Chemical vapor infiltration rates of ZrO2 into MoSi2 porous bodies and comparison with model calculation

Article abstract of DOI:10.1111/j.1151-2916.2002.tb00300.x

Zirconia (ZrO₂) was chemical vapor infiltrated (CVI) into a partially sintered MoSi₂ body (preform) by using zirconium n-propoxide (Zr(OC₃H₇)₄) as a gas precursor. Infiltration distances at different conditions were compared with the calculated results. Chemical vapor deposition (CVD) film growth rates of ZrO₂ were measured, and the data were incorporated into the model calculations. Two models were used to analyze the observed infiltration distances. Initially a conventional model assuming a pore with constant radius (SP model) was used. With this model, it was possible to predict the approximate infiltration distance. However, the model cannot predict pore closure and the infiltration distances for a variety of CVI conditions. Secondly, a newly proposed model (PC model) from a previous paper was applied to calculate the infiltration distance. Using this model, it was possible to predict the occurrence of pore closure or the formation of the deposition layer on the perform surface.

Full text of DOI:10.1111/j.1151-2916.2002.tb00300.x

J. Am. Ceram. Soc., 85 [6] 1477–84 (2002)
journal
Chemical Vapor Infiltration Rates of ZrO2 into
MoSi2 Porous Bodies and Comparison with Model Calculation
Noboru Yoshikawa†
Department of Metallurgy, Graduate School of Engineering, Tohoku University,
02 Aza-Aoba, Aramaki, Aoba-ku, Sendai, Japan 980-8579
James W. Evans
Department of Materials Science and Mineral Engineering, University of California, Berkeley, California 94720
due to transformation toughening.16–19 The present study at-
tempted to incorporate ZrO2 into a partially sintered porous body
of MoSi2 by CVI to fabricate composite materials with improved
properties. A metal-organic (MO) precursor was utilized for the
CVI of ZrO2, as MO precursors are known to be effective in
obtaining excellent step coverage20 and lower deposition temper-
ature21 than chloride precursors. The excellent step coverage of
MO is favorable for deposition of thin films in multilayered
structures with narrow trenches in electronic devices. In the
present study, we chose to fill in the fine pore networks in porous
preforms. By selecting an appropriate MO precursor, it is possible
to achieve a low deposition temperature and deposition of ZrO2
without an oxygen gas source,22 which prevents the oxidation of
MoSi2 during the process. In this study, ZrO2 was incorporated
without any additive oxides for stabilization of ZrO2, such as
Y2O3, to simplify the reaction systems.
This paper describes our attempts at CVI using this reactive
system and sets out an analysis of the infiltration kinetics. Several
models exist, with which to analyze the CVI process. The simplest
model23,24 (SP model) assumes a straight single pore with a
constant radius to represent the pore structure of the preform. The
other models25,26 treat gas flow and mass transfer in a porous body
and the porosity variations are calculated. To consider changes in
the porosity and the pore structures during CVI in the models, it is
necessary to handle the effect of pore closures. In a previous
paper,27 a model (PC model) was presented for analysis of CVI
infiltration distances considering the pore closure effect, using a
tapered pore geometry constructed from the preform pore size
distributions. In this paper, the PC model was applied to an actual
CVI system, and comparisons were made between the calculated
and the experimental infiltration distances. To obtain the reaction
rates of the CVI process, CVD rates for ZrO2 films on a flat
surface using the same MO precursor were measured under
different deposition conditions, and these rates were incorporated
into the simulation model.
Zirconia (ZrO2) was chemical vapor infiltrated (CVI) into a
partially sintered MoSi2 body (preform) by using zirconium
n-propoxide (Zr(OC3H7)4) as a gas precursor. Infiltration
distances at different conditions were compared with the
calculated results. Chemical vapor deposition (CVD) film
growth rates of ZrO2 were measured, and the data were
incorporated into the model calculations. Two models were
used to analyze the observed infiltration distances. Initially a
conventional model assuming a pore with constant radius (SP
model) was used. With this model, it was possible to predict the
approximate infiltration distance. However, the model cannot
predict pore closure and the infiltration distances for a variety
of CVI conditions. Secondly, a newly proposed model (PC
model) from a previous paper was applied to calculate the
infiltration distance. Using this model, it was possible to
predict the occurrence of pore closure or the formation of the
deposition layer on the preform surface.
I. Introduction
HEMICAL vapor infiltration (CVI) is an important processes for
C
fabricating ceramic-matrix composite materials.1,2 Ceramic
preforms consisting of either fibers or particulates are filled with
ceramics at lower temperatures than their melting (or sublimation)
temperature.3 Generally, the process temperature is also lower than
the sintering temperature of these materials. The low processing
temperature has many advantages especially during the fabrication
of continuous filament ceramic composites (CFCCs), for which
large numbers of CVI studies have been performed so far, both by
experiments4–6 and by means of computer simulations.7–9
In our study, CVI was used to incorporate ZrO2 into partially
sintered molybdenum disilicide (MoSi2) porous bodies (preforms)
and the infiltration kinetics were investigated. The current CVI
system has been selected according to the following factors:
MoSi2 is well known as an intermetallic compound which
possesses excellent creep10,11 and oxidation resistance above 1000
K.12,13 Sintered MoSi2 bodies are currently used as heating
elements and have the potential for use as a high-temperature
structural material, while the poor room-temperature properties of
MoSi2 limit its use in structural applications.14,15
In this study, CVI experiments were conducted under different
conditions using two types of MoSi2 preforms with different
porosities and pore size distributions. The infiltrated microstruc-
tures were observed using SEM-EDX and the infiltration distances
were measured from the micrographs. The observed distances
were compared with the results calculated using the conventional
(SP) model, and with the PC model.
ZrO2 ceramics also possess refractory properties, and have
higher fracture resistance and flexural strength than most ceramics,
II. Experimental Procedure
(1) Preparation of MoSi2 Porous Bodies
T. M. Besmann—contributing editor
Porous preforms were fabricated from MoSi2 powders (Wako
Chemical, Inc.) with two different particle sizes: (a) fine-grained
powder with an average particle size of 2–5 ␮m and (b) a
coarse-grained powder with an average particle size of 6–12 ␮m.
The powders were cold isostatically pressed at 2 MPa in rubber
molds. The green compacts were then sintered at 1373 K for
Manuscript No. 188374. Received July 25, 2000; approved March 15, 2002.
†On leave as a research investigator abroad supported by the Japanese Ministry of
Education, Science, Sports and Culture.
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Journal of the American Ceramic Society—Yoshikawa and Evans
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7200 s in an Ar atmosphere. Although the sintered bodies were
porous, they had enough strength to be handled for the CVI
operations. Porosity and pore size distribution of the preforms
were measured using Hg porosimetry. These data were used for
constructing tapered pores in PC model simulations, which will be
discussed later. The measured porosities (pr) and average pore
radii (rav) are as follows: (a) fine grain, pr ϭ 29%, rav ϭ 0.963 ␮m;
(b) coarse grain, pr ϭ 32.5%, rav ϭ 3.25 ␮m.
The measured pore size distributions are shown in Fig. 1. The
coarse-grained preforms have larger pore radii than the fine-
grained preforms. The MoSi2 preforms were machined into cylin-
ders 4 mm in diameter and 5–10 mm long.
well-defined. Both the CVD and the CVI processes were con-
ducted at a reduced pressure. The experimental conditions are
shown in Table I. Long CVI processing times are common31,32
during the industrial fabrication of composites. However, in our
study, short CVI processing times were used to keep the process
pressure constant during the experiments. CVI process times of
less than 1 h were used. CVI infiltration distances were obtained
under conditions of comparatively higher deposition rates.
The as-infiltrated state of the ZrO2 was amorphous for all CVI
temperatures that we studied. Therefore, these materials would not
be expected to show transformation toughening. In a previous
work, an annealing heat treatment was performed and the resulting
mictrostructural changes were studied.33 Nanosized tetragonal
ZrO2 grains were obtained by annealing, which contributed to
transformation toughening. Optimum CVI conditions were dis-
cussed, with respect to the current process.
(2) Precursor Selection for CVD and CVI Methods
Both CVD and CVI were used for obtaining ZrO2 deposits.
Zirconium n-propoxide (Zr(OC3H7)4 or Zr(n-Pr)4) was selected as
the precursor in this study, for the following reasons:28,29 (1) It has
a relatively high vapor pressure, which provides a constant stable
vapor pressure during deposition. (2) It is available at a reasonable
price. (3) It can be directly decomposed to produce ZrO2 deposits,
without an additional oxygen gas source. Deposition of ZrO2
occurs, according to the following overall reaction:
(4) Measurement of Film Thickness and
Microstructural Observations
The thickness of the CVD ZrO2 films was measured using an
interferometer attached to an optical microscope. The infiltrated
preform bodies were cross-sectioned for observation by SEM. The
compositional distributions were measured using EDX and the
distance infiltrated was determined from the SEM micrographs. To
measure the lengths of pores that start from the outer surface of the
preform, SEM images were digitally recorded using a scanner and
analyzed using image analysis software (Photoshop, NIH Image)
installed in a personal computer (Macintosh, iMac). The measured
lengths of about 15 pores in one photograph were averaged (in five
images) to construct the tapered pore used in the PC model
analysis.
Zr(OC3H7)4͑g͒ ϭ ZrO2͑s͒ ϩ 4C3H6͑g͒ ϩ 2H2O͑g͒
Vaporized Zr(n-Pr)4 is transported into the reactor with a He
carrier gas. The choice of He allowed us to obtain better sensitivity
in the analysis of the output gas from the reactor, using gas
chromatography.
(3) CVD, CVI Experiments
The apparatus used in this work is illustrated in Fig. 2. The
vaporization temperature of the Zr(n-Pr)4 was held constant at 418
K (vapor pressure: 13 Pa), and the concentration of the precursor
was controlled by the process pressure. The effect of process
pressure on concentration will be discussed along with the CVD
kinetics in a later section. The reactor consisted of a stainless steel
tube 10 mm in diameter and 300 mm long, heated by a Nicrome
tube furnace. A gas chromatograph was connected to the outlet of
the reactor.
CVD was used to deposit ZrO2 films on polished Si wafers
placed in the reactor, as shown in Fig. 2. The film thicknesses were
large enough to ignore any differences between the interaction of
gas species with Si and MoSi2. This will be discussed later. The
present tubular CVD reactor configuration was selected to obtain
the film growth rate distributions.30 The MoSi2 preforms were also
placed at a position in the reactor, where the film growth rates were
III. Results
(1) CVD-ZrO2 Film Growth Rates
An example of the distribution of the film growth rate in the
reactor is shown in Fig. 3. The growth rate has a maximum in the
region close to the inlet (about 7 ϫ 10Ϫ2 m), where the substrate
temperature was constant and was equal to the setup value. For the
series of CVD experiments, films having thicknesses of 0.5–5 ␮m
were considered for the growth measurements and there was a
near-linear increase in thickness with the deposition time. There-
fore, the growth rate was simply defined as a quotient of the film
thickness divided by deposition time. In the current study, the
MoSi2 preforms were placed in this peak location, and the
maximum film growth rates with changed deposition conditions
were investigated
The relationship between CVD growth rate and substrate
temperature is shown in Fig. 4. The growth rate increased in a
temperature range from 573 to 673 K. A decrease in growth rate
was observed at 723 K. Above 700 K, particle formation in the gas
phase occurred which may be relevant to the apparent decrease in
the film growth rates.
The film growth rates obtained at different process pressures are
plotted in Fig. 5(a). The growth rate increases with decreasing
process pressure. Output gas from the reactor was sampled and the
gas composition was analyzed by means of gas chromatography.
The concentration of propylene (C3H6) in the output gas is also
plotted with respect to the process pressure in Fig. 5(a). The
concentration of C3H6 increases as the process pressure decreases.
Considering the fact that the Zr(n-Pr)4 vapor pressure (13 Pa at 418
K) is much lower than the process pressure (Ͼ1.3 kPa), more
precursor was supplied to the reactor at the lower process pressures
because the gas flow rate was kept constant. Therefore, the
precursor concentration in the reactor was greater at lower process
pressures, resulting in faster film growth rates. Precursor-saturated
gas from the vaporizer is transferred to the reactor, with the
volume of the carrier gas flow per unit time, in other words the
linear velocity, being roughly inversely proportional to the process
pressure, assuming ideal gas behavior. It follows that the supplied
per unit time is also inversely proportional to the process pressure.
Fig. 1. Intrusion volume and differential pore volumes of coarse- and
fine-grained preforms, obtained by Hg porosimetry.

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Chemical Vapor Infiltration Rates of ZrO2 into MoSi2 Porous Bodies
1479
Fig. 2. Schematic illustration of apparatus.
Precursor concentration was calculated using the equation C ϭ
56.8/p (mol/m3) (p in pascals). Film growth rates are plotted in Fig.
5(b), with respect to the precursor concentration. A linear relation-
ship is apparent within the limited range of the operation condi-
tions studied.
From the CVD film growth rate experiments, a reaction rate
equation was obtained, which is expressed assuming a first-order
equation in Eq. (1). According to the sensitivity study performed
for the reaction order, the selection has important effects on the
predictions; however, it was not necessarily easy to assign the
other reaction orders over the wide range of concentrations. As it
does not seem very fruitful to construct a complicated reaction
model, considering the nature of fictitious pores, a first-order
reaction was assumed in the present study. The reaction rate
constant ks, which is used in the model analysis of CVI rates, was
determined to be consistent with real experimental values, under
different conditions.
hand in Fig. 6(b) at 1.3 kPa and 673 K, a surface deposition layer
was observed and the infiltrated distance was smaller.
Figures 6(c) and (d) show the infiltrated microstructures of the
fine-grained preforms. Infiltration distances were generally much
smaller than those into the coarse-grained preforms. Surface
deposition layers were commonly observed. An infiltration dis-
tance of less than 50 ␮m was observed in Fig. 6(c) at 2.6 kPa and
673 K. However, as shown in Fig. 6(d), an increased infiltration
depth of 80 to 100 ␮m was achieved by decreasing the reaction
temperature to 600 K, and using an even higher concentration (at
1.3 kPa).
The measured infiltration distances for different processing
conditions are plotted as a function of process pressure as open
marks in Fig. 7. The data are scattered, especially in the case of the
coarse-grained preforms. Infiltration distances at 13 kPa were
lower than at 2.6 kPa, because of a lower diffusion constant. No
surface deposition layers were observed at 13 kPa on either
perform under any conditions. The largest infiltration distances
were obtained at 2.6 kPa.
R͑mol/(m2s)) ϭ ks⅐C
(1)
The film growth rate was converted into reaction rate, using the
following relationship:
IV. Discussion
R͑mol/(m2s)) ϭ R͑nm/s͒ ϫ 4.55 ϫ 10Ϫ5
To interpret the observed CVI distances, calculations were
performed to obtain the concentration distributions in the tapered
pores and the conditions resulting in pore closures. Initially,
analysis by a conventional single straight pore (SP) model was
conducted; then the PC model was used to account for the pore
closure. The experimental results are discussed in comparison with
the calculations.
assuming the density and molecular weight of ZrO2 to be 5.6 ϫ
103kg/m3 and 0.123 kg.
(2) Infiltration Distances of ZrO2 into MoSi2 Preforms
Cross sections of the composites were observed using SEM and
the compositional distributions near the surface were measured
using EDX. The compositional profiles and SEM micrographs for
four different CVI conditions are shown in Fig. 6. Since Si had a
spatial distribution similar to that of Mo, and O to that of Zr, the
Si and O profiles were omitted. Near the preform surface (right-
hand sides in Figs. 6(a–d)), Zr concentrations are high and Mo
concentrations are low. These areas correspond to the ZrO2
infiltrated regions.
CVI microstructures of the coarse-grained preforms are shown
in Figs. 6(a,b). Infiltration distances of about 400 ␮m were
obtained at 2.6 kPa and 673 K, as shown in Fig. 6(a). On the other
Table I. Experimental Conditions
CVD
CVI
Gas flow rate, QT (ϫ10Ϫ6 m3⅐sϪ1
Vaporization temperature, Tv (K)
Deposition temperature, T (K)
Process pressure, P (kPa)
)
3.3
3.3
481
481
573–773
1.3–26.7
600–673
1.3–13.3
Fig. 3. Temperature profile and distribution of film growth rates along
the axial direction of the tubular reactor.

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Vol. 85, No. 6
the total pore volume (V) and the total pore surface (S), as shown
in Eqs. (3).
2
r0 ϭ
av ϭ
(3a)
(3b)
av
S
V
The values of r0 for coarse- and fine-grained performs are given in
Section II(1). The diffusion constant, D, was calculated using Eq.
(4), in which contributions from both molecular diffusion (DM)
and Knudsen diffusion (DK)35 were included. DM and DK were
calculated using Eqs. (5) and (6).
1
1
1
ϭ
ϩ
(4)
D
DM DK
1
1
C*⅐ T3
ϩ
Fig. 4. Relationship between substrate temperature and film growth rate.
ͩ
ͪ
ͱ
MZr͑n-Pr͒
p␴2⍀
MHe
4
D
M ϭ
(5)
(1) Analysis of the Infiltration Distance Using the SP Model
where C* is a constant, T is temperature, p is pressure, M is the
molecular weight, and ␴ and ⍀ are Lennard-Jones parameters.36
(A) Description of the Model: Using this model, the concen-
tration distribution can be obtained on termination of infiltration
due to pore closure at the inlet. The infiltrated distance extends
from the inlet position to the point of zero concentration. The
concentration distributions depend on hSP, which is expressed in
Eq. (2). To obtain hSP, values of the reaction rate constant ks, the
precursor diffusion constant D, the pore size r0, and the value of
representative length L have to be specified.
1/ 2
2
3
8RT
DK ϭ
⅐r
(6)
ͩ ͪ
␲MZr͑n-Pr͒
4
where R is the gas constant, and r is the pore radius.
Selection of the specific length L is somewhat arbitrary, because
the tortuosity factors of the porous preforms are not known. In the
present case, the radius of the cylindrical preforms was selected as
the specific length. The concentration distributions were obtained
by solving a differential equation presented in the previous work
(Eq. (1) in Ref. 27).
(B) Calculated Results: The concentration profiles are plot-
ted in Fig. 8, for different hSP values, corresponding to different
CVI conditions in terms of (a) preforms and temperatures and (b)
pressures. The measured infiltration distances are shown in Fig. 7.
The calculated infiltration distance was 300–400 ␮m (Fig. 8(a)) at
2.6 kPa and 673 K, which is a reasonable estimate for the
coarse-grained preform, but the calculated distances for the fine-
grained preforms were larger than those that were observed
experimentally.
k
2ks
h
SP ϭ L
ϭ L
(2)
ͱ ͱ
D
r0D
where
2ks
k ϭ
r0
The rate constant ks was obtained from CVD experiments, as
discussed previously. The average pore radius r0 was determined34
from Hg porosimetry measurements, using the measured value of
Fig. 5. (a) Influence of process pressure on film growth rate (circles) and C3H6 concentration (squares) in the output gas. (b) Effect of Zr(n-Pr)4
concentration on the film growth rate. (T ϭ 673 K, QT ϭ 3.3 ϫ 10Ϫ6 m3⅐sϪ1.)

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Chemical Vapor Infiltration Rates of ZrO2 into MoSi2 Porous Bodies
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Fig. 6. SEM photographs and EDX profiles of the ZrO2-infiltrated MoSi2 preforms under different conditions. Analyzed regions are shown by arrows: (a)
at p ϭ 1.3 kPa, T ϭ 673 K, into coarse-grained preform; (b) at p ϭ 2.6 kPa, T ϭ 673 K, into coarse-grained preform; (c) at p ϭ 2.6 kPa, T ϭ 673 K, into
fine-grained preform; (d) at p ϭ 1.3 kPa, T ϭ 600 K, into fine-grained preform.
The concentration profiles into the coarse-grained preforms at
1.3 and 2.6 kPa were almost the same, while the profile for 13 kPa
deviated somewhat from the others (Fig. 8(b)). The diffusion
constants at 1.3 and 2.6 kPa are almost the same and are dominated
by Knudsen diffusion, while at 13 kPa molecular diffusion plays
the major role. Pressure dependence for the fine-grained preforms
was obtained at both 673 and 600 K.
Estimates of the infiltration distances were obtainable using the
SP model, despite the approximate selection of the L value. Using
this model, it was not possible to predict the formation of closed

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(A) Pore Size Distribution and Pore Construction: Tapered
pores were constructed based on the pore size distributions of the
fine- and coarse-grained preforms (as shown in Fig. 1). Lengths of
the pores were determined by microstructural observation.
The calculated pore radius for the coarse-grained preform is
shown in Fig. 9. In this case, a crooked point (P1) exists (indicated
by an arrow in Fig. 9(a)); this point corresponds to a radius of 4
␮m. An example of the microstructure of the coarse-grained
preform is shown in Fig. 10(a). The image was magnified and the
contrast was inverted to emphasize the pore structure, as shown in
Fig. 10(b). Pores that started from the preform surface and ended
in radii of 4 ␮m were observed, and the lengths were measured by
image analysis. Examples of the measured lengths are indicated in
Fig. 10(b).
The average pore length was determined to be ϳ21 ␮m, by
averaging the measured pore lengths from SEM photographs. The
lengths of pores with radii greater than 4 ␮m were adjusted to be
21 ␮m. Thus, the total pore length was 1212 ␮m. Considering the
tortuous nature of the pores in this microstructure, the more
intimate procedures in the image analysis might yield a less
approximate value of the total pore length leading to better model
predictions.
Direct microstructural observation was not possible in the
fine-grained preforms, due to the limited resolution of the photo-
graphs. The total pore length was determined for the total pore
volume of the fictitious pore to accord with the porosity difference
from the coarse-grained preform. The calculated total pore length
in the fine-grained preform was 2955 ␮m. The tapered pores of
fine-grained preform have large openings at the inlet, and thus the
radius is larger than that in the coarse-grained preform. There is
also a position (P2) close to the inlet where the pore radius
increases rapidly.
Fig. 7. Measured (open marks) and calculated (closed marks) infiltration
distances into different preforms at different temperatures and process
pressures.
pores inside the preform nor was the effect of inlet concentration
on infiltration distance accounted for, even though it is critical as
shown previously in Figs. 6(a) and (b). These limitations stem
from the nature of the SP model, which does not account for the
structural changes in the pores during the process.
(2) Analysis of the Infiltration Distance Using the PC Model
The PC model was used to account for changes in the pore
structure during infiltration and to show how difficult it is to fill
the fine pores. In this analysis, a tapered pore was constructed
based on the pore size distribution of the preform body.
The method used to construct the tapered pore is as described in
the previous work.27
(B) Calculated Results for the Change of Fictitious Pore
Shapes and Concentration Distributions: In calculations using
the PC model, the CVD reaction rate constant ks (Eq. (1)) was
incorporated as well as the dependence of the Knudsen diffusion
constant on the pore radius, as shown in Eq. (6). The simulation
was performed using the following hPC parameter (Eq. (11):
2ks⅐dx
h
PC ϭ
(7)
D
where dx is the pore segment length and is defined as the total pore
length divided by 50. These segments were further divided into 50
nodes for the numerical calculation of the mass balance. The
concentration and the pore radius at the first node of the segments
were updated at every iteration of the numerical simulation. The
time step was taken to be 50 s and the simulation was performed
to calculate the CVI rates in the real CVI time schedules.
Calculated results of the concentration distributions and the pore
radii distributions (pore shapes) are shown in Fig. 11, for the same
CVI conditions as the four SEM-EDX profiles in Fig. 6.
Fig. 8. Calculated (normalized) concentration distribution by SP model:
(a) at 2.6 kPa, in different preforms; (b) in coarse-grained preforms at
different pressures.
Fig. 9. Fictitious pore shapes constructed from the pore size distributions
of coarse- and fine-grained preforms.

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1483
Fig. 10. (a) SEM photograph of coarse-grained preform and (b) a magnified view of point (P) area in the SEM image (left; (a)), which was utilized for image
analysis. Length of pore paths (1–4) were measured and the values are shown in the figure.
In Figs. 11(a) and (b), the calculated results of infiltration into
coarse-grained preforms at different process pressures are shown.
The infiltration distances at 1.3 and 2.6 kPa were similar to each
other, because the diffusion constants were similar, as noted in
Section IV(1)(B) (for Fig. 8(b)). Changes in the process pressure
affected the inlet concentration of the precursor as previously
noted. Calculated results at 1.3 kPa indicate pore closure occurs
after infiltration times of between 2.4 and 3.6 ks, while no pore
closure (surface deposition layer) was predicted at 2.6 kPa, which
agreed with the observations (Fig. 6(a) and (b)). The calculated
infiltration distances are plotted in Fig. 7 with closed marks.
The calculations were performed for the fine-grained preforms,
and the results are plotted in Figs. 11(c) and (d). Pore closure was
predicted at p ϭ 1.3 kPa and both T ϭ 673 and 600 K, and also at
p ϭ 2.6 kPa, T ϭ 673 K, which agreed with the experiments. As
shown in Fig. 7, the infiltration distances in the fine-grained
preforms were also similar at 1.3 and 2.6 kPa, but larger than at
13.3 kPa, because of the decrease in the diffusion constant at 13.3
kPa. A reduction in the reaction rate constant (ks) at 600 K resulted
in the infiltration distances being a little larger than at 673 K.
The calculated results have a tendency to overestimate the
distances. This requires the detection limits of EDX to be taken
into consideration. Signals from thin ZrO2 deposits inside the
preform are probably buried in the noise, and consequently some
infiltrated areas would not be identified in the profiles. Some other
effects might become significant even at an earlier stage in the
Fig. 11. Calculated concentration (inner graph) and fictitious pore radius variation (outer graph) with CVI time under different CVI conditions: (a) 673 K,
2.6 kPa, coarse-grained preform; (b) 673 K, 1.3 kPa, coarse-grained preform; (c) 673 K, 2.6 kPa, fine-grained preform; (d) 600 K, 1.3 kPa, fine-grained
preform.

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6W. J. Lackey, S. Vaidyaraman, and K. L. More, “Laminated C–SiC Matrix
Composites by CVI,” J. Am. Ceram. Soc., 80, 113–16 (1997).
process, such as choking in the bottlenecked pores or two-
dimensional diffusion effects in the winding pores, as discussed in
the preceding paper.27 Precision in determination of the total pore
length (L or dx in Eq. (7)) might affect the predictions, as the
change of hPC. The pore shape dependence on the process time
might be influenced by the selection. On the other hand, it
might be possible to predict to some extent what radii of pores
become closed pores, if the pore size distribution data are properly
input into the model. A first-order equation was assumed in a
limited range of CVI conditions in the present study. Better
prediction and further extension of the infiltration condition of the
model are expected, if more detailed reaction kinetics are taken
into consideration.
7X. Hou, H. Li, Y. Chen, and K. Li, “Modeling of Chemical Vapor Infiltration
Process for Fabrication of Carbon/Carbon Composites by Finite Difference Methods,”
Carbon, 37, 669–77 (1999).
8S. Vaidyaraman, W. J. Lackey, P. K. Agrawal, and T. L. Starr, “1-D Model for
Forced Flow–Thermal Gradient Chemical Vapor Infiltration Process for Carbon/
Carbon Composites,” Carbon, 34, 1123–33 (1996).
9T. L. Starr, “Advances in Modeling of the Chemical Vapor Infiltration Processes,”
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10M. Singh and A. Bose, “Molybdenum Disilicide Matrix Composites”; pp. 95–109
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Materials Society—American Institute of Mining, Metallurgical, and Petroleum
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V. Conclusions
13P. J. Meschter, “Oxidation of MoSi2/TiB2 and MoSi2/Al2O3 Mixtures,” Scr.
Metall., 25, 1065–69 (1991).
ZrO2 was incorporated into partially sintered MoSi2 preforms
by CVI. Infiltration distances into preforms with different poros-
ities processed under different conditions were measured by means
of SEM-EDX depth profiling. The infiltration distances were
compared with simulation models, where the reaction rates ob-
tained in the CVD experiments were utilized. The following
conclusions were obtained:
(1) CVD-ZrO2 film growth rate increased with substrate
temperature in the range between 573 and 673 K and decreased
with increasing process pressure.
(2) The infiltration distance in the coarse-grained preforms
was larger than that in the fine-grained preforms. The infiltration
distance was largest at 2.6 kPa, because surface deposition layers
formed at 1.3 kPa, and due to larger diffusion rates at 2.6 kPa than
at 13 kPa.
(3) A conventional straight single pore (SP) model was
applied to account for the infiltration distances. It was possible to
obtain reasonable estimates of the infiltration distances. However,
the model was not able to predict the extended conditions of the
CVI process.
14K. Hayashi, M. Yoneyama, and Y. Okamoto, “Mechanical Properties of
MoSi2/ZrO2 Composites at Room Temperature” (in Jpn.), J. Ceram. Soc. Jpn., 104
[6] 550–55 (1996).
15R. Suryanarayanan, S. M. L. Sastry, and K. L. Jerina, “Mechanical Properties of
Molybdenum Disilicide Based Materials Consolidated by Hot Isostatic Pressing
(HIP),” Acta Met. Mater., 42, 3751–57 (1994).
16A. H. Heuer, N. Claussen, W. M. Kriven, and M. Ruhle, “Stability of Tetragonal
Zirconia Particles in Ceramic Materials,” J. Am. Ceram. Soc., 65, 642–50 (1982) .
17F. F. Lange, “Transformation Toughening, Parts I, II, III, IV, and V,” J. Mater.
Sci., 17, 225–63 (1982).
18Y. M. Liang and J. H. Zhao, “Effect of Zirconia Particle Size Distribution on the
Toughness of Zirconia-Containing Ceramics,” J. Mater. Sci., 34 [9] 2175–81 (1999).
19W. Soboyejo, D. Brooks, L. C. Chen, and R. Lederich, “Transformation
Toughening and Fracture Behavior of Molybdenum Disilicide Composite Reinforced
with Partially Stabilized Zirconia,” J. Am. Ceram. Soc., 78 [6] 1481–88 (1995).
20M. de Keijser and G. J. M. Dormans, “Chemical Vapor Deposition of Electro-
ceramic Thin Films,” Mater. Res. Soc. Bull., 21 [6] 37–43 (1996).
21L. A. Ryabova, “Thin Films from Organometallic Compounds”; pp. 589–642 in
Current Topics in Materials Science, Vol. 7. Edited by E. Kalidis. North-Holland
Publishing, Amsterdam, Netherlands, 1981.
22C. H. Peng and S. B. Desu, “Metalorganic Chemical Vapor Deposition of
Ferroelectric Pb(Zr,Ti)O3 Thin Films,” J. Am. Ceram. Soc., 77 [7] 1799–812 (1994).
23S. Middleman, “The Interaction of Chemical Kinetics and Diffusion in the
Dynamics of Chemical Vapor Infiltration,” J. Mater. Res., 4 [6] 1515–24 (1989) .
24Y. S. Lin and A. J. Burggraaf, “Modeling and Analysis of CVD Process in Porous
Media for Ceramic Composite Preparation,” Chem. Eng. Sci., 46 [12] 3067–80
(1990).
(4) The CVI distances were analyzed using the PC model.
Tapered pores were constructed based on the measured pore size
distributions. Calculated infiltration distances were compared with
the experimental data. The model was able to predict the occur-
rence of pore closure at different pressures and temperatures,
which agreed with experimental observations.
25S. V. Sotircos, “Dynamic Modeling of Chemical Vapor Infiltration,” AIChE J.,
37 [9] 1365–78 (1991).
26N. H. Tai and T. W. Chou, “Modeling of an Improved Chemical Vapor
Infiltration Process for Ceramic Composites Fabrication,” J. Am. Ceram. Soc., 73 [6]
1489–98 (1990).
27N. Yoshikawa and J. W. Evans, “Modeling of Chemical Vapor Infiltration Rate
Considering a Pore Size Distribution,” J. Am. Ceram. Soc., 85 [6] 1485–91 (2002).
28D. C. Bradley, “Metal Alkoxides as Precursors for Electronic and Ceramic
Materials,” Chem. Rev., 89 [6] 1317–22 (1989).
Acknowledgment
29D. C. Bradley and M. M. Faktor, “Pyrolysis of Metal Alkoxides: I, Thermal
Stability of Some Zirconium Alkoxides,” J. Appl. Chem., 9 [8] 435–39 (1959).
30N. Yoshikwa and A. Kikuchi, “Discussion on Microstructure of Chemical-Vapor-
Deposited TiN Films Based on the Calculated Gaseous Concentration Distribution in
the Reactor,” J. Mater. Res., 10 [11] 2801–807 (1995).
We wish to acknowledge the Japanese Ministry of Education, Science Sports and
Culture, whose support allowed this collaborative work to be undertaken.
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