolysis of SiO vapor yields three different types of product
morphology: nano-sized powder, whiskers, and crystals.
The method for
supplying ammonia into a reaction zoon is one of the most important factors
influencing the formation of nano-sized silicon nitride powder.
Geometries of
reactant feeders also affect the morphologies of product silicon nitride powder.
It has also been proved that ammonia plays a more important role in the
conversion of SiO vapor into Si3N4 than intermediates (NH and NH2) or N2-H2 gas
mixtures, as products of ammonia dissociation, do [Vongpayabal, 2003].
It is thus
important to maintain ammonia in its molecular form in the high temperature
reaction environment, where ammonia tends to dissociate. Obviously, to suppress
the ammonia dissociation, keeping the residence time of ammonia in the high
temperature environment is essential.
Short residence time can be achieved in
microchannel reactors.
2.3 Ammonia Dissociation
Ammonia dissociates into nitrogen and hydrogen at high temperature as
10
2NH3 (g) = N2 (g) +3H2 (g)
Based on the study of ammonia dissociation kinetics at temperatures ranging from
1185℃ to 1382℃, using a 1/4” alumina (Al₂O₃) tube, the ammonia dissociation
rate has been found to be represented by [Lin and Kimura, 2003]
− rA = k C A1/ 3
where CA is the ammonia concentration in mol/m3. The rate constant k is given as
k = 4.46 ×10 9 e − 246000 / R T
(mol/m )
3 2/3
/s
The dissociation of ammonia described above is mostly promoted by the tube wall
heterogeneously.
Once ammonia comes into a reaction zone with surrounding inert gas flow,
the heterogeneous ammonia dissociation is reduced, because of the reduction of
contact frequency of ammonia with the solid surface due to the supply of inert gas.
Thus, the homogeneous thermal decomposition of ammonia should also be taken
11
into consideration.
The homogeneous thermal decomposition of ammonia was studied using
stainless-steel shock tube with mixtures of ammonia and inert gas argon [Roose, et.
al., 1980].
Because the true mechanism is complex, the rate of thermal
decomposition of ammonia has been represented based on the following simplified
mechanism:
k₁
NH3 (g) + M = NH2 (g)+H +M
k₂
NH3 (g) + M = NH + H2 (g) + M
where M is argon gas.
Their experimental results are represented, at temperature
in the range from 2200 K to 3450 K, as
k1 = 2.52 ×10 16 e − 47200 / T
k2 = 3.46 ×10 6
cm3 /mole ⋅ s
cm3 /mole ⋅ s
at 2798 K
12
It is obvious that k1 / k2 > 100 over the temperature range from 2200 K to
3450 K. The rate of thermal decomposition of ammonia can then be represented
in the range of temperature investigated by [Roose, et al.,1980]
− rA = k1 [ NH3 ]
3/ 2
[ Ar ]1 / 2
mol/cm3 ⋅ s
2.4 Macro-scale Reactor versus Microchannel Reactor.
The biggest differences between the macro-scale reactor, used by
Vongpayabal [2003], and microchannel reactors used in this research are not only
the diameters of reactor tubes but also the length of reacting zone. Though the
diameter of the tube supplying SiO vapor in the microchannel reactor is at least
one-order-of-magnitude smaller, the linear gas velocities through the reactor tubes
are on the same order of magnitude.
On the other hand, the mean residence time
of reactant gas mixture in the reacting zone in the microchannel reactor can be two
orders of magnitude smaller than the macro-scale reactor because of the confined
heating zone used for the microchannel reactor.
13
The average particle size of product powder (silicon nitride) is strongly
affected by the residence time of reactant gas mixture [Vongpayabal and Kimura,
2005]. The average particle size of product powder obtained in the macro-scale
reactor, providing a mean residence time of 0.2 – 0.7 seconds, ranges from about 25
nm to about 120 nm [Vongpayabal, 2003].
The biggest advantage of using
microchannel reactors is a smaller particle size expected from shorter residence
time.
In addition, the configurations of microchannel reactor allow the residence
time to be narrowly distributed, leading to narrowly distributed particle sizes.
2.5 Objectives of This Research
The major objectives of this research are to test the feasibility of operating
microchannel reactors and to investigate effects of reactor size and operating
parameters on the size of product nano-sized silicon nitride powder. The major
attempts of this research are listed below:
1.
to prove that nano-sized silicon nitride powder can be synthesized in
microchannel reactors,
14
2.
to compare the size of product powder obtained in microchannel
reactors with that obtained in macro-scale reactor in terms of mean
residence time, and
3.
to propose scaleable microchannel reactor configurations.
15
CHAPTER 3 EXPERIMENTAL APPARATUS AND PROCEDURE
3.1 Reactor Configurations
3.1.1 Vertical Microchannel Reactors
Two types of vertical microchannel reactors were first built. Four tubes of
different sizes were vertically arranged, as illustrated in Figure 3.1: from the inner
to outer tubes, a 0.508 mm ID tube connected to a 3.96 mm ID tube for SiO vapor
generation, annular argon gas feeder, ammonia feeder, and furnace tube (3.125” ID).
The set of bottom three tubes is a combination of smallest alumina tubes
commercially available and used as a microchannel reactor.
To minimize the product attachment to reactor walls, argon flows through the
annular space between the two tubes for supplying the respective reactants as well
as the space outside the ammonia supply tube in the furnace tube. SiO particles
were placed in a 3.96 mm inner diameter tube to which a 508 µm inner diameter
tube was connected for SiO vapor supply.
16
OD, mm ID, mm Length, mm
OD, mm
ID, mm Length, mm
4.78
3.18
50.8
19.1
14.3
2.39
1.60
63.5
12.7
1.27
0.508
76.2
6.35
914
9.53
1016
3.96
1118
Figure 3.1 Dimensional details of individual tubes used
for vertical microchannel reactor.
17
This whole set of SiO vapor/argon/ammonia gas-feeders was placed in the 200 mm
long uniform temperature zone in an electric furnace, in which the temperature
variation is within 5℃ [Vongpayabal, 2003], as shown in Figure 3.2 (a).
To restrict the gas flow and modify the residence time distribution, a
collection coupler was placed at the outlet of the microchannel reactor, as
illustrated in Figure 3.2 (b). The main objective of this coupler is to confine the
reacting zone inside of the coupler receptacle and discharge the product through the
guide tube as quickly as possible to the low temperature zone, namely for
quenching the product.
It is important to control the SiO feed rate from SiO vapor generator in order
to investigate the kinetics of SiO-NH₃ reaction.
The SiO vapor feed rate is
controlled by the quality and quantity of SiO particles placed in the SiO generator,
the carrier gas argon flow rate, and the temperature.
of an average size of 300 µm were used.
In this research, SiO particles
In each run, 0.2 – 0.25 grams of fresh
SiO particles were placed in the SiO generator, and the set of microchannel reactor
was then inserted in the uniform temperature zone in the furnace. The volumetric
flow rate of argon gas into the SiO generator was fixed at 105 cm3/s.
18
Ar
Ar
NH3
Thermocouple
Temperature
Controller
T
P
Pressure
Gage
Electric Furnace
SiO -Vapor
Generator
Uniform
Temperature Zone
SiO Particles
Furnace Tube
Gas Outlet
Filter
Vacuum
Pump
Figure 3.2 (a) Schematic diagram of vertical microchannel reactor
set-up with no collection coupler.
19
Ar
Ar
NH3
Thermocouple
Temperature
Controller
T
P
Pressure
Gage
Electric Furnace
SiO -Vapor
Generator
Uniform
Temperature Zone
SiO Particles
Furnace Tube
Gas Outlet
Filter
Vacuum
Pump
Figure 3.2 (b) Schematic diagram of vertical microchannel reactor
set-up with a collection coupler.
20
The electric furnace has three heating zones, and the temperature is measured
with an R-type thermocouple. A heating rate of 10℃/min and cooling rate of
30℃/min were set in the controller program. SiO generation was started, when
the reactor temperature reached the prescribed temperature, by feeding argon gas
through the SiO generator, and terminated by stopping the argon gas feed.
3.1.2 Horizontal Microchannel Reactors
Controlling the residence time of reactant mixture using the configurations
described above is very much limited because the whole set of microchannel
reactor is in the furnace high temperature zone. To reduce the residence time
substantially and to quench the reactant gas as well as the product powder, a
microchannel reactor with its own heating unit was built in this research. The
combination of tubes is the same as that for the vertical microchannel reactor, as
illustrated in Figure 3.3.
However, the outside of the entire microchannel reactor
set is wound with a 0.5 mm diameter Pt-13% Rh wire which is covered with
alumina cement, as illustrated in Figure 3.4.
21
OD, cm
19.1
12.7
6.35
ID, mm Length, mm
OD, mm
ID, mm
914
4.78
3.18
50.8
9.53
1016
2.39
1.60
63.5
3.96
1118
1.27
0.508
76.2
14.3
Length, mm
Figure 3.3 Dimensional details of individual tubes used for horizontal
microchannel reactor.
22
Heating Element (13% Rh/Pt)
200 mm
Ar
TC
NH3
Ar
Ar
SiO
50 mm
Furnace Tube
2.40 mm
0.50 mm
1.60 mm
Ar
1.27 mm
3.18 mm
Figure 3.4 Detailed structure of horizontal microchannel reactor
with its own heating unit.
23
This entire set was placed in a 29 mm inner diameter alumina tube mounted
in an unheated horizontal furnace.
In the configurations illustrated in Figure 3.5
(a), the product-reactant mixture is quenched as soon as it comes out of the reacting
zone, namely the microchannel reactor. Thus, the reaction time is limited to the
residence time inside the microchannel reactor.
To effectively collect the product
powder, a collection coupler was placed right downstream the microchannel reactor
set, as illustrated in Figure 3.5 (b). The entire horizontal microchannel reactor is
shown in Figure 6.
3.2 Procedures of Reaction Experiment
The effective temperature for utilizing SiO vapor for synthesizing nano-sized
silicon nitride powder has been found in the range from 1310℃ to 1390℃
[Vongpayabal, 2003].
In this research, a midpoint of 1350°C was selected as the
standard temperature for SiO generation and hence for the ammonolysis reaction.
24
Gas
Outlet
Pressure Gage
P
Ar
Electric Furnace
(unheated)
NH3
SiO Particles
Furnace Tube
Vacuum
Pump
Filter
Thermocouple
T
Ar
Temperature Controller
Figure 3.5 (a) Schematic diagram of horizontal microchannel reactor
with no collection coupler.
25
Gas
Outlet
Pressure Gage
P
Ar
Electric Furnace
(unheated)
NH3
SiO Particles
Furnace Tube
Vacuum
Pump
Filter
Thermocouple
T
Ar
Temperature Controller
Figure 3.5 (b) Schematic diagram of horizontal microchannel reactor
with collection coupler.
26
Microchannel
Reactor/Heate
Supporter
Stopper
Argon Feeder
Thermocouple
Power Supply
Figure 3.6. Picture of horizontal microchannel reactor with its own
heating unit.
27
A small amount of SiO particles (0.2 – 0.25 g) were first placed in the SiO
generator, which was then inserted in the annular argon feeder to make up a set of
microchannel reactor.
The set was installed in the vertical furnace tube of electric
furnace for heating or in the horizontal furnace tube for isolating the microchannel
reactor from the atmosphere, and then heated to the prescribed temperature of
1350°C. The heating rate was set at 10°C per min.
When any types of reactors described above were used, the pressure drop
through the SiO generator became very high at the reaction temperature.
The feed
rate of argon gas was controlled so that the linear velocity of argon gas containing
SiO vapor through the smallest tube was 47.0 m/s and the pressure drop of argon
through the SiO generator was maintained below about 50 kPa. The volumetric
flow rates of ammonia as well as annular argon were also adjusted so that both the
linear velocities were 45 – 50. m/s.
The method for ammonia supply plays an important role in the ammonolysis
reaction converting SiO into silicon nitride.
The dissociation of ammonia
decreases the rate of silicon nitride synthesis.
However, the residence time of
ammonia in the reacting zone is very small in the microchannel reactors (a few
28
microseconds), and the estimated fraction of ammonia dissociation (mostly by
heterogeneous dissociation) based on the residence time was 1–2%. Consequently,
the feed of ammonia was about 12 times in excess of stoichiometric ratio over SiO.
The product powder was collected with a paper filter of 0.5 µm average pores,
mounted in the exhaust line. Because an accumulation of product powder caused
an increase in the pressure drop through the filter, the effluent stream from the filter
was connected to a vacuum pump to enhance the collection of product powder, and
at the same time the system pressure was maintained at pressure slightly above the
atmospheric pressure.
The reaction in a vertical microchannel reactor was carried out for 1 hour at
1350°C by starting ammonia gas feed first, argon gas feed through the annular
space, and then argon gas feed through the SiO generator. The argon gas feed
through the annular space between the SiO generator and Ammonia feeder was to
prevent the product attachment at the SiO generator outlet. The flow of argon in
the furnace tube was maintained throughout the reaction run to prevent attachment
of product powder on the furnace tube wall. The linear velocity in the furnace
tube was set to be about 5.0 cm/s.
29
During the one-hour reaction time, the SiO generation rate was expected to
remain constant [Lin and Kimura, 1996].
After the one-hour operation, the
reaction was terminated by stopping the SiO generation, ammonia feed, then the
annular argon feed. The flow of argon through the furnace tube was maintained
but at a low rate until the reactor cooled down to room temperature.
Two horizontal microchannel reactors were built for reactions runs.
The
same procedures as those for the horizontal microchannel reactors were applied to
the horizontal microchannel reactors. However, after starting the reaction, the
heating element was broken in 10 – 15 min. The same problem happened in both
the horizontal microchannel reactors.
The Pt-13% Rd heating element has been known to be weak in the reduction
environment containing hydrogen, causing hydrogen pit formation.
In addition,
SiO vapor tends to react with Pt at high temperature to form platinum silicide,
leading to wire breakage. There seems to have been permiation of hydrogen and
SiO vapor through the ceramic tubes used.
It is important to use a different
material as the heating element, such as molybdenum disilicide, for longer and
stable operation.
30
3.3 Characterization of Product Powder
The product morphology was examined by transmission electron microscopy
(TEM). Small pieces of filter paper were cut out together with product powder
from each filter and inserted in a plastic bottle half filled with ethyl alcohol. The
plastic bottles were sonicated for 1 min for powder dispersion. Ethyl alcohol with
dispersed powder was sampled with a micropipette, and a small droplet of alcohol
was placed on a copper screen, followed by alcohol vaporization, and the copper
screen was used for TEM observation.
TEM photographs were scanned into digital pictures, which were then further
enlarged for printing hard copies.
Individual particles observed in each picture
were measured with a ruler and analyzed for average sizes.
31
CHAPTER 4 EXPERIMENTAL RESULTS AND DISCUSSIONS
4.1 SiO Vapor Generation versus Product Yields
It was revealed by several experimental runs that the amount of product
powder was much less than the amount of product estimated based on the decrease
in the mass of SiO particles placed in the SiO generator.
It is suspected that loss
of product powder through the filter and attachment to the furnace tube wall as well
as the exhaust line wall might have caused this difference.
However, small
amounts of product collected and small decreases in SiO mass did not allow any
accuracy analysis of data in terms of product yields.
Because testing the
feasibility of using microchannel reactors is one of the major objectives, any further
investigation was not made in this research.
The pressure drop through the bed of SiO particles became almost
one-order-of-magnitude larger at the reaction temperature than the pressure drop at
room temperature. The changes in physical properties of argon gas, mostly the
viscosity, seems to have caused the increase in the pressure drop.
32
4.2 Nano-Sized Si3N4 Power Synthesis
4.2.1 Product morphologies
Figures 4.1 shows sample TEM pictures of nano-sized powder obtained in
different types of microchannel reactors: (a) vertical reactor with no collection
coupler, (b) vertical reactor with collection couple, (c) horizontal reactor with no
collection coupler, and (d) horizontal reactor with collection coupler.
It is not very
easy to differentiate the types of reactor based on the particles produced.
However,
particles obtained in the vertical microchannel reactor without a collection coupler
[Figure 4.1 (a)] are somewhat more widely distributed than those obtained in the
vertical microchannel reactor with a collection coupler [Figure 4.1 (b)]. On the
other hand, particles obtained in both the type of horizontal microchannel reactors
are smaller, in general, than those obtained in both the vertical microchannel
reactors.
SiO vapor sublimated in the reactor reacts with NH3 to form nano-sized
silicon nitride powder. However, if SiO is not consumed in the ammonolysis
33
reaction, it remains unreacted and condenses to nano-sized particles [Lin, 1996].
In the macro-sized reactor having the residence time greater than about 150 ms, the
fractional conversion of SiO is above 95%.
However, all the microchannel
reactors used in this research have the residence time less than a few ms, and the
fractional conversion of SiO is unknown.
The content of SiO in the product nano-sized powder may be measured by the
decrease in sample mass due to SiO sublimation when the sampled product is
heated to 1350°C. However, because the amounts of product obtained in the
current research were very small, the SiO sublimation experiment was not possible.
It should be noted that the particles shown in the TEM pictures may contain SiO
particles.
It will be important to make measurable amounts of product for SiO
content analysis in the future.
One of the major objectives of this research is to test the feasibility of
operating microchannel reactors. Because it was demonstrated that all the types
of microchannel reactors could be operated without such problems as plugging of
microchannels with nano-sized particles or whiskers, analyzing the SiO content
was not attempted any further.
34
Figure 4.1 (a) TEM picture of particles obtained in the vertical
microchannel reactor with no collection coupler.
35
Figure 4.1 (b) TEM picture of particles obtained in the vertical
microchannel reactor with collection coupler
36
Figure 4.1 (c) TEM picture of particles obtained in the horizontal
microchannel reactor with no collection coupler.
37
Figure 4.1 (d) TEM picture of particles obtained in the horizontal
microchannel reactor with collection coupler.
38
4.2.2 Effects of residence time
The residence time of reactant gas mixture plays a major role in the formation
of nano-sized particles and their sizes. For the vertical microchannel reactor with
no collection coupler, it is not easy to define the mean residence time, because the
velocity depends on the expansion of reactant gas mixture after it comes out of the
microchannel reactor, where the temperature is still high enough.
If the reactant
gas mixture forms a jet stream and it goes thought the distance between the SiO
feeder outlet and the bottom of uniform temperature zone, defined as the reacting
zone, the mean residence time could be as short as 4 ms. However, the actual
mean residence time could be larger, though the actual values is not known.
For the vertical microchannel reactor with a collection coupler, the flow of
reactant-gas mixture is confined in the collection coupler. The mean residence
time can be estimated dividing the length of 1/2” coupler tube, 10 cm, by the
average linear velocity of total gas flow in the coupler tube, yielding about 80 ms.
For the horizontal microchannel reactors, the residence time can be calculated
by dividing the distance between the SiO generator outlet and the end of heated
39
zone by the linear gas velocity of total gas through the outermost tube. The mean
residence should not depend on whether the reactor has a collection coupler or not.
These values are listed in Table 4.1 together with average sizes of particles
obtained in the respective reactor settings. The average particle size goes down to
about 10 nm when the mean residence time approaches zero.
Figure 4.2 plots the
average particle size obtained in this research against the individual mean residence
time together with data obtained in a macro-scale reactor by Vongpayabal [2003].
The operating temperature is all 1350°C.
The data obtained in this research
scatter mostly because of the uncertainty of mean residence time. However, it is
still indicated that the microchannel reactor can make smaller nano-sized particles
when the residence time is limited short.
There is a critical size of particles that can grow rather than disassembling
back to smaller clusters or molecules.
It is evidenced in the TEM pictures that
many small particles actually exist, having diameters on the order of a few
nanometers. These small particles could be of critical size.
It is implied that
about 10 nm obtained in the microchannel reactors is still larger than the possible
critical size for particles to grow, which will be estimated in the following chapter.
40
Table 4.1. Correlations between mean residence time and mean particle size
obtained in different types of microchannel reactors.
Mean
Average
Residence
Particle Size,
Time, msec
nm
1350
0.2
10.3
1300
0.2
20.2
1350
4.0
21.0
1350
79.9
53.2
1300
82.5
52.8
Temperature,
°C
Horizontal
microchannel
reactor
Without
coupler
With coupler
Without
Vertical
coupler
microchannel
reactor
With coupler
41
120
Average particle size, nm
100
80
60
40
Vongpayabal [2003]
Current Work
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Residence time, sec
Figure 4.2 Average particle size varying with mean residence time.
0.8
42
4.2.3 Effects of Temperature
The reaction was carried out at two different temperatures: 1300℃ and
1350℃. The average particle sizes of product powder obtained in the horizontal
microchannel reactor are different by a factor of about two. However, it is not
clear if this difference is attributed to the collection coupler or temperature. The
average particle sizes of product powder obtained in the vertical microchannel
reactor with a collection coupler do not depend much on the reaction temperature.
In general, high temperature enhances burst nucleation, leading to the
formation of more, smaller particles, while low temperature enhances slow
nucleation as well as growth, leading to larger particles. However, in the regime
close to the formation of particles of critical size, the growth under restricted
residence time is not well understood yet.
Any further discussion on the
temperature dependency of nano-sized particle formation needs to be made based
on more data collected at different temperatures in the identical reactor settings of
microchannel reactor.
Further study is needed.
43
5. Discussion
5.1 Critical Size for Stable Growth
It is expected that making particle sizes smaller is possible by reducing the
residence time of reactant gas mixture. However, how small the particles could be
is not known.
It is attempted in this chapter to estimate the minimum size of
particles that can grow.
One may estimate the critical radius for a nucleus to become stable based on
classical thermodynamics [Kathmann, et. al., 2000], assuming that the system is at
thermodynamic equilibrium represented by the following stoichiometric reactions:
3SiO (g) + 4NH3 (g) = Si3N4 (g) + 3H2O (g) + 3H2 (g)
Si3N4 (g) = Si3N4 (s)
It is assumed that silicon nitride molecules are formed first as intermediate gaseous
44
species and then condense to solid phase, and that there is equilibrium between the
gaseous-phase and solid-phase.
The chemical potentials of individual species at equilibrium are correlated as
µSi N
3
4 (g)
+ 3 µ H2O (g) + 3 µ H2 (g) − 3 µSiO (g) − 4 µ NH3 (g) = 0
µSi N
3
4 (s)
− µSi3N4 (g) = 0
(1)
(2)
The chemical potential of ideal gaseous species i is given by
µi = µio + R T ln
Pi
P0
(3)
where µio is the chemical potential of species i at its standard state, Pi is the
partial pressure of species i, P0 is the system pressure, R is the universal gas
constant, and T is the absolute temperature.
The activity of solid silicon nitride is assumed to be unity, and the chemical
potential is equal to its chemical potential at the standard state. Or
45
µSi N
3
4 (s)
= µSi∗ 3N4 ( s )
(4)
where µSi∗ 3N4 ( s ) is the chemical potential of silicon nitride at its standard state.
The Gibbs free energy of silicon nitride changes when its phase changes from
gaseous state to solid state, and its change is given by
∆ G = ( µSi N
3
4 (s)
− µSi3N4 ( g ) ) nSi3N4 + 4 π r 2 σ
(5)
where nSi3N4 is the number of moles of silicon nitride that transfer from the vapor
phase to the solid phase, σ is the surface tension, and r is the radius of nucleus
that has formed. At the equilibrium, ∆ G is minimum with respect to nSi3N4 .
Thus, differentiating ∆ G with respect to nSi3N4 yields
d ∆G
=0
d nSi3N4
(6)
Also, with the density, ρ, of the nucleus and the molecular weight, M Si3N4 of
silicon nitride, the mass of nucleus is correlated to the number of moles of silicon
46
nitride in the nucleus in terms of nucleus radius by the following equation:
4
π r 3 ρ = M Si 3 N 4 ⋅ n Si 3 N 4
3
(7)
The following Kelvin's equation is then obtained for the critical nucleus
radius r ∗ , combining Eqs. (1) – (7) [see Appendix I]:
R T ln
3
4
PSiO
PNH
3
PH32 O PH32 P0 K P
=
2 M Si 3 N 4 σ
ρ r∗
(8)
where K P is the equilibrium constant for the following stoichiometry:
3SiO (g) + 4NH3 (g) = Si3N4 (s) + 3H2O (g) + 3H2 (g)
(9)
The value of K P is obtained at any temperature by the Gibbs free energies of
formation, heats of formation, and temperature dependencies of constant-pressure
heat capacity of individual species.
Under the typical operating conditions at 1350°C, the physical properties and
47
parameters contained in Eq. (8) are estimated as indicated in Table 5.1 with their
individual sources.
48
Table 5.1 Physical properties needed for Kelvin’s equation.
Parameters
Magnitude
Units
Sources
PSiO (g)
~ 400
Pa
PNH 3 (g)
7.66 ×104
Pa
PH 2 (g)
1.62 ×10 4
Pa
PH 2 O (g)
0 .2
Pa
Impurity water in ammonia
P0
1.013 ×105
Pa
Operating pressure
M Si 3 N 4
140
g/mol
Molecular weight of Si3N4
ρ
~3
g/cm3
Density of Si3N4
σ
100 ~ 200
dynes/cm
ln K P
25
−
Brady, 1959
Ammonia dissociation based on
plug flow assumption
Order-of-magnitude estimate
Lin, 1995
49
The partial pressures of NH3 and H2 were estimated by the dissociation of
NH3 at the given temperature [Lin and Kimura, 1996; Lin, 1995], mostly by the
heterogeneous dissociation.
The plug flow is assumed to find the extent of
dissociation taking place in the residence time. The partial pressure of water is
based on the purity of gases used in this research, namely, 2 ppm in ammonia.
Note that water in the argon used was 1 ppm.
rough order-of-magnitude estimate.
The surface tension used is a very
Because the critical radius is directly
proportional to the surface tension, as shown in Eq. (8), this could cause a
significant error.
With these values, the critical radius is estimated to be 4-8 D, i.e. 0.4-0.8 nm.
The volume of silicon nitride molecule, Vm , obtained based on the assumption that
each molecule is spherical, gives roughly the critical number of molecules in a
cluster so that it becomes stable and can grow as
4 ∗3
4
πr
π ( 4 ~ 8×10− 8 ) 3
v
∗
= 3
= 3
= 4 ~ 28
i =
Vm
Vm
7.75×10− 23
∗
( 10 )
50
Though the accuracy of estimation is not very high, it is implied that the
critical diameter of nucleus (2r*) that can grow is on the order of a few nanometers.
As evidenced in the TEM pictures, there are many small particles having
diameters of a few nanometers. The critical size is hence considered to be close to
the estimated size, and the larger average particle size is attributed to size
distributions, containing both large and small particles, resulting from residence
time distributions.
One of advantages of using microchannel reactors is achieving a narrowly
confined residence time distributions, leading to narrow particle size distributions.
However, because of the very small amount of product obtained, there are
possibilities that other factors might have influenced the product properties.
It is
important to design and build an assembly of multiple microchannel reactors so
that measurable amounts of product can be collected for detailed analysis, including
not only the size distribution analysis but also the SiO content analysis.
Once a
significant amount of nano-sized powder is synthesized, sintered parts can also be
made for characterizing the sintered parts.
Further study is needed.
51
5.2 Scalable Microchannel Reactors
One of major objectives is to propose scalable structures for microchannel
reactors.
It has been proved that microchannel reactors can be used for this
unique high-temperature gas-phase reaction to precipitate nano-sized powder
without causing serious problems, such as plugging of microchannels.
This
section attempts to propose some potential structures for building scalable
microchannel reactors.
The key features of microchannel reactors for this particular reaction system
include:
(1)
SiO generation
(2)
microchannel for feeding SiO vapor into a reacting zone
(3)
microchannel for ammonia supply into the reacting zone
(4)
annular space between the SiO and ammonia supplied into microchannels
(5)
reacting zone where SiO and ammonia merge and react
(6)
quenching of reactant/product mixtures to terminate not only the reaction
and but also the particle growth.
52
These requirements may be satisfied by a stack of plates with multiple holes
aligned in grooved channels, as illustrated in Figure 5.1 (a).
A single layer is
schematically illustrated in Figure 5.1 (b). The whole set needs to be heated by a
heating unit which only heats the multiple microchannel reactors, so that the
reactant gas mixture and product particles are quenched when they go out of the
reacting zone, as illustrated in Figure 5.1 (c).
There are several technical issues to be addressed.
One of major challenges
is the material to be used. Though alumina is apparently a suitable material,
technologies to drill micron-sized holes through plates and to make micron-sized
grooves to be used as channels, both economically, have not been established yet.
There are some potential methods, such as a laser beam method or mechanical
drilling/grooving.
However, none of these has been tried yet.
Gluing the three plates to the individual gas feeding tubes is another problem.
Alumina glue currently available is somewhat porous, and sealing gas is not
complete. Also, the strengths of the glue may be an issue when the microchannel
reactor unit is used for a certain length of time at elevated temperature.
In this study, annular argon gas was used for preventing the growth of
53
whiskers at the SiO feeder outlet. This may not be necessary in microchannel
reactors. Further study is indispensable.
54
SiO Particles
Porous
Plate
SiO Feeder
Ar Channel
Ar Feeder
NH3 Channel
NH3 Feeder
Reacting
Zone
Figure 5.1 (a) Schematic diagram of multiple microchannel reactors.
55
Figure 5.1 (b) Unit component for multiple-layer microchannel reactor.
56
Ar Feed
NH3 Feed
SiO Particles
Figure 5.1 (c) Set of multiple microchannel reactors.
Heating Unit
Heating Unit
Ar Feed
57
CHAPTER 6 CONCLUSIONS AND RECOMMENDATION
FOR FUTURE WORK
6.1 Conclusions
Four types of microchannel reactors were built, using a combination of
smallest alumina tubes commercially available, for testing the feasibility of
applying microchannel reactors to the ammonolysis of SiO for producing
nano-sized silicon nitride powder.
The experimental results are summarized
below.
(1)
All the microchannel reactors built for this study could be operated
without any serious problems, such as clogging of microchannels with
whiskers or nano-sized powder.
(2)
The reduction of residence time and quenching of reactant/product mixture
decreased the average particle size down to about 10 nm under the
conditions used in this research.
(3)
The smallest size for particles to grow was estimated based on
thermodynamic consideration and found to be on the same order of
58
magnitude as those observed in TEM pictures.
(4)
Potential structures for scalable microchannel reactors were proposed for
future study.
6.2 Recommendation to Future Work
There are a number of problems that could not be resolved in this study.
To
realize mass production of nano-sized silicon nitride powder via the ammonolysis
of SiO vapor, the following items need to be clarified.
(1)
Build a set of multiple microchannel reactors for its test.
(2)
Produce a measurable amount of nano-sized silicon nitride powder for
analyzing the SiO content in the product as well as the size distributions
and average sizes.
(3)
Based on measurable amounts of product, reexamine the correlation
between the particle size and residence time.
(4)
Make sintered pieces from nano-sized silicon nitride powder for
characterization of mechanical properties of sintered parts.
59
BIBLIOGRAPHY
Allaire, F. and S. Dallaire, “Synthesis and Characterization of Silicon Nitride
Powders Produced in a D.C. Thermal Plasma Reactor,” J. mater. Sci. , 26
[24], 6736-6740 (1991).
Andrievski, R. A., ”Review: Nanocrystalline High Melting Point Compound-based
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Barsoum, M., P. Kangutar, and M. J. Koczak, ”Nitridation Mechanism of Powder
Compacts,” Ceram. Eng. Sci. Proc., 10 [7-8], 794-806 (1989).
Barsoum, M., P. Kangutar, and M. J. Koczak, ”Nitridation Kinetics and
Thermodynamics of Silicon Powder Compacts,” J. Am. Ceram. Soc. Proc.,
74 [6], 1248-1253 (1991).
Brady, G. W., ”A study of amorphous SiO,” J. Phys. Chem., 63[7], 1119-1120
(1959).
Danforth, S. C., W. Symons, K. J. Nilsen, and R. L. Riman, ”Processing of Dense,
High-Purity, Additive-free SiliconNitride,” Proceedings of Ceramic
Powder Processing Science, 2’nd International Conference, Bavaria,
495-502 (1988).
Danforth, S. C. and J. S. Haggerty, ”Synthesis of Ceramic Powders by Laser Driven
Reactions,” Ceram. Eng. Sci. Proc., 2[7-8], 466 (1981).
Gleiter, H., ”Nanocrystalline Materials,” Prog. Mater. Sci., 33 [4], 223-315 (1989).
Hisao, H. and K. Kondo, “Shock-Compacted Si3N4 Nanocrystalline Ceramics:
Mechanism of Consolidation and Transition from α- to β-form,” J. Am.
Ceram. Soc., 77 [2], 487-492 (1994).
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Kathmann,S.M., G. K. Schenter, and B.C. Garrett, “Dynamical Nucleation Theory,”
pp.197-200, in Nucleation and Atmospheric Aerosols 2000, vol. 534,
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(AIP Conference Proceedings), 2000.
Lee, C. J. and D. J. Kim, “Effect of α-Si3N4 Particle Size on the Microstructure
Evolution of Si3N4 Ceramics,” J. Am. Ceram. Soc., 82[3], 753-756 (1999).
Lin, D.C., “Kinetic study on the synthesis of Si3N4 via the ammonolysis of SiO
vapor,” Ph.D. dissertation, Oregon State University, 1995.
Lin, D.C. and S. Kimura, “Kinetics of Silicon Monoxide Ammonolysis for
Nanophase Silicon Nitride Synthesis,” J. Am. Ceram. Soc., 79[11],
2947-2955(1996).
Maalmi, M. and A. Varma, ”Intrinsic Nitridation Kinetics of High-Purity Silicon
Powder,” AIChE. J, 42[12], 3477-3483 (1996).
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Shock Tubes Waves,” Proc. Int. Symp., 12th, 476-485(1980)
Vongpayabal, P., “Kinetics of nano-sized Si3N4 powder synthesis via ammonolysis
of SiO vapor,” Ph.D. Dissertation, Oregon State University, (2003)
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Nano-sized Silicon Nitride Powder Synthesis,” Powder Technology, 156,
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61
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62
APPENDICES
Appendix I
Consider the first stage of equilibrium in the sequence:
3SiO (g) + 4NH3 (g) = Si3N4 (g) + 3H2O (g) + 3H2 (g)
The equilibrium of this reaction can be represented in terms of chemical potential
by Eq. (1) as
µSi
3 N 4 (g)
+ 3 µH 2 O (g) + 3 µ H 2 (g) − 3 µSiO (g) − 4 µ NH 3 (g) = 0
(1)
Substituting Eq. (3) for individual species, except Si3N4 (g), into Eq. (1) gives
µ Si N
3
o
o
o
o
= 3 µ SiO
(g ) + 4 µ NH 3 ( g ) − 3 µ H 2 O (g ) − 3 µ H 2 (g ) + R T ln
4 (g )
3
4
PSiO
(g ) PNH 3 (g )
PH32 O (g ) PH32 (g ) P0
(A-1)
Next, consider the overall equilibrium for the ammonolysis of SiO vapor to
63
form silicon nitride in its solid phase, represented by Eq. (9):
3SiO (g) + 4NH3 (g) ↔ Si3N4 (s) + 3H2O (g) + 3H2 (g)
(9)
Then, the equilibrium of this reaction is represented in terms of chemical potentials
of individual species, as the combination of Eqs. (1) and (2), by
µSi
3 N 4 (s)
+ 3 µH 2 O (g) + 3 µH 2 (g) − 3 µSiO (g) − 4 µ NH 3 (g) = 0
(A-2)
Substituting Eqs. (3) and (4) for individual species into (A-2) above yields
µSi∗
3N4
(s )
o
o
o
o
= 3 µ SiO
(g ) + 4 µ NH 3 ( g ) − 3 µ H 2 O (g ) − 3 µ H 2 (g ) + R T ln K P
(A-3)
where KP is the equilibrium constant for the reaction represented by Eq. (9):
3
4
 PSiO
g ) PNH3 ( g )
(
KP =  3
 PH O (g ) PH3 (g ) P0
2
2




 eq
(A-4)
64
Differentiating Eq. (5) with respect to nSi 3 N 4 and setting the derivative equal
to zero, as Eq. (6), gives
µSi
3N4
(s )
− µSi 3 N 4 (g ) + 8 π r σ
dr
=0
d nSi 3 N 4
(A-5)
Rearranging Eq. (7) to explicitly represent r in terms of nSi 3 N 4 , one has
 3 M Si 3 N 4 nSi 3 N 4
r = 
4π ρ





1/ 3
(A-6)
Taking the derivative of Eq. (A-6) with respect to r and representing nSi 3 N 4 in
terms of r using Eq. (7), then one has
M Si3 N 4
dr
=
d nSi3 N 4 4 π ρ r 2
Substituting (A-7) into (A-5), one has with r replaced by r*
(A-7)
65
µSi
3N4
(s )
− µSi 3 N 4 (g ) =
2 σ M Si 3 N 4
ρ r*
(A-8)
Knowing that µSi3N4 ( s ) = µSi∗ 3N4 ( s ) as indicated by Eq. (4) and substituting Eqs.
(A-1) and (A-3) into Eq. (A-8), one finally has Eq. (8) as
R T ln
3
4
PSiO
PNH
3
3
H 2O
P
3
H2
P P0 K P
=
2 M Si 3 N 4 σ
ρ r∗
(8)